T O T A L C R O S S S E C T I O N S , E L A S T I C S C A T T E R I N G O B S E R V A B L E S A N D D I R E C T R E C O N S T R U C T I O N O F

S C A T T E R I N G M A T R I X I N n p I N T E R A C T I O N S B E T W E E N 0.8 A N D 1.1 G E V A T S A T U R N E I I

J. BALL, PH. CHESNY, M. COMBET, J . M . FONTAINE, R. KUNNE, C . D . LAC*), J. L. SANS

Laboratoire National SATURNE, CNRS/ IN2P3 et CEA/DSM, CF_,-Saclay, F-91191 Gif-sur-Yvette Cedex, France

J. BYSTRICKY, P. CHAUMETTE, J. DER~GEL, F. LEHAR, M . C . LEMAIRE, A. DE LESQUEN, M. DE MALI, F. PERROT-KUNNE, L. VAN ROSSUM

CEA DAPNIA, CE Saclay, F-91191 Gif-sur-Yvette Cedex, France

P. BACH**), PH. DEMIERRE, G. GAILLARD?), R. HESS, D. RAPIN, PH. SORMANI:~), B. VUARIDEL

DPNC, University of Geneva, 24, quai Ernest-Ansermet, 1211 Geneva 4, Switzerland

J . P . GOUDOUR

C.E.N.B., Doma/ne du Haut-Vigneau, F-33170 Gradignan, France

R. BINZ, A. KLETT, R. PESCHINA-KLETT, E. ROSSLE, H. SCHMITT

Faculty o f Physics, Freiburg University, D-7800 Freiburg im Br., Germany

L.S. BARABASH, Z. JANOUTw B . A . KHACHATUROV, YU. A. Usov

LNP-JINR, Dubna, 101000 Moscow, P.O.Box 79, Russian Federation

D. LOPIANO, H. SPINKA

ANL-HEP, 9700 South Cass Avenue, Argonne, I11 60439, USA

V. GHAZIKHANIAN, C. WHITTEN

UCLA, 405 H//gard Ave., Los Angeles, CA 90024, USA

Received 4 July 1994

Neutron-proton total cross section differences with the beam and target polarizations orientated either transversally or longitudinally with respect to the beam direction, as

*) Present address: Inst. Nat. des Telecommunications, 9, rue Charles Fourier, 91011 Evry, France. **) Present address: Coll~ge Rousseau, 16A, av. du Bouchet, 1209 Geneva, Switzerland. t) Present address: Schlumberger Ind., 87, rte de Grigny, 91130 Ris Orangis, France. ~) Present address: Bralnsoft Consulting S.A., Cusinand 46, 1285 Athenaz, Switzerland. w Present address: Faculty of Nuclear Sciences and Physical Engineering, Czech Technical Uni-

versity, B~ehov~ 7, 11519 Praha 1, Czech Republic.

Czechoslovak Journal of Physics, Vol. 45 (1995), No. 1 23

J. Ball et M.

well as 11 spin dependent elastic scattering observables measured at SATURNE [I as a function of energy and angle are presented. A major part of results was measured using the quasimonoenergetic polarized neutron beam and/or the polarized proton target. A small part of data was obtained using a polarized deuteron beam considered as a beam of quasifree neutrons and protons. The present paper represents a review of measured observables. Several sets of present data are compared with results obtained in other laboratories below 0.8 GeV. Imaginary parts of spin dependent forward amplitudes for np scattering and for the isospin state I = 0 were determined. First direct reconstruction of the np scattering matrix at 0.84 GeV is shown.

1 I n t r o d u c t i o n

A review of the nucleon-nucleon scattering situation in the intermediate energy region below 30 GeV was presented in ref. [1]. A large amount of new results for np elastic scattering and transmission experiments at intermediate energies appeared recently. A considerable part of them was measured at SATURNE II using the intense polarized beam of free neutrons obtained by a break-up of accelerated po- larized deuterons. The total cross section differences Acrw and Act L were measured in a large energy region [2-4]. Below 0.8 GeV differential cross sections at medium and large scattering angles have been accurately measured for many years now in different laboratories. Measurements at small angles, however, have been scarce. At SATURNE II, the small angle elastic np differential cross section at 378,481,532, 582, 633, 683, 708, 784, 834, 884, 934, 985, 1085 and l135MeV was measured by Saclay and Gatchina groups [5], resulting in 585 experimental points. In this exper- iment, neutrons were scattered at small angles inside a high-pressure drift chamber IKAR which measured the slow recoil proton angle and pa th length in the gas. The same experimental set-up completed by two large neutron counters was used to determine the np analyzing power at 0.633, 0.784, 0.834, 0.934 and 0.985 GeV [5,6]. Most of spin dependent observables were measured by the "NUCLEON-NUCLEON GROUP" (NN), either in quasielastic [7,8,9], or in elastic [10-15] np scattering (90 and 1646 data points, respectively). For these measurements the polarized deuteron or neutron beams and the Saclay polarized proton target (PPT) were used. The a im of SATURNE II experimental program is a reconstruction of scattering matr ix either via the phase shift analysis (PSA), or by a direct determination of scattering amplitudes.

In the present review, the spin-dependent total cross section differences and np ==~ np scattering results of the NN group are reported. The notat ion of observables and the scattering ampli tude representation as in ref. [16] are used.

2 P o l a r i z e d b e a m a n d p o l a r i z e d t a r g e t

A small part of np data was measured with a polarized deuteron beam considered as a beam of quasifree proton and neutrons. For such a beam the polarizations of protons and neutrons in accelerated deuterons are equal and the ratio of the quasielastic pp to np asymmetries is idependent on the deuteron beam polarization.

24 Czech. J. Phys. 45 (1995)

T o t a ! c r o s s s e c t i o n s . . .

Using the NN beam-line polarimeter and assuming that the quasielastic pp ana- lyzing power is the same as that for pp elastic scattering, we determined the polar- ization of the protons and neutrons in the deuterons. It was equal to 0.577 + 0.003 (the error is statistical only) and it was found to be independent on the deuteron beam energy [7]. This is in agreement with the absence of any deuteron depolarizing resonance at SATURNE II. The proton and neutron polarizations agree with the measurement of the deuteron beam polarization, undertaken at very low energy.

The angular dependence of several observables (Aoo,~o, Aoo,~,~, Aoosk) in quasifree pp scattering agrees with the fit to free pp data and one can assume that this also holds for np scattering.

At SATURNE II, a free neutron beam was first built for the IKAR experiment [5,6] and later for the NN program [2].The characteristics of both beain~ are simi- lar. Vector-polarized deuterons were broken up on a 20 cm thick Be target. For the NN beam line [2,3] the protons, outgoing from the production target, are swept away by a magnetic field, while the remaining neutron beam goes through a spin- rotating solenoid and precessing magnets. This allows to orient the neutron polar- ization along any of the three orthogonal directions ~ (vertical), ~" (sideways) and /~ (longitudinal). The neutron beam is defined by 8 meters of collimators inserted into the 17.5m long neutron beam line. The beam spot at the target was either 20m m or 30mm in diameter. The MIMAS booster increases the SATURNE II polarized deuteron beam intensity up to 3 x 1011 deuterons/spill providing up to 6 • 107 neutrons/spi l l /cm 2 on the target.

A. Boudard and C. Wilkin calculated in 1987 the polarization of the "break- up" neutrons in the forward direction, using the results from refs. [7,17,18]. They predicted a value of 0.59 at SATURNE II. Experimentally we have measured it by comparing the beam analyzing power Aoono and the target analyzing power Aooo,~, measured with a polarized neutron beam and unpolarized proton target and vice versa. The slope of the angular dependence of Aoono near the zero-crossing point must be equal to that of Aooo,~ which is independent of the beam polarization. The comparison was done at 477 MeV [11], i.e., at the very energy where a precise test of isospin invariance Aoono(np) = Aooon(np) has been done at TRIUMF [19]. This comparison gives the beam polarization PB = 0.59 + 0.02 for the "break- up" neutrons in perfect agreement with the calculations of Boudard and Wilkin. Later, the same values were obtained at several higher energies and the error of PB decreased considerably.

The neutron beam enters the 35 mm thick, 40 mm wide and 49 mm high P P T [20]. The target material was Pentanol-1, with a typical proton polarization PT = 85%. The relaxation time of the target was ~ 30 days at 38 mK in a holding field of 0.33 Tesla. The P P T polarization may be also oriented in any of the if, ~" or /~ directions (only the vertical and longitudinal target spin directions were employed). The experiments using an incident deuteron beam were done with the P P T 44 mm long and 20 mm in diameter [21].

Czech. J. Phys. 45 (1995) 25

J. Ball et al.

3 T o t a l c ros s s e c t i o n d i f f e r e n c e s for n p s c a t t e r i n g

The np total cross section differences A0" T and A~rL were determined for the first time in 1987 at SATURNE II [2]. These results were completed by new mea- surements for each observable [3,4]. Results were obtained at 11 energies for A~rw and at 10 energies for AaL. The total cross section differences were measured si- multaneously with other spin-dependent np elastic scattering observables.

The experimental set-up and its electronics were described in refs. [2-4]. The beam monitor, upstream from the PPT, and the transmission detector were of similar design. The 40 to 60 mm thick CH2 convertors are placed immediately after large veto scintillators, and charged particles emitted forward are detected by two counters in coincidence. The solid angle subtended by the transmission detector at the center of the target was ~2 = 2.5 msr for most of measurements. The difference between the value measured a t / 2 = 2.5 msr and the mo" L at ~2 = 0 ~ is estimated to be less than 0.05 mb. This is smaller than the experimental errors in the experiment. The effects due to misalignment and transverse beam polarization cancel in the simple average between measurements with opposite target polarizations [22]. A check with ~-type beam and k-type target at 0.84 GeV gives (0.12-4-0.74)mb.

The Saclay results were soon followed by PSI measurements in the energy region from 140 to 590MeV. The latter used a similar counter set-up, but completely different electronics. A polarized neutron beam with a continuous energy spectrum [23] was used so that Atrw or AO'L data were collected simultaneously over the entire energy range 140-590 MeV [24].

The observable AO-L has also been measured at five energies at LAMPF. The measurements were done with a quasi-monoenergetic polarized neutron beam pro- duced in pd ~ n + X scattering of longitudinally polarized protons. A large neutron counter hodoscope was used because of the small neutron beam intensity. Prelimi- nary results are given in ref. [25], the final results were recently reported in ref. [26].

Figures la,b show the energy dependence of all existing measurements for O ' l t o t :

--A~rT/2 and --ACrL, respectively. One can notice an excellent agreement between all data sets. A dip at .~ 600 MeV for both observables is less pronounced than for the analogous pp quantities. A very broad maximum can be observed at ~ 0.9 GeV in --AtrL energy dependence.

In fact, the first AaL results were obtained in 1981 in a quasifree pn transmis- sion measurements at the ANL-ZGS [27]. This experiment measured AtrL (pd) and AaL (pp) by transmission of polarized protons through a partially deuterated po- larized target. Taking a simple difference between pd and pp results, corrected only for beam and target polarizations and for Coulomb-nuclear rescattering including deuteron break-up, yields data in fairly good agreement with the Saclay, PSI and LAMPF results. The Glauber-type rescattering increases the difference. Including more sophisticated corrections increases the disagreement between the data from refs. [2-4,24,26] and the results of ref. [27], as shown in [3,26].

In the past no serious difference has ever been found between elastic and quasielas- tic scattering observables and all a t tempts to correct quasifree scattering have

26 Czech. J. Phys. 45 (1995)

Total cross s e c t i o n s . . .

o)

6! 4

2

-2

-4

-6

-8 012' ~ ' ' ' ' ' J_.~ t 0.4 0.6 0.8 1.0 1.2

Tki n (GeV)

301 ' ,

2~ I io~

o!,, o'.~

' i " l i

q

-&6 L (n-p) ] "1 ?

!

i

i ~ i

Tt ~ t 1.1

�9 SATURNE tl o PSI + LAMPF

+ '0.2 0:3 ' 0.~, 'o:s '0.'6 ' 0'7 ' o:s ' 0:9 ' 1:0

Tkin(GeV)

Fig. 1. Energy dependence of a) a]tot(np) and b) --AO'L(np). �9 - - S A T U R N E II [3]; v - - S A T U R N E II [4]; o - - PSI [24]; + - - LAMPF [ 2 6 ] .

failed. Surprizing results were obtained at PSI [23] which show that the polarization transfer parameters Konno, and Kok%o for the pC =~ n + X reaction at angles close to 180 ~ CM, have practially the same energy dependences as the observables for free np scattering.

4 I s o s p i n I = 0 t o t a l cross s e c t i o n s

From the measured observables ~0tot, AO'T and A~L for pp and np transmission it is possible to determine the I = 0 total cross sections. Since the corresponding pp observables are known, the np quantities presented above were used for these calculations. Figures 2a and 2b show the energy behavior of O'ltot and --AtTL , respectively. The LAMPF results, plotted in Fig. 2b (crosses) slightly differ from

Czech. J. Phys. 45 (1995) 27

J. Ball et al.

2

E o

-2

- 4

a)

4 --t

-6

-a!

-10

r i i i i I i i

Eltot ]=0

iIt ..... i/i t-- I I L ~ L I I I I I I

0.2 0.4 0.6 0.8 1.0 1.2 Tkin(GeV)

40~ �84 ,

3O

20

10

-10

b)

( f i , , , , ,

-Ag L (I=0)

�9 SATURNE II

o PSI + LAMPF

! ! 1

+'t*TI . . . . . . . . . . . . . . . . . -

0,2 04 0.6 0.8 10 12

Tkin(GeV)

Fig. 2. Energy dependence of a) Chtot(I = 0) and b) - - A a L (I = 0). �9 - - SATURNE II [3,4]; o - - PSI [24]; + - - LAMPF [26].

--Ao" L ( I : 0) data, listed in ref. [26]. This is due to the fact that in the present calculations a phase shift analysis fit to all existing data was used, whereas in ref. [26] the SATURNE II --ACrL (pp) results were omitted. The difference is within the errors. Shapes of chtot and - A c t L observables for I = 0 state are similar to those observed for the corresponding np observables. A dip at ~ 0.6 GeV is well pronounced as it was found also in the energy dependence of similar pp quantities. In the past the dip for pp observables was at tr ibuted to a possible resonance in the 1 D2 partial wave. Present results show that no resonance can be at t r ibuted to this partial wave, which is absent in I = 0 amplitudes. This question is. discussed in refs. [3,26].

5 S p i n d e p e n d e n t o b s e r v a b l e s

In the NN program at SATURNE II, 11 spin dependent np observables were measured at 840, 880, 940, 1000 and l l 0 0 M e V in a large angular range in order to determine directly the np scattering amplitudes. Some dedicated measurements were also performed at other energies.

The apparatus, the experimental set-up, the ON-LINE and OFF-LINE analyses are described in ref. [28]. The two arm spectrometer comprising trigger counters and hodoscopes, 8 M W P C ' s and an analyzing magnet was used. Neutrons scattered at

28 Czech. J. Phys. 45 (1995)

Total c r o s s s e c t i o n s . . .

angles below 90 ~ CM were detected in a large neutron counter hodoscope having a detection efficiency of about 20 % and the angular resolution +0.22 ~ lab horizontally and 4-0.35 ~ vertically. Transverse components of recoil proton polarization were determined by rescattering on a carbon analyzer 5 to 6 cm thick. Neutrons scattered at large angles may also be converted into charged particles )roduced in the same carbon block. For such events the detection efficiency is considerably smaller.

03

0.2 ~ , =0.84 GeV ~ T ~ ~ -r ~

o

-0.1 '

-0,2

-0.3

-0.4

-os , , ' do' '12o 1 OCM (deg)

I ; I I ] I ; 1

Aoono =Aooon -] n-p -~

J

180

Fig. 3. Angular dependence of A . . . . ( n p ) a t 0 . 8 4 G e V . �9 - - P P T ref. [12]; o - - CH2 ref. [12]; c rosses ( x ) - - ref. [7]; c rosses (+ ) - - refs. [5,6].

0.4

0.3

0.2

0.1

I I ~ I ; I I k b i t q I T I I i I J " A ~ 1 7 6 1 7 6 1 7 6 4

o Aooon PPT

+ Aoono CH 2 -lt

0.94, GeV

n -p i 0 . . . . . . . . . . " ~ . . . . . . . . . . . . . . . . .

-0.2 t -

-0.:

- 0 , l I I I I I I I I t i t I r !

0 30 60 90 120 150 180 0CM (deg)

Fig. 4. Angular dependence of A . . . . ( np ) a n d A . . . . ( n p ) a t 0.94 G e V [11]. �9 - - A . . . . (r ip) using P P T ; o - - A . . . . ( n p ) using P P T ; + - - A . . . . ( n p ) using CH2 .

Czech, d. Phys. 45 (1995) 29

Q}

J. Ball et al.

0k n-p I 1 ii 0 . ~ . . . . . . .

02 II 01 / /

0 . . . . . .

-0.1

-0.2

-0.: [ i l i I I I I 0 30 GO 90 120 150 180

8cM(deg)

07 , , ~ ,

O6 Aoonn

0.5 n-p

I,I GeV O.4

0.3

02 f 0.I

-0,2

"0'3 t- -0.4

~) ' ' . . . . . 9'o' '~ '~o'' 0 30 60 I 0 I 180 eCM(deg)

Fig. 5. Angular dependence of A . . . . a) around 0.80 GeV (o -- S A T U R N E II [13]; o - - L A M P F [29]; + - - S A T U R N E II [9]) and b) at 1.10 GeV [13].

In order to correctly monitor measurements with two opposite target polarization directions, a CH2 target 3 to 10 mm thick was positioned downstream from the PPT. Particles scattered either on the P P T or on the CH2 target produce independent triggers, but all tracks are detected in the same MWPC's.

The observables Aoono and Aooo,~ were measured separately at 0.447, 0.880, 0.910 and 0.940 GeV [11]. Altogether 208 experimental points were determined. The same

30 Czech. J. Phys. 45 (1995)

Total cross sections...

Q)

0 ' 1, ! 0.2

0 . . . . . . :'- . . . . . . . 4k-

- 0.2 "~, ! i - 0 . 4 \ \ / I -~

\ /

- 0.6 " ' - /

_ 0 8 0 t i i s I I I I 1 t r i I 3 0 6 0 9 0 120 150 180

O c M ( d e g )

1.0 ' J I I ] ' ' ' ' ' ' / ' ' ' ' '

o.+

O~ 1 eV

0.4

0 :-- - ' - - ~ . . . . . . . . . . . . .

_ 0 . 2 0 t ~ , L i, i i l z I ~ i i ~ I I i l 3 0 6 0 9 0 120 150 180

8 C M ( d e g )

Fig. 6. Results of Aoo~k(np) around a) 0.80GeV (e - - 0.80GeV [15]; o - - 0.788GeV, LAMPF [30]; solid line - - Saclay-Geneva PSA 1993 including the present points; dashed line - - ref. [31]; dot-dashed line - - ref. [32]) and b) 1.00 GeV (e - - 1.00 GeV

[15]; o - - 0.98 GeV [10]; dot-dashed line - - PSA [32]).

observables, assuming Ao,,no = Aooon, were measured at 0.312, 0.363, 0.800, 0.840, 0.860, 0.877, 0.880, 0.910, 0.940, 1.00, 1.08 and 1.10 GeV [23]. These measurements provided 379 experimentM points. The observable Aoono measured with the addi- tional CI-I2 target, simultaneously with the P P T measurements, provided 117 data points. In addition, 62 Aoon,, data points were determined in quasielastic np scat- tering at 0.544, 0.719, 0.725, 0.744, 0.794, 0.800, 0.850, 0.894, 0.950 and 1.00 GeV, using a polarized deuteron beam.

Figure 3 compares analyzing power Aoono = Aooon measured with the PPT, Aoono data obtained with the CH2 target from ref. [12], quasielastic Aoo, o data from ref. [7] and the IKAR results at small angles [5,6] around 0.84 GeV. In Fig. 4 are shown the results of the beam and target analyzing powers Aoono and Aooo~

C z e c h . J . P h y s . 4 5 ( 1 9 9 5 ) 3 1

J. Ball et al.

! . . . . . i . . . . . . . . . . Aoos i

- 0 2 "~

e) -0"60 30 60 90 120 150 180

e c M ( d e g )

0.6 Aoos k

0.4 n-p

i L ]

o2 I I t . . ~ . I

o ~ ' : - - - - i . . . . . . . . . .

-02 =1.10 GeV I ' i q

b) - O . & ~ , , , ' 6 ' 0 ' ' 9 t ~ i , , i 1 ] 4 0 30 0 120 150 180 eCM (deg)

Fig. 7. Results of Aoo~k(np) around a) 0.80GeV (o I 0.80GeV SATURNE II [15]; o - - 0.794 GeV, SATURNE II [9]; + - - 0.788 GeV, LAMPF [30]; • - - 0.788 GeV, LAMPF [33]; solid line - - Saclay-Geneva PSA 1993 including the present points; dashed line - - ref. [31]; dot-dashed line - - r e f . [32]) and b) 1.10GeV [15] (o - - 1.10GeV; o - - 1.08 GeV;

dot-dashed line - - PSA [32]).

measured with the P P T and Aoono data, measured using the CH2 target at 0.94 GeV [11]. Different results are in excellent agreement. The da ta above 90~ were measured using the neut ron charge exchange on the carbon block and their errors are large.

The angular dependence of the elastic scat ter ing spin correlat ion A ...... (np) was measured at 0.800, 0.840, 0.860, 0.'880, 0.910, 0.940, 1.00, 1.08 and 1.10GeV [13]. Measurements provided 323 experimental da ta points. This observable was also measured in quasielastic scat ter ing of polarized deuterons on a P P T at 0.744 and 0 .794GeV [9] (12 points). Figures 5a,b show Aoonn data at 0.80 and 1.10 GeV, re- spectively. Around 0.8 GeV the S A T U R N E II results f rom refs. [9,13] are compared with the elastic scat ter ing da ta f rom L A M P F [29].

Note tha t A . . . . (np) values f rom 0.15 to 0.65 GeV in the angular region between 40 ~ and 150" CM are positive. The angular dependence shows two maxima, one in the forward hemisphere, another in the backward one, separate by a min imum close to 90 ~ CM. The Aoon,~(np) observable as a funct ion of the scat ter ing angle

32 Czech. J. Phys. 45 (1995)

- T - - - 1 - 7 - Q - ~ - - T r l - - - ] - -

o.8~ "*r*', "- 0,6 "

0.4 Donon n - p

Q2 0.80 GeV

0 I I F-4--4:--t--+-+- 1.0

0.6!

04 0.91 GeV

0.2

0 L L _ ~ L ~ L I ~LJ~ l I__-L 0 30 60

T o ~ a l c r o s s sectlons. . .

--1 I '1--I--I-0" ~ I 4.--rq---~---T--T ~ , n ]r r I ' l " - I ~ u--F-TT]

.......... ....... i .... ........... ; - " . . . . . . . " i " +-

J

0.84 GeV 0 8 8 GeV ~ 0 8 8 GeV i -

f

L L l L J L L L ~ . L A [ t L & % [ L L I I s L I I 0 30 60 0 30 60 0 30 60 90

OCM (deg)

Fig. 8. D . . . . (np) at 8 energies [14], Sofid l ine--- Saclau PSA 1993 including the present points; dashed line --- ref. [31]; dot-dashed line - - ref. [32].

0.6

0.4~

02!

-0 .2

0A

0.2

0 i

- 0 . 2~

- 0.4

0

- q - - F l - I I T - -T -1 - - . 7 -Tq - -q -q -q - -7 -q - -T -T - - r - - i ~ -~F - -T - -Fq - - I - I--T--r-- i I "T I l ~ ]

K oooo I 4 / -~ o.~oov

/ / O " 80 0 eV - - I / 0 . 8 4 GeV- / I / I J / " 0 I s 8 OeV 4

~arS-4--F-4---~H-+--E~-~Jf-Jr--~---I---~L-4--4 T--~-J-,-4--+~t-4--+-4 - - --~=-,-~--F-FF-4 i [ -t

. . . . . ~ 7 . . . . . . .

0.91 GeV L a L --L--L_L_• J..

30 60

/ /

0.94 GeV ._~_l_,J_ 1 I _k_A__L_

0 30 60 0

10 GeV

_L ~_J.__L_LJ_. ~ 30 60 0

OCM (deg)

I

I~i GeY

_LA._.LJ_~__J__LJ_. 30 80 90

Fig. 9. K . . . . (np) at 8 energies. LirLes are as in Fig. 8; �9 - - S A T U R N E II [14]; 0 - - 0.788 GeV, L A M P F [34].

Czech. J. Phys. 45 (1995) 3.3

J. Ball et al.

0.4

0.2

0

-0.2

K O S " S O J.

_~176 ........ t - - . - , . I " - ' -

0.80 GeV 1 0.84 GeV 0.8B GeV

0.4

0.2

0

-0.2

-0.,~

-0.6 0

Fig . 10.

0,94 GeV -~+~:-.i ='---"1.o o+v .... 30 60 90 0 30 60 90 0 30 60 90

0cM(deg)

Ko,%o(nP) a t 6 e n e r g i e s . L i n e s a r e a.s in F ig . 8; �9 - - S A T U R N E II [14];

o - - 0 . 78 8 G e V , L A M P F [35].

-0.2 ",, i / - 0.4 '~ t

0. 80 G eV ", J ' , ,, -0.6 "--" . - + - - + - ~

ot a : : : : j ! t ....

- 0 . 4 t I t L 0

f - - ] l"

/

X.., . ,/"

....... / /

O.8Z, GeV

/ / .~"

-'-"-'<-]~-T- . . . . . . . 10 GeV l

_L--LI l 1 M _ _ I ~ t _ - L 30 60 90 0 30 60 90 0

8CM (deg)

~ 1 |

/ f - - /"

-. /

, t++,+ \ /

0.88 GeV

L "~ ' - ~+'"

"-~, . . . . . . . . . . . .

1.1 GeV I I

30 60 90

Fig . 11. Ko~%o(np) a t 6 e n e r g i e s . L i n e s a r e a s in F ig . 8; �9 - - S A T U R N E II [14];

o - - 0 . 7 8 8 G e V , L A M P F [35].

34 Czech. J. Phys. 45 (1995)

T o t a l c r o s s s e c t i o n s . . .

1.0 , i i i i i I i i i i i i i i i i i

0 8 D~176 ,

/ |

/ /

/ r

0.2 / 0 .80 GeV 0 8 4 GeV /

0 ' ' I I i I I I I I I I ] i

[

0.2~ 0.94 GeV 1.0 GeV

~ 'oh' '9 'oo' '3o' ' ' i o ' '9'oo 0CM (deg)

I I I I I I I I I J

- . . . . . . . . itf t 0.88 GeV

I

\

1.1 GeV

l I I I I I I I I 30 60 90

Fig. 12. D o / , o k ( n p ) at 6 energies. Lines are as in Fig. 8; �9 - - S A T U R N E II [14].

0.2

0

-0.2

-0.4

-0.6

0.8

0.6

0.4

] I J 1 1 | I I l I I l I I I I I I I l l I I I I

0.6 Nonsk ' / ' " ' k

f , 'P l 'P

I / / " .7" . , / . / " / "

0.84 GeV 0 .88 GeV

I I ] I I I I I I I t I ' ' ' ' I I I : II

4 ,

-0.

0.2

, GeV

t I I i ' I

I I

0.94 ( eV

q , I i

1.00 GeV

q~

1.10 GeV l i

I I a I I ! l I l I i I I I I I I I I 1 I I [ I ~ ! , L ~ J ~

30 60 90 0 30 60 90 O 30 6 0 90 OCM (deg)

Fig. 13. No,~,k(np) at 6 energies. Lines are as in Fig. 8; �9 - - S A T U R N E II [14].

Czech. J. Phys. 45 ( 1 9 9 5 ) 3 5

J. Ball e t a l .

crosses zero towards negative values close to 150 ~ at all energies. This shape changes above 0.8 GeV, where the second maximum vanishes and the angular de- pendence crosses zero from positive to negative values at about 90 ~ CM. A minimum is observed around 120 ~ CM, then the angular dependence crosses zero towards pos- itive values. Close to 180~ values become again negative, as indicated by preliminary results at SATURNE II. The forward maximum and the backward nfinimum are more and more pronounced with increasing energy (Figs. 5a,b).

The angular dependence of Aookk(np) was measured at 0.312, 0.630, 0.800, 0.840, 0.880, 0.940, 0.980, 1.00, 1.08 and 1.10 GeV [10,15]. In these measurements 256 data points were determined. The results from ref. [10] represent the first existing mea- surement of this observable. The Aookk results at 0.80 and 1.00 GeV are plotted in Figs. 6a,b and compared with the LAMPF [30] and phase shift analyses (PSA) pre- dictions. The Saclay-Geneva energy-dependent PSA [31] from 1987 (dashed line) contains only few spin dependent data existing at that time. The new fixed-energy PSA (solid line) uses all available data (Saclay-Geneva 1993). Both PSA were car- ried out up to 0.8 GeV only. The Arndt 's PSA [32] below 1.3 GeV contains the new np LAMPF results and previously published Saclay quasi-elastic data [7--9] (dot-dashed line).

The Aoo, k(np) results were obtained in elastic np scattering at 0.800, 0.840, 0.880, 0.940, 1.00, 1.08 and 1.10GeV [15]. Altogether 203 data were measured Another 16 points were measured in quasielastic scattering at 0.744 and 0.794 GeV. This observable at 0.80 and 1.11GeV is plotted in Figs. 7a,b, respectively, and compared with LAMPF [30,33] and with the same PSA predictions.

The measured np rescattering observables (altogether 160 data points) are treated in ref. [14]. The observables Donon and Ko,,)o at 8 energies are shown in Figs. 8

--I I T--T--T--T--F-7--T--

04 N o n k k

o.2! ~-P r I

0 . . . . . z . : "

-o.2;; I I 0.80 GeV

- 0.4 0.4 i ~--) ) -l--l--I[ I 1

~ ..... . . . . . .

0 30 60 90

! ' I 7 - 7 - - - 7 - - ~ I ) | | i I " ' F - - i - - 7 - 7 - -

.-I-_.L_LLI---L.z__A--L. ~ I I I~ l L I I_ 30 60 90 0 30 60 90

ecM(deg)

Fig. 14. Nonkk(np) at 6 energies. Lines are as in Fig. S; �9 - - SATURNE II [14].

36 Czech. J. Phys. 45 (1995)

Total cross sections . . .

and 9, respectively. Kormo results at 0 .80GeV are compared with L A M P F da ta [34] at 0.788 GeVo Results for Ko, , , o and Kos,,ko at 6 energies are shown in Figs. 10 and 11. At 0.80 GeV they are compared with L A M P F da ta [35]. The rescat ter ing observables Do,,,ok , No.n,k and Nonkk at 6 energies are p lo t ted in Figs. 12,13 and 14, respectively. The observable Do,,ok was measured in two different exper iments and averaged results are shown. All the da ta in Figs. 8 to 14 are compared with the PSA predictions. Any np spin correlation parameters and rescat ter ing observables above 0.80 GeV were measured at S A T U R N E II only.

6 A m p l i t u d e s n p , I = 0 a n d I = 1 i n t h e f o r w a r d d i r e c t i o n

At zero degree, only 3 independent complex scat ter ing ampli tudes :remain, there- fore at least 6 independent experimental quanti t ies are required to directly compute

0.8

0.6

0.4

0.2

0

-0.2

Im c(O ~ n-p

. . . . . . . . -+-;T..-___F+___ Im d(O ~

0 . . . . . . . . . . . . . . . . . . . . . . . . . . . n-p

-0.2

-o.o t +

-0.8 I I I J I I

0 02 04 0.6 , # > , h ,

0.8 1.0

-0.

-0 .

1.01 t II ~ - F - q - q - - 1 1 ~ L , J ~ I

F Y ;m c(0 ~ o.:

I 1.2 0 0.2 0,4 0.6 0.8 1.0 12 1/-,

Tkin(GeV) Tki n (GeV)

-0

- 0

- 0

-0

Fig. 15 Fig. 16

Fig. 15. Invariant scattering amplitudes Im c(np) and Im d(np) at 0 ~ o - - SATURNE II [3]; �9 - - SATURNE I[ [4]; crosses (+) - - PSI [24].

Fig. 16. Invariant scattering amplitudes Im c and Im d at 0". �9 - - I = 0 [3,4]; o - - I = 0, PSI [24]; crosses (+) - - I = 1 [36]; solid line - - I = 1 [31,37].

Czech. J. Phys. 45 (1995) 37

J. B a l l e t al.

the amplitudes. But only three total cross sections, o'0tot , A f t T and i 0 " L c a n be measured at 0 ~ Optical theorems give access to the imaginary parts of scattering amplitudes (a + b), c and d via measurements of cr0tot, AO" T and A a L [16]. The energy dependence of the amplitudes c(np) and d(np) is plotted in Fig. 15. Using the relation A m p ( I = O) = 2Amp(np ) - A m p ( p p ) one can extract the amplitudes for I = 0 isospin state. This is shown in Fig. 16 for the amplitudes Im c(I = O) and Im d( I -- 0), respectively. The energy dependence for I = 0 parts was calcu- lated from the data [3,4,24]. The I = 1 imaginary parts were calculated using the Saclay-Geneva phase shift analyses [31,36,37].

"

0.84 GeV

IQJ 1 0 ~ I ! e

+

]bl

0 ; ; I I f I 1

0 t I I I r 1

0 I I I ~ I

0 L I I I Z 0 30 60

eCM(deg)

180 l 1 , , i j I I

9o ~

0 . . . . . . . . . . . - - ~ - . . . . . . .

1 -9o ~o I

- 1 8 0 I I I I I [ I 180

901 ~, o

OI !

-90] ~. %

qSOI 1801 1 I I I I I

~ 901

~" ao~ ......... ~I ~190 ~Pc

,vv"A~' ' ' ' '

- 1 8 0 ~ - I I I I 1 I I I - I 0 30 60 90

OCM(deg)

9O

Fig . 17. A b s o l u t e v a l u e s a n d r e l a t i v e p h a s e s o f n p i n v a r i a n t a m p l i t u d e s 0 . 8 4 G e V . F o u r

d i f f e r e n t s y m b o l s d e n o t e o b t a i n e d p r e l i m i n a r y s o l u t i o n s .

38 Czech. J. Phys. 45 (1995)

T o t a l c r o s s s e c t i o n s . . .

7 Amplitude analysis of np elastic scattering

The available linearly independent observables together with the known elastic np differential cross sections [38,39] form complete sets, which allow the direct reconstructions of the scattering mat r ix [1,16]. This reconstruction at 0.84 GeV is demonstrated in Fig. 17, where absolute values and relative phases of invariant amplitudes a, b, c, d and e(r = 0, Re e = [el) are plotted. Four different solutions were found. Two of them (+ and x) are inconsistent with solutions at other angles. The preliminary results shown here represent the first numerical direct ampli tude analysis for the np system. It remains uncertain whether the accuracy of some observables will be sufficient to get unique solutions at all energies.

8 Conclusions

One cannot say that at intermediate energies there exist enough of np elastic scattering data for a "good" PSA or for a direct amplitude analysis solution at any energy. Even for the spin independent observables there is a lack of total inelastic or total elastic np cross sections, the reaction np --* np~r ~ remains badly determined and the elastic differential np cross section data between 30* and 130" CM above 0.8 GeV are rare. Results measured by the NN group at SATURNE lI, providing altogether 1757 data points, will contribute considerably to the world da ta bank and give a possibility to correctly extend the PSA up to 1.1.GeV. The results allowed, for the first time, the direct reconstructions of the np scattering matr ix . Nevertheless, new data are needed and well selected nucleon-nucleon experiments at different energies will improve our knowledge of nucleon-nucleon interactions. Structures in NN scattering must be studied not only on the basis of the energy and angular dependences of observables, but also on the basis of scattering amplitudes, if it will be possible.

We acknowledge support for this work from J. Arvieux, R. Beurtey, P. Borgeaud, P. A. Chamouard, A. Fleury, E. Heer, J. M. Laget, L. Musflek, L. Price, N. A. Russakovich, J. Saudinos, and J. Tolar. Discussions with J. Franz, J.M. Lagniel, C. Lechanoine-Leluc, G. Milleret, I. Strakovsky, and Y. Terrien have solved several problems. The exploitation of the polarized target owes a lot to G. Guillier, Ph. Marlet and J. Mommejat. We thank T. Lambert, E. Perrin, J. Poupard and J. P. Richeux for their efficient help in preparation of the experiment and the SATURNE II crew for unusual accelerator operations. Finally, we express our gratitude to Franqoise Haroutel, who efficiently helped overcome all ad- ministrative requirements concerning a large international colaboration. This work was partly supported by the Swiss National Science Foundation and by the US Department of Energy Contract No. W-31-109-ENG-38.

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40 Czech. J. Phys. 45 (1995)