inis.jinr.ruinis.jinr.ru/sl/ntblib/jinr-p17-85-665.pdf18 kon. i . 06beamh eh hbim mhctmtyt . rj18 ph...
TRANSCRIPT
18 Kon I 06beAMH eH HbiM
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HO CTpeMHTCR YMeHIshyO0156 Lv (11J6 OQI23 t (W) O O~O i (IY) 00 23 L (Y) L
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)
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TIp aTOM YMeHhwaeTCR MaKCRMantHaR HBTeaCKBHOCT~H KOr~a ~~ tlgt
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Tgt t r77 + r2 ( (37)
lJHCJI9BH09 HCCJIe~OB8lHe qopyJru (22 ) o lllJCblB8lOIllel qoplY mmy~ca H
OoSHKH (36) n OItTBsJlllllaeT C~8JIB1ilWiI BHBO~ (eM T3OJUlllY) PaCIeT 110shy
Ka3HBa9 qro B CJIy1laeAl~ = 300 CJIeItOBaT8JIIHOrn -- OOI89
III
7t T a 6 ~ H ua CpaBHeHHe 3HallelIIlli BpeMeHH 3aneplKKH RMIlY1Ihca rrnj
IIOJIYlelllUlX lHCneHHHM HC~e~OB8HReM qoPMYJIll (22)
C OU9HKOtt ( 36) H TaKlKe C on9HKoi1 (27) l3ollllilrumoshy
JIYJlUlaTo BJl1lliICJIeHIDI BHIIOIIHeFlli MR CJIYlM II z 300 tn = 00189 co ~ = 00033 ~
---------------================ - - ---~- (x 1( ~) Pe3Y~TaT
GueRRa (36) OneHKa (27)~ rnCJIeHHoroT t (gtlt i l old RCCJIenOB8HRR E-ll
46 2 3 2 3 245
42 2 34 2 34 251
39 24 2 38 260
3 6 2 45 2 42 271
32 25 2 45 286
2 9 2 58 2 41 3 08
26 2 63 2 04 345
16 2 40 HeIIpHJlleImMa HeIIpIDlleHmm -------- ========
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HIlA r ynOBJIeTOOpJlIiIlRX YCJIOBHll (37)(T e Tgt 0026) tmcrreHlIlDll HCshy
I h 51 CJlenOBaIDleNl MOlilliO TaKii(e UOKa3aTh ITO
B CJIYllae HeOUHOpOlJflOrO BpeM8Hl1 JKl13Hl1 13 shy1 JIYID T8JIe~i T IIopilllKa t T~ t m i1
410 7d(T-Tm)~ 1cpopMYJIa (22 ) ]d B0001l16
rOBopR p ellleHHe YPaBH9IDlH (I ) OIrncrmashy
lOT BCe-laKH Hem U- r op6aTIcM HMTIYJIhC 7 C YMeHhmeHHOH aMJ1JlliTy~o~i H YMeHbllleHHH310 I BpeM6H ffi~ nOCT~eIDlH ~a ( cMpac 4 5)
Ha pRc 5 nOKa3aHO rrOB9~9Hl19 HMDY~ca
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t IDIT9HCKBHOCTH HSJIYshy 1eHIIR IIOJIYleHHM IIpa
IlICJI9HBOM psmeHIDl YPaBshya8H1IJl 0) MJf napaMsljlOB N =2 100 L =O69 middot m - 5
- ]IL Ln 167 H~ - T = Tn-gt - K t N X
110l f LL t reI) K = 2(IT) A =4shy
0 1 3 t (HC )1 CUI) k = 60Y)
I
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ro YJlIKPeHHR JIHHIDI Ha ltIoIMY BpeMH 3aneplUW H llJIHTeJIbHOCTh HMIIYJIbca
upa BpeMeHax ilOPMKa bull PaCCMOTpHM Tenepb KaJ BenyT ce6R IDIBepcHf
ltR~ (I )l R RHTeHCHBHOCTh Ii 3JIYle1mR f (I ) B IltHTepBaJIe 60JIbnmx BpeMeH
i gtgt (3~eCb rrpennOJIaraJIOCb R8] H pamme ITO T Memme BpeMeshy
1m C110HTaHHOro paCTI8JlB I OT~eJIbHoro H3JIYlaTe~ )
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H3 (I) B lIpeIU10JIOJi eHIDl 0 rrpeo6JI8JlaHIDI CB6Pn3JIYlBT6JIbHOH KOMTIOHeHshy
Ttl H8Jl oOHlHol1 HeKorepeHTHoH Tallt R8] TIpH Z raquo i rrpRB6~eHHOe Bpe-
ME -( ) COrJIaCHO (23) rrpHlmMa6T rrp6n9JThHOe 3HBleHllt6
7 (1 )gt 1 ) = I (38)
TO H3 (21) ( 22) lloJIYla6M
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HeKOTOpaR OCTaTOH8H HHB6pcHR H CBH3aHHaR C He~ HeBarryl8HH8H 3HeprHR
3anBCeHHafi B CHCT9M8 B HalaJThHWt MOMeHT 3To eCTh RBJIeillle 3BMe~eilllR
CBepXR3JIYeHlIR 06YCJIosneHHo8 H60~OpOnHllM ymKp6HH6M nKHRH2 OHO
MOE6T rrpHBO~Tb K TaR HB3HBaeMOMY orpBHHleHHOMY CBepXlI3JIYl6~2 5~ npH KOTOPOM H6 BCR B TOJIbKO He6oJIbmaH laCTb 3HeprKH CHCTeMH BTOMOB
Korep6HTHO H3JIyaeTCR
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KorepeHTHHH a o61lUIllli rrpo1l6CC R8] B~O H 3 CTPYKTYPH ypaBHeHllR
(I) B cwry MaJIOCTlI 3KC lIOH61~Horo llaKTOpa 2 - tr) ( H
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H3JIYleHHR - II~(t c (42 )I ( f )- t~
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TalltHM 06pa30M B lIHTepBaJIe ~ gtgt I HMeeT MeCTO JIKJIlb
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He3aBHCHMO JJPyr OT JJPyra C xapaKTepHHM BpeMeHeM J He 3aBHCJ1ll1IDl OT
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5 KpBlep o nplDleBlDolOcn pe3YJIbTa1OB
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I ~
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no~eHHUX B sect 3 pe 3YJIbTaTOB RBnR8TCR BIlIO~eHRe COOTHOm6HBR (29)
Z IN ( - i t1 ) ltL i 3~6Cb B6JlHmHll 1 H ~ ollpe~eruooT BpeMR 3auepuw H ItJmTemshy
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CTBeHHO 3aBHCHMOCTH 3TlJX B~H OT ~c~a H~aTaneH B reoMeTpBshy
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j c gy7 IV 3f~ J 1
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L gtgt Lp -= ~x (If ) (48)36)1Sshy
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3~eCb IjJyHKIUfl )( (_~ ) orrpe~eMBTCfl RaR pemeHHB ypaBH6HIR
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B pa60Te I MH JlCIIOJIL30BaHH p~ ynpomeliHH KOTOpue cnpaBe~u TOJILshy
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ro 6o~rnesectjPaRTepHoro BpeMeHH H3MeHeHllfl 8MTInMTynH O~ B 06pa3ue
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1 Bogolubov NN( j r ) Pam Le Kien Shumovsky AS Physica1984
128A No 1 2 p82-98
2 Groas M Earo che S PhysRep 1982 v93 No5 p301-396
15
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
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) til C- f2 X +Z R ~(oraquoTH - (5)t kC C -r Ll pound - ltIZ (ojgt
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I (-t) = - fir -It lt~ (-traquo (b)
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2
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V2 M8KCKMaJILHO~ HHTeHCHBHOCTH CBl1neTeJIbCTByeT npoCTO 0 nOffBneHHH
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KOJIJI9KTHBffiD( flBJIeHl1i1 rne Korep9HTHoC Tb HOOKT na c cl1BHilli
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eX == I II K = IDO (l ) COO80 (IT) 300 (111 ) shy
I = lit to
PlH~B~ XapaKTep H o6ycshy
lIOEneHa BHelliHHM areHTOM B nposhy
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eT ITO cymecTBOBaHHe CBepXR3XYshy
leHRR MO~O TpaKTOB8Th K8K pe3YJIbshy
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(10-2) tiro JlPyrHMH mmoJIRMB J3JIaronapR B38Hshy
MOlIeJicTBIDIM aTOMOB 1epe3 nOJIe H3shy
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3
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( T ) (lu)
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~ I
t t (I V (II)11-shyI II r
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lltIZt t) ~ t-
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lt AI) ( Iraquo -lt - IV ILl
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= Exp - --=- e-y (- tj )r (1111 klt (0 gtt- ill) (
n03TOMY
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(15)2 (
rne JltOHCTaHTa S Oflpe)leJIHeTCH YCJlOBl1eM CIIiliBaHl1fl C peweHl1eM (3) B
o 6JIac Ill t ltlt T OTC Kl)la HeTPY)JHo nOJIYlJ1Th flO qJOpMyJIe (b) BblpaJReHl1e
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l (
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l )HC 2 ~3 qop lly JIU 11 plfCYHllta BI1)JHO 1TO JeT BJrnHHJ fl HeODHopoIIHOro
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M8HTax (cM7~ 3 11 TaM ~e ~TepaTypy) X
Tenep 0603HatrnM lepe3 trllt MOMeHT BpeMeHJ llpJ KOTOPOM BblpaJKeshy
wl e B npaBoli laCTJ1 YlJaBHemUl ( 16) l(OCTlfraeT MaKC1MaJIbHOrO 3HaleHHH
TaKaf BeJIHUlHa t onp e)leJIHeT BpeMR 3aQelJlKlltl1 oBepXli3JIyqBTeJUHoro
l1Ml1Ymiddot1hca np yqeTe lICOlHolJOIIHom ytlMpeHPl1I JIHHIDI YprulHeHHe Mil Hee
e CTh lt1--0-7 2 7V - t 1 elY a -~-t e 1eN1 ) e - o (17) vf T ( v t i
5
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50 HKH BH~CJl9HI1H B~shy
llOJIHeHii no JoptYJIe (~2) ~ MQaMe poundaMH T =- 0 N ( 1 I 5 lA (Ill IO N ( ill t 11I~= 30G t = 0 0 09 ~ bull40 f = 0 0033 J I=Vi l-
30 TaK KaK ypaBlIoHlHI (14 ) - ( 16 ) (lwm nOJJ1eHtl B llperrUOJIome shyHRH 0 npellc6peltUlMov M8JIOCTll
B1uraun l-I8KOIepeHTHoI O H3JIyle shy
HHfI B ypaBl leHRI ( I ) TO JIe rKO
BHJJCTb iTO yCJlOBl1eM TIIlI1MeHJIIshy
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~l fl ~ltR~ (~gt2 e- t~4
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60JI1gttnlIY HCJlO H3JlYl8TeJreA ( Nxgt gtgt n llOJUlOCTlgt1l BO 36~eR8 bull T e lt R ~ p-= 11 2- H BltlIBJt BRTHp830BBHClWX LlleHOB TaR hiM lTD
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B8lIrut C (15) (16) nOJl1lBeM
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(20)
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ltR~ (+) - r th 2 ~AI (lti - t-In )] ) (21)
6
I ) ~ IV~r~ - t T 7
shy- rt = E (I (-11 r JU ( )- CC-Ia )
v (v (22)
me T eCTh llpKBenemme BP9MH
--_ --1 )== ( i _ t- i IT) ( 23)
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JyEK8TO B pa60Te4 nOCBRmeHHOa HCCJIeuo~ paanK~~ PexHMOB
cBspxaarryqeHKR B KrJroo6paaHoH cpeue Ha OCHOBe ypaBHSmrR nnR yrJla MOxa
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1 ~I LTgt ( 1 (24 )T - (_
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CHMYM8 nOBeneHHe 3TOA ~~ XMeeT cJIe~ B~n
~ r Jt ((It ) - t~) - lt( ell [ J1 (25)22 1 rne BeJmlUIHa
- T (1- = (A
i ( l t) ) = ~ ~ (26) t - (InI (~-il f I
~ f)
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n J ~
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7
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T ~-- ) C- If ~ ( JI (28)
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llPH STOM MaKCHManbHaH HHTeHCRBHOCTb HanyqeRHfl RMeeT B~
If ~ J 1-shy
I 11 ( I I - ) - T - -- shyO A L L IV lt ~-rn _ - _ 177 (30)
rna
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J gt (4 gt- 1 c (31)111 ( 77 middot) n il rlt - r h ) (
3TO 03HaQaeT iTO HeOnHOponHOe ymRpeHRe JllfHIDI ITpIffiOnHT K yB9JIKlemoo
IlJIlTe~HOCTH CBepXH3JIYlaTeJThHoro HMIIYJIICa Ltv BpeMeHR 3anep(KH
T k 11 yMeHbmeHID) MaKCBMyMa HHTeHCHBaOCTR HanyqeHRR j - ~ B qaCTshy
a~~ CJIyiae KOrna Traquo i IDIIeeM rrpoCTO tf- - 7 ~ T _ ~ _ 17 V AI 1 )1
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ypaBHeHRR (17 ) CJIen~ 06pa30M
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HRXJ c T H COrJIaCHO onpenMemm (23) RMeeM
T - tn (-( f I ) T-I c (32)177 I n T
C npyroH CTOPOHH ypaBHeHRe (17) rraeT
TNe 1- _ (I f) - ern lT - - f h (33)
J 71
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~ fshy(t _ L Lj (34 )~ - - (h -shy ) ~fshy
A (N
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1 16
14
12
10 1213 16 20 24 28
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lW no qoINY~8M ( 2 6)R (36) lIlIH CJIyiM t-rn = 10 0v bull
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HOTOHHO y6HBa~ro rrOBeneHllfl
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13 IloBeneHRe B o6JIacTRT Tt lt 13 03HaiaeT iTO CJImllKOM
tn 6o~woe ~flHRe HOOnaOponHOra
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nBHHHM DHO cymeCTBeHHO OTJIHqaeTshy
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Ta lIlIH CJIYlM T gt ern CM bull qopshy
MYJIY (3I) H OT pe3YJIbTaTOB npyshy
lRX aBTOPOB2-4i llpHOOla TaKOlt
OC06eHHOCTH rrOBeneHKR 3aBRCRMOCshy
TH f rH r OT T 3aKJITOiaeTCfl B CJIeshy
nyDIIleM
~3BeCTHO iTO B npouecce H3shy
JIYleBIDl l1MelOT MeCTO ItBa npoTKBOshy
UO~OlKma KOHKypHpyDIIRX ifaKTOpa
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napS B3aHMoneHCTBRIl iepe3 no~e R
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T gtgtc rJIaBHYIgt POJII RIpaeTn 7
tpaKTOP qa3RpOBKR 06YCJIOBIDlllIHi
11 l)
cBepXRanyqaTe~Hoe IIOshy
lIt)1 Io Be~8HHe HMny~ca ~aKshy
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10 mm ITpHBOmrT K 38Me~shy
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6 CYMMapHoro ~O~HOro
MOMeHTa aTOMOB ~e~oshy
BaTemHO K YB8JmI9mm
Bp9M9HH 3anepxKH HMshyJ itshy
rry~ca I rH bull A Ror~a
T IIpH6mmaeTcR K tr~ 2 L 6 8 10 c~ecTBeHHyD po~ Hashy
~aeT HrpaTh npyroa ( 10-2) t To centaRTop - ne~3HPOBKa
~IIo~ea aTOMOB TaR
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HO CTpeMHTCR YMeHIshyO0156 Lv (11J6 OQI23 t (W) O O~O i (IY) 00 23 L (Y) L
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)
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TIp aTOM YMeHhwaeTCR MaKCRMantHaR HBTeaCKBHOCT~H KOr~a ~~ tlgt
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YCJIOBH9 eCTh H KpHTepKH llpRMeHHMOCTH (36 ) KaK rrpH6~eHHR BHcwero ITOshy
PRJ(Ka Ho C ~yroH CTOPOHH IIOCKO~KY B peaJiIlliX CHCTSMax A-~gt I TO
~1 Al raquo 1 n 03TOMy ~ raquo 1 BCJI9ItC TBe 3TOro OueHllta (36 ) xopomo
OllltCHBaeT 3HaqSIU9 BpeM9HH 3aneparot CBepXll 3JIyUlreJrhHoro HMJIy~ca ( 22) IIJlH 60JIS9 CJIaOOM YCJIOBIDI 18M YCJlOB1I9 (29)
Tgt t r77 + r2 ( (37)
lJHCJI9BH09 HCCJIe~OB8lHe qopyJru (22 ) o lllJCblB8lOIllel qoplY mmy~ca H
OoSHKH (36) n OItTBsJlllllaeT C~8JIB1ilWiI BHBO~ (eM T3OJUlllY) PaCIeT 110shy
Ka3HBa9 qro B CJIy1laeAl~ = 300 CJIeItOBaT8JIIHOrn -- OOI89
III
7t T a 6 ~ H ua CpaBHeHHe 3HallelIIlli BpeMeHH 3aneplKKH RMIlY1Ihca rrnj
IIOJIYlelllUlX lHCneHHHM HC~e~OB8HReM qoPMYJIll (22)
C OU9HKOtt ( 36) H TaKlKe C on9HKoi1 (27) l3ollllilrumoshy
JIYJlUlaTo BJl1lliICJIeHIDI BHIIOIIHeFlli MR CJIYlM II z 300 tn = 00189 co ~ = 00033 ~
---------------================ - - ---~- (x 1( ~) Pe3Y~TaT
GueRRa (36) OneHKa (27)~ rnCJIeHHoroT t (gtlt i l old RCCJIenOB8HRR E-ll
46 2 3 2 3 245
42 2 34 2 34 251
39 24 2 38 260
3 6 2 45 2 42 271
32 25 2 45 286
2 9 2 58 2 41 3 08
26 2 63 2 04 345
16 2 40 HeIIpHJlleImMa HeIIpIDlleHmm -------- ========
7 t = 00033 ooell1B (-no qopfyJIe (36) ~OBOJIbHO XopoWO cor~acyshy8TCR C TO~ pe 3YJIbTaTOM HCCJIe~OB8HRR qopMy~ (22) MR Bcex 8Haqeshy
HIlA r ynOBJIeTOOpJlIiIlRX YCJIOBHll (37)(T e Tgt 0026) tmcrreHlIlDll HCshy
I h 51 CJlenOBaIDleNl MOlilliO TaKii(e UOKa3aTh ITO
B CJIYllae HeOUHOpOlJflOrO BpeM8Hl1 JKl13Hl1 13 shy1 JIYID T8JIe~i T IIopilllKa t T~ t m i1
410 7d(T-Tm)~ 1cpopMYJIa (22 ) ]d B0001l16
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1 Bogolubov NN( j r ) Pam Le Kien Shumovsky AS Physica1984
128A No 1 2 p82-98
2 Groas M Earo che S PhysRep 1982 v93 No5 p301-396
15
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
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KaH aCl1MMeTpii fl CBepXli 3JIJaTeJIbHOrO HMTIyJIbca Ha6JIID)JaeTCH B 3KcnepMshy
M8HTax (cM7~ 3 11 TaM ~e ~TepaTypy) X
Tenep 0603HatrnM lepe3 trllt MOMeHT BpeMeHJ llpJ KOTOPOM BblpaJKeshy
wl e B npaBoli laCTJ1 YlJaBHemUl ( 16) l(OCTlfraeT MaKC1MaJIbHOrO 3HaleHHH
TaKaf BeJIHUlHa t onp e)leJIHeT BpeMR 3aQelJlKlltl1 oBepXli3JIyqBTeJUHoro
l1Ml1Ymiddot1hca np yqeTe lICOlHolJOIIHom ytlMpeHPl1I JIHHIDI YprulHeHHe Mil Hee
e CTh lt1--0-7 2 7V - t 1 elY a -~-t e 1eN1 ) e - o (17) vf T ( v t i
5
PtC 2 ~JIa cBepo3JIYlashyreJThHOlO fMIIYJIbCa IT1JI1Il010 Yle le BJIIDlHKfI neorrHOshyp OllHoro YJUHPeHlu l ID1shy
50 HKH BH~CJl9HI1H B~shy
llOJIHeHii no JoptYJIe (~2) ~ MQaMe poundaMH T =- 0 N ( 1 I 5 lA (Ill IO N ( ill t 11I~= 30G t = 0 0 09 ~ bull40 f = 0 0033 J I=Vi l-
30 TaK KaK ypaBlIoHlHI (14 ) - ( 16 ) (lwm nOJJ1eHtl B llperrUOJIome shyHRH 0 npellc6peltUlMov M8JIOCTll
B1uraun l-I8KOIepeHTHoI O H3JIyle shy
HHfI B ypaBl leHRI ( I ) TO JIe rKO
BHJJCTb iTO yCJlOBl1eM TIIlI1MeHJIIshy
MOCTJ I1 X flIlJlRe TC fl HepaBSHCTBO
~l fl ~ltR~ (~gt2 e- t~4
2 5 8 gt i 1 + i (i 1f ) (I8 ) 2 lt - I
(1 0-2) tIto
nS J f j TN ~- t 1 ~ ] lt- R-r (1 ) c ) ~ t (19)2 -- t
BePHeMCH K 60JIee ueTMbHOMY paCCMOTpemm ypaBHeHlrl (I5 ) (16) ITpenrroJIOXlIM bull lTO B H8l8JIhllllA MOMeHT t = 0 CHCTeMa C uOCTaTOlHO
60JI1gttnlIY HCJlO H3JlYl8TeJreA ( Nxgt gtgt n llOJUlOCTlgt1l BO 36~eR8 bull T e lt R ~ p-= 11 2- H BltlIBJt BRTHp830BBHClWX LlleHOB TaR hiM lTD
rL~ I Toma B 06ttaCTJII t ltlt T llpHMeHJIIMH yprulHemm ( II) IToCJIe ClJlHshy
B8lIrut C (15) (16) nOJl1lBeM
T - -t rnb = 2lv
(20)
CJIeuOBaTeJThHO ypBBHemUJ (15) (16) MOSHO nepellHcaTb B BlII(e
ltR~ (+) - r th 2 ~AI (lti - t-In )] ) (21)
6
I ) ~ IV~r~ - t T 7
shy- rt = E (I (-11 r JU ( )- CC-Ia )
v (v (22)
me T eCTh llpKBenemme BP9MH
--_ --1 )== ( i _ t- i IT) ( 23)
O~eTRM aneClgt ITO cJxlp1YJUl (22 ) BnepBlle 6wta nOJIYieH8 BomrcIJ81nlO 11
JyEK8TO B pa60Te4 nOCBRmeHHOa HCCJIeuo~ paanK~~ PexHMOB
cBspxaarryqeHKR B KrJroo6paaHoH cpeue Ha OCHOBe ypaBHSmrR nnR yrJla MOxa
060aH8lHM lepea t j) peweHife YPaB09HHH ( 1) = ~ CorJIacno (23) RMeeM
1 ~I LTgt ( 1 (24 )T - (_
HeTPYJJHO BllIJen lTO B TOUle i~ TJ ) ~ rth 1-mJ 4JHry_ tV
PHPyrgtIlIBJl B llpBBO~ laCTH yp8BHeHlJR ( 22) HMeeT oCTpIiA llHllt B6Jm3il M8Kshy
CHMYM8 nOBeneHHe 3TOA ~~ XMeeT cJIe~ B~n
~ r Jt ((It ) - t~) - lt( ell [ J1 (25)22 1 rne BeJmlUIHa
- T (1- = (A
i ( l t) ) = ~ ~ (26) t - (InI (~-il f I
~ f)
OnpeneJIR6T CTenem cnana C mrna C npyroi CTOpoHli CTSnSHD R3MeSemrR
3KCUOHeflIOlBJThHoro cJaKTOpa t(j1I- tiT) B ITp8BOA ttaCTH (22) X8prultTampshypB 3yeTcR BeJDflHlIol T IT0 3TOMY JISIKO BllI(eTb lTO TOni M8Kcnryshyhla -f l1Jl8BOl laCTB ypaBHeffiHJ (22 ) 6yneT 6lIH3M R -t 4 bull T e
n J ~
T ~ -t T 117 ~ 17-1 J) T- T ) (27)
rH
7
ecnR Burro~eTcR yc~oBHe ~CnO~30BaHHe STO~ qopMy~ BMeCTe C (24) H (26) rraeT OKOffqaTanDHHa
T ~-- ) C- If ~ ( JI (28)
KOTopoe cor~aCHO (26) SKBRBMeHTHO CJIenyJOlDeMY shy~~ ltlt i (29)
~ -t-I - C
llPH STOM MaKCHManbHaH HHTeHCRBHOCTb HanyqeRHfl RMeeT B~
If ~ J 1-shy
I 11 ( I I - ) - T - -- shyO A L L IV lt ~-rn _ - _ 177 (30)
rna
CpaBHeHRe qoJlMY~ ( 26) (27) (30) C qoNYJI8M1I (II) naeT
- -f - -~
J gt (4 gt- 1 c (31)111 ( 77 middot) n il rlt - r h ) (
3TO 03HaQaeT iTO HeOnHOponHOe ymRpeHRe JllfHIDI ITpIffiOnHT K yB9JIKlemoo
IlJIlTe~HOCTH CBepXH3JIYlaTeJThHoro HMIIYJIICa Ltv BpeMeHR 3anep(KH
T k 11 yMeHbmeHID) MaKCBMyMa HHTeHCHBaOCTR HanyqeHRR j - ~ B qaCTshy
a~~ CJIyiae KOrna Traquo i IDIIeeM rrpoCTO tf- - 7 ~ T _ ~ _ 17 V AI 1 )1
I lTD l1 gtltlUlaeTCR DoJIee TOiHM OueHKa lIlIH BpeMeHR 38shy- U ~ hvlt nepxKR MOlleT 6HTb uOJIYieaa Ha OCHOBe upn6JIR1teHHoro pemeHRfl
ypaBHeHRR (17 ) CJIen~ 06pa30M
0603H8iIDII 1r 7 - -tTl = L1 bull BBlUY MaJIOCTR BeJIRllRlill L1 no CpaBHe-
HRXJ c T H COrJIaCHO onpenMemm (23) RMeeM
T - tn (-( f I ) T-I c (32)177 I n T
C npyroH CTOPOHH ypaBHeHRe (17) rraeT
TNe 1- _ (I f) - ern lT - - f h (33)
J 71
llO)lCTaBRY Tenepy (32) B (33) C yieTOM MMOCTH ~ UOJIYlllM
~ fshy(t _ L Lj (34 )~ - - (h -shy ) ~fshy
A (N
rne ~TeJIIHOCTb HMDYJIIca ~ A-OIlJlCIlBaeTCfl qoIHYJIol (26) OTCIlna
DeeM gtl )~f- oc-- gtf
f h-gt = Igt - C IV 0 [1(- th -K (35 )r
J-~ pe3Y~TaT lIlIH m
j -----L Jf _J
HI TI In -1_ II
L shyI ( r-t TT- Trn
aT~ TNI
6
5
4 ]
oL--~-----------shy
12 16 20 24 28 Tt m
~tm (
1 16
14
12
10 1213 16 20 24 28
Ttm
PRC 3 SaBHCRMOCTH IlJIlTeJThHOCTR lOOIYJIIca Z- (a)R WeMeshyHR 3auepxKH f (6) OT HeshyO)UIoponaoro BpeueHll U 3HR r BlARcJIeHRR BWlOJIHeshy
lW no qoINY~8M ( 2 6)R (36) lIlIH CJIyiM t-rn = 10 0v bull
~t- ) (r1 ~- ~ J (36)
- 0 17 ( v
~ - of SaBRCRMOCTI t H I IV OT Heonshy
aopoIllloro BpeMeHR lU3HR HanyqBTeshy
JIeM T OIllICaHHM qopfyJIBMI
(26) H (36) nOKa3aHa H8 pHC 3
lIlIH CJIYUlR 1 = 10 (V bull H3 PHshycyaxa BRnBO iTO B OTJIRqRe OT MOshy
HOTOHHO y6HBa~ro rrOBeneHllfl
~ 7 (- JcentyHKllHR i (T) rn shyo6JranaeT MaKCRMyMOM B TOiKe Iz=
13 IloBeneHRe B o6JIacTRT Tt lt 13 03HaiaeT iTO CJImllKOM
tn 6o~woe ~flHRe HOOnaOponHOra
yumpeHldSl JIHHKH ITpilllOnHT He K yBeshy
JIHieHRD a K yMeHbmeHHD BpeMeHH
3aueJllKKR IDIIUyJIIca A aTO C nepshy
Bora B3r~a ORa3HBaeTCfl HeoxHshy
nBHHHM DHO cymeCTBeHHO OTJIHqaeTshy
CS OT nOJIYieHHoro BHIlle pe3YJIITashy
Ta lIlIH CJIYlM T gt ern CM bull qopshy
MYJIY (3I) H OT pe3YJIbTaTOB npyshy
lRX aBTOPOB2-4i llpHOOla TaKOlt
OC06eHHOCTH rrOBeneHKR 3aBRCRMOCshy
TH f rH r OT T 3aKJITOiaeTCfl B CJIeshy
nyDIIleM
~3BeCTHO iTO B npouecce H3shy
JIYleBIDl l1MelOT MeCTO ItBa npoTKBOshy
UO~OlKma KOHKypHpyDIIRX ifaKTOpa
~3RpoBKa ~o~el aTOMOB 6JIaIOshy
napS B3aHMoneHCTBRIl iepe3 no~e R
neqaaHpOBKa HX Bc~enCTBHe pa3JIRshy
~ co6CTBeHHHX iaCTOT ITpH Heo~shy
HOPO)(HOM ynmpemm JIHHB1l Ko rna
T gtgtc rJIaBHYIgt POJII RIpaeTn 7
tpaKTOP qa3RpOBKR 06YCJIOBIDlllIHi
11 l)
cBepXRanyqaTe~Hoe IIOshy
lIt)1 Io Be~8HHe HMny~ca ~aKshy
TOp ~8~3KpOBKH ~IIOshy
~e~ CBff3aHHHH C H90~shy12 HOPOlOWM ynmp9HHeM Jmshy
10 mm ITpHBOmrT K 38Me~shy
neHKID YCTaHOan9HHR 8 MaKCHMEUnBOB BEllllfUnibI
6 CYMMapHoro ~O~HOro
MOMeHTa aTOMOB ~e~oshy
BaTemHO K YB8JmI9mm
Bp9M9HH 3anepxKH HMshyJ itshy
rry~ca I rH bull A Ror~a
T IIpH6mmaeTcR K tr~ 2 L 6 8 10 c~ecTBeHHyD po~ Hashy
~aeT HrpaTh npyroa ( 10-2) t To centaRTop - ne~3HPOBKa
~IIo~ea aTOMOB TaR
PlIe 4 RaK TaKru neltIa3lfPOBKa 3aBHCIlMOCTI OT BpeMeHH t HBTeHClmshyHOCTH HanyqeHBR (22) ITpH C~HOM BnHshy BHSHBaeT 3aTyxBHH9 CYMshymum H80ltHOpoIHoro ymap8HHR 1IlllIlm MapHoro ~O~Horo MOshy( T - T) BWlHCJIeHHR BIffiOIIHeHH C IIapBM8Tp8MH-C)- = 300 7~= 0 0189 t M8HTa H C~e~OBaTe~shyTmiddot c 0 0033 to middot f = deg0169 7 ( I)
HO CTpeMHTCR YMeHIshyO0156 Lv (11J6 OQI23 t (W) O O~O i (IY) 00 23 L (Y) L
() = N M ( WHTh HHTeHcKBHOCTh H3shy
)
~eHHH no 3KcnoH9~shyaJiIHOMy 3aKOHY TO BpeMR nOCTIDK6HHH mnta ~HallHHaeT YMsmUJaTnCJJ
TIp aTOM YMeHhwaeTCR MaKCRMantHaR HBTeaCKBHOCT~H KOr~a ~~ tlgt
HMYl8HHe nepeCTaeT 61gtlTb CBepXH3JIYIaT8JI1IDlM ( CM pHC 4) OTClllla ~erKO rrOHRTh nOBe~eHHe ifiyHKIUH 1 -N (T) ITOllta3aHHOe Ha pRC 36
PaCCMOTpHM TeIIepI YCJIOBHe ITpHM9HHMOC TH oueHXH ( 36) HeTpYlUo BHshy~eTh qTO OueHKa ( 27) c~8nyeT H3 (36) ITPH yC~OBKH (29 ) TaR ITO 3TO
YCJIOBH9 eCTh H KpHTepKH llpRMeHHMOCTH (36 ) KaK rrpH6~eHHR BHcwero ITOshy
PRJ(Ka Ho C ~yroH CTOPOHH IIOCKO~KY B peaJiIlliX CHCTSMax A-~gt I TO
~1 Al raquo 1 n 03TOMy ~ raquo 1 BCJI9ItC TBe 3TOro OueHllta (36 ) xopomo
OllltCHBaeT 3HaqSIU9 BpeM9HH 3aneparot CBepXll 3JIyUlreJrhHoro HMJIy~ca ( 22) IIJlH 60JIS9 CJIaOOM YCJIOBIDI 18M YCJlOB1I9 (29)
Tgt t r77 + r2 ( (37)
lJHCJI9BH09 HCCJIe~OB8lHe qopyJru (22 ) o lllJCblB8lOIllel qoplY mmy~ca H
OoSHKH (36) n OItTBsJlllllaeT C~8JIB1ilWiI BHBO~ (eM T3OJUlllY) PaCIeT 110shy
Ka3HBa9 qro B CJIy1laeAl~ = 300 CJIeItOBaT8JIIHOrn -- OOI89
III
7t T a 6 ~ H ua CpaBHeHHe 3HallelIIlli BpeMeHH 3aneplKKH RMIlY1Ihca rrnj
IIOJIYlelllUlX lHCneHHHM HC~e~OB8HReM qoPMYJIll (22)
C OU9HKOtt ( 36) H TaKlKe C on9HKoi1 (27) l3ollllilrumoshy
JIYJlUlaTo BJl1lliICJIeHIDI BHIIOIIHeFlli MR CJIYlM II z 300 tn = 00189 co ~ = 00033 ~
---------------================ - - ---~- (x 1( ~) Pe3Y~TaT
GueRRa (36) OneHKa (27)~ rnCJIeHHoroT t (gtlt i l old RCCJIenOB8HRR E-ll
46 2 3 2 3 245
42 2 34 2 34 251
39 24 2 38 260
3 6 2 45 2 42 271
32 25 2 45 286
2 9 2 58 2 41 3 08
26 2 63 2 04 345
16 2 40 HeIIpHJlleImMa HeIIpIDlleHmm -------- ========
7 t = 00033 ooell1B (-no qopfyJIe (36) ~OBOJIbHO XopoWO cor~acyshy8TCR C TO~ pe 3YJIbTaTOM HCCJIe~OB8HRR qopMy~ (22) MR Bcex 8Haqeshy
HIlA r ynOBJIeTOOpJlIiIlRX YCJIOBHll (37)(T e Tgt 0026) tmcrreHlIlDll HCshy
I h 51 CJlenOBaIDleNl MOlilliO TaKii(e UOKa3aTh ITO
B CJIYllae HeOUHOpOlJflOrO BpeM8Hl1 JKl13Hl1 13 shy1 JIYID T8JIe~i T IIopilllKa t T~ t m i1
410 7d(T-Tm)~ 1cpopMYJIa (22 ) ]d B0001l16
rOBopR p ellleHHe YPaBH9IDlH (I ) OIrncrmashy
lOT BCe-laKH Hem U- r op6aTIcM HMTIYJIhC 7 C YMeHhmeHHOH aMJ1JlliTy~o~i H YMeHbllleHHH310 I BpeM6H ffi~ nOCT~eIDlH ~a ( cMpac 4 5)
Ha pRc 5 nOKa3aHO rrOB9~9Hl19 HMDY~ca
TIOJIY1leHH0 e llpn den9HH OM PemeHliIK11 J 10 I
1middot~1I PHc 5 3aBHCHMOCTb OT BpeY9HH
t IDIT9HCKBHOCTH HSJIYshy 1eHIIR IIOJIYleHHM IIpa
IlICJI9HBOM psmeHIDl YPaBshya8H1IJl 0) MJf napaMsljlOB N =2 100 L =O69 middot m - 5
- ]IL Ln 167 H~ - T = Tn-gt - K t N X
110l f LL t reI) K = 2(IT) A =4shy
0 1 3 t (HC )1 CUI) k = 60Y)
I
- shyypaBHeIDfl (1 ) ME CJIYlaH -=- 1u)- t= = 0(lt -1(
i 167 HC 1 = 1- If ltA- bull
4 IIOBeleHHe lIH1eaCHBHOCTlI l3JIYl9HIDr IlpH 60JThlJlliX BpeMeHax ( traquo T ) 3aMe~eHHe cBepXH3JIYleHHE H OCTa1O~8H HHBepcan Hace~eHHOC1e
MIl 110npo6HO o6cy JlHll B ITpe1U4llYllleM naparpa4Je BJIrunme HeOllHOpoIlltOshy
ro YJlIKPeHHR JIHHIDI Ha ltIoIMY BpeMH 3aneplUW H llJIHTeJIbHOCTh HMIIYJIbca
upa BpeMeHax ilOPMKa bull PaCCMOTpHM Tenepb KaJ BenyT ce6R IDIBepcHf
ltR~ (I )l R RHTeHCHBHOCTh Ii 3JIYle1mR f (I ) B IltHTepBaJIe 60JIbnmx BpeMeH
i gtgt (3~eCb rrpennOJIaraJIOCb R8] H pamme ITO T Memme BpeMeshy
1m C110HTaHHOro paCTI8JlB I OT~eJIbHoro H3JIYlaTe~ )
06paTHM CHalaJIB BIDIMaPHe Ha ypaBHeHIUI ( 21) ( 22) l1oJIYleHHlle
H3 (I) B lIpeIU10JIOJi eHIDl 0 rrpeo6JI8JlaHIDI CB6Pn3JIYlBT6JIbHOH KOMTIOHeHshy
Ttl H8Jl oOHlHol1 HeKorepeHTHoH Tallt R8] TIpH Z raquo i rrpRB6~eHHOe Bpe-
ME -( ) COrJIaCHO (23) rrpHlmMa6T rrp6n9JThHOe 3HBleHllt6
7 (1 )gt 1 ) = I (38)
TO H3 (21) ( 22) lloJIYla6M
t - f 0 7lt R (t) gt ~ ---7 - ~ 11 - ) Z t gt gt I A- ) f ~
t- ltlt i~ (39 )
shyi (I )jtgt ( t -- (
3TO 03HBlaeT ITO no HCTel8HHB BpeMeHH 3Ha~TeJIDHO npeBHmaIDmero
Heo6xo]tHMoe lIIlR nOJIHoli ~eqa3HpoBKH H3JIYlaT8JI8ii OCTB8TCR 8rne
HeKOTOpaR OCTaTOH8H HHB6pcHR H CBH3aHHaR C He~ HeBarryl8HH8H 3HeprHR
3anBCeHHafi B CHCT9M8 B HalaJThHWt MOMeHT 3To eCTh RBJIeillle 3BMe~eilllR
CBepXR3JIYeHlIR 06YCJIosneHHo8 H60~OpOnHllM ymKp6HH6M nKHRH2 OHO
MOE6T rrpHBO~Tb K TaR HB3HBaeMOMY orpBHHleHHOMY CBepXlI3JIYl6~2 5~ npH KOTOPOM H6 BCR B TOJIbKO He6oJIbmaH laCTb 3HeprKH CHCTeMH BTOMOB
Korep6HTHO H3JIyaeTCR
IIPH BpeM6Hax T ~ 0 raquo T I1IaBHyD POJIb B H3JIY8mm Brpa6 Ite He
KorepeHTHHH a o61lUIllli rrpo1l6CC R8] B~O H 3 CTPYKTYPH ypaBHeHllR
(I) B cwry MaJIOCTlI 3KC lIOH61~Horo llaKTOpa 2 - tr) ( H
CBH3aHHOro C HHM KOJIJIeKTRBHoro lJIeHB aTO ypaBHeHll6 nepeXOnBT B CJIeshy
~ee
~ ZR~ Ii raquo == - i (x v r lt R t raquo1 (40 )(_ 2 )
12
OTC)JJa nOrylaeM peDle1me IJ)lR HHBepCJm ( A~ (I ) gtB 06JIaCTH
~ ~ gtgt jt L-
I I gt( It t (V[- ( (41)lt- r ~ It )gt l - )
r~e llOCTOHHHaH orrpene~eTcR YCJIOBHeM CmRBaEHR C peWe1meM (21) B 06JIaCTH r COOTBeTCTBy1Ornee BIl1l8lKe1me IJ)lR HHTeHCHBHOCTH
H3JIYleHHR - II~(t c (42 )I ( f )- t~
OTIRCHBaeT H3B6CTHli aKC110He~HHil 3aKOH pacrrana
TalltHM 06pa30M B lIHTepBaJIe ~ gtgt I HMeeT MeCTO JIKJIlb
o6wmoe HeKor6peHTHoe Cn OHTaHHOe H3jlYleIDf8 Kor~a_ a T OMll p acIIaJJaJOTcR
He3aBHCHMO JJPyr OT JJPyra C xapaKTepHHM BpeMeHeM J He 3aBHCJ1ll1IDl OT
UlCJIa aTOMOB Ii
3aMe TlM lTO npH 1gt lI3 ltIoPMYJIH (41) nOJIYlBeM
-t A gt I (43)lt Rz 10gt1raquo_ ~ shy )
0Ashy( -
B cJIYiae OTCYTCTBHR HOOIIHOPOllHoro ynm-peHru JIlIlflm RMeeM A = I
( eM1 ) I103TorlY
~ (44)( ~ (rxraquo[
)
= - 3 TO 03Ha~aeT ~TO BCR 3HeprRR 3aTIaCeHHaR B CHCTeMe B HalaJIbHHfi Meshy
MeHT Bp8MeHn nepeillJIa B 3Hep~ H~8HnR B CHYlBe H80~OPOnHOro
ynm-peHHR JlHHID BKJI8Jl aHTH)630HaHCHIlX lJIeHOB B r aMKJIbTOilllaHe B38ID10shy
~6~CTBBR npHBOnBT K ~ ~ T IT03TOMY
IvIV rC (45)( k) (cgtu) gt shy ) L
Tlt~ --
HepaBeHCTBO ( 4 5 ) o3Ha~a8T ITO B pe3y~bTaTe ~n He-
OIIHOPO~oro ymHp8HKR JIlIHlIH nOCJIe np01l8cca HarryqeHRff OCTBeTCR eme Beshy
RM HHBep CKH H CBR38RHaR C Hea HeHarryqeHHaH 3HeprHR
5 KpBlep o nplDleBlDolOcn pe3YJIbTa1OB
3aKaHlHBaH p acCMOTlJ8HHe BJIJUlIDIR H60lIliOpoJtHOro ynm-pemrn JIHIDm Ha
cBepXR3JIY8 TeJIbHWi mmyJIbC cltlxJp1YJIKPy eM KPHTepHH TIpBM9tmMOCTlI IIOJrYshy
leHHUX B sectsect 2-4 p e3YJIbTaTOB lIJm npoCTOThI 6yl9M orpaImlItBaTbCR cTj-
I ~
~aeM ROr~a pa60~ 06~eM B ROTOPOM HaXO~CH HarryqaTe~ MeeT Hrshy
~006pa3HyID ~PMY
KaK 6blJIO YRa3aHO p erneHlle (21) )JJllI mrnep cID HaCeJIeHHOCTBH
ltJltc (t) H Blip8leIDle HBTaHCltJllOCTlJ f31Iyiemm (22) B o CSJracTlI t T crrpaBell)IID3Il lOJIhRO Torna ROr~a BIDIOJIIDI8TCR YCJlOBH6 (18) C Iij)yroA
CTOPOlill lIpH ~OnOJIHHTemHOM npe~lIOJIOlltemm (23) WIH BpeMeHil 3aneJlliUGI
mmyJILC8 cnpaBenmIBII OneHlUl (27) JIB ( 35 ) a Mfl )llIHTemHOCTlJ-f mmyJIbC8 T--ou eRRa (26) EMil nO~CT8BlIM (27 ) B rrpaBYRJ l8CTD (21) TO no~ymM
( R~ (-t ) gt ( 0TICj )(c1 (1) GJ(yOT
310 OSHa~eT ~TO yc~oBHe (18) aBTOMaT~eCKH BIDIo~eTCH ec~ BNshy
no~eTCR ycnoBlIe (29) C~e~OBaTeJILHo 0 6lIlHM KpHTepHeM llpHMeHilMocTIil
no~eHHUX B sect 3 pe 3YJIbTaTOB RBnR8TCR BIlIO~eHRe COOTHOm6HBR (29)
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HOCTD HMIIYJILca IIpH OTCyTCTBHlf Heo~oponHoro yumpeHIDI JIlUlllI COOTB6Tshy
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j c gy7 IV 3f~ J 1
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r~e = VIv - IIJIOTHOCTL B3JIyla TeJIel B pa60~eM 06beMe Vc A L 01shycnna MOlltliO nep eIIHcaTL YCJIOBHe nplWelfilMOCTH (29) B BHIJe
L gtgt Lp -= ~x (If ) (48)36)1Sshy
I middot ~
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COrJIBCHO (46) 3KBRBMeHTHO CJIeJlY1OOeMY
J p1~L raquo1 (50)7lt0shy
t)
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B pa60Te I MH JlCIIOJIL30BaHH p~ ynpomeliHH KOTOpue cnpaBe~u TOJILshy
RO Mfl CJIa60 MeHmOOerocR B rrpe~Max 06pasU1l IIOM IT03TOMY Jl)IHTeJIL-
HOCTb uponecca xapaRTepll3yeMaR B6XJllJlHOH (~ ~o~a 6UTb HaMHOshy
ro 6o~rnesectjPaRTepHoro BpeMeHH H3MeHeHllfl 8MTInMTynH O~ B 06pa3ue
ic = L C 3 ~TO 03Ha~aeT KPJlTepKlf ApeKRJl-KypTeHca 8
L L C ~I (51)
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1 Bogolubov NN( j r ) Pam Le Kien Shumovsky AS Physica1984
128A No 1 2 p82-98
2 Groas M Earo che S PhysRep 1982 v93 No5 p301-396
15
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
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orr~fMM Inc 1) 1JmiddotiJ11C (j ) nl (lB(J1 ~Jffia TO1h ~O MR HeOOJliJU Bl-IJ shy
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l (
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B8lIrut C (15) (16) nOJl1lBeM
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Tgt t r77 + r2 ( (37)
lJHCJI9BH09 HCCJIe~OB8lHe qopyJru (22 ) o lllJCblB8lOIllel qoplY mmy~ca H
OoSHKH (36) n OItTBsJlllllaeT C~8JIB1ilWiI BHBO~ (eM T3OJUlllY) PaCIeT 110shy
Ka3HBa9 qro B CJIy1laeAl~ = 300 CJIeItOBaT8JIIHOrn -- OOI89
III
7t T a 6 ~ H ua CpaBHeHHe 3HallelIIlli BpeMeHH 3aneplKKH RMIlY1Ihca rrnj
IIOJIYlelllUlX lHCneHHHM HC~e~OB8HReM qoPMYJIll (22)
C OU9HKOtt ( 36) H TaKlKe C on9HKoi1 (27) l3ollllilrumoshy
JIYJlUlaTo BJl1lliICJIeHIDI BHIIOIIHeFlli MR CJIYlM II z 300 tn = 00189 co ~ = 00033 ~
---------------================ - - ---~- (x 1( ~) Pe3Y~TaT
GueRRa (36) OneHKa (27)~ rnCJIeHHoroT t (gtlt i l old RCCJIenOB8HRR E-ll
46 2 3 2 3 245
42 2 34 2 34 251
39 24 2 38 260
3 6 2 45 2 42 271
32 25 2 45 286
2 9 2 58 2 41 3 08
26 2 63 2 04 345
16 2 40 HeIIpHJlleImMa HeIIpIDlleHmm -------- ========
7 t = 00033 ooell1B (-no qopfyJIe (36) ~OBOJIbHO XopoWO cor~acyshy8TCR C TO~ pe 3YJIbTaTOM HCCJIe~OB8HRR qopMy~ (22) MR Bcex 8Haqeshy
HIlA r ynOBJIeTOOpJlIiIlRX YCJIOBHll (37)(T e Tgt 0026) tmcrreHlIlDll HCshy
I h 51 CJlenOBaIDleNl MOlilliO TaKii(e UOKa3aTh ITO
B CJIYllae HeOUHOpOlJflOrO BpeM8Hl1 JKl13Hl1 13 shy1 JIYID T8JIe~i T IIopilllKa t T~ t m i1
410 7d(T-Tm)~ 1cpopMYJIa (22 ) ]d B0001l16
rOBopR p ellleHHe YPaBH9IDlH (I ) OIrncrmashy
lOT BCe-laKH Hem U- r op6aTIcM HMTIYJIhC 7 C YMeHhmeHHOH aMJ1JlliTy~o~i H YMeHbllleHHH310 I BpeM6H ffi~ nOCT~eIDlH ~a ( cMpac 4 5)
Ha pRc 5 nOKa3aHO rrOB9~9Hl19 HMDY~ca
TIOJIY1leHH0 e llpn den9HH OM PemeHliIK11 J 10 I
1middot~1I PHc 5 3aBHCHMOCTb OT BpeY9HH
t IDIT9HCKBHOCTH HSJIYshy 1eHIIR IIOJIYleHHM IIpa
IlICJI9HBOM psmeHIDl YPaBshya8H1IJl 0) MJf napaMsljlOB N =2 100 L =O69 middot m - 5
- ]IL Ln 167 H~ - T = Tn-gt - K t N X
110l f LL t reI) K = 2(IT) A =4shy
0 1 3 t (HC )1 CUI) k = 60Y)
I
- shyypaBHeIDfl (1 ) ME CJIYlaH -=- 1u)- t= = 0(lt -1(
i 167 HC 1 = 1- If ltA- bull
4 IIOBeleHHe lIH1eaCHBHOCTlI l3JIYl9HIDr IlpH 60JThlJlliX BpeMeHax ( traquo T ) 3aMe~eHHe cBepXH3JIYleHHE H OCTa1O~8H HHBepcan Hace~eHHOC1e
MIl 110npo6HO o6cy JlHll B ITpe1U4llYllleM naparpa4Je BJIrunme HeOllHOpoIlltOshy
ro YJlIKPeHHR JIHHIDI Ha ltIoIMY BpeMH 3aneplUW H llJIHTeJIbHOCTh HMIIYJIbca
upa BpeMeHax ilOPMKa bull PaCCMOTpHM Tenepb KaJ BenyT ce6R IDIBepcHf
ltR~ (I )l R RHTeHCHBHOCTh Ii 3JIYle1mR f (I ) B IltHTepBaJIe 60JIbnmx BpeMeH
i gtgt (3~eCb rrpennOJIaraJIOCb R8] H pamme ITO T Memme BpeMeshy
1m C110HTaHHOro paCTI8JlB I OT~eJIbHoro H3JIYlaTe~ )
06paTHM CHalaJIB BIDIMaPHe Ha ypaBHeHIUI ( 21) ( 22) l1oJIYleHHlle
H3 (I) B lIpeIU10JIOJi eHIDl 0 rrpeo6JI8JlaHIDI CB6Pn3JIYlBT6JIbHOH KOMTIOHeHshy
Ttl H8Jl oOHlHol1 HeKorepeHTHoH Tallt R8] TIpH Z raquo i rrpRB6~eHHOe Bpe-
ME -( ) COrJIaCHO (23) rrpHlmMa6T rrp6n9JThHOe 3HBleHllt6
7 (1 )gt 1 ) = I (38)
TO H3 (21) ( 22) lloJIYla6M
t - f 0 7lt R (t) gt ~ ---7 - ~ 11 - ) Z t gt gt I A- ) f ~
t- ltlt i~ (39 )
shyi (I )jtgt ( t -- (
3TO 03HBlaeT ITO no HCTel8HHB BpeMeHH 3Ha~TeJIDHO npeBHmaIDmero
Heo6xo]tHMoe lIIlR nOJIHoli ~eqa3HpoBKH H3JIYlaT8JI8ii OCTB8TCR 8rne
HeKOTOpaR OCTaTOH8H HHB6pcHR H CBH3aHHaR C He~ HeBarryl8HH8H 3HeprHR
3anBCeHHafi B CHCT9M8 B HalaJThHWt MOMeHT 3To eCTh RBJIeillle 3BMe~eilllR
CBepXR3JIYeHlIR 06YCJIosneHHo8 H60~OpOnHllM ymKp6HH6M nKHRH2 OHO
MOE6T rrpHBO~Tb K TaR HB3HBaeMOMY orpBHHleHHOMY CBepXlI3JIYl6~2 5~ npH KOTOPOM H6 BCR B TOJIbKO He6oJIbmaH laCTb 3HeprKH CHCTeMH BTOMOB
Korep6HTHO H3JIyaeTCR
IIPH BpeM6Hax T ~ 0 raquo T I1IaBHyD POJIb B H3JIY8mm Brpa6 Ite He
KorepeHTHHH a o61lUIllli rrpo1l6CC R8] B~O H 3 CTPYKTYPH ypaBHeHllR
(I) B cwry MaJIOCTlI 3KC lIOH61~Horo llaKTOpa 2 - tr) ( H
CBH3aHHOro C HHM KOJIJIeKTRBHoro lJIeHB aTO ypaBHeHll6 nepeXOnBT B CJIeshy
~ee
~ ZR~ Ii raquo == - i (x v r lt R t raquo1 (40 )(_ 2 )
12
OTC)JJa nOrylaeM peDle1me IJ)lR HHBepCJm ( A~ (I ) gtB 06JIaCTH
~ ~ gtgt jt L-
I I gt( It t (V[- ( (41)lt- r ~ It )gt l - )
r~e llOCTOHHHaH orrpene~eTcR YCJIOBHeM CmRBaEHR C peWe1meM (21) B 06JIaCTH r COOTBeTCTBy1Ornee BIl1l8lKe1me IJ)lR HHTeHCHBHOCTH
H3JIYleHHR - II~(t c (42 )I ( f )- t~
OTIRCHBaeT H3B6CTHli aKC110He~HHil 3aKOH pacrrana
TalltHM 06pa30M B lIHTepBaJIe ~ gtgt I HMeeT MeCTO JIKJIlb
o6wmoe HeKor6peHTHoe Cn OHTaHHOe H3jlYleIDf8 Kor~a_ a T OMll p acIIaJJaJOTcR
He3aBHCHMO JJPyr OT JJPyra C xapaKTepHHM BpeMeHeM J He 3aBHCJ1ll1IDl OT
UlCJIa aTOMOB Ii
3aMe TlM lTO npH 1gt lI3 ltIoPMYJIH (41) nOJIYlBeM
-t A gt I (43)lt Rz 10gt1raquo_ ~ shy )
0Ashy( -
B cJIYiae OTCYTCTBHR HOOIIHOPOllHoro ynm-peHru JIlIlflm RMeeM A = I
( eM1 ) I103TorlY
~ (44)( ~ (rxraquo[
)
= - 3 TO 03Ha~aeT ~TO BCR 3HeprRR 3aTIaCeHHaR B CHCTeMe B HalaJIbHHfi Meshy
MeHT Bp8MeHn nepeillJIa B 3Hep~ H~8HnR B CHYlBe H80~OPOnHOro
ynm-peHHR JlHHID BKJI8Jl aHTH)630HaHCHIlX lJIeHOB B r aMKJIbTOilllaHe B38ID10shy
~6~CTBBR npHBOnBT K ~ ~ T IT03TOMY
IvIV rC (45)( k) (cgtu) gt shy ) L
Tlt~ --
HepaBeHCTBO ( 4 5 ) o3Ha~a8T ITO B pe3y~bTaTe ~n He-
OIIHOPO~oro ymHp8HKR JIlIHlIH nOCJIe np01l8cca HarryqeHRff OCTBeTCR eme Beshy
RM HHBep CKH H CBR38RHaR C Hea HeHarryqeHHaH 3HeprHR
5 KpBlep o nplDleBlDolOcn pe3YJIbTa1OB
3aKaHlHBaH p acCMOTlJ8HHe BJIJUlIDIR H60lIliOpoJtHOro ynm-pemrn JIHIDm Ha
cBepXR3JIY8 TeJIbHWi mmyJIbC cltlxJp1YJIKPy eM KPHTepHH TIpBM9tmMOCTlI IIOJrYshy
leHHUX B sectsect 2-4 p e3YJIbTaTOB lIJm npoCTOThI 6yl9M orpaImlItBaTbCR cTj-
I ~
~aeM ROr~a pa60~ 06~eM B ROTOPOM HaXO~CH HarryqaTe~ MeeT Hrshy
~006pa3HyID ~PMY
KaK 6blJIO YRa3aHO p erneHlle (21) )JJllI mrnep cID HaCeJIeHHOCTBH
ltJltc (t) H Blip8leIDle HBTaHCltJllOCTlJ f31Iyiemm (22) B o CSJracTlI t T crrpaBell)IID3Il lOJIhRO Torna ROr~a BIDIOJIIDI8TCR YCJlOBH6 (18) C Iij)yroA
CTOPOlill lIpH ~OnOJIHHTemHOM npe~lIOJIOlltemm (23) WIH BpeMeHil 3aneJlliUGI
mmyJILC8 cnpaBenmIBII OneHlUl (27) JIB ( 35 ) a Mfl )llIHTemHOCTlJ-f mmyJIbC8 T--ou eRRa (26) EMil nO~CT8BlIM (27 ) B rrpaBYRJ l8CTD (21) TO no~ymM
( R~ (-t ) gt ( 0TICj )(c1 (1) GJ(yOT
310 OSHa~eT ~TO yc~oBHe (18) aBTOMaT~eCKH BIDIo~eTCH ec~ BNshy
no~eTCR ycnoBlIe (29) C~e~OBaTeJILHo 0 6lIlHM KpHTepHeM llpHMeHilMocTIil
no~eHHUX B sect 3 pe 3YJIbTaTOB RBnR8TCR BIlIO~eHRe COOTHOm6HBR (29)
Z IN ( - i t1 ) ltL i 3~6Cb B6JlHmHll 1 H ~ ollpe~eruooT BpeMR 3auepuw H ItJmTemshy
HOCTD HMIIYJILca IIpH OTCyTCTBHlf Heo~oponHoro yumpeHIDI JIlUlllI COOTB6Tshy
CTBeHHO 3aBHCHMOCTH 3TlJX B~H OT ~c~a H~aTaneH B reoMeTpBshy
~ecKOro rIsKTo pa ~ Blip8leHl ~~Jr~ (II ) Blm lrultTopa 12 6wx rrpHshy76miJKeHHo IIOJI IeH PeJlepoM 11 36eplIIl IJ)UI p a3JIRIHHX MaKpocROlIllleClGIX
ROHqJHryp~ ~pIi pa6olero 06beM8 )lnR Kpyr~oro IJJIHHHoro ItWnnlllJla C
lIHCJIOM ~eHeJIR IIOp~ I xopome~ amtpoKCRMaJJHei CJIyXJT Bllp8teHlle
~2 -x=
S Araquo ( ~_ ) ( A I- 1FA A ~4 ) (46 )1 ~
3nech A L -COOTBeTCTB~e llHO~ OCHOB8HHR B ~a~a ) -IllIIDla BOJIBH B3J1YleHlUI )-fCIIOJIb3YR (II ) Il (46 ) nO1IJl86M 2-7
j c gy7 IV 3f~ J 1
1- t th 3el ltL (47)
It It S)
r~e = VIv - IIJIOTHOCTL B3JIyla TeJIel B pa60~eM 06beMe Vc A L 01shycnna MOlltliO nep eIIHcaTL YCJIOBHe nplWelfilMOCTH (29) B BHIJe
L gtgt Lp -= ~x (If ) (48)36)1Sshy
I middot ~
HJIll z j (~- )I raquofr = ~ A)L (49)
3~eCb IjJyHKIUfl )( (_~ ) orrpe~eMBTCfl RaR pemeHHB ypaBH6HIR
j ~
LO )( gt- i Ie 81 Jr- 2 T
B CJIym6 KOr na TaKOe pemeHR6 cymecTByeT (T e KOrna Tc e ) B rrpoTHmlOM CJIyTlBB (Kor na Tgt e ~ ) MeeM rrpoClO _k -= if
Be3~e B 3TOH p a60T6 MI rrpe~o~~ ~TO ~C~O HanyqaTe~eH ~OCshy
TaTO~O 6 0JILmoe ~T06H BIDIOJIHamp)lOCb YC~OBHe II gtgt i A B c~ae Kpyr~oro IJ1IIHHoro ~a C ~CJIOM ~eH6JU UOP1mRa I 3TO y~BHe
COrJIBCHO (46) 3KBRBMeHTHO CJIeJlY1OOeMY
J p1~L raquo1 (50)7lt0shy
t)
ITocne~ee yc~oBHe KOTopoe He06xo~0 ~TlBaTh CBR3aHO C TaM
iTO llpll oi~eHll1 ypaBHeHHR (I) Ha OCHOBe KJlHeTHleCKKX ypaaHeHHii
B pa60Te I MH JlCIIOJIL30BaHH p~ ynpomeliHH KOTOpue cnpaBe~u TOJILshy
RO Mfl CJIa60 MeHmOOerocR B rrpe~Max 06pasU1l IIOM IT03TOMY Jl)IHTeJIL-
HOCTb uponecca xapaRTepll3yeMaR B6XJllJlHOH (~ ~o~a 6UTb HaMHOshy
ro 6o~rnesectjPaRTepHoro BpeMeHH H3MeHeHllfl 8MTInMTynH O~ B 06pa3ue
ic = L C 3 ~TO 03Ha~aeT KPJlTepKlf ApeKRJl-KypTeHca 8
L L C ~I (51)
)JJllI IIpHMaHHMOCTH IIO~6HHIlX pesYJrbTaToB )-fCIIOJIL3YR REHoe BIIP~eHHe
LN B (47 ) MOJl(HO nepeIIHCaTb (5D B B~e
L z L_ I JT c- (52)kfJ 3 i ) (
Jl lITepaTy p8
1 Bogolubov NN( j r ) Pam Le Kien Shumovsky AS Physica1984
128A No 1 2 p82-98
2 Groas M Earo che S PhysRep 1982 v93 No5 p301-396
15
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
-I737
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II 8HTR0PJi 1985 rOla
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111 J XU 1 11Y 4 IIH R
11 111 1 1 11 110 11 111 I l lIII1H 1JJ1R
111 1 I I1 I 1I1 Il l lllMl llIIMIlCTII
P lIl 1M liI Tli i1i ll I TIO IH 1 111 Kll il 1 111111 nIHilI
11111 amp11 If II r JIIA lytlHa 19 8 )
llepeBoA i1 II H
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into I II 1III u k ll i II g
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bull 1 ~ )JIIleni II ~ I i oI tl-gt 1 1YlIn1 r y of t he pul St f I I li n I lly I i 1110 1 111 1 pilI St middot durashy
tion 111 11 1111 j l1 t I1 ~ il y th middot rt la r dashyI i (Ill tf 1 1 _ p middot i hl ~ middot i ti l t IlIl pound 1 r Cs idu-
I I 111111 1111 i 110 a 11 1y l i il l middotX l rl f i l1h r t he pll l d 1111 I I I v il l l d i lY (middot d i illll lgt hnv 1)1 ( 11 e tashyhI i l ll l
11 10 iI ( I fr rll r llllmiddot d 11 h i Lahoralory o f T Ill l rl I I NIt
Preprint of the In H i llJtt l u r Nuo l car Kesearch Dubna 1985
PtC 2 ~JIa cBepo3JIYlashyreJThHOlO fMIIYJIbCa IT1JI1Il010 Yle le BJIIDlHKfI neorrHOshyp OllHoro YJUHPeHlu l ID1shy
50 HKH BH~CJl9HI1H B~shy
llOJIHeHii no JoptYJIe (~2) ~ MQaMe poundaMH T =- 0 N ( 1 I 5 lA (Ill IO N ( ill t 11I~= 30G t = 0 0 09 ~ bull40 f = 0 0033 J I=Vi l-
30 TaK KaK ypaBlIoHlHI (14 ) - ( 16 ) (lwm nOJJ1eHtl B llperrUOJIome shyHRH 0 npellc6peltUlMov M8JIOCTll
B1uraun l-I8KOIepeHTHoI O H3JIyle shy
HHfI B ypaBl leHRI ( I ) TO JIe rKO
BHJJCTb iTO yCJlOBl1eM TIIlI1MeHJIIshy
MOCTJ I1 X flIlJlRe TC fl HepaBSHCTBO
~l fl ~ltR~ (~gt2 e- t~4
2 5 8 gt i 1 + i (i 1f ) (I8 ) 2 lt - I
(1 0-2) tIto
nS J f j TN ~- t 1 ~ ] lt- R-r (1 ) c ) ~ t (19)2 -- t
BePHeMCH K 60JIee ueTMbHOMY paCCMOTpemm ypaBHeHlrl (I5 ) (16) ITpenrroJIOXlIM bull lTO B H8l8JIhllllA MOMeHT t = 0 CHCTeMa C uOCTaTOlHO
60JI1gttnlIY HCJlO H3JlYl8TeJreA ( Nxgt gtgt n llOJUlOCTlgt1l BO 36~eR8 bull T e lt R ~ p-= 11 2- H BltlIBJt BRTHp830BBHClWX LlleHOB TaR hiM lTD
rL~ I Toma B 06ttaCTJII t ltlt T llpHMeHJIIMH yprulHemm ( II) IToCJIe ClJlHshy
B8lIrut C (15) (16) nOJl1lBeM
T - -t rnb = 2lv
(20)
CJIeuOBaTeJThHO ypBBHemUJ (15) (16) MOSHO nepellHcaTb B BlII(e
ltR~ (+) - r th 2 ~AI (lti - t-In )] ) (21)
6
I ) ~ IV~r~ - t T 7
shy- rt = E (I (-11 r JU ( )- CC-Ia )
v (v (22)
me T eCTh llpKBenemme BP9MH
--_ --1 )== ( i _ t- i IT) ( 23)
O~eTRM aneClgt ITO cJxlp1YJUl (22 ) BnepBlle 6wta nOJIYieH8 BomrcIJ81nlO 11
JyEK8TO B pa60Te4 nOCBRmeHHOa HCCJIeuo~ paanK~~ PexHMOB
cBspxaarryqeHKR B KrJroo6paaHoH cpeue Ha OCHOBe ypaBHSmrR nnR yrJla MOxa
060aH8lHM lepea t j) peweHife YPaB09HHH ( 1) = ~ CorJIacno (23) RMeeM
1 ~I LTgt ( 1 (24 )T - (_
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CHMYM8 nOBeneHHe 3TOA ~~ XMeeT cJIe~ B~n
~ r Jt ((It ) - t~) - lt( ell [ J1 (25)22 1 rne BeJmlUIHa
- T (1- = (A
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n J ~
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rH
7
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T ~-- ) C- If ~ ( JI (28)
KOTopoe cor~aCHO (26) SKBRBMeHTHO CJIenyJOlDeMY shy~~ ltlt i (29)
~ -t-I - C
llPH STOM MaKCHManbHaH HHTeHCRBHOCTb HanyqeRHfl RMeeT B~
If ~ J 1-shy
I 11 ( I I - ) - T - -- shyO A L L IV lt ~-rn _ - _ 177 (30)
rna
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- -f - -~
J gt (4 gt- 1 c (31)111 ( 77 middot) n il rlt - r h ) (
3TO 03HaQaeT iTO HeOnHOponHOe ymRpeHRe JllfHIDI ITpIffiOnHT K yB9JIKlemoo
IlJIlTe~HOCTH CBepXH3JIYlaTeJThHoro HMIIYJIICa Ltv BpeMeHR 3anep(KH
T k 11 yMeHbmeHID) MaKCBMyMa HHTeHCHBaOCTR HanyqeHRR j - ~ B qaCTshy
a~~ CJIyiae KOrna Traquo i IDIIeeM rrpoCTO tf- - 7 ~ T _ ~ _ 17 V AI 1 )1
I lTD l1 gtltlUlaeTCR DoJIee TOiHM OueHKa lIlIH BpeMeHR 38shy- U ~ hvlt nepxKR MOlleT 6HTb uOJIYieaa Ha OCHOBe upn6JIR1teHHoro pemeHRfl
ypaBHeHRR (17 ) CJIen~ 06pa30M
0603H8iIDII 1r 7 - -tTl = L1 bull BBlUY MaJIOCTR BeJIRllRlill L1 no CpaBHe-
HRXJ c T H COrJIaCHO onpenMemm (23) RMeeM
T - tn (-( f I ) T-I c (32)177 I n T
C npyroH CTOPOHH ypaBHeHRe (17) rraeT
TNe 1- _ (I f) - ern lT - - f h (33)
J 71
llO)lCTaBRY Tenepy (32) B (33) C yieTOM MMOCTH ~ UOJIYlllM
~ fshy(t _ L Lj (34 )~ - - (h -shy ) ~fshy
A (N
rne ~TeJIIHOCTb HMDYJIIca ~ A-OIlJlCIlBaeTCfl qoIHYJIol (26) OTCIlna
DeeM gtl )~f- oc-- gtf
f h-gt = Igt - C IV 0 [1(- th -K (35 )r
J-~ pe3Y~TaT lIlIH m
j -----L Jf _J
HI TI In -1_ II
L shyI ( r-t TT- Trn
aT~ TNI
6
5
4 ]
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12 16 20 24 28 Tt m
~tm (
1 16
14
12
10 1213 16 20 24 28
Ttm
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lW no qoINY~8M ( 2 6)R (36) lIlIH CJIyiM t-rn = 10 0v bull
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- 0 17 ( v
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aopoIllloro BpeMeHR lU3HR HanyqBTeshy
JIeM T OIllICaHHM qopfyJIBMI
(26) H (36) nOKa3aHa H8 pHC 3
lIlIH CJIYUlR 1 = 10 (V bull H3 PHshycyaxa BRnBO iTO B OTJIRqRe OT MOshy
HOTOHHO y6HBa~ro rrOBeneHllfl
~ 7 (- JcentyHKllHR i (T) rn shyo6JranaeT MaKCRMyMOM B TOiKe Iz=
13 IloBeneHRe B o6JIacTRT Tt lt 13 03HaiaeT iTO CJImllKOM
tn 6o~woe ~flHRe HOOnaOponHOra
yumpeHldSl JIHHKH ITpilllOnHT He K yBeshy
JIHieHRD a K yMeHbmeHHD BpeMeHH
3aueJllKKR IDIIUyJIIca A aTO C nepshy
Bora B3r~a ORa3HBaeTCfl HeoxHshy
nBHHHM DHO cymeCTBeHHO OTJIHqaeTshy
CS OT nOJIYieHHoro BHIlle pe3YJIITashy
Ta lIlIH CJIYlM T gt ern CM bull qopshy
MYJIY (3I) H OT pe3YJIbTaTOB npyshy
lRX aBTOPOB2-4i llpHOOla TaKOlt
OC06eHHOCTH rrOBeneHKR 3aBRCRMOCshy
TH f rH r OT T 3aKJITOiaeTCfl B CJIeshy
nyDIIleM
~3BeCTHO iTO B npouecce H3shy
JIYleBIDl l1MelOT MeCTO ItBa npoTKBOshy
UO~OlKma KOHKypHpyDIIRX ifaKTOpa
~3RpoBKa ~o~el aTOMOB 6JIaIOshy
napS B3aHMoneHCTBRIl iepe3 no~e R
neqaaHpOBKa HX Bc~enCTBHe pa3JIRshy
~ co6CTBeHHHX iaCTOT ITpH Heo~shy
HOPO)(HOM ynmpemm JIHHB1l Ko rna
T gtgtc rJIaBHYIgt POJII RIpaeTn 7
tpaKTOP qa3RpOBKR 06YCJIOBIDlllIHi
11 l)
cBepXRanyqaTe~Hoe IIOshy
lIt)1 Io Be~8HHe HMny~ca ~aKshy
TOp ~8~3KpOBKH ~IIOshy
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10 mm ITpHBOmrT K 38Me~shy
neHKID YCTaHOan9HHR 8 MaKCHMEUnBOB BEllllfUnibI
6 CYMMapHoro ~O~HOro
MOMeHTa aTOMOB ~e~oshy
BaTemHO K YB8JmI9mm
Bp9M9HH 3anepxKH HMshyJ itshy
rry~ca I rH bull A Ror~a
T IIpH6mmaeTcR K tr~ 2 L 6 8 10 c~ecTBeHHyD po~ Hashy
~aeT HrpaTh npyroa ( 10-2) t To centaRTop - ne~3HPOBKa
~IIo~ea aTOMOB TaR
PlIe 4 RaK TaKru neltIa3lfPOBKa 3aBHCIlMOCTI OT BpeMeHH t HBTeHClmshyHOCTH HanyqeHBR (22) ITpH C~HOM BnHshy BHSHBaeT 3aTyxBHH9 CYMshymum H80ltHOpoIHoro ymap8HHR 1IlllIlm MapHoro ~O~Horo MOshy( T - T) BWlHCJIeHHR BIffiOIIHeHH C IIapBM8Tp8MH-C)- = 300 7~= 0 0189 t M8HTa H C~e~OBaTe~shyTmiddot c 0 0033 to middot f = deg0169 7 ( I)
HO CTpeMHTCR YMeHIshyO0156 Lv (11J6 OQI23 t (W) O O~O i (IY) 00 23 L (Y) L
() = N M ( WHTh HHTeHcKBHOCTh H3shy
)
~eHHH no 3KcnoH9~shyaJiIHOMy 3aKOHY TO BpeMR nOCTIDK6HHH mnta ~HallHHaeT YMsmUJaTnCJJ
TIp aTOM YMeHhwaeTCR MaKCRMantHaR HBTeaCKBHOCT~H KOr~a ~~ tlgt
HMYl8HHe nepeCTaeT 61gtlTb CBepXH3JIYIaT8JI1IDlM ( CM pHC 4) OTClllla ~erKO rrOHRTh nOBe~eHHe ifiyHKIUH 1 -N (T) ITOllta3aHHOe Ha pRC 36
PaCCMOTpHM TeIIepI YCJIOBHe ITpHM9HHMOC TH oueHXH ( 36) HeTpYlUo BHshy~eTh qTO OueHKa ( 27) c~8nyeT H3 (36) ITPH yC~OBKH (29 ) TaR ITO 3TO
YCJIOBH9 eCTh H KpHTepKH llpRMeHHMOCTH (36 ) KaK rrpH6~eHHR BHcwero ITOshy
PRJ(Ka Ho C ~yroH CTOPOHH IIOCKO~KY B peaJiIlliX CHCTSMax A-~gt I TO
~1 Al raquo 1 n 03TOMy ~ raquo 1 BCJI9ItC TBe 3TOro OueHllta (36 ) xopomo
OllltCHBaeT 3HaqSIU9 BpeM9HH 3aneparot CBepXll 3JIyUlreJrhHoro HMJIy~ca ( 22) IIJlH 60JIS9 CJIaOOM YCJIOBIDI 18M YCJlOB1I9 (29)
Tgt t r77 + r2 ( (37)
lJHCJI9BH09 HCCJIe~OB8lHe qopyJru (22 ) o lllJCblB8lOIllel qoplY mmy~ca H
OoSHKH (36) n OItTBsJlllllaeT C~8JIB1ilWiI BHBO~ (eM T3OJUlllY) PaCIeT 110shy
Ka3HBa9 qro B CJIy1laeAl~ = 300 CJIeItOBaT8JIIHOrn -- OOI89
III
7t T a 6 ~ H ua CpaBHeHHe 3HallelIIlli BpeMeHH 3aneplKKH RMIlY1Ihca rrnj
IIOJIYlelllUlX lHCneHHHM HC~e~OB8HReM qoPMYJIll (22)
C OU9HKOtt ( 36) H TaKlKe C on9HKoi1 (27) l3ollllilrumoshy
JIYJlUlaTo BJl1lliICJIeHIDI BHIIOIIHeFlli MR CJIYlM II z 300 tn = 00189 co ~ = 00033 ~
---------------================ - - ---~- (x 1( ~) Pe3Y~TaT
GueRRa (36) OneHKa (27)~ rnCJIeHHoroT t (gtlt i l old RCCJIenOB8HRR E-ll
46 2 3 2 3 245
42 2 34 2 34 251
39 24 2 38 260
3 6 2 45 2 42 271
32 25 2 45 286
2 9 2 58 2 41 3 08
26 2 63 2 04 345
16 2 40 HeIIpHJlleImMa HeIIpIDlleHmm -------- ========
7 t = 00033 ooell1B (-no qopfyJIe (36) ~OBOJIbHO XopoWO cor~acyshy8TCR C TO~ pe 3YJIbTaTOM HCCJIe~OB8HRR qopMy~ (22) MR Bcex 8Haqeshy
HIlA r ynOBJIeTOOpJlIiIlRX YCJIOBHll (37)(T e Tgt 0026) tmcrreHlIlDll HCshy
I h 51 CJlenOBaIDleNl MOlilliO TaKii(e UOKa3aTh ITO
B CJIYllae HeOUHOpOlJflOrO BpeM8Hl1 JKl13Hl1 13 shy1 JIYID T8JIe~i T IIopilllKa t T~ t m i1
410 7d(T-Tm)~ 1cpopMYJIa (22 ) ]d B0001l16
rOBopR p ellleHHe YPaBH9IDlH (I ) OIrncrmashy
lOT BCe-laKH Hem U- r op6aTIcM HMTIYJIhC 7 C YMeHhmeHHOH aMJ1JlliTy~o~i H YMeHbllleHHH310 I BpeM6H ffi~ nOCT~eIDlH ~a ( cMpac 4 5)
Ha pRc 5 nOKa3aHO rrOB9~9Hl19 HMDY~ca
TIOJIY1leHH0 e llpn den9HH OM PemeHliIK11 J 10 I
1middot~1I PHc 5 3aBHCHMOCTb OT BpeY9HH
t IDIT9HCKBHOCTH HSJIYshy 1eHIIR IIOJIYleHHM IIpa
IlICJI9HBOM psmeHIDl YPaBshya8H1IJl 0) MJf napaMsljlOB N =2 100 L =O69 middot m - 5
- ]IL Ln 167 H~ - T = Tn-gt - K t N X
110l f LL t reI) K = 2(IT) A =4shy
0 1 3 t (HC )1 CUI) k = 60Y)
I
- shyypaBHeIDfl (1 ) ME CJIYlaH -=- 1u)- t= = 0(lt -1(
i 167 HC 1 = 1- If ltA- bull
4 IIOBeleHHe lIH1eaCHBHOCTlI l3JIYl9HIDr IlpH 60JThlJlliX BpeMeHax ( traquo T ) 3aMe~eHHe cBepXH3JIYleHHE H OCTa1O~8H HHBepcan Hace~eHHOC1e
MIl 110npo6HO o6cy JlHll B ITpe1U4llYllleM naparpa4Je BJIrunme HeOllHOpoIlltOshy
ro YJlIKPeHHR JIHHIDI Ha ltIoIMY BpeMH 3aneplUW H llJIHTeJIbHOCTh HMIIYJIbca
upa BpeMeHax ilOPMKa bull PaCCMOTpHM Tenepb KaJ BenyT ce6R IDIBepcHf
ltR~ (I )l R RHTeHCHBHOCTh Ii 3JIYle1mR f (I ) B IltHTepBaJIe 60JIbnmx BpeMeH
i gtgt (3~eCb rrpennOJIaraJIOCb R8] H pamme ITO T Memme BpeMeshy
1m C110HTaHHOro paCTI8JlB I OT~eJIbHoro H3JIYlaTe~ )
06paTHM CHalaJIB BIDIMaPHe Ha ypaBHeHIUI ( 21) ( 22) l1oJIYleHHlle
H3 (I) B lIpeIU10JIOJi eHIDl 0 rrpeo6JI8JlaHIDI CB6Pn3JIYlBT6JIbHOH KOMTIOHeHshy
Ttl H8Jl oOHlHol1 HeKorepeHTHoH Tallt R8] TIpH Z raquo i rrpRB6~eHHOe Bpe-
ME -( ) COrJIaCHO (23) rrpHlmMa6T rrp6n9JThHOe 3HBleHllt6
7 (1 )gt 1 ) = I (38)
TO H3 (21) ( 22) lloJIYla6M
t - f 0 7lt R (t) gt ~ ---7 - ~ 11 - ) Z t gt gt I A- ) f ~
t- ltlt i~ (39 )
shyi (I )jtgt ( t -- (
3TO 03HBlaeT ITO no HCTel8HHB BpeMeHH 3Ha~TeJIDHO npeBHmaIDmero
Heo6xo]tHMoe lIIlR nOJIHoli ~eqa3HpoBKH H3JIYlaT8JI8ii OCTB8TCR 8rne
HeKOTOpaR OCTaTOH8H HHB6pcHR H CBH3aHHaR C He~ HeBarryl8HH8H 3HeprHR
3anBCeHHafi B CHCT9M8 B HalaJThHWt MOMeHT 3To eCTh RBJIeillle 3BMe~eilllR
CBepXR3JIYeHlIR 06YCJIosneHHo8 H60~OpOnHllM ymKp6HH6M nKHRH2 OHO
MOE6T rrpHBO~Tb K TaR HB3HBaeMOMY orpBHHleHHOMY CBepXlI3JIYl6~2 5~ npH KOTOPOM H6 BCR B TOJIbKO He6oJIbmaH laCTb 3HeprKH CHCTeMH BTOMOB
Korep6HTHO H3JIyaeTCR
IIPH BpeM6Hax T ~ 0 raquo T I1IaBHyD POJIb B H3JIY8mm Brpa6 Ite He
KorepeHTHHH a o61lUIllli rrpo1l6CC R8] B~O H 3 CTPYKTYPH ypaBHeHllR
(I) B cwry MaJIOCTlI 3KC lIOH61~Horo llaKTOpa 2 - tr) ( H
CBH3aHHOro C HHM KOJIJIeKTRBHoro lJIeHB aTO ypaBHeHll6 nepeXOnBT B CJIeshy
~ee
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12
OTC)JJa nOrylaeM peDle1me IJ)lR HHBepCJm ( A~ (I ) gtB 06JIaCTH
~ ~ gtgt jt L-
I I gt( It t (V[- ( (41)lt- r ~ It )gt l - )
r~e llOCTOHHHaH orrpene~eTcR YCJIOBHeM CmRBaEHR C peWe1meM (21) B 06JIaCTH r COOTBeTCTBy1Ornee BIl1l8lKe1me IJ)lR HHTeHCHBHOCTH
H3JIYleHHR - II~(t c (42 )I ( f )- t~
OTIRCHBaeT H3B6CTHli aKC110He~HHil 3aKOH pacrrana
TalltHM 06pa30M B lIHTepBaJIe ~ gtgt I HMeeT MeCTO JIKJIlb
o6wmoe HeKor6peHTHoe Cn OHTaHHOe H3jlYleIDf8 Kor~a_ a T OMll p acIIaJJaJOTcR
He3aBHCHMO JJPyr OT JJPyra C xapaKTepHHM BpeMeHeM J He 3aBHCJ1ll1IDl OT
UlCJIa aTOMOB Ii
3aMe TlM lTO npH 1gt lI3 ltIoPMYJIH (41) nOJIYlBeM
-t A gt I (43)lt Rz 10gt1raquo_ ~ shy )
0Ashy( -
B cJIYiae OTCYTCTBHR HOOIIHOPOllHoro ynm-peHru JIlIlflm RMeeM A = I
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)
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ynm-peHHR JlHHID BKJI8Jl aHTH)630HaHCHIlX lJIeHOB B r aMKJIbTOilllaHe B38ID10shy
~6~CTBBR npHBOnBT K ~ ~ T IT03TOMY
IvIV rC (45)( k) (cgtu) gt shy ) L
Tlt~ --
HepaBeHCTBO ( 4 5 ) o3Ha~a8T ITO B pe3y~bTaTe ~n He-
OIIHOPO~oro ymHp8HKR JIlIHlIH nOCJIe np01l8cca HarryqeHRff OCTBeTCR eme Beshy
RM HHBep CKH H CBR38RHaR C Hea HeHarryqeHHaH 3HeprHR
5 KpBlep o nplDleBlDolOcn pe3YJIbTa1OB
3aKaHlHBaH p acCMOTlJ8HHe BJIJUlIDIR H60lIliOpoJtHOro ynm-pemrn JIHIDm Ha
cBepXR3JIY8 TeJIbHWi mmyJIbC cltlxJp1YJIKPy eM KPHTepHH TIpBM9tmMOCTlI IIOJrYshy
leHHUX B sectsect 2-4 p e3YJIbTaTOB lIJm npoCTOThI 6yl9M orpaImlItBaTbCR cTj-
I ~
~aeM ROr~a pa60~ 06~eM B ROTOPOM HaXO~CH HarryqaTe~ MeeT Hrshy
~006pa3HyID ~PMY
KaK 6blJIO YRa3aHO p erneHlle (21) )JJllI mrnep cID HaCeJIeHHOCTBH
ltJltc (t) H Blip8leIDle HBTaHCltJllOCTlJ f31Iyiemm (22) B o CSJracTlI t T crrpaBell)IID3Il lOJIhRO Torna ROr~a BIDIOJIIDI8TCR YCJlOBH6 (18) C Iij)yroA
CTOPOlill lIpH ~OnOJIHHTemHOM npe~lIOJIOlltemm (23) WIH BpeMeHil 3aneJlliUGI
mmyJILC8 cnpaBenmIBII OneHlUl (27) JIB ( 35 ) a Mfl )llIHTemHOCTlJ-f mmyJIbC8 T--ou eRRa (26) EMil nO~CT8BlIM (27 ) B rrpaBYRJ l8CTD (21) TO no~ymM
( R~ (-t ) gt ( 0TICj )(c1 (1) GJ(yOT
310 OSHa~eT ~TO yc~oBHe (18) aBTOMaT~eCKH BIDIo~eTCH ec~ BNshy
no~eTCR ycnoBlIe (29) C~e~OBaTeJILHo 0 6lIlHM KpHTepHeM llpHMeHilMocTIil
no~eHHUX B sect 3 pe 3YJIbTaTOB RBnR8TCR BIlIO~eHRe COOTHOm6HBR (29)
Z IN ( - i t1 ) ltL i 3~6Cb B6JlHmHll 1 H ~ ollpe~eruooT BpeMR 3auepuw H ItJmTemshy
HOCTD HMIIYJILca IIpH OTCyTCTBHlf Heo~oponHoro yumpeHIDI JIlUlllI COOTB6Tshy
CTBeHHO 3aBHCHMOCTH 3TlJX B~H OT ~c~a H~aTaneH B reoMeTpBshy
~ecKOro rIsKTo pa ~ Blip8leHl ~~Jr~ (II ) Blm lrultTopa 12 6wx rrpHshy76miJKeHHo IIOJI IeH PeJlepoM 11 36eplIIl IJ)UI p a3JIRIHHX MaKpocROlIllleClGIX
ROHqJHryp~ ~pIi pa6olero 06beM8 )lnR Kpyr~oro IJJIHHHoro ItWnnlllJla C
lIHCJIOM ~eHeJIR IIOp~ I xopome~ amtpoKCRMaJJHei CJIyXJT Bllp8teHlle
~2 -x=
S Araquo ( ~_ ) ( A I- 1FA A ~4 ) (46 )1 ~
3nech A L -COOTBeTCTB~e llHO~ OCHOB8HHR B ~a~a ) -IllIIDla BOJIBH B3J1YleHlUI )-fCIIOJIb3YR (II ) Il (46 ) nO1IJl86M 2-7
j c gy7 IV 3f~ J 1
1- t th 3el ltL (47)
It It S)
r~e = VIv - IIJIOTHOCTL B3JIyla TeJIel B pa60~eM 06beMe Vc A L 01shycnna MOlltliO nep eIIHcaTL YCJIOBHe nplWelfilMOCTH (29) B BHIJe
L gtgt Lp -= ~x (If ) (48)36)1Sshy
I middot ~
HJIll z j (~- )I raquofr = ~ A)L (49)
3~eCb IjJyHKIUfl )( (_~ ) orrpe~eMBTCfl RaR pemeHHB ypaBH6HIR
j ~
LO )( gt- i Ie 81 Jr- 2 T
B CJIym6 KOr na TaKOe pemeHR6 cymecTByeT (T e KOrna Tc e ) B rrpoTHmlOM CJIyTlBB (Kor na Tgt e ~ ) MeeM rrpoClO _k -= if
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TaTO~O 6 0JILmoe ~T06H BIDIOJIHamp)lOCb YC~OBHe II gtgt i A B c~ae Kpyr~oro IJ1IIHHoro ~a C ~CJIOM ~eH6JU UOP1mRa I 3TO y~BHe
COrJIBCHO (46) 3KBRBMeHTHO CJIeJlY1OOeMY
J p1~L raquo1 (50)7lt0shy
t)
ITocne~ee yc~oBHe KOTopoe He06xo~0 ~TlBaTh CBR3aHO C TaM
iTO llpll oi~eHll1 ypaBHeHHR (I) Ha OCHOBe KJlHeTHleCKKX ypaaHeHHii
B pa60Te I MH JlCIIOJIL30BaHH p~ ynpomeliHH KOTOpue cnpaBe~u TOJILshy
RO Mfl CJIa60 MeHmOOerocR B rrpe~Max 06pasU1l IIOM IT03TOMY Jl)IHTeJIL-
HOCTb uponecca xapaRTepll3yeMaR B6XJllJlHOH (~ ~o~a 6UTb HaMHOshy
ro 6o~rnesectjPaRTepHoro BpeMeHH H3MeHeHllfl 8MTInMTynH O~ B 06pa3ue
ic = L C 3 ~TO 03Ha~aeT KPJlTepKlf ApeKRJl-KypTeHca 8
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1 Bogolubov NN( j r ) Pam Le Kien Shumovsky AS Physica1984
128A No 1 2 p82-98
2 Groas M Earo che S PhysRep 1982 v93 No5 p301-396
15
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
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A (N
rne ~TeJIIHOCTb HMDYJIIca ~ A-OIlJlCIlBaeTCfl qoIHYJIol (26) OTCIlna
DeeM gtl )~f- oc-- gtf
f h-gt = Igt - C IV 0 [1(- th -K (35 )r
J-~ pe3Y~TaT lIlIH m
j -----L Jf _J
HI TI In -1_ II
L shyI ( r-t TT- Trn
aT~ TNI
6
5
4 ]
oL--~-----------shy
12 16 20 24 28 Tt m
~tm (
1 16
14
12
10 1213 16 20 24 28
Ttm
PRC 3 SaBHCRMOCTH IlJIlTeJThHOCTR lOOIYJIIca Z- (a)R WeMeshyHR 3auepxKH f (6) OT HeshyO)UIoponaoro BpeueHll U 3HR r BlARcJIeHRR BWlOJIHeshy
lW no qoINY~8M ( 2 6)R (36) lIlIH CJIyiM t-rn = 10 0v bull
~t- ) (r1 ~- ~ J (36)
- 0 17 ( v
~ - of SaBRCRMOCTI t H I IV OT Heonshy
aopoIllloro BpeMeHR lU3HR HanyqBTeshy
JIeM T OIllICaHHM qopfyJIBMI
(26) H (36) nOKa3aHa H8 pHC 3
lIlIH CJIYUlR 1 = 10 (V bull H3 PHshycyaxa BRnBO iTO B OTJIRqRe OT MOshy
HOTOHHO y6HBa~ro rrOBeneHllfl
~ 7 (- JcentyHKllHR i (T) rn shyo6JranaeT MaKCRMyMOM B TOiKe Iz=
13 IloBeneHRe B o6JIacTRT Tt lt 13 03HaiaeT iTO CJImllKOM
tn 6o~woe ~flHRe HOOnaOponHOra
yumpeHldSl JIHHKH ITpilllOnHT He K yBeshy
JIHieHRD a K yMeHbmeHHD BpeMeHH
3aueJllKKR IDIIUyJIIca A aTO C nepshy
Bora B3r~a ORa3HBaeTCfl HeoxHshy
nBHHHM DHO cymeCTBeHHO OTJIHqaeTshy
CS OT nOJIYieHHoro BHIlle pe3YJIITashy
Ta lIlIH CJIYlM T gt ern CM bull qopshy
MYJIY (3I) H OT pe3YJIbTaTOB npyshy
lRX aBTOPOB2-4i llpHOOla TaKOlt
OC06eHHOCTH rrOBeneHKR 3aBRCRMOCshy
TH f rH r OT T 3aKJITOiaeTCfl B CJIeshy
nyDIIleM
~3BeCTHO iTO B npouecce H3shy
JIYleBIDl l1MelOT MeCTO ItBa npoTKBOshy
UO~OlKma KOHKypHpyDIIRX ifaKTOpa
~3RpoBKa ~o~el aTOMOB 6JIaIOshy
napS B3aHMoneHCTBRIl iepe3 no~e R
neqaaHpOBKa HX Bc~enCTBHe pa3JIRshy
~ co6CTBeHHHX iaCTOT ITpH Heo~shy
HOPO)(HOM ynmpemm JIHHB1l Ko rna
T gtgtc rJIaBHYIgt POJII RIpaeTn 7
tpaKTOP qa3RpOBKR 06YCJIOBIDlllIHi
11 l)
cBepXRanyqaTe~Hoe IIOshy
lIt)1 Io Be~8HHe HMny~ca ~aKshy
TOp ~8~3KpOBKH ~IIOshy
~e~ CBff3aHHHH C H90~shy12 HOPOlOWM ynmp9HHeM Jmshy
10 mm ITpHBOmrT K 38Me~shy
neHKID YCTaHOan9HHR 8 MaKCHMEUnBOB BEllllfUnibI
6 CYMMapHoro ~O~HOro
MOMeHTa aTOMOB ~e~oshy
BaTemHO K YB8JmI9mm
Bp9M9HH 3anepxKH HMshyJ itshy
rry~ca I rH bull A Ror~a
T IIpH6mmaeTcR K tr~ 2 L 6 8 10 c~ecTBeHHyD po~ Hashy
~aeT HrpaTh npyroa ( 10-2) t To centaRTop - ne~3HPOBKa
~IIo~ea aTOMOB TaR
PlIe 4 RaK TaKru neltIa3lfPOBKa 3aBHCIlMOCTI OT BpeMeHH t HBTeHClmshyHOCTH HanyqeHBR (22) ITpH C~HOM BnHshy BHSHBaeT 3aTyxBHH9 CYMshymum H80ltHOpoIHoro ymap8HHR 1IlllIlm MapHoro ~O~Horo MOshy( T - T) BWlHCJIeHHR BIffiOIIHeHH C IIapBM8Tp8MH-C)- = 300 7~= 0 0189 t M8HTa H C~e~OBaTe~shyTmiddot c 0 0033 to middot f = deg0169 7 ( I)
HO CTpeMHTCR YMeHIshyO0156 Lv (11J6 OQI23 t (W) O O~O i (IY) 00 23 L (Y) L
() = N M ( WHTh HHTeHcKBHOCTh H3shy
)
~eHHH no 3KcnoH9~shyaJiIHOMy 3aKOHY TO BpeMR nOCTIDK6HHH mnta ~HallHHaeT YMsmUJaTnCJJ
TIp aTOM YMeHhwaeTCR MaKCRMantHaR HBTeaCKBHOCT~H KOr~a ~~ tlgt
HMYl8HHe nepeCTaeT 61gtlTb CBepXH3JIYIaT8JI1IDlM ( CM pHC 4) OTClllla ~erKO rrOHRTh nOBe~eHHe ifiyHKIUH 1 -N (T) ITOllta3aHHOe Ha pRC 36
PaCCMOTpHM TeIIepI YCJIOBHe ITpHM9HHMOC TH oueHXH ( 36) HeTpYlUo BHshy~eTh qTO OueHKa ( 27) c~8nyeT H3 (36) ITPH yC~OBKH (29 ) TaR ITO 3TO
YCJIOBH9 eCTh H KpHTepKH llpRMeHHMOCTH (36 ) KaK rrpH6~eHHR BHcwero ITOshy
PRJ(Ka Ho C ~yroH CTOPOHH IIOCKO~KY B peaJiIlliX CHCTSMax A-~gt I TO
~1 Al raquo 1 n 03TOMy ~ raquo 1 BCJI9ItC TBe 3TOro OueHllta (36 ) xopomo
OllltCHBaeT 3HaqSIU9 BpeM9HH 3aneparot CBepXll 3JIyUlreJrhHoro HMJIy~ca ( 22) IIJlH 60JIS9 CJIaOOM YCJIOBIDI 18M YCJlOB1I9 (29)
Tgt t r77 + r2 ( (37)
lJHCJI9BH09 HCCJIe~OB8lHe qopyJru (22 ) o lllJCblB8lOIllel qoplY mmy~ca H
OoSHKH (36) n OItTBsJlllllaeT C~8JIB1ilWiI BHBO~ (eM T3OJUlllY) PaCIeT 110shy
Ka3HBa9 qro B CJIy1laeAl~ = 300 CJIeItOBaT8JIIHOrn -- OOI89
III
7t T a 6 ~ H ua CpaBHeHHe 3HallelIIlli BpeMeHH 3aneplKKH RMIlY1Ihca rrnj
IIOJIYlelllUlX lHCneHHHM HC~e~OB8HReM qoPMYJIll (22)
C OU9HKOtt ( 36) H TaKlKe C on9HKoi1 (27) l3ollllilrumoshy
JIYJlUlaTo BJl1lliICJIeHIDI BHIIOIIHeFlli MR CJIYlM II z 300 tn = 00189 co ~ = 00033 ~
---------------================ - - ---~- (x 1( ~) Pe3Y~TaT
GueRRa (36) OneHKa (27)~ rnCJIeHHoroT t (gtlt i l old RCCJIenOB8HRR E-ll
46 2 3 2 3 245
42 2 34 2 34 251
39 24 2 38 260
3 6 2 45 2 42 271
32 25 2 45 286
2 9 2 58 2 41 3 08
26 2 63 2 04 345
16 2 40 HeIIpHJlleImMa HeIIpIDlleHmm -------- ========
7 t = 00033 ooell1B (-no qopfyJIe (36) ~OBOJIbHO XopoWO cor~acyshy8TCR C TO~ pe 3YJIbTaTOM HCCJIe~OB8HRR qopMy~ (22) MR Bcex 8Haqeshy
HIlA r ynOBJIeTOOpJlIiIlRX YCJIOBHll (37)(T e Tgt 0026) tmcrreHlIlDll HCshy
I h 51 CJlenOBaIDleNl MOlilliO TaKii(e UOKa3aTh ITO
B CJIYllae HeOUHOpOlJflOrO BpeM8Hl1 JKl13Hl1 13 shy1 JIYID T8JIe~i T IIopilllKa t T~ t m i1
410 7d(T-Tm)~ 1cpopMYJIa (22 ) ]d B0001l16
rOBopR p ellleHHe YPaBH9IDlH (I ) OIrncrmashy
lOT BCe-laKH Hem U- r op6aTIcM HMTIYJIhC 7 C YMeHhmeHHOH aMJ1JlliTy~o~i H YMeHbllleHHH310 I BpeM6H ffi~ nOCT~eIDlH ~a ( cMpac 4 5)
Ha pRc 5 nOKa3aHO rrOB9~9Hl19 HMDY~ca
TIOJIY1leHH0 e llpn den9HH OM PemeHliIK11 J 10 I
1middot~1I PHc 5 3aBHCHMOCTb OT BpeY9HH
t IDIT9HCKBHOCTH HSJIYshy 1eHIIR IIOJIYleHHM IIpa
IlICJI9HBOM psmeHIDl YPaBshya8H1IJl 0) MJf napaMsljlOB N =2 100 L =O69 middot m - 5
- ]IL Ln 167 H~ - T = Tn-gt - K t N X
110l f LL t reI) K = 2(IT) A =4shy
0 1 3 t (HC )1 CUI) k = 60Y)
I
- shyypaBHeIDfl (1 ) ME CJIYlaH -=- 1u)- t= = 0(lt -1(
i 167 HC 1 = 1- If ltA- bull
4 IIOBeleHHe lIH1eaCHBHOCTlI l3JIYl9HIDr IlpH 60JThlJlliX BpeMeHax ( traquo T ) 3aMe~eHHe cBepXH3JIYleHHE H OCTa1O~8H HHBepcan Hace~eHHOC1e
MIl 110npo6HO o6cy JlHll B ITpe1U4llYllleM naparpa4Je BJIrunme HeOllHOpoIlltOshy
ro YJlIKPeHHR JIHHIDI Ha ltIoIMY BpeMH 3aneplUW H llJIHTeJIbHOCTh HMIIYJIbca
upa BpeMeHax ilOPMKa bull PaCCMOTpHM Tenepb KaJ BenyT ce6R IDIBepcHf
ltR~ (I )l R RHTeHCHBHOCTh Ii 3JIYle1mR f (I ) B IltHTepBaJIe 60JIbnmx BpeMeH
i gtgt (3~eCb rrpennOJIaraJIOCb R8] H pamme ITO T Memme BpeMeshy
1m C110HTaHHOro paCTI8JlB I OT~eJIbHoro H3JIYlaTe~ )
06paTHM CHalaJIB BIDIMaPHe Ha ypaBHeHIUI ( 21) ( 22) l1oJIYleHHlle
H3 (I) B lIpeIU10JIOJi eHIDl 0 rrpeo6JI8JlaHIDI CB6Pn3JIYlBT6JIbHOH KOMTIOHeHshy
Ttl H8Jl oOHlHol1 HeKorepeHTHoH Tallt R8] TIpH Z raquo i rrpRB6~eHHOe Bpe-
ME -( ) COrJIaCHO (23) rrpHlmMa6T rrp6n9JThHOe 3HBleHllt6
7 (1 )gt 1 ) = I (38)
TO H3 (21) ( 22) lloJIYla6M
t - f 0 7lt R (t) gt ~ ---7 - ~ 11 - ) Z t gt gt I A- ) f ~
t- ltlt i~ (39 )
shyi (I )jtgt ( t -- (
3TO 03HBlaeT ITO no HCTel8HHB BpeMeHH 3Ha~TeJIDHO npeBHmaIDmero
Heo6xo]tHMoe lIIlR nOJIHoli ~eqa3HpoBKH H3JIYlaT8JI8ii OCTB8TCR 8rne
HeKOTOpaR OCTaTOH8H HHB6pcHR H CBH3aHHaR C He~ HeBarryl8HH8H 3HeprHR
3anBCeHHafi B CHCT9M8 B HalaJThHWt MOMeHT 3To eCTh RBJIeillle 3BMe~eilllR
CBepXR3JIYeHlIR 06YCJIosneHHo8 H60~OpOnHllM ymKp6HH6M nKHRH2 OHO
MOE6T rrpHBO~Tb K TaR HB3HBaeMOMY orpBHHleHHOMY CBepXlI3JIYl6~2 5~ npH KOTOPOM H6 BCR B TOJIbKO He6oJIbmaH laCTb 3HeprKH CHCTeMH BTOMOB
Korep6HTHO H3JIyaeTCR
IIPH BpeM6Hax T ~ 0 raquo T I1IaBHyD POJIb B H3JIY8mm Brpa6 Ite He
KorepeHTHHH a o61lUIllli rrpo1l6CC R8] B~O H 3 CTPYKTYPH ypaBHeHllR
(I) B cwry MaJIOCTlI 3KC lIOH61~Horo llaKTOpa 2 - tr) ( H
CBH3aHHOro C HHM KOJIJIeKTRBHoro lJIeHB aTO ypaBHeHll6 nepeXOnBT B CJIeshy
~ee
~ ZR~ Ii raquo == - i (x v r lt R t raquo1 (40 )(_ 2 )
12
OTC)JJa nOrylaeM peDle1me IJ)lR HHBepCJm ( A~ (I ) gtB 06JIaCTH
~ ~ gtgt jt L-
I I gt( It t (V[- ( (41)lt- r ~ It )gt l - )
r~e llOCTOHHHaH orrpene~eTcR YCJIOBHeM CmRBaEHR C peWe1meM (21) B 06JIaCTH r COOTBeTCTBy1Ornee BIl1l8lKe1me IJ)lR HHTeHCHBHOCTH
H3JIYleHHR - II~(t c (42 )I ( f )- t~
OTIRCHBaeT H3B6CTHli aKC110He~HHil 3aKOH pacrrana
TalltHM 06pa30M B lIHTepBaJIe ~ gtgt I HMeeT MeCTO JIKJIlb
o6wmoe HeKor6peHTHoe Cn OHTaHHOe H3jlYleIDf8 Kor~a_ a T OMll p acIIaJJaJOTcR
He3aBHCHMO JJPyr OT JJPyra C xapaKTepHHM BpeMeHeM J He 3aBHCJ1ll1IDl OT
UlCJIa aTOMOB Ii
3aMe TlM lTO npH 1gt lI3 ltIoPMYJIH (41) nOJIYlBeM
-t A gt I (43)lt Rz 10gt1raquo_ ~ shy )
0Ashy( -
B cJIYiae OTCYTCTBHR HOOIIHOPOllHoro ynm-peHru JIlIlflm RMeeM A = I
( eM1 ) I103TorlY
~ (44)( ~ (rxraquo[
)
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MeHT Bp8MeHn nepeillJIa B 3Hep~ H~8HnR B CHYlBe H80~OPOnHOro
ynm-peHHR JlHHID BKJI8Jl aHTH)630HaHCHIlX lJIeHOB B r aMKJIbTOilllaHe B38ID10shy
~6~CTBBR npHBOnBT K ~ ~ T IT03TOMY
IvIV rC (45)( k) (cgtu) gt shy ) L
Tlt~ --
HepaBeHCTBO ( 4 5 ) o3Ha~a8T ITO B pe3y~bTaTe ~n He-
OIIHOPO~oro ymHp8HKR JIlIHlIH nOCJIe np01l8cca HarryqeHRff OCTBeTCR eme Beshy
RM HHBep CKH H CBR38RHaR C Hea HeHarryqeHHaH 3HeprHR
5 KpBlep o nplDleBlDolOcn pe3YJIbTa1OB
3aKaHlHBaH p acCMOTlJ8HHe BJIJUlIDIR H60lIliOpoJtHOro ynm-pemrn JIHIDm Ha
cBepXR3JIY8 TeJIbHWi mmyJIbC cltlxJp1YJIKPy eM KPHTepHH TIpBM9tmMOCTlI IIOJrYshy
leHHUX B sectsect 2-4 p e3YJIbTaTOB lIJm npoCTOThI 6yl9M orpaImlItBaTbCR cTj-
I ~
~aeM ROr~a pa60~ 06~eM B ROTOPOM HaXO~CH HarryqaTe~ MeeT Hrshy
~006pa3HyID ~PMY
KaK 6blJIO YRa3aHO p erneHlle (21) )JJllI mrnep cID HaCeJIeHHOCTBH
ltJltc (t) H Blip8leIDle HBTaHCltJllOCTlJ f31Iyiemm (22) B o CSJracTlI t T crrpaBell)IID3Il lOJIhRO Torna ROr~a BIDIOJIIDI8TCR YCJlOBH6 (18) C Iij)yroA
CTOPOlill lIpH ~OnOJIHHTemHOM npe~lIOJIOlltemm (23) WIH BpeMeHil 3aneJlliUGI
mmyJILC8 cnpaBenmIBII OneHlUl (27) JIB ( 35 ) a Mfl )llIHTemHOCTlJ-f mmyJIbC8 T--ou eRRa (26) EMil nO~CT8BlIM (27 ) B rrpaBYRJ l8CTD (21) TO no~ymM
( R~ (-t ) gt ( 0TICj )(c1 (1) GJ(yOT
310 OSHa~eT ~TO yc~oBHe (18) aBTOMaT~eCKH BIDIo~eTCH ec~ BNshy
no~eTCR ycnoBlIe (29) C~e~OBaTeJILHo 0 6lIlHM KpHTepHeM llpHMeHilMocTIil
no~eHHUX B sect 3 pe 3YJIbTaTOB RBnR8TCR BIlIO~eHRe COOTHOm6HBR (29)
Z IN ( - i t1 ) ltL i 3~6Cb B6JlHmHll 1 H ~ ollpe~eruooT BpeMR 3auepuw H ItJmTemshy
HOCTD HMIIYJILca IIpH OTCyTCTBHlf Heo~oponHoro yumpeHIDI JIlUlllI COOTB6Tshy
CTBeHHO 3aBHCHMOCTH 3TlJX B~H OT ~c~a H~aTaneH B reoMeTpBshy
~ecKOro rIsKTo pa ~ Blip8leHl ~~Jr~ (II ) Blm lrultTopa 12 6wx rrpHshy76miJKeHHo IIOJI IeH PeJlepoM 11 36eplIIl IJ)UI p a3JIRIHHX MaKpocROlIllleClGIX
ROHqJHryp~ ~pIi pa6olero 06beM8 )lnR Kpyr~oro IJJIHHHoro ItWnnlllJla C
lIHCJIOM ~eHeJIR IIOp~ I xopome~ amtpoKCRMaJJHei CJIyXJT Bllp8teHlle
~2 -x=
S Araquo ( ~_ ) ( A I- 1FA A ~4 ) (46 )1 ~
3nech A L -COOTBeTCTB~e llHO~ OCHOB8HHR B ~a~a ) -IllIIDla BOJIBH B3J1YleHlUI )-fCIIOJIb3YR (II ) Il (46 ) nO1IJl86M 2-7
j c gy7 IV 3f~ J 1
1- t th 3el ltL (47)
It It S)
r~e = VIv - IIJIOTHOCTL B3JIyla TeJIel B pa60~eM 06beMe Vc A L 01shycnna MOlltliO nep eIIHcaTL YCJIOBHe nplWelfilMOCTH (29) B BHIJe
L gtgt Lp -= ~x (If ) (48)36)1Sshy
I middot ~
HJIll z j (~- )I raquofr = ~ A)L (49)
3~eCb IjJyHKIUfl )( (_~ ) orrpe~eMBTCfl RaR pemeHHB ypaBH6HIR
j ~
LO )( gt- i Ie 81 Jr- 2 T
B CJIym6 KOr na TaKOe pemeHR6 cymecTByeT (T e KOrna Tc e ) B rrpoTHmlOM CJIyTlBB (Kor na Tgt e ~ ) MeeM rrpoClO _k -= if
Be3~e B 3TOH p a60T6 MI rrpe~o~~ ~TO ~C~O HanyqaTe~eH ~OCshy
TaTO~O 6 0JILmoe ~T06H BIDIOJIHamp)lOCb YC~OBHe II gtgt i A B c~ae Kpyr~oro IJ1IIHHoro ~a C ~CJIOM ~eH6JU UOP1mRa I 3TO y~BHe
COrJIBCHO (46) 3KBRBMeHTHO CJIeJlY1OOeMY
J p1~L raquo1 (50)7lt0shy
t)
ITocne~ee yc~oBHe KOTopoe He06xo~0 ~TlBaTh CBR3aHO C TaM
iTO llpll oi~eHll1 ypaBHeHHR (I) Ha OCHOBe KJlHeTHleCKKX ypaaHeHHii
B pa60Te I MH JlCIIOJIL30BaHH p~ ynpomeliHH KOTOpue cnpaBe~u TOJILshy
RO Mfl CJIa60 MeHmOOerocR B rrpe~Max 06pasU1l IIOM IT03TOMY Jl)IHTeJIL-
HOCTb uponecca xapaRTepll3yeMaR B6XJllJlHOH (~ ~o~a 6UTb HaMHOshy
ro 6o~rnesectjPaRTepHoro BpeMeHH H3MeHeHllfl 8MTInMTynH O~ B 06pa3ue
ic = L C 3 ~TO 03Ha~aeT KPJlTepKlf ApeKRJl-KypTeHca 8
L L C ~I (51)
)JJllI IIpHMaHHMOCTH IIO~6HHIlX pesYJrbTaToB )-fCIIOJIL3YR REHoe BIIP~eHHe
LN B (47 ) MOJl(HO nepeIIHCaTb (5D B B~e
L z L_ I JT c- (52)kfJ 3 i ) (
Jl lITepaTy p8
1 Bogolubov NN( j r ) Pam Le Kien Shumovsky AS Physica1984
128A No 1 2 p82-98
2 Groas M Earo che S PhysRep 1982 v93 No5 p301-396
15
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
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cBepXRanyqaTe~Hoe IIOshy
lIt)1 Io Be~8HHe HMny~ca ~aKshy
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10 mm ITpHBOmrT K 38Me~shy
neHKID YCTaHOan9HHR 8 MaKCHMEUnBOB BEllllfUnibI
6 CYMMapHoro ~O~HOro
MOMeHTa aTOMOB ~e~oshy
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Bp9M9HH 3anepxKH HMshyJ itshy
rry~ca I rH bull A Ror~a
T IIpH6mmaeTcR K tr~ 2 L 6 8 10 c~ecTBeHHyD po~ Hashy
~aeT HrpaTh npyroa ( 10-2) t To centaRTop - ne~3HPOBKa
~IIo~ea aTOMOB TaR
PlIe 4 RaK TaKru neltIa3lfPOBKa 3aBHCIlMOCTI OT BpeMeHH t HBTeHClmshyHOCTH HanyqeHBR (22) ITpH C~HOM BnHshy BHSHBaeT 3aTyxBHH9 CYMshymum H80ltHOpoIHoro ymap8HHR 1IlllIlm MapHoro ~O~Horo MOshy( T - T) BWlHCJIeHHR BIffiOIIHeHH C IIapBM8Tp8MH-C)- = 300 7~= 0 0189 t M8HTa H C~e~OBaTe~shyTmiddot c 0 0033 to middot f = deg0169 7 ( I)
HO CTpeMHTCR YMeHIshyO0156 Lv (11J6 OQI23 t (W) O O~O i (IY) 00 23 L (Y) L
() = N M ( WHTh HHTeHcKBHOCTh H3shy
)
~eHHH no 3KcnoH9~shyaJiIHOMy 3aKOHY TO BpeMR nOCTIDK6HHH mnta ~HallHHaeT YMsmUJaTnCJJ
TIp aTOM YMeHhwaeTCR MaKCRMantHaR HBTeaCKBHOCT~H KOr~a ~~ tlgt
HMYl8HHe nepeCTaeT 61gtlTb CBepXH3JIYIaT8JI1IDlM ( CM pHC 4) OTClllla ~erKO rrOHRTh nOBe~eHHe ifiyHKIUH 1 -N (T) ITOllta3aHHOe Ha pRC 36
PaCCMOTpHM TeIIepI YCJIOBHe ITpHM9HHMOC TH oueHXH ( 36) HeTpYlUo BHshy~eTh qTO OueHKa ( 27) c~8nyeT H3 (36) ITPH yC~OBKH (29 ) TaR ITO 3TO
YCJIOBH9 eCTh H KpHTepKH llpRMeHHMOCTH (36 ) KaK rrpH6~eHHR BHcwero ITOshy
PRJ(Ka Ho C ~yroH CTOPOHH IIOCKO~KY B peaJiIlliX CHCTSMax A-~gt I TO
~1 Al raquo 1 n 03TOMy ~ raquo 1 BCJI9ItC TBe 3TOro OueHllta (36 ) xopomo
OllltCHBaeT 3HaqSIU9 BpeM9HH 3aneparot CBepXll 3JIyUlreJrhHoro HMJIy~ca ( 22) IIJlH 60JIS9 CJIaOOM YCJIOBIDI 18M YCJlOB1I9 (29)
Tgt t r77 + r2 ( (37)
lJHCJI9BH09 HCCJIe~OB8lHe qopyJru (22 ) o lllJCblB8lOIllel qoplY mmy~ca H
OoSHKH (36) n OItTBsJlllllaeT C~8JIB1ilWiI BHBO~ (eM T3OJUlllY) PaCIeT 110shy
Ka3HBa9 qro B CJIy1laeAl~ = 300 CJIeItOBaT8JIIHOrn -- OOI89
III
7t T a 6 ~ H ua CpaBHeHHe 3HallelIIlli BpeMeHH 3aneplKKH RMIlY1Ihca rrnj
IIOJIYlelllUlX lHCneHHHM HC~e~OB8HReM qoPMYJIll (22)
C OU9HKOtt ( 36) H TaKlKe C on9HKoi1 (27) l3ollllilrumoshy
JIYJlUlaTo BJl1lliICJIeHIDI BHIIOIIHeFlli MR CJIYlM II z 300 tn = 00189 co ~ = 00033 ~
---------------================ - - ---~- (x 1( ~) Pe3Y~TaT
GueRRa (36) OneHKa (27)~ rnCJIeHHoroT t (gtlt i l old RCCJIenOB8HRR E-ll
46 2 3 2 3 245
42 2 34 2 34 251
39 24 2 38 260
3 6 2 45 2 42 271
32 25 2 45 286
2 9 2 58 2 41 3 08
26 2 63 2 04 345
16 2 40 HeIIpHJlleImMa HeIIpIDlleHmm -------- ========
7 t = 00033 ooell1B (-no qopfyJIe (36) ~OBOJIbHO XopoWO cor~acyshy8TCR C TO~ pe 3YJIbTaTOM HCCJIe~OB8HRR qopMy~ (22) MR Bcex 8Haqeshy
HIlA r ynOBJIeTOOpJlIiIlRX YCJIOBHll (37)(T e Tgt 0026) tmcrreHlIlDll HCshy
I h 51 CJlenOBaIDleNl MOlilliO TaKii(e UOKa3aTh ITO
B CJIYllae HeOUHOpOlJflOrO BpeM8Hl1 JKl13Hl1 13 shy1 JIYID T8JIe~i T IIopilllKa t T~ t m i1
410 7d(T-Tm)~ 1cpopMYJIa (22 ) ]d B0001l16
rOBopR p ellleHHe YPaBH9IDlH (I ) OIrncrmashy
lOT BCe-laKH Hem U- r op6aTIcM HMTIYJIhC 7 C YMeHhmeHHOH aMJ1JlliTy~o~i H YMeHbllleHHH310 I BpeM6H ffi~ nOCT~eIDlH ~a ( cMpac 4 5)
Ha pRc 5 nOKa3aHO rrOB9~9Hl19 HMDY~ca
TIOJIY1leHH0 e llpn den9HH OM PemeHliIK11 J 10 I
1middot~1I PHc 5 3aBHCHMOCTb OT BpeY9HH
t IDIT9HCKBHOCTH HSJIYshy 1eHIIR IIOJIYleHHM IIpa
IlICJI9HBOM psmeHIDl YPaBshya8H1IJl 0) MJf napaMsljlOB N =2 100 L =O69 middot m - 5
- ]IL Ln 167 H~ - T = Tn-gt - K t N X
110l f LL t reI) K = 2(IT) A =4shy
0 1 3 t (HC )1 CUI) k = 60Y)
I
- shyypaBHeIDfl (1 ) ME CJIYlaH -=- 1u)- t= = 0(lt -1(
i 167 HC 1 = 1- If ltA- bull
4 IIOBeleHHe lIH1eaCHBHOCTlI l3JIYl9HIDr IlpH 60JThlJlliX BpeMeHax ( traquo T ) 3aMe~eHHe cBepXH3JIYleHHE H OCTa1O~8H HHBepcan Hace~eHHOC1e
MIl 110npo6HO o6cy JlHll B ITpe1U4llYllleM naparpa4Je BJIrunme HeOllHOpoIlltOshy
ro YJlIKPeHHR JIHHIDI Ha ltIoIMY BpeMH 3aneplUW H llJIHTeJIbHOCTh HMIIYJIbca
upa BpeMeHax ilOPMKa bull PaCCMOTpHM Tenepb KaJ BenyT ce6R IDIBepcHf
ltR~ (I )l R RHTeHCHBHOCTh Ii 3JIYle1mR f (I ) B IltHTepBaJIe 60JIbnmx BpeMeH
i gtgt (3~eCb rrpennOJIaraJIOCb R8] H pamme ITO T Memme BpeMeshy
1m C110HTaHHOro paCTI8JlB I OT~eJIbHoro H3JIYlaTe~ )
06paTHM CHalaJIB BIDIMaPHe Ha ypaBHeHIUI ( 21) ( 22) l1oJIYleHHlle
H3 (I) B lIpeIU10JIOJi eHIDl 0 rrpeo6JI8JlaHIDI CB6Pn3JIYlBT6JIbHOH KOMTIOHeHshy
Ttl H8Jl oOHlHol1 HeKorepeHTHoH Tallt R8] TIpH Z raquo i rrpRB6~eHHOe Bpe-
ME -( ) COrJIaCHO (23) rrpHlmMa6T rrp6n9JThHOe 3HBleHllt6
7 (1 )gt 1 ) = I (38)
TO H3 (21) ( 22) lloJIYla6M
t - f 0 7lt R (t) gt ~ ---7 - ~ 11 - ) Z t gt gt I A- ) f ~
t- ltlt i~ (39 )
shyi (I )jtgt ( t -- (
3TO 03HBlaeT ITO no HCTel8HHB BpeMeHH 3Ha~TeJIDHO npeBHmaIDmero
Heo6xo]tHMoe lIIlR nOJIHoli ~eqa3HpoBKH H3JIYlaT8JI8ii OCTB8TCR 8rne
HeKOTOpaR OCTaTOH8H HHB6pcHR H CBH3aHHaR C He~ HeBarryl8HH8H 3HeprHR
3anBCeHHafi B CHCT9M8 B HalaJThHWt MOMeHT 3To eCTh RBJIeillle 3BMe~eilllR
CBepXR3JIYeHlIR 06YCJIosneHHo8 H60~OpOnHllM ymKp6HH6M nKHRH2 OHO
MOE6T rrpHBO~Tb K TaR HB3HBaeMOMY orpBHHleHHOMY CBepXlI3JIYl6~2 5~ npH KOTOPOM H6 BCR B TOJIbKO He6oJIbmaH laCTb 3HeprKH CHCTeMH BTOMOB
Korep6HTHO H3JIyaeTCR
IIPH BpeM6Hax T ~ 0 raquo T I1IaBHyD POJIb B H3JIY8mm Brpa6 Ite He
KorepeHTHHH a o61lUIllli rrpo1l6CC R8] B~O H 3 CTPYKTYPH ypaBHeHllR
(I) B cwry MaJIOCTlI 3KC lIOH61~Horo llaKTOpa 2 - tr) ( H
CBH3aHHOro C HHM KOJIJIeKTRBHoro lJIeHB aTO ypaBHeHll6 nepeXOnBT B CJIeshy
~ee
~ ZR~ Ii raquo == - i (x v r lt R t raquo1 (40 )(_ 2 )
12
OTC)JJa nOrylaeM peDle1me IJ)lR HHBepCJm ( A~ (I ) gtB 06JIaCTH
~ ~ gtgt jt L-
I I gt( It t (V[- ( (41)lt- r ~ It )gt l - )
r~e llOCTOHHHaH orrpene~eTcR YCJIOBHeM CmRBaEHR C peWe1meM (21) B 06JIaCTH r COOTBeTCTBy1Ornee BIl1l8lKe1me IJ)lR HHTeHCHBHOCTH
H3JIYleHHR - II~(t c (42 )I ( f )- t~
OTIRCHBaeT H3B6CTHli aKC110He~HHil 3aKOH pacrrana
TalltHM 06pa30M B lIHTepBaJIe ~ gtgt I HMeeT MeCTO JIKJIlb
o6wmoe HeKor6peHTHoe Cn OHTaHHOe H3jlYleIDf8 Kor~a_ a T OMll p acIIaJJaJOTcR
He3aBHCHMO JJPyr OT JJPyra C xapaKTepHHM BpeMeHeM J He 3aBHCJ1ll1IDl OT
UlCJIa aTOMOB Ii
3aMe TlM lTO npH 1gt lI3 ltIoPMYJIH (41) nOJIYlBeM
-t A gt I (43)lt Rz 10gt1raquo_ ~ shy )
0Ashy( -
B cJIYiae OTCYTCTBHR HOOIIHOPOllHoro ynm-peHru JIlIlflm RMeeM A = I
( eM1 ) I103TorlY
~ (44)( ~ (rxraquo[
)
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MeHT Bp8MeHn nepeillJIa B 3Hep~ H~8HnR B CHYlBe H80~OPOnHOro
ynm-peHHR JlHHID BKJI8Jl aHTH)630HaHCHIlX lJIeHOB B r aMKJIbTOilllaHe B38ID10shy
~6~CTBBR npHBOnBT K ~ ~ T IT03TOMY
IvIV rC (45)( k) (cgtu) gt shy ) L
Tlt~ --
HepaBeHCTBO ( 4 5 ) o3Ha~a8T ITO B pe3y~bTaTe ~n He-
OIIHOPO~oro ymHp8HKR JIlIHlIH nOCJIe np01l8cca HarryqeHRff OCTBeTCR eme Beshy
RM HHBep CKH H CBR38RHaR C Hea HeHarryqeHHaH 3HeprHR
5 KpBlep o nplDleBlDolOcn pe3YJIbTa1OB
3aKaHlHBaH p acCMOTlJ8HHe BJIJUlIDIR H60lIliOpoJtHOro ynm-pemrn JIHIDm Ha
cBepXR3JIY8 TeJIbHWi mmyJIbC cltlxJp1YJIKPy eM KPHTepHH TIpBM9tmMOCTlI IIOJrYshy
leHHUX B sectsect 2-4 p e3YJIbTaTOB lIJm npoCTOThI 6yl9M orpaImlItBaTbCR cTj-
I ~
~aeM ROr~a pa60~ 06~eM B ROTOPOM HaXO~CH HarryqaTe~ MeeT Hrshy
~006pa3HyID ~PMY
KaK 6blJIO YRa3aHO p erneHlle (21) )JJllI mrnep cID HaCeJIeHHOCTBH
ltJltc (t) H Blip8leIDle HBTaHCltJllOCTlJ f31Iyiemm (22) B o CSJracTlI t T crrpaBell)IID3Il lOJIhRO Torna ROr~a BIDIOJIIDI8TCR YCJlOBH6 (18) C Iij)yroA
CTOPOlill lIpH ~OnOJIHHTemHOM npe~lIOJIOlltemm (23) WIH BpeMeHil 3aneJlliUGI
mmyJILC8 cnpaBenmIBII OneHlUl (27) JIB ( 35 ) a Mfl )llIHTemHOCTlJ-f mmyJIbC8 T--ou eRRa (26) EMil nO~CT8BlIM (27 ) B rrpaBYRJ l8CTD (21) TO no~ymM
( R~ (-t ) gt ( 0TICj )(c1 (1) GJ(yOT
310 OSHa~eT ~TO yc~oBHe (18) aBTOMaT~eCKH BIDIo~eTCH ec~ BNshy
no~eTCR ycnoBlIe (29) C~e~OBaTeJILHo 0 6lIlHM KpHTepHeM llpHMeHilMocTIil
no~eHHUX B sect 3 pe 3YJIbTaTOB RBnR8TCR BIlIO~eHRe COOTHOm6HBR (29)
Z IN ( - i t1 ) ltL i 3~6Cb B6JlHmHll 1 H ~ ollpe~eruooT BpeMR 3auepuw H ItJmTemshy
HOCTD HMIIYJILca IIpH OTCyTCTBHlf Heo~oponHoro yumpeHIDI JIlUlllI COOTB6Tshy
CTBeHHO 3aBHCHMOCTH 3TlJX B~H OT ~c~a H~aTaneH B reoMeTpBshy
~ecKOro rIsKTo pa ~ Blip8leHl ~~Jr~ (II ) Blm lrultTopa 12 6wx rrpHshy76miJKeHHo IIOJI IeH PeJlepoM 11 36eplIIl IJ)UI p a3JIRIHHX MaKpocROlIllleClGIX
ROHqJHryp~ ~pIi pa6olero 06beM8 )lnR Kpyr~oro IJJIHHHoro ItWnnlllJla C
lIHCJIOM ~eHeJIR IIOp~ I xopome~ amtpoKCRMaJJHei CJIyXJT Bllp8teHlle
~2 -x=
S Araquo ( ~_ ) ( A I- 1FA A ~4 ) (46 )1 ~
3nech A L -COOTBeTCTB~e llHO~ OCHOB8HHR B ~a~a ) -IllIIDla BOJIBH B3J1YleHlUI )-fCIIOJIb3YR (II ) Il (46 ) nO1IJl86M 2-7
j c gy7 IV 3f~ J 1
1- t th 3el ltL (47)
It It S)
r~e = VIv - IIJIOTHOCTL B3JIyla TeJIel B pa60~eM 06beMe Vc A L 01shycnna MOlltliO nep eIIHcaTL YCJIOBHe nplWelfilMOCTH (29) B BHIJe
L gtgt Lp -= ~x (If ) (48)36)1Sshy
I middot ~
HJIll z j (~- )I raquofr = ~ A)L (49)
3~eCb IjJyHKIUfl )( (_~ ) orrpe~eMBTCfl RaR pemeHHB ypaBH6HIR
j ~
LO )( gt- i Ie 81 Jr- 2 T
B CJIym6 KOr na TaKOe pemeHR6 cymecTByeT (T e KOrna Tc e ) B rrpoTHmlOM CJIyTlBB (Kor na Tgt e ~ ) MeeM rrpoClO _k -= if
Be3~e B 3TOH p a60T6 MI rrpe~o~~ ~TO ~C~O HanyqaTe~eH ~OCshy
TaTO~O 6 0JILmoe ~T06H BIDIOJIHamp)lOCb YC~OBHe II gtgt i A B c~ae Kpyr~oro IJ1IIHHoro ~a C ~CJIOM ~eH6JU UOP1mRa I 3TO y~BHe
COrJIBCHO (46) 3KBRBMeHTHO CJIeJlY1OOeMY
J p1~L raquo1 (50)7lt0shy
t)
ITocne~ee yc~oBHe KOTopoe He06xo~0 ~TlBaTh CBR3aHO C TaM
iTO llpll oi~eHll1 ypaBHeHHR (I) Ha OCHOBe KJlHeTHleCKKX ypaaHeHHii
B pa60Te I MH JlCIIOJIL30BaHH p~ ynpomeliHH KOTOpue cnpaBe~u TOJILshy
RO Mfl CJIa60 MeHmOOerocR B rrpe~Max 06pasU1l IIOM IT03TOMY Jl)IHTeJIL-
HOCTb uponecca xapaRTepll3yeMaR B6XJllJlHOH (~ ~o~a 6UTb HaMHOshy
ro 6o~rnesectjPaRTepHoro BpeMeHH H3MeHeHllfl 8MTInMTynH O~ B 06pa3ue
ic = L C 3 ~TO 03Ha~aeT KPJlTepKlf ApeKRJl-KypTeHca 8
L L C ~I (51)
)JJllI IIpHMaHHMOCTH IIO~6HHIlX pesYJrbTaToB )-fCIIOJIL3YR REHoe BIIP~eHHe
LN B (47 ) MOJl(HO nepeIIHCaTb (5D B B~e
L z L_ I JT c- (52)kfJ 3 i ) (
Jl lITepaTy p8
1 Bogolubov NN( j r ) Pam Le Kien Shumovsky AS Physica1984
128A No 1 2 p82-98
2 Groas M Earo che S PhysRep 1982 v93 No5 p301-396
15
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
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11 10 iI ( I fr rll r llllmiddot d 11 h i Lahoralory o f T Ill l rl I I NIt
Preprint of the In H i llJtt l u r Nuo l car Kesearch Dubna 1985
- shyypaBHeIDfl (1 ) ME CJIYlaH -=- 1u)- t= = 0(lt -1(
i 167 HC 1 = 1- If ltA- bull
4 IIOBeleHHe lIH1eaCHBHOCTlI l3JIYl9HIDr IlpH 60JThlJlliX BpeMeHax ( traquo T ) 3aMe~eHHe cBepXH3JIYleHHE H OCTa1O~8H HHBepcan Hace~eHHOC1e
MIl 110npo6HO o6cy JlHll B ITpe1U4llYllleM naparpa4Je BJIrunme HeOllHOpoIlltOshy
ro YJlIKPeHHR JIHHIDI Ha ltIoIMY BpeMH 3aneplUW H llJIHTeJIbHOCTh HMIIYJIbca
upa BpeMeHax ilOPMKa bull PaCCMOTpHM Tenepb KaJ BenyT ce6R IDIBepcHf
ltR~ (I )l R RHTeHCHBHOCTh Ii 3JIYle1mR f (I ) B IltHTepBaJIe 60JIbnmx BpeMeH
i gtgt (3~eCb rrpennOJIaraJIOCb R8] H pamme ITO T Memme BpeMeshy
1m C110HTaHHOro paCTI8JlB I OT~eJIbHoro H3JIYlaTe~ )
06paTHM CHalaJIB BIDIMaPHe Ha ypaBHeHIUI ( 21) ( 22) l1oJIYleHHlle
H3 (I) B lIpeIU10JIOJi eHIDl 0 rrpeo6JI8JlaHIDI CB6Pn3JIYlBT6JIbHOH KOMTIOHeHshy
Ttl H8Jl oOHlHol1 HeKorepeHTHoH Tallt R8] TIpH Z raquo i rrpRB6~eHHOe Bpe-
ME -( ) COrJIaCHO (23) rrpHlmMa6T rrp6n9JThHOe 3HBleHllt6
7 (1 )gt 1 ) = I (38)
TO H3 (21) ( 22) lloJIYla6M
t - f 0 7lt R (t) gt ~ ---7 - ~ 11 - ) Z t gt gt I A- ) f ~
t- ltlt i~ (39 )
shyi (I )jtgt ( t -- (
3TO 03HBlaeT ITO no HCTel8HHB BpeMeHH 3Ha~TeJIDHO npeBHmaIDmero
Heo6xo]tHMoe lIIlR nOJIHoli ~eqa3HpoBKH H3JIYlaT8JI8ii OCTB8TCR 8rne
HeKOTOpaR OCTaTOH8H HHB6pcHR H CBH3aHHaR C He~ HeBarryl8HH8H 3HeprHR
3anBCeHHafi B CHCT9M8 B HalaJThHWt MOMeHT 3To eCTh RBJIeillle 3BMe~eilllR
CBepXR3JIYeHlIR 06YCJIosneHHo8 H60~OpOnHllM ymKp6HH6M nKHRH2 OHO
MOE6T rrpHBO~Tb K TaR HB3HBaeMOMY orpBHHleHHOMY CBepXlI3JIYl6~2 5~ npH KOTOPOM H6 BCR B TOJIbKO He6oJIbmaH laCTb 3HeprKH CHCTeMH BTOMOB
Korep6HTHO H3JIyaeTCR
IIPH BpeM6Hax T ~ 0 raquo T I1IaBHyD POJIb B H3JIY8mm Brpa6 Ite He
KorepeHTHHH a o61lUIllli rrpo1l6CC R8] B~O H 3 CTPYKTYPH ypaBHeHllR
(I) B cwry MaJIOCTlI 3KC lIOH61~Horo llaKTOpa 2 - tr) ( H
CBH3aHHOro C HHM KOJIJIeKTRBHoro lJIeHB aTO ypaBHeHll6 nepeXOnBT B CJIeshy
~ee
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OTC)JJa nOrylaeM peDle1me IJ)lR HHBepCJm ( A~ (I ) gtB 06JIaCTH
~ ~ gtgt jt L-
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r~e llOCTOHHHaH orrpene~eTcR YCJIOBHeM CmRBaEHR C peWe1meM (21) B 06JIaCTH r COOTBeTCTBy1Ornee BIl1l8lKe1me IJ)lR HHTeHCHBHOCTH
H3JIYleHHR - II~(t c (42 )I ( f )- t~
OTIRCHBaeT H3B6CTHli aKC110He~HHil 3aKOH pacrrana
TalltHM 06pa30M B lIHTepBaJIe ~ gtgt I HMeeT MeCTO JIKJIlb
o6wmoe HeKor6peHTHoe Cn OHTaHHOe H3jlYleIDf8 Kor~a_ a T OMll p acIIaJJaJOTcR
He3aBHCHMO JJPyr OT JJPyra C xapaKTepHHM BpeMeHeM J He 3aBHCJ1ll1IDl OT
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3aMe TlM lTO npH 1gt lI3 ltIoPMYJIH (41) nOJIYlBeM
-t A gt I (43)lt Rz 10gt1raquo_ ~ shy )
0Ashy( -
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( eM1 ) I103TorlY
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)
= - 3 TO 03Ha~aeT ~TO BCR 3HeprRR 3aTIaCeHHaR B CHCTeMe B HalaJIbHHfi Meshy
MeHT Bp8MeHn nepeillJIa B 3Hep~ H~8HnR B CHYlBe H80~OPOnHOro
ynm-peHHR JlHHID BKJI8Jl aHTH)630HaHCHIlX lJIeHOB B r aMKJIbTOilllaHe B38ID10shy
~6~CTBBR npHBOnBT K ~ ~ T IT03TOMY
IvIV rC (45)( k) (cgtu) gt shy ) L
Tlt~ --
HepaBeHCTBO ( 4 5 ) o3Ha~a8T ITO B pe3y~bTaTe ~n He-
OIIHOPO~oro ymHp8HKR JIlIHlIH nOCJIe np01l8cca HarryqeHRff OCTBeTCR eme Beshy
RM HHBep CKH H CBR38RHaR C Hea HeHarryqeHHaH 3HeprHR
5 KpBlep o nplDleBlDolOcn pe3YJIbTa1OB
3aKaHlHBaH p acCMOTlJ8HHe BJIJUlIDIR H60lIliOpoJtHOro ynm-pemrn JIHIDm Ha
cBepXR3JIY8 TeJIbHWi mmyJIbC cltlxJp1YJIKPy eM KPHTepHH TIpBM9tmMOCTlI IIOJrYshy
leHHUX B sectsect 2-4 p e3YJIbTaTOB lIJm npoCTOThI 6yl9M orpaImlItBaTbCR cTj-
I ~
~aeM ROr~a pa60~ 06~eM B ROTOPOM HaXO~CH HarryqaTe~ MeeT Hrshy
~006pa3HyID ~PMY
KaK 6blJIO YRa3aHO p erneHlle (21) )JJllI mrnep cID HaCeJIeHHOCTBH
ltJltc (t) H Blip8leIDle HBTaHCltJllOCTlJ f31Iyiemm (22) B o CSJracTlI t T crrpaBell)IID3Il lOJIhRO Torna ROr~a BIDIOJIIDI8TCR YCJlOBH6 (18) C Iij)yroA
CTOPOlill lIpH ~OnOJIHHTemHOM npe~lIOJIOlltemm (23) WIH BpeMeHil 3aneJlliUGI
mmyJILC8 cnpaBenmIBII OneHlUl (27) JIB ( 35 ) a Mfl )llIHTemHOCTlJ-f mmyJIbC8 T--ou eRRa (26) EMil nO~CT8BlIM (27 ) B rrpaBYRJ l8CTD (21) TO no~ymM
( R~ (-t ) gt ( 0TICj )(c1 (1) GJ(yOT
310 OSHa~eT ~TO yc~oBHe (18) aBTOMaT~eCKH BIDIo~eTCH ec~ BNshy
no~eTCR ycnoBlIe (29) C~e~OBaTeJILHo 0 6lIlHM KpHTepHeM llpHMeHilMocTIil
no~eHHUX B sect 3 pe 3YJIbTaTOB RBnR8TCR BIlIO~eHRe COOTHOm6HBR (29)
Z IN ( - i t1 ) ltL i 3~6Cb B6JlHmHll 1 H ~ ollpe~eruooT BpeMR 3auepuw H ItJmTemshy
HOCTD HMIIYJILca IIpH OTCyTCTBHlf Heo~oponHoro yumpeHIDI JIlUlllI COOTB6Tshy
CTBeHHO 3aBHCHMOCTH 3TlJX B~H OT ~c~a H~aTaneH B reoMeTpBshy
~ecKOro rIsKTo pa ~ Blip8leHl ~~Jr~ (II ) Blm lrultTopa 12 6wx rrpHshy76miJKeHHo IIOJI IeH PeJlepoM 11 36eplIIl IJ)UI p a3JIRIHHX MaKpocROlIllleClGIX
ROHqJHryp~ ~pIi pa6olero 06beM8 )lnR Kpyr~oro IJJIHHHoro ItWnnlllJla C
lIHCJIOM ~eHeJIR IIOp~ I xopome~ amtpoKCRMaJJHei CJIyXJT Bllp8teHlle
~2 -x=
S Araquo ( ~_ ) ( A I- 1FA A ~4 ) (46 )1 ~
3nech A L -COOTBeTCTB~e llHO~ OCHOB8HHR B ~a~a ) -IllIIDla BOJIBH B3J1YleHlUI )-fCIIOJIb3YR (II ) Il (46 ) nO1IJl86M 2-7
j c gy7 IV 3f~ J 1
1- t th 3el ltL (47)
It It S)
r~e = VIv - IIJIOTHOCTL B3JIyla TeJIel B pa60~eM 06beMe Vc A L 01shycnna MOlltliO nep eIIHcaTL YCJIOBHe nplWelfilMOCTH (29) B BHIJe
L gtgt Lp -= ~x (If ) (48)36)1Sshy
I middot ~
HJIll z j (~- )I raquofr = ~ A)L (49)
3~eCb IjJyHKIUfl )( (_~ ) orrpe~eMBTCfl RaR pemeHHB ypaBH6HIR
j ~
LO )( gt- i Ie 81 Jr- 2 T
B CJIym6 KOr na TaKOe pemeHR6 cymecTByeT (T e KOrna Tc e ) B rrpoTHmlOM CJIyTlBB (Kor na Tgt e ~ ) MeeM rrpoClO _k -= if
Be3~e B 3TOH p a60T6 MI rrpe~o~~ ~TO ~C~O HanyqaTe~eH ~OCshy
TaTO~O 6 0JILmoe ~T06H BIDIOJIHamp)lOCb YC~OBHe II gtgt i A B c~ae Kpyr~oro IJ1IIHHoro ~a C ~CJIOM ~eH6JU UOP1mRa I 3TO y~BHe
COrJIBCHO (46) 3KBRBMeHTHO CJIeJlY1OOeMY
J p1~L raquo1 (50)7lt0shy
t)
ITocne~ee yc~oBHe KOTopoe He06xo~0 ~TlBaTh CBR3aHO C TaM
iTO llpll oi~eHll1 ypaBHeHHR (I) Ha OCHOBe KJlHeTHleCKKX ypaaHeHHii
B pa60Te I MH JlCIIOJIL30BaHH p~ ynpomeliHH KOTOpue cnpaBe~u TOJILshy
RO Mfl CJIa60 MeHmOOerocR B rrpe~Max 06pasU1l IIOM IT03TOMY Jl)IHTeJIL-
HOCTb uponecca xapaRTepll3yeMaR B6XJllJlHOH (~ ~o~a 6UTb HaMHOshy
ro 6o~rnesectjPaRTepHoro BpeMeHH H3MeHeHllfl 8MTInMTynH O~ B 06pa3ue
ic = L C 3 ~TO 03Ha~aeT KPJlTepKlf ApeKRJl-KypTeHca 8
L L C ~I (51)
)JJllI IIpHMaHHMOCTH IIO~6HHIlX pesYJrbTaToB )-fCIIOJIL3YR REHoe BIIP~eHHe
LN B (47 ) MOJl(HO nepeIIHCaTb (5D B B~e
L z L_ I JT c- (52)kfJ 3 i ) (
Jl lITepaTy p8
1 Bogolubov NN( j r ) Pam Le Kien Shumovsky AS Physica1984
128A No 1 2 p82-98
2 Groas M Earo che S PhysRep 1982 v93 No5 p301-396
15
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
-I737
PY1WIU1Cb JIOCTYffiIJI a B 113laTMbCKilli OTl8JI
II 8HTR0PJi 1985 rOla
16
PI 7-8)-665 IIMI IYJ Il 1
1111111111111
1tlH1Yll h c a npH
111 1 r~II I11 11t IIM II YI U C J YMe llhshy
111 J XU 1 11Y 4 IIH R
11 111 1 1 11 110 11 111 I l lIII1H 1JJ1R
111 1 I I1 I 1I1 Il l lllMl llIIMIlCTII
P lIl 1M liI Tli i1i ll I TIO IH 1 111 Kll il 1 111111 nIHilI
11111 amp11 If II r JIIA lytlHa 19 8 )
llepeBoA i1 II H
r 17-Rr hfl5 l l ~ 111 1
into I II 1III u k ll i II g
1 I lv i ll llr n il h -~ i ll x llnill Ed I IiIlIInlII i I jlI b c (a cl lIi II i II has
bull 1 ~ )JIIleni II ~ I i oI tl-gt 1 1YlIn1 r y of t he pul St f I I li n I lly I i 1110 1 111 1 pilI St middot durashy
tion 111 11 1111 j l1 t I1 ~ il y th middot rt la r dashyI i (Ill tf 1 1 _ p middot i hl ~ middot i ti l t IlIl pound 1 r Cs idu-
I I 111111 1111 i 110 a 11 1y l i il l middotX l rl f i l1h r t he pll l d 1111 I I I v il l l d i lY (middot d i illll lgt hnv 1)1 ( 11 e tashyhI i l ll l
11 10 iI ( I fr rll r llllmiddot d 11 h i Lahoralory o f T Ill l rl I I NIt
Preprint of the In H i llJtt l u r Nuo l car Kesearch Dubna 1985
~aeM ROr~a pa60~ 06~eM B ROTOPOM HaXO~CH HarryqaTe~ MeeT Hrshy
~006pa3HyID ~PMY
KaK 6blJIO YRa3aHO p erneHlle (21) )JJllI mrnep cID HaCeJIeHHOCTBH
ltJltc (t) H Blip8leIDle HBTaHCltJllOCTlJ f31Iyiemm (22) B o CSJracTlI t T crrpaBell)IID3Il lOJIhRO Torna ROr~a BIDIOJIIDI8TCR YCJlOBH6 (18) C Iij)yroA
CTOPOlill lIpH ~OnOJIHHTemHOM npe~lIOJIOlltemm (23) WIH BpeMeHil 3aneJlliUGI
mmyJILC8 cnpaBenmIBII OneHlUl (27) JIB ( 35 ) a Mfl )llIHTemHOCTlJ-f mmyJIbC8 T--ou eRRa (26) EMil nO~CT8BlIM (27 ) B rrpaBYRJ l8CTD (21) TO no~ymM
( R~ (-t ) gt ( 0TICj )(c1 (1) GJ(yOT
310 OSHa~eT ~TO yc~oBHe (18) aBTOMaT~eCKH BIDIo~eTCH ec~ BNshy
no~eTCR ycnoBlIe (29) C~e~OBaTeJILHo 0 6lIlHM KpHTepHeM llpHMeHilMocTIil
no~eHHUX B sect 3 pe 3YJIbTaTOB RBnR8TCR BIlIO~eHRe COOTHOm6HBR (29)
Z IN ( - i t1 ) ltL i 3~6Cb B6JlHmHll 1 H ~ ollpe~eruooT BpeMR 3auepuw H ItJmTemshy
HOCTD HMIIYJILca IIpH OTCyTCTBHlf Heo~oponHoro yumpeHIDI JIlUlllI COOTB6Tshy
CTBeHHO 3aBHCHMOCTH 3TlJX B~H OT ~c~a H~aTaneH B reoMeTpBshy
~ecKOro rIsKTo pa ~ Blip8leHl ~~Jr~ (II ) Blm lrultTopa 12 6wx rrpHshy76miJKeHHo IIOJI IeH PeJlepoM 11 36eplIIl IJ)UI p a3JIRIHHX MaKpocROlIllleClGIX
ROHqJHryp~ ~pIi pa6olero 06beM8 )lnR Kpyr~oro IJJIHHHoro ItWnnlllJla C
lIHCJIOM ~eHeJIR IIOp~ I xopome~ amtpoKCRMaJJHei CJIyXJT Bllp8teHlle
~2 -x=
S Araquo ( ~_ ) ( A I- 1FA A ~4 ) (46 )1 ~
3nech A L -COOTBeTCTB~e llHO~ OCHOB8HHR B ~a~a ) -IllIIDla BOJIBH B3J1YleHlUI )-fCIIOJIb3YR (II ) Il (46 ) nO1IJl86M 2-7
j c gy7 IV 3f~ J 1
1- t th 3el ltL (47)
It It S)
r~e = VIv - IIJIOTHOCTL B3JIyla TeJIel B pa60~eM 06beMe Vc A L 01shycnna MOlltliO nep eIIHcaTL YCJIOBHe nplWelfilMOCTH (29) B BHIJe
L gtgt Lp -= ~x (If ) (48)36)1Sshy
I middot ~
HJIll z j (~- )I raquofr = ~ A)L (49)
3~eCb IjJyHKIUfl )( (_~ ) orrpe~eMBTCfl RaR pemeHHB ypaBH6HIR
j ~
LO )( gt- i Ie 81 Jr- 2 T
B CJIym6 KOr na TaKOe pemeHR6 cymecTByeT (T e KOrna Tc e ) B rrpoTHmlOM CJIyTlBB (Kor na Tgt e ~ ) MeeM rrpoClO _k -= if
Be3~e B 3TOH p a60T6 MI rrpe~o~~ ~TO ~C~O HanyqaTe~eH ~OCshy
TaTO~O 6 0JILmoe ~T06H BIDIOJIHamp)lOCb YC~OBHe II gtgt i A B c~ae Kpyr~oro IJ1IIHHoro ~a C ~CJIOM ~eH6JU UOP1mRa I 3TO y~BHe
COrJIBCHO (46) 3KBRBMeHTHO CJIeJlY1OOeMY
J p1~L raquo1 (50)7lt0shy
t)
ITocne~ee yc~oBHe KOTopoe He06xo~0 ~TlBaTh CBR3aHO C TaM
iTO llpll oi~eHll1 ypaBHeHHR (I) Ha OCHOBe KJlHeTHleCKKX ypaaHeHHii
B pa60Te I MH JlCIIOJIL30BaHH p~ ynpomeliHH KOTOpue cnpaBe~u TOJILshy
RO Mfl CJIa60 MeHmOOerocR B rrpe~Max 06pasU1l IIOM IT03TOMY Jl)IHTeJIL-
HOCTb uponecca xapaRTepll3yeMaR B6XJllJlHOH (~ ~o~a 6UTb HaMHOshy
ro 6o~rnesectjPaRTepHoro BpeMeHH H3MeHeHllfl 8MTInMTynH O~ B 06pa3ue
ic = L C 3 ~TO 03Ha~aeT KPJlTepKlf ApeKRJl-KypTeHca 8
L L C ~I (51)
)JJllI IIpHMaHHMOCTH IIO~6HHIlX pesYJrbTaToB )-fCIIOJIL3YR REHoe BIIP~eHHe
LN B (47 ) MOJl(HO nepeIIHCaTb (5D B B~e
L z L_ I JT c- (52)kfJ 3 i ) (
Jl lITepaTy p8
1 Bogolubov NN( j r ) Pam Le Kien Shumovsky AS Physica1984
128A No 1 2 p82-98
2 Groas M Earo che S PhysRep 1982 v93 No5 p301-396
15
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
-I737
PY1WIU1Cb JIOCTYffiIJI a B 113laTMbCKilli OTl8JI
II 8HTR0PJi 1985 rOla
16
PI 7-8)-665 IIMI IYJ Il 1
1111111111111
1tlH1Yll h c a npH
111 1 r~II I11 11t IIM II YI U C J YMe llhshy
111 J XU 1 11Y 4 IIH R
11 111 1 1 11 110 11 111 I l lIII1H 1JJ1R
111 1 I I1 I 1I1 Il l lllMl llIIMIlCTII
P lIl 1M liI Tli i1i ll I TIO IH 1 111 Kll il 1 111111 nIHilI
11111 amp11 If II r JIIA lytlHa 19 8 )
llepeBoA i1 II H
r 17-Rr hfl5 l l ~ 111 1
into I II 1III u k ll i II g
1 I lv i ll llr n il h -~ i ll x llnill Ed I IiIlIInlII i I jlI b c (a cl lIi II i II has
bull 1 ~ )JIIleni II ~ I i oI tl-gt 1 1YlIn1 r y of t he pul St f I I li n I lly I i 1110 1 111 1 pilI St middot durashy
tion 111 11 1111 j l1 t I1 ~ il y th middot rt la r dashyI i (Ill tf 1 1 _ p middot i hl ~ middot i ti l t IlIl pound 1 r Cs idu-
I I 111111 1111 i 110 a 11 1y l i il l middotX l rl f i l1h r t he pll l d 1111 I I I v il l l d i lY (middot d i illll lgt hnv 1)1 ( 11 e tashyhI i l ll l
11 10 iI ( I fr rll r llllmiddot d 11 h i Lahoralory o f T Ill l rl I I NIt
Preprint of the In H i llJtt l u r Nuo l car Kesearch Dubna 1985
3 AllnpeeB AB EMeJIbHHOB B l~ VUIMHCKJ1ij Kl A YloHI980 TI3I B~n 4 c653- 694
4 Bonitmiddot8cio R Lugiato LA PhysRev1n 5 V 1A No 5 p1 5 07shy152 1 v 1 2 A No2 p87-5 91J
5 Nac Gi lli vray J C oeld )yl ~ Ph)s J(ev 1976 v14A NO3 P11(9- 1185
6 Mac GillimiddotJray Je Peld 11 hysRev 198 1 v23A No3 P1334- 134 9
7 Rehl er iE Eberl y JH PhysHev1970 vA No 5 1730-1737
b Artc ch1 F f Court ens E Phts ~eV I970 v A2 No ~ I7JO_
-I737
PY1WIU1Cb JIOCTYffiIJI a B 113laTMbCKilli OTl8JI
II 8HTR0PJi 1985 rOla
16
PI 7-8)-665 IIMI IYJ Il 1
1111111111111
1tlH1Yll h c a npH
111 1 r~II I11 11t IIM II YI U C J YMe llhshy
111 J XU 1 11Y 4 IIH R
11 111 1 1 11 110 11 111 I l lIII1H 1JJ1R
111 1 I I1 I 1I1 Il l lllMl llIIMIlCTII
P lIl 1M liI Tli i1i ll I TIO IH 1 111 Kll il 1 111111 nIHilI
11111 amp11 If II r JIIA lytlHa 19 8 )
llepeBoA i1 II H
r 17-Rr hfl5 l l ~ 111 1
into I II 1III u k ll i II g
1 I lv i ll llr n il h -~ i ll x llnill Ed I IiIlIInlII i I jlI b c (a cl lIi II i II has
bull 1 ~ )JIIleni II ~ I i oI tl-gt 1 1YlIn1 r y of t he pul St f I I li n I lly I i 1110 1 111 1 pilI St middot durashy
tion 111 11 1111 j l1 t I1 ~ il y th middot rt la r dashyI i (Ill tf 1 1 _ p middot i hl ~ middot i ti l t IlIl pound 1 r Cs idu-
I I 111111 1111 i 110 a 11 1y l i il l middotX l rl f i l1h r t he pll l d 1111 I I I v il l l d i lY (middot d i illll lgt hnv 1)1 ( 11 e tashyhI i l ll l
11 10 iI ( I fr rll r llllmiddot d 11 h i Lahoralory o f T Ill l rl I I NIt
Preprint of the In H i llJtt l u r Nuo l car Kesearch Dubna 1985