laser stark spectroscopy of phosphine

Vol. 4, No. 7/July 1987/J. Opt. Soc. Am. B 1145

Laser Stark spectroscopy of phosphine

Kojiro Takagi, Katsumi Itoh, Eiji Miura, and Shoichi Tanimura

Department of Physics, Toyama University, Gofuku, Toyama 930, Japan

Received January 6, 1987; accepted March 24, 1987

A laser Stark spectrum of PH3 has been observed by using 12C1602, 13C1602, 12C1802, and N2 0 lasers. Coincidenceshave been found for 44 v2 band lines and 31 v4 band lines for Stark fields up to 60 kV/cm. Zero-field frequencies ofthe v2 and v4 band lines and several AjA2 splittings in the v2 and v4 states have been determined. Effective dipolemoments for rotational levels in the v2 and v4 states have been determined and analyzed by taking into account themixing of the states resulting from the Coriolis interaction between the v2 and V4 states and by introducing thetransverse dipole moment between the two states.

INTRODUCTION

The 2 and v4 vibration rotation bands of phosphine weremeasured by Hoffman et al.' and analyzed by taking intoaccount the Coriolis interaction between the v2 and V4 states.Later these bands were measured with higher resolution andanalyzed in more detail by Yin and Rao.2 More recently,Tarrago et al.3 studied all the transitions with J _ 20 in thesebands and determined the molecular constants.

Laser Stark spectra of the v2 and V4 bands of phosphineusing a CO2 laser were first observed by Shimizu.4 Later,several lines in these bands were studied by Di Lonardo andTrombetti5 to determine the dipole moments of the v2 and v4states. More recently, the AlA2 splittings for J, K = 4, 3 and9, 3 in the v2 state were measured by Carlotti et al.6 using asub-Doppler laser Stark method.

The study of the v2 and v4 bands of phosphine is of practi-cal importance related to the development of opticallypumped far-infrared lasers. Malk et al.

7 reported 16 C02pump lines that produced lasing for phosphine.

To study the v2 and V4 bands more systematically by laserStark spectroscopy, we have observed the laser Stark spectraof these bands, using all the 12C1 6 0 2, 13C1602, 12C1802, andN2 0 laser lines available to us with Stark fields up to 60 kV/cm. Using the sub-Doppler resolution of Lamb-dip tech-niques, Stark components were easily resolved and identi-fied. About 500 Stark resonances have been identified for44 v2 and 31 v4 band lines. During the study of the qP(5, 3)line in the v2 fundamental band, an infrared-infrared doubleresonance caused by the accidental overlapping of V2 qP(5, 3)and 2v 2 -v2 qp(4, 3) was observed and was reported earlier.8 9

In this paper all the observed Stark resonances and theresults frQm their analysis are reported. It was found thatthe effective dipole moment changes greatly with rotationallevels in the v4 state. This change is explained by the mixingof the wave functions because of the Coriolis interactionbetween the v2 and V4 states and by the introduction of thetransverse dipole moment between the two states.

EXPERIMENT

The laser Stark spectrometer used is similar to that de-scribed by Freund et al.10 The laser cavity of 2.7-m lengthconsists of a concave mirror (radius of curvature, 10 m;

reflectivity, 90%) and a plane grating (150 lines/mm, blazedat 10.6 m). The water-cooled gain tube of 2.2-m effectivelength was used for either a flowing-gas system for normalCO2 or N20 operations or a semisealed system for isotopic13C1602 and l2Cl802 operations. The laser was operated onthe following lines:

12C160 2: 1OP(4)-1OP(46), 1OR(2)-lOR(48),9R(4)-9R(46);13C 60 2 : OP(4)-1OP(46), 1R(4)-1OR(40),9R(6)-9R(32);12C1802: OP(8)-lOP(38), OR(8)-lOR(34),9R(6)-9R(38);N20: P(5)-P(37), R(4)-R(36).

9P(4)-9P(48),

9P(8)-9P(38),

9P(6)-9P(46),

The laser was stabilized on the gain maximum with a lock-in stabilizer (Lansing 80-214).

The Stark plates in the absorption cell are made of chro-mium-coated glass plates of 25-cm length and are separatedby six spacers of 1-mm nominal thickness. The electrodeseparation was calibrated to be 1.0000(7) mm by measuringthe double-resonance signals of phosphine. 8 9 A dc biasvoltage of 0-6000 V was applied to one of the plates, anda sawtooth voltage of 0-1000 V was applied to the other.The bias voltage was measured through a 1000:1 voltagedivider (Fluke 80-E), and the sweep voltage was measureddirectly by a digital voltmeter. A sine-wave voltage at 10kHz was used for modulation. The peak-to-peak amplitudeof the modulation was 1-10 V for the observation of Lambdips and 50-100 V for the observation of Doppler-broadenedsignals. In all the measurements the laser beam was reflect-ed back after passing through the cell to permit observationof Lamb dips. The beam was detected by a HgCdTe detec-tor, and the signal was processed by a phase-sensitive detec-tor. The beam polarization was perpendicular to the Starkfield (selection rule AM = ±1). The pressure of phosphinein the absorption cell was 3-15 mTorr.

OBSERVED SPECTRUM

Some characteristic signals are shown in Figs. 1-3. In Fig. 1laser Stark resonances of the qp(4, 3) transition in the v2band for the normal CO2 1OP(6) line are shown as typical

0740-3224/87/071145-14$02.00 © 1987 Optical Society of America

Takagi et al.

1146 J. Opt. Soc. Am. B/Vol. 4, No. 7/July 1987Tagieal

7.7

I I

-, I i

.4..,,. I. ~ L.

LL !,j,~~~~~~~~~-0-tvr+3 .~~~ '.1

. 4...:. . q I ; I ,� 7 1 , ; � � 'i : i

. I .I " , ; ; � � I- d - ;_-- i ;- _i I I � I IcI . j1'. J_ i.I , . -1111. I lw�

Fig. 1. Laser Stark signal Of V2 qp(4, 3), using the C02 1OP(6) laserline showing Doppler-limited lines and Lamb dips. The PH, pres-sure was 0.007 Torr; modulation voltage at 10 kHz was 10 V (peak topeak); the time constant of the phase-sensitive detector (PSD) was0.1 sec.

; !~~~~~ , ~~ I -

4I-- -

t771

- "Il.- - 1N. I 1 1- .. 11 11 - - 11 1. -, .- - 1 1.J ... I-, , "..... . .4 ". _� " I - __ � 111. I -A� . �

I . I C)

.-. . . .. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . .. . 2 j.. .. .. .

Fig. 2. Laser Stark signal Of V4 PM(, 5), using the C18 0 2 9P(44) laserline. Lanip dips and collision-induced center dips (weaker fea-tures) are shown. The PH, pressure was 0.015 Torr; modulationvoltage was 8 V (peak to peak); the PSD time constant was 0.1 sec.

signals for the 2 qp(J), or R(J) line. Lamb dips are ob-served at the centers of Doppler-broadened absorption lines.The assignment for each component (' - M") is given atthe bottom of the signal. Two Lamb dips are resolved at thecenter of the feature near 3000 V. Figure 2 shows the PP(7,5) transition in the P4 band for the C1802 9P(44) laser line inwhich one broad signal is resolved into many Lamb dips.The weak features at the center of two neighboring Lambdips are collision-induced center dips." Figure 3 shows apart of the qp(7, 3) transition in the v2 band for the "3CO2IOR(14) laser line. Two dips, 1 and 2, originate from theAjA2 splitting in the lower state of the transition, and dips 3and 4 originate from the AIA2 splitting in the upper state.The relevant energy-level scheme is given in Fig. 4. Thetransitions corresponding to the four dips mentioned aboveare shown.

Observed transitions are given in Tables 1 and 2. Table lists observed Stark resonances for transitions with theStark effect approximately linear with the electric field.Their assignments; observed resonant fields Eob,, and differ-ences between observed and calculated fields AE = E~b -

EcaIc are shown. The method used to calculate the resonantfield EaIc is given below. Table 2 lists transitions withnonlinear Stark effects that are due to the AjA2 splittings.Along with assignments and observed resonant fields, fre-quency differences - , are given, where PI is a laser fre-quency and vP, is the separation in frequency units betweenthe centers of AjA2 doublets in the excited and ground vibra-tional states. The difference P - v is a hypothetical Starkshift for no AjA2 splittings, as is shown below.4 .... - -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.......

- -- ------......

4'

..0 ...

Fig. 3. A part of laser Stark signal f 2 q(7, 3), using the 13CO2

1OR(14) laser line. Two sharp features, and 2, originate from theAjA2 doublet in the lower level, and two features, 3 and 4, originatefrom the one in the upper level involved in the transition. A weakerfeature at 3900 V is a cross-over center dip.

1-11.1--.1-_ __ .1-1 ... I I..''.- 1-11, ....... ....... _-_-.--_-

I . - - --- _11 .... . .. _-_-_.______ ___ ...... _- .

Takagi et al.


ANALYSIS AND RESULTS

Since the dipole moment of phosphine is relatively small, theobserved Stark shifts are less than 0.1 cm-1 for most of thetransitions. For the rotation-vibrational levels of symme-try species E, Stark shifts are approximately linear and canbe calculated by perturbation theory, because they are muchsmaller than rotational spacings. For some levels of speciesA for which AjA2 splittings are larger than the homogeneousbroadening, however, Stark shifts are not linear and must becalculated more rigorously. So we treat the Stark shift forthese two cases separately.

Linear Stark EffectFor E levels or A levels whose AjA2 splittings are negligible,the Stark shift for a level with J, K, M at the electric field E isgiven by

AW = -EMK/J(J + 1) + (A + BM2)E2,

L

C E

Fig. 4. The energy-level scheme relevant to the transitions shownin Fig.3. The energy levels for (v2, J, K) = (1,6,3) and (0,7,3) forM= ±1 and ±0 are shown, and the levels with MI > 1 are not shown,where M is negative for the upper component and is positive for thelower component of an AjA2 doublet.

where the first term is the main term and the second term isa small second-order correction.

Observed transitions are analyzed by the following meth-od: For an observed laser Stark line with J', K', M' - J,K", M", the Stark shift is given byIP -Vm = (C'M' -C"M")E + S(E),

Table 1. Observed Stark Resonances in PH3 for E Levels and A Levels with Small A1A2 Splittings

Assignment Resonant Field (V/cm) Assignment Resonant Field (V/cm)

M Ml Eobs A.E M" Eobs AE

1921lr% 1OR(30) PP(13, 11)-% ,--k2

1OP(28) QP(6,4)-5-4-3-2-1

1OP(6) QP(4, 3)32103

1OR(8) QQ(15, 8)M + 1

1OR(14) PP(13, 13)1087654321

1OR(30) QQ(9, 5)M-1

-4-3-2-1

0

210

-14

2677430876365084463257495

1010712997181903019930332

M

20-3-2

-2311

-9-210-2

0

48920a

976543210

M

352873886240929432254579148650518755557059858

-48-15

21938304

-17-18

45107a

7

6543210

-1-2-3-4-5-6

1OR(32) QQ(8, 4)M-1

1OR(34) QQ(14, 12)M - 1

1OR(36) QQ(11, 9)M-1

1OR(42) PP(12, 11)876543

65

43210

-1-2-3-4-5-6-7

M

M

2144122488236402489126316279182971631757341403679040019438744843954151

(2)

111415

-10-8

10

-627

-48-18

29-12

11

9951a

2128a

54045aM

7

65

432

268982825429718313593341835541

6343

-18-76

7952

(continued overleaf)

M

-i

-o+0

+1

v 2 J K

1 63

0 7 3

-1-o+0

1(1)

I

Takagi et al.

1148 J. Opt. Soc. Am. B/Vol. 4, No. 7/July 1987

Table 1. Continued

Assignment Resonant Field (V/cm) Assignment Resonant Field (V/cm)Eab AE M' M" Eobs AE

210

-1-2-3

9P(26) QR(5, 4)-4-3-2

9P(26) PP(7, 7)6543210

-1-2-3

9P(24) QR(5, 5)4321065

-34

9P(22) RP(11, 7)65

104938271

9P(18) RP(10, 2)-7-6-9-5-8-4-7-3-6-2-5-1-4

0

9P(18) PP(7,5)54

10

-1-2-3-4

-5-4-3

543210

-1-2-3-4

5432154

-23

54

113

1029180

378224064544026478915240357904

430144962158547

16792182641997122024246262785332065377174592958655

43064970587771609216

12941215936331764075

24810280032942232188341063786640520459224991358369

-6-5

-10-4-9-3-8-2-7-1-6

0-5

1

43

6807770485958815

10023103031198112437149661564519829210452952232053

4160444088

-116-103

195813-3

2723

-33

-11142

-22201619

-37-710

-7-6-4

-26-20-13

1042

19-11-24-14-1

61

-6127

-60-32-49-39-43-48-65-21-32

4-39

329139

0-3

3210

9P(8) RP(9, 5)76548372615

9P(6) PP(7, 1)-6-5-4-3-2-1

0

9P(4) QR(7, 7)654

9R(6) QR(8,8)-7-6-5-4

9R(8) RP(7, 4)6546

9R(10) QR(9, 7)-7-6-5-4-3-2-1

0-10-9-8-7

9R(10) QR(10, 4)-7-6-5-4-3-2

210

-1

65439281706

-7-6-5-4-3-2-1

765

-8-7-6-5

5437

-8-7-6-5-4-3-2-1-9-8-7-6

-8-7-6-5-4-3

46896500665370657905

1981622341255142973130007356453604144469450925913660226

5827666077029144

113571488922044

487925392560239

44041480195285558745

34918402934760558172

64907064773885589574

10863125261482418138233343269554756

363573940442994473495260359098

5-3

10

-3814

12026

7-7-1

2-2

-16141

-1725-9

0

-46

-3

14-19

23

-6320

-22-14-13-8

1141137-5-9

-3116

-27-13-84540

-39

Takagi et al.


Table 1. Continued

Assignment Resonant Field (V/cm) Assignment Resonant Field (V/cm)

M AP ~~Eobs AR M Ml' Eobs AR

9R(14) QR(9,8)543210

1098

9R(18) QR(10, 7)-9-8-7-6-5-4-3-2-1

9R(32) QR(12,6)-9-8-7-6-5-4-3-2

9R(36) QR(11, 9)-10-9-8-7

9R(38) RP(4,1)3

9R(40) PP(3,2)210

-1

9R(42) RP(4,2)-3-2-3-1-2

13CI6 02

1OP(40) QP(11, 2)-9-8-7-6-5-4-3-2-1

-10

654321987

-10-9-8-7-6-5-4-3-2

-10-9-8-7-6-5-4-3

-11-10-9-8

2

10

-1-2

-2-1-4

0-3

-8-7-6-5-4-3-2-1

0-11

124511378415396174452014223825290903743952296

279863009232480351333845642164469435270360276

3464836958395974264546197503905541861573

49957531855683761072

-22-2

-11-15-418-344

-23

-123-27

43-11113-18

67-42-20

-7-4-2

485

-2-4

35

-147

53762

41743426724332843583

1349818579211052984436972

10065108511159312598141341562417547198992307027707

-9

125

-17

814

-4-2

106126-25-75196139129-4

-143-250

-9-8

1OP(26) QP(11, 9)-10-9

-8-7-6

1OP(22) QP(11, 10)-5-4-3-2-1

-10-9

-8-7

1OP(16) QP(10, 8)98765432

1OP(12) QP(10, 9)-9

-8-7-6-5-4-3-2-1

0

1OP(8) QP(9,6)-8-7-6-5-4-3-2

1OR(12) QP(7, 1)-6-5-4-3-2-1

1OR(16) QP(7,4)-6-5-4-3-2

-10-9

-9

-8-7-6-5

3461946951

4426747446510625534360352

110871232413915159291855422376280253739156350

-4-3-2-1

0-11-10-9-8

87654321

-8-7-6-5-4-3-2-1

01

-7-6-5-4-3-2-1

-5-4-3-2-1

0

-5-4-3

-2-1

2603228130305863346137042413194679354005

20357220432396626251290253245936780424495017661541

30126328603615440177.451975164760254

272203050934891406014869260622

3312937282426254972859701

-341301

-613

-1512-4

-45-44

43415-224

-152

-19-213

-1650

-11-29

11

-3615171517251

-18-65

38

-3-8

1760

-3

44-41

12-36

29-5

-509

-3-1


0

0

Takagi et al.

1150 J. Opt. Soc. Am. B/ol. 4, No. 7/July 1987

Table 1. Continued

Assignment Resonant Field (V/cm) Assignment Resonant Field (V/cm)Al M" EQb6 AR 1 M" Eobs AR

1OR(28) QP(6, 1) IOR(18) QQ(12, 8)-5-4-3-2-1-5-4

9P(32) QQ(10, 9)M-I

9P(28) QQ(11, 11)M+ 1

9P(16) PP(11,9)109876

9R(8) QR(3, 1)-2

9R(10) QR(3,3)-2

9R(16) PP(8,8)-7-6-5-4-3-2-1

012

9R(20) PP(10, 2)98765432

12C'802

1OP(28) QP(5, 2)-4-3-2-1

0-4

1-3

10R(10) QP(2, 1)101

1OR(16) QQ(11, 6)M + 1

40954708552167388781

1232020718

152

-37-48

70-51

24

29957a

34118a

4783150216526765528658200

56817

56556

22940246262663228948317023503939152443955120560524

2420325595271922906831044334213625139536

966611576144801924228916289165754757800

315594409482

-10461859

-52

-11-25

9966

-516-6-4

5-17-11

61-25-30

152

372240-6601

-34-15

-1021

M+ 1

1OR(22) QQ(13, 10)M-i

1OR(26) QQ(10, 7)M + 1

9P(44) PP(7, 5)543210

-1-2-3-4-5-6

9P(34) RP(9,5)-8-7-6

9P(18) RP(7,4)65465

9P(14) PP(5,2)432

9P(8) RP(6, 4)54354132

9R(10) RP(4,2)-3-2-3-1-2

9R(20) RP(3, 1)22

*1

9R(22) PP(2,2)1

9R(34) PQ(7, 7)-6-5

29223a -4

M

M

11572a

40940a

M

43210

-1-2-3-4-5-6-7

-7-6-5

54376

543

8719a

347836863921418844964847525857446334705879599127

-4-3-2-1

2110250

-4

430064776953740

2198525366299693660147037

448835052057819

4285512261707339

10096118711603239218

43265043

-2-1-4

0-3

130

1245617157194962756034125

4-6

2

2

2-2-3

2

1-2

1

-130

-101-61742

-174

-30

11-1-4

329114620057116

0

-7-6-5

-311

55173

491485313457831

1-2

1

0

0

CD2

0

N

ro

-4-3-2-1

0-6-5

M

M

98765

-3

-3

-6-5-4-3-2-1

0123

109876543

-3-2-1

01

-52

-4

0-1

2

M

Takagi et al.


Table 1. Continued

Assignment Resonant Field (V/cm)M' M" Eob 8 AE

N2 0

P(30) QP(9, 8)-8 -7 14797 -82-7 -6 16208 -24-6 -5 17869 14-5 -4 19859 21-4 -3 22321 4-3 -2 25478 -28-2 -1 29769 13-1 0 35742 33

-8 -9 44741 -37-7 -8 59820 28

R(21) QP(4, 3)-3 -2 27105 -5-2 -1 34912 6-1 0 49016 -2

R(32) QP(3, 1)2 1 45736

R(33) QP(3,2)-2 -1 564 -4*-1 0 844 -7

0 1 1708 6

-2 -3 1708 4

a Lamb dips with various M's overlap at one resonant field.

where v1 is the laser frequency, v'm is the zero-field transition

frequency, C' =-'K'/J'(J' + 1), C" = -,4"K"/J"(J" + 1),and S(E) = (A' + B'M2 - A" - B"M" 2 )E2. It is assumed

here that the dipole moment in the ground state is hz" =0.57395(3) D, as given by Davies et al.12 for any J" and K".The second-order correction S(E) can be calculated withsufficient accuracy by a second-order perturbational the-ory13 with rotational constants given in Ref. 3 or by a more

rigorous calculation discussed below. Thus the unknownvalues in Eq. (2) are C' and vm. When a series of N Stark

components Mi'- Mi" is observed at the electric fields Ei for

i = 1-N for the transition J', K' - J", K", the following Nequation is obtained:

y = (Mi'x - C"1Mj)Ej + Si(Ei)

where y = vI - ,m and x = C'. Hence the observation

equation for x and y is

(D

(D

00xLNm05

M

[y - (E)](Mi'x - C"Mi") = Ei

These equations become linear for Ax = x - x0 and Ay = y -

ye, with appropriate initial values x0 and yo, which are solved

by the least-squares method. The effective dipole momentof the J', K' state is given by

,u = xJ'(J' + 1)/0.50345K', (5)

where p' and x are in debeyes and in megahertz per volt perinverse centimeter, respectively. The numerical factor of

Table 2. Observed Stark Resonances in PH3 for A Levels with Large AA2 Splittings

Assignmenta Eobs VI - Vb Assignmenta Eobs i -PCb

l' Ml" (V/cm) (MHz) l' Ml" (V/cm) (MHz)

12c16f,, 9P(10) RP(9, 3)

1OP(18) QP(5, 3)-4-3-2-1-1-0-4

0-3

1

9P(24) RP(11, 3)1098765432

9P(20) PP(8, 3)-7-6-5-4-3

-3-2-1

0-0

1-5

1-4

2

10135121651520720259203043039030408305076097861142

200192159323784263472948933593391434707259724

11109876543

87654

2560829501347844237654184

878.2878.4878.3878.2878.4878.3877.8878.3877.3878.3

-2970.8-2975.5-2971.9-2971.0-2971.7-2971.6-2971.3-2971.8-2971.0

4955.64955.64955.34955.54954.8

876543210

9R(10) UP(6, 0)543

9R(22) UP(5, 0)-4-3-2-1

9R(30) RP(5, 3)-4-3-4-3

-9-8-7-6-5-4-3-2-1

654

53296020690281329886

12574171682715658496

306533831651062

10938145952188943991

5432

-3-2-5-4

21090263643515452914

-2516.8-2516.4-2514.6-2515.7-2516.8-2517.3-2515.2-2517.2-2515.2

-5877.6-5879.0-5879.4

2536.12537.42534.92536.2

3056.03054.23058.93062.9


Takagi et al,

(i = 1 2, - -, N) 3)

(i = 1 2_ .. , N) - 4)


Table 2. ContinuedAssignmenta Eobs Pvt-'b Assignmenta Eobs v - vPb

l' M" (V/cm) (MHz) l' M" (V/cm) (MHz)

13C1602

1OR(14)654321

1

06

-0

-0

QP(7, 3)

9P(14) PP(13,3)1211109876543

12C1802

9P(46) PP(8, 3)-7-6-5-4

9P(36) RP(9, 3)-3-2-1

9P(34) UP(8, 0)76

9P(32) QR(8, 3)-9-8-6-5-1-2

76

54321

-00

-17

-1

-13-12-11-10-9-8-7-6-5-4

17467196582249426208314513899139613512635233653611

15392166941822120070223302516328822337184072751127

34305395284664156853

366113915148453

8765

-4-3-2

87

5180860428

17301956216325368554

105031382015097

87762187

-811.7-811.9-812.9-811.8-811.8-811.6-811.4-811.7-811.3-811.6

-6707.7-6708.0-6707.5-6707.7-6707.6-6707.5-6707.5-6707.2-6709.7-6708.1

6358.46357.36357.66356.2

1149.11149.01149.0

-7299.8-7298.5

387.1385.8386.6385.7387.2385.7385.9385.5

-1-1

90

-28

9P(28) RP(8, 3)-7-6-5-4-3-2-1-7-6-5-4

9P(16) UP(6, 0)54321

9P(10) QR(11, 3)-12-11-10-9

9P(6) UP(5, 0)43

9R(12) QR(14, 3)-6-5-2-4-1-3

9R(32) RP(2, 0)-1-1

a The quantum number M is negative for the upper component and is positive for the lower component of an A1A2 doublet.b VI is a laser frequency, and v, is a separation (in megahertz) between centers of A1A2 doublets in the excited and ground vibrational states.

0.50345 has been used in the present work, as it has beenused for the determination of the ground-state dipole mo-ment of PH3 in Ref. 12. When this factor is changed to arecent value of 0.5034036, all the values of dipole momentsdetermined in the present work and the ground-state dipolemoment in Ref. 12 are to be multiplied by 1.00009.

The procedure to determine v - i'm and ' in the presentwork is similar to those given by Di Lonardo and Tromnbetti,5

Weber and Terhune,14 and Weber.15 However, it is uniquein that the right-hand side of the observation equation [Eq.

(4)] is the resonant electric field, the directly measuredquantity, so that the variance of the resonant fields is mini-mized in the least-squares method.

In Table 1, the differences Eobs- Ecalc corresponding toEq. (4) are given. The results of the analysis are given inTables 3 and 4, where v - and the effective dipole mo-ment ,', as given by Eq. (5), are given. The quoted errorsgiven in parentheses are 2.5 times the standard deviation.The laser frequencies used to obtain i'm were taken fromRefs. 16-18.

120

-081

-17

1872129743351633841940694454625201654224

8765432

-8-5-4-3

896910356122481499319320271504540259188416824804656520

65432

400650006671

1000320007

386.7387.9389.1389.1388.9386.7388.0389.2

2602.82602.42601.92601.92602.02603.02603.72603.72596.02601.32601.9

-819.4-818.5-819.0-818.9-819.9

5916.45917.95919.55918.4

-8257.3-8257.6

1576.91577.01577.21576.71576.71576.6

6681.56681.6

111098

54

42047460825097256994

3558947413

-5-4-3-3-2-2

108141368816294187742419129907

-20

2844528718

Takagi et al.


Stark Shifts in the Presence of AA 2 SplittingsThe energy levels for components of an AjA2 doublet at theelectric field E are similar to those of a K-type doublet13 andare given by

W = Wo i [(s/2)2 + (CME) 2 1/2 + (A + BM 2)E2, (6)

where Wo is the doublet center, s is the doublet separation, C= -,K/J(J + 1), and A and B are second-order Stark coeffi-cients resulting from the perturbation from levels other thanthe AjA2 doublet. In Table 2, upper and lower componentlevels are designated by negative M and positive M, respec-tively.

We denote here the separation (in frequency units) be-tween the centers of the upper and lower A1A2 doubletsinvolved in a transition by vc. This center frequency corre-sponds to the hypothetical transition frequency with noAjA2 splittings. For the observed laser Stark line withJ'K'M' - J"K"M", the frequency difference vI - v, is givenby

Table 3. Tb

Transition

QP(11.2)QP(11.9)QP(11.10)QP(10.8)QP(10.9)QP(9.6)QP(9.8)QP(7.1)QP(7.4)QP(6.1)QP(6.4)QP(5.2)QP(4.3)QP(4.3)QP(3.1)QP(3.2)QQ(15.8)QP(2.1)QQ(11.6)QQ(12.8)QQ(13.10)QQ(9.5)QQ(10.7)QQ(8.4)QQ(14.12)QQ(11.9)QQ(10.9)QQ(11.11)QR(3.1)QR(3.3)QR(5.4)QR(5.5)QR(7.7)QR(8.8)QR(9.7)QR(10.4)QR(9.8)QR(10.7)QR(12.6)QR(11.9)

V- vc = [(s'/2) 2 + (C'M'E) 2]1"2 + (A' + B'M' 2)E2

- [[(s"/2)2 + (C"M"E)2]1/2 + (A" + B"M"2)E2],(7)

where s' and s" are the doublet separations in the upper andthe lower A1A2 doublets, respectively. For no A1 A2 split-

tings (s' = s" = 0), Eq. (7) reduces to Eq. (2), used for thelinear Stark effect. The Stark shift for the ground-statelevel can be calculated by using s" reported in Refs. 12 and19 and A" and B" calculated by a perturbational treatment.For the 2 or 4 state the value of the dipole moment isestimated by a method mentioned below. The calculationof A' and B' was discussed in the previous section. Thus s' isthe only unknown parameter in Eq. (7).

When the AjA2 splitting in an upper doublet is observedby two transitions, M = +0 - -1 and -0 - -1, as is shownin Fig. 3 for qp(7, 3), the splitting s' is determined so that itgives the same vi - i' value for these two transitions. The

We4

NCDCD

5

(D00WFOdMne+

e v2 Band of PH3 and Effective Dipole Moment in the 2 State (A1A2 Doublet Lines Are Excluded)

Laser Vm - i (MHz) Pm (cm-') ' (D)

"CO2 1OP(40)"CO2 1OP(26)3CO2 1OP(22)3CO2 1OP(16)3CO2 1OP(12)3CO2 1OP(8)N2 0 P(30)"CO2 1OR(12)3CO2 1OR(16)3CO2 1OR(28)

CO2 1OP(28)C1802 1OP(28)CO2 1OP(6)N 2O R(21)N 2 0 R(32)N 2 0 R(33)CO2 1bR(8)C1802 1OR(10)C1802 1OR(16)C1802 1OR(18)C1802 1OR(22)CO2 1OR(30)C1802 1OR(26)CO2 1OR(32)CO2 1OR(34)CO2 1OR(36)3CO2 9P(32)3CO2 9P(28)3CO2 9R(8)3CO2 9R(10)

CO2 9P(26)CO2 9P(24)CO2 9P(4)CO2 9R(6)CO2 9R(10)CO2 9R(10)CO2 9R(14)CO2 9R(18)CO2 9R(32)CO2 9R(36)

-122.0(1.5)-2608.(11)-486.5(1.1)1638.8(4.1)

-1451.2(1.7)-1738.5(0.9)-1144.7(2.0)-418.2(1.2)

-2053.2(1.7)-83.8(0.9)

-2211.6(3.8)-556.1(0.6)1315.9(0.7)

-3524.6(5.4)3340.8-81.9(0.8)471.2457.6(1.2)383.8171.5

-649.9-724.1

160.3-159.7-35.1

-1064.6-708.2

822.22432.27348.53543.8(7.1)-445.0(0.2)

-4110.(11)3395.(14)332.3(0.5)828.6(2.8)

-611.7(0.9)1293.1(4.7)873.5(0.3)

2499.(11)

878.429 52(25)891.486 95(40)895.134 34(25)900.423 31(30)903.701 33(25)906.994 85(25)912.321 10(25)923.097 38(25)925.855 42(25)933.877 90(25)936.729 98(30)944.978 18(25)956.228 88(25)956.229 00(30)964.572 65(40)965.174 88(25)967.722 95(30)974.175 57(25)977.763 11(30)978.899 08(30)981.076 98(30)982.071 38(30)983.201 10(30)983.246 92(30)984.382 05(30)985.452 80(30)989.049 19(30)993.070 02(30)

1024.448 87(30)1026.023 39(45)1041.397 28(30)1043.148 40(25)1060.433 57(45)1069.127 34(50)1071.894 85(25)1071.911 41(25)1074.626 09(25)1077.345 65(30)1085.794 58(25)1088.031 66(45)

0.57397(57)0.57345(69)0.57362(8)0.57360(53)0.57447(33)0.57372(12)0.57367(12)0.57361(89)0.57426(23)0.57282(76)0.57438(61)0.57400(11)0.57403(10)0.57404(69)(0.57398)a0.5737(23)0.57394b0.57396(74)0.5739360.573951,0.57395b0.57409(0.5739580.57397b0.57395170.57395b0.57394b0.57397b

(0.57396)a(0.57396)a(0.57395)a0.57407(10)0.57409(82)0.5738(11)0.57418(5)0.57377(97)0.57391(7)0.5738(11)0.57509(9)0.57393(84)

a Dipole moment calculated by Eq. (15) used to anal-ze this transition.b Uncertainty is not given because only one resonant field is observed.

Takagi et al.

1154 J. Opt. Soc. Am. B/Vol. 4, No. 7/July 1987 Takagi et al.

Table 4. The 4 Band of PH3 and Effective Dipole Moment in the V4 State (AIA2 Doublet Lines Are Excluded)Transition Laser vm - i (MHz) m (cm-') yt (D)

PP(13.13) C02 1OR(14) 1339.9(1.6) 971.974 95(25) 0.57758(19)PP(13.11) C02 1OR(30) 554.9(0.3) 982.114 04(25) 0.57846(5)PP(12.11) C02 1OR(42) 902.4(1.1) 988.676 73(25) 0.57751(24)PP(11.9) 13CO2 9P(16) 1695.(29) 1004.336 41(100) 0.5808(19)PP(8.8) 13CO2 9R(16) -1424.0(0.4) 1029.787 63(25) 0.57812(6)PP(10.2) 13CO2 9R(20) -254.7(0.8) 1032.386 01(25) 0.83338(89)PP(7.7) C02 9P(26) 1158.2(0.7) 1041.317 71(25) 0.57826(9)RP(11.7) C02 9P(22) 1228.9(0.6) 1045.062 66(25) 0.57436(8)RP(10.2) C02 9P(18) -168.2(0.5) 1048.655 20(25) 0.47720(53)PP(7.5) C1802 9P(44) 125.0(0.1) 1048.710 58(25) 0.58019(4)PP(7.5) C02 9P(18) 1493.2(0.2) 1048.710 62(25) 0.58005(3)RP(9.5) C02 9P(8) 1420.3(0.8) 1057.347 54(25) 0.57155(10)RP(9.5) C802 9P(34) -3420.(27) 1057.347 85(95) 0.5718(19)PP(7.1) C02 9P(6) 113.4(0.2) 1058.952 50(25)RP(7.4) C02 9R(8) 3611.4(1.8) 1070.582 77(25) 0.57450(11)RP(7.4) C1802 9P(18) 2273.5(0.9) 1070.582 89(25) 0.57455(7)PP(5.2) C802 9P(14) -1586.0(0.6) 1073.525 96(25) 0.60436(17)RP(6.4) C1802 9P(8) 566.4(8.0) 1078.061 31(60) 0.5774(10)RP(4.1) C02 9R(38) 5980. 1089.200 59(45) (0.55578)aPP(3.2) C02 9R(40) 2070.2(1.5) 1090.097 42(25) 0.57934(34)RP(4.2) C02 9R(42) -2160.4(1.6) 1090.958 13(25) 0.57752(22)RP(4.2) C1802 9R(10) -1996.0(2.0) 1090.958 08(25) 0.57765(29)RP(3.1) C1802 9R(20) 5560.5(2.9) 1097.336 08(25) 0.57413(24)PP(2.2) C1802 9R(22) 8067.5 1098.586 49(60) (0.57904)aPQ(7.7) C1802 9R(34) 3222.3(2.3) 1105.019 30(25) 0.57871(16)

a Dipole moment calculated by Eq. (15) used to analyze this transition.

Table 5. AA2 Doublet Transitions in the 2 and 4 Bands and AIA2 Splittings in the 2 and 4 States of PH3A 2 - A (MHz)

Transition v (cm-') J K I Obs. Calc.a

QP(5.3) A2-Aj 945.950 96(25) 4 3 3.4 + 0.5 2.5Al-A2 945.950 91(25)

QP(7.3) A 2 -Aj 924.555 02(25) 6 3 36.3 1.0 26.2Al-A2 924.554 24(25)

QR(8.3) A2-A1 1059.140 27(25) 9 3 -321.7 1.0 -227.6Al-A2 1059.150 06(25)

QR(11.3) A-Ab 1076.376 46(90) 12 3 (1300)c 972.0QR(14.3) A-A 2 1092.290 43(30) 15 3 -4000 250 -2898.6RP(2.0) A2-Aj 1103.813 14(30) 1 1 1 10 4 9 8 .9 d 10 541.4UP(5.0) A-Ab 1079.767 66(30) 4 4 1 (200)c 170.2RP(5.3) A-Ab 1084.533 21(30) 4 4 1 (200)cUP(6.0) A-Ab 1072.079 86(40) 5 4 1 -580 140 -547.4PP(8.3) A 2-Aj 1046.739 49(60) 7 2 -1 3000 150 2852.8UP(8.0) A-Alb 1057.705 41(30) 7 4 1 (-2426)c -2286.6RP(8.3) Al-A 2 1062.447 82(50) 7 4 1 -2426 20RP(9.3) A2 -Aj 1055.773 12(25) 8 4 1 3901 + 10 3712.4

Al-A2 1055.644 89(25)RP(11.3) Al-A2 1043.132 16(30) 10 4 1 7990 100 7646.0PP(13.3) A2-Aj 1006.080 14(30) 12 2 -1 -11 320 1400 -11 477.8

0 Calculated with the constants in Ref. 3.b Frequency between the centers of A1A2 doublets in the upper state and the lower state.c Assumed AA2 splitting used to calculate - v in Table 2.d Observed by microwave spectroscopy.20 This value was used to analyze this transition.

splittings for qp(5, 3), qP(7, 3), and qR(8, 3) have been deter-mined in this way.

When only one component for the AIA2 doublet transi-tions is observed, s' is determined in the following way. Foran appropriate value for s', Eq. (7) gives frequency differ-ences - for all the M' - M" resonant voltages. Thesplitting s' is determined so that these Pi - v, values show a

minimum deviation from the average. The uncertainty in s'is estimated by the change in s' required to make the devi-ation three times as large as at the minimum. In some caseswhen one or two components of a doublet transitions werestudied by two laser lines independently [e.g., PP(8, 3), rp(9,3), u(5, 0), and uP(6, 0)], the consistency of the two resultswas taken into consideration in the determination of s'. The


values for - c listed in Table 2 were obtained for s'determined in this way. In the case when the change of s'does not change the deviation for vi - ic appreciably, the PI-VC value in Table 2 is calculated with an appropriately as-sumed s'. For the analysis of the rP(2, 0) transition, the s'value observed by microwave spectroscopy 2 0 was used.

The results of the analysis are summarized in Table 5. Inthis table the center frequencies vc are given as A - A for

some transitions. For those transitions the transition fre-quencies were not well determined from the observed reso-nant fields, but center frequencies were, nevertheless, welldetermined.

DISCUSSION

Observed FrequenciesThe accuracy of the observed frequencies is limited by sever-al factors. The error of the voltage measurement is includedin AE in Table 1. The main part of AE comes from thefluctuation of the laser frequency during the voltage mea-surement. The errors in the observed frequencies comingfrom AE are given as quoted errors in vim - v in Tables 3 and4.

Uncertainty also arises from the procedure used to deter-mine zero-field frequencies from observed resonant volt-ages. The dipole moment in the ground state is assumed tobe constant for all the states studied here. For low J, Ktransitions the assumption causes uncertainties smallerthan quoted ones for PI- vm in Tables 3 and 4. For higher J,K it may cause uncertainties comparable with or larger thanquoted ones. The second-order term S(E) in Eq. (2) is asmall correction of a few magahertz or less. In the prelimi-nary analysis the constants A and B in Eq. (1) calculated byperturbational treatment were used. To test the accuracy ofthis treatment, the Stark effects of all the observed transi-tions were calculated by solving the secular equations ob-tained from the Hamiltonian matrix given by Tarrago et al.,3

and the effective second-order coefficients were determinednumerically. In the final analysis these coefficients wereused. However, the results obtained are the same within thequoted errors for the two analyses, except for a few cases.

For transitions involving levels with AjA2 splittings, thezero-field frequencies are not well determined in several

cases. This arises from the fact that the Stark shifts are notaffected much by the amount of the AjA2 splittings when theshifts are larger than the splittings.

Finally, the uncertainties of the observed frequencies inTables 3-5 are directly affected by the instability of laserfrequency, which is estimated to be r7 MHz.

The accuracy of the observed frequencies is tested by theagreement of the two frequencies of one transition observedindependently by two laser lines for qP(4, 3), PP(7, 5), rp(9,

5), rp(7, 4), and rp(4, 2) in Tables 3 and 4. The two frequen-cies agree well within the quoted uncertainties. However,these transitions are of relatively low J, K, and for transi-tions with J > 10 the uncertainty coming from the inappro-priate assumption for the constancy of the ground-statedipole moment may exceed the quoted error.

AA 2 Splittings in the v2 and v4 StatesThe observed AjA2 splittings for K = 3 in the V2 state havebeen given in Table 5 for J = 4,6, 9, 15. The splittings have

been determined by observing the split resonant fields corre-sponding to the AjA2 splittings in the V2 state for J = 4, 6, 9[-0 - 1 and 0 - 1 for qp(5, 3) and qR(8, 3) and 0 - -1 and-0 - -1 for qP(7, 3) in Table 2]. The splitting for J = 4measured by the same method as reported here has alreadybeen reported,6 with which our value agrees. The splittingfor J = 9 has been reported to be 317.5(5) MHz, 6 which

differs slightly from the value in Table 5. The value inTable 5 is considered to be more precise because the splitresonant fields were measured. The splitting for J = 15listed in Table 5 has a large uncertainty because it was

estimated from the observation of one component of theAjA2 split transitions. The splitting for J, K = 5, 3 in the V2

state was recently measured by Chen et al.2

1 to be 13.22 MHzby using a microwave sideband of a CO2 laser as an infraredsource. In Table 5, the calculated values with the molecularconstants given in Ref. 3 are listed for comparison; they are

1.4 times smaller than the observed values.Several AjA2 splittings for the v4 state have also been given

with their estimated uncertainties in Table 5.

Dipole MomentThe effective dipole moments given in Tables 3 and 4 aresummarized in Table 6. When two values are available forone state, the one with better accuracy is listed. Table 6shows that, for the v2 state, the effective dipole moment doesnot vary much for the rotational states studied. The effec-tive dipole moment for the v4 state, however, varies muchbeyond experimental uncertainties with rotational states.This variation is not systematic for rotational quantumnumbers J, K and cannot be understood by a rotationaldependence of the type j = AO + jijJ(J + 1) + AKK 2. Themain part of the variation is explained as due to the mixingof the symmetric-top wave functions of the same or thedifferent vibrational states resulting from vibration-rota-tion interaction. The wave function for a rotation-vibra-tional level is given by

(8)= ak1J, k)11, 0, + bJ k') 0, 1, ),k k'

where IJ, k) is a rotational wave function and 1v2, V4, 1) is a

vibrational wave function. The Stark-effect Hamiltonianfor the electric field E along the space-fixed Z axis is

H =-AZXZZE, (9)

where , is the dipole moment along the molecular symme-try axis and XzZ is a direction cosine. The first-order Stark

effect is given by

W1()= (i0IHt) =-J(J +1) [ 2 > ak2k + A4 bkA']

(10)

where ,2 and A4 are the permanent dipole moments in the v2

and v4 states, respectively. The wave function in Eq. (8) isobtained by diagonalizing the Hamiltonian matrix in Ref. 3.

The effective dipole moment thus calculated for appropriatevalues for ,2 and A4 explains the main part of the variation ofdipole moments in the v4 state, but some discrepancies stillremain between the observed and calculated dipole mo-ments.

M

(D

0

eFP

004NCD

Takagi et al.


Table 6. Effective Dipole Moments (D) in the v2 and 4 States of PH3

J K I Mobs. Mcalc. Ao - Ac (go - Mc)a J K 1 Mobs. Mcalc. Mo - Ac (Mo - a

V2 = 1 12 9 0.5739(8)b 0.5739 0.0000 (0.0002)1 1 0.5740(7) 0.5740 0.0000 (-0.0002) 13 6 0.5751(1)b 0.5740 0.0011 (0.0015)2 1 0.5740 13 10 0.5740b 0.5740 0.0000 (0.0002)2 2 0.5737(23)b 0.5740 -0.0003 (-0.0004) 14 12 0.5740b 0.5739 0.0000 (0.0002)3 3 0.5740(1) 0.5740 0.0001 (-0.0001) 15 3 0.57374 1 0.5740 (0.0000) 15 8 0.5739b 0.5740 -0.0001 (0.0003)4 2 0.5740(1) 0.5740 0.0000 (0.0000)4 3 0.5740(1) 0.5740 0.0000 (-0.0001) V4 = 15 1 0.5728(8)b 0.5740 -0.0011 (-0.0012) 1 1 1 0.57885 4 0.5744(6) 0.5740 0.0004 (0.0003) 2 1 -1 0.5793(3) 0.5795 -0.0001 (0.0001)6 1 0.5736(9) 0.5740 -0.0003 (-0.0003) 2 2 1 0.5741(2) 0.5738 0.0003 (0.0022)6 3 0.5740 3 3 1 0.5775(2) 0.5764 0.0012 (0.0031)6 4 0.5743(2) 0.5740 0.0003 (0.0003) 4 1 -1 0.6044(2) 0.6047 -0.0004 (-0.0038)6 5 0.5741(1) 0.5740 0.0001 (0.0001) 4 4 1 0.57548 4 0.5740 0.5739 0.0000 (0.0001) 5 4 1 0.57038 6 0.5737(1) 0.5739 -0.0002 (-0.0002) 5 5 1 0.5774(10)b 0.5775 0.0001 (0.0020)8 7 0.5741(8) 0.5739 0.0002 (0.0001) 6 4 -1 0.5801(1) 0.5806 -0.0005 (-0.0007)8 8 0.5737(1) 0.5739 -0.0003 (-0.0004) 6 5 1 0.5746(1) 0.5740 0.0005 (0.0030)9 3 0.5738 6 6 -1 0.5783(1) 0.5790 -0.0008 (0.0006)9 5 0.5740 0.5739 0.0001 (0.0002) 7 2 -1 0.61669 8 0.5736(5) 0.5739 -0.0003 (-0.0003) 7 4 1 0.55199 9 0.5745(3) 0.5739 0.0005 (0.0005) 7 6 -1 0.5787(2) 0.5793 -0.0006 (0.0001)

10 2 0.5740(6) 0.5739 0.0000 (0.0003) 7 7 -1 0.5781(1) 0.5790 -0.0009 (0.0005)10 7 0.5742(1) 0.5739 0.0002 (0.0004) 8 4 1 0.539910 8 0.5739(1) 0.5739 0.0000 (0.0001) 8 6 1 0.5716(1) 0.5711 0.0005 (0.0035)10 9 0.5735(7) 0.5739 -0.0005 (-0.0005) 9 1 -1 0.8334(9) 0.8330 0.0004 (-0.0103)10 10 0.5736(1) 0.5739 -0.0003 (-0.0004) 9 3 1 0.4772(5) 0.4776 -0.0004 (0.0042)11 4 0.5738(10)b 0.5739 -0.0002 (0.0001) 10 4 1 0.515611 6 0.5739b 0.5740 0.0000 (0.0002) 10 8 -1 0.5808(19)b 0.5799 0.0009 (0.0009)11 7 0.5738(11)b 0.5740 -0.0002 (0.0000) 10 8 1 0.5744(1) 0.5738 0.0006 (0.0035)11 9 0.5740b 0.5739 0.0000 (0.0001) 11 10 -1 0.5775(2)b 0.5792 -0.0017 (-0.0011)11 11 0.5740b 0.5739 0.0001 (0.0000) 12 2 -1 0.714712 3 0.5739 12 10 -1 0.5785(1)b 0.5797 -0.0012 (-0.0013)12 8 0.5740b 0.5740 0.0000 (0.0002) 12 12 -1 0.5776(2)b 0.5790 -0.0014 (0.0000)

a The values for yj - M in parentheses are for the least-squares analysis withb This value is removed from the least-squares analysis.

To produce better agreement, the transverse dipole mo-ment at is introduced here in a way similar to that given byMills et al.

2 2

The transverse dipole moment is assumed to be expressedas

A. il.y = dq 2 [q4 (l) ± iq4 (2 )], (11)

where d is a constant, q2 is the normal coordinate for the v2state, and q4(1) and q4(

2) are those for the 4 state. TheHamiltonian in Eq. (9) is modified as

two parameters, M2 and M4.

in the phase convention of Ref. 3. Equation (13) is rewrittenas

W = OMEl) (aK 2 + b4 + cad,J(J + 1) (14)

where Ko is a representative K, that is, K appearing as anenergy level, and a = Sk ak 2k/Ko, b = k' bk'2k'/Ko, and c =Ek ak[bk+1/f(J, k) - bk-,Vf(J, k - 1)]/Ko. The effectivedipole moment, as determined in Tables 3 and 4, is given by

H = -,uXzE - (.Xz + sYXY)E. (12)

This Hamiltonian has matrix elements between IJ, k)I1, 0, 0)and IJ, k 1) 10, 1, 1), like the Coriolis interaction betweenthe 2 and 4 states, and can contribute to the linear Starkeffect when the two interacting states are mixed with theCoriolis interaction. The linear Stark effect is given by

W= W(0) - ME$ Ya k[ b k + f_Jk)J(J + 1) E [

-bk.,Vf(J, k-1)], (13)

where f(J, k) J(J + 1) - k(k + 1) and

At = (1, 0, Ax - il0, 1, 1) = -(1, 0I OlM + AYl0, 1, -1)

A = a 2 + b 4 + C9t. (15)

Using the wave function calculated by the constants givenin Ref. 3, the constants a, b, and c can be calculated. Thedipole moments 2, 4, and At are determined by fitting theobserved effective dipole moments to Eq. (15) by the least-squares method.

The result of the fitting is given in Table 6. In the fitting,a few dipole-moment measurements considered to havelarge uncertainties are removed. Also, the levels with J > 10are removed to avoid the complexity coming from the J, Kdependence of the dipole moment. The dipole moments forthe remaining levels are treated with equal weight. For thev2 state, the calculated dipole moment changes only littlewith rotational levels and generally agrees well with the

Takagi et al.


Table 7. Dipole Moments in the V2 and V4 States ofPH3 (D)a

2 114 Mt

0.57420(27) 0.57904(32) -0.01100(92)

a The errors quoted are 2.5 times the standard deviation.

observed values. For the 4 state the agreement is not sogood as for the i' 2 state. However, the calculated valuesexplain the large change of the dipole moment satisfactorily.The result of the least-squares analysis with two parameters,$2 and A4, by Eq. (10) is shown in parentheses in the lastcolumn of Table 6. [The dipole moments determined are $2

= 0.57494(143) D and A4 = 0.57764(168) D.] It is seen that

the introduction of At decreases the deviation $0 - /c for thev4 state. In this table calculated values are given for somelevels whose dipole moments were not measured but wereestimated to enable us to analyze observed transitions.

The dipole moments of the v2 and v4 states of PH3 havealready been measured by di Lonardo and Trombetti forseveral v2 band lines and two v4 band lines, using the laserStark method.5 The observed values agree with our ob-served effective dipole moments fairly well. The dipolemoment for the v2 state has been obtained as $2 = 0.5740(2)D from the mean value of effective dipole moments of sever-al levels. For the v4 state, the dipole moments were deter-mined from the effective dipole moments of the (J, K, 1) = (6,6, -1) and (7, 7, -1) levels, because these two levels are notconnected by the Coriolis interaction with the 1'2 state andare considered to be of pure K = 6 and K = 7, respectively, inthe v4 state. From the effective dipole moments of theselevels, the dipole moment 4 has been determined as0.5784(1) D. The corresponding value of ,u4 obtained fromour measurement is 0.5782(1) D. The value of A4 given inTable 7, which gives a better fit to the effective dipole mo-ments of many rotational levels, is a little larger than thesevalues.

CONCLUSIONS

The v2 and i 4 bands of PH3 have been studied by laser Starkspectroscopy, using 12C1602, 13C160 2, 12C1802, and N2 0 la-sers. The precise transition frequencies and several A1A2splittings have been reported. The dipole moments of

phosphine for the 2 and v4 states and the transverse dipolemoment between these states have been determined.

ACKNOWLEDGMENT

This research was supported in part by a Grant-in-Aid forScientific Research from the Ministry of Education, Science,and Culture of Japan.

REFERENCES

1. J. M. Hoffman, H. H. Nielsen, and K. N. Rao, Z. Elektrochem.64, 606 (1960).

2. P. K. L. Yin and K. N. Rao, J. Mol. Spectrosc. 51, 199 (1974).3. G. Tarrago, M. Dang-Nhu, and A. Goldman, J. Mol. Spectrosc.

88, 311 (1981).4. F. Shimizu, J. Phys. Soc. Jpn. 38, 293 (1975).5. G. di Lonardo and A. Trombetti, Chem. Phys. Lett. 76, 307

(1980).6. N. Carlotti, G. di Lonardo, and A. Trombetti, J. Chem. Phys. 78,

1670 (1983).7. E. G. Malk, J. W. Niesen, D. F. Parsons, and P. D. Coleman,

IEEE J. Quantum Electron. QE-14, 544 (1978).8. K. Takagi, Chem. Phys. Lett. 112, 302 (1984).9. K. Tanaka, K. Harada, T. Tanaka, and K. Takagi, Chem. Phys.

Lett. 119, 447 (1985).10. S. M. Freund, G. Duxbury, M. Romheld, J. T. Tiedje, and T.

Oka, J. Mol. Spectrosc. 52, 38 (1974).11. J. W. C. Johns, A. R. W. Mckellar, T. Oka, and M. R6mheld, J.

Chem. Phys. 62, 1488 (1975).12. P. B. Davies, R. M. Neuman, S. C. Wofsy, and W. Klemperer, J.

Chen. Phys. 55, 3564 (1971).13. C. H. Townes and A. L. Shawlow, Microwave Spectroscopy

(McGraw-Hill, New York 1955).14. W. H. Weber and R. W. Terhune, J. Chem. Phys. 78, 6422

(1983).15. W. H. Weber, J. Mol. Spectrosc. 107, 405 (1984).16. C. Freed, L. C. Bradley, and R. G. O'Donnell, IEEE J. Quantum

Electron. QE-16, 1195 (1980).17. F. R. Petersen, E. C. Beaty, and C. R. Pollock, J. Mol. Spectrosc.

102, 112 (1983).18. B. G. Whitford, K. J. Siemsen, H. D. Riccius, and G. R. Hanes,

Opt. Commun. 14, 70 (1975).19. A. G. Maki, R. L. Sams, and W. B. Olsen, J. Chem. Phys. 58,4502

(1973).20. A. Guarnieri, F. Scappini, and G. di Lonardo, Chem. Phys. Lett.

82, 321 (1981).21. Y. Chen, J. M. Frye, and T. Oka, J. Opt. Soc. Am. B 3, 935

(1986).22. I. M. Mills, J. K. G. Watson, and W. L. Smith, Mol. Phys. 16,329

(1969).(continued overleaf)

DCD

D

0

00

N

Takagi et al.


Kojiro Takagi Eiji MiuraKojiro Takagi received the B.S. degree in1958, the M.S. degree in 1960, and thePh.D. degree in 1964, all in physics, fromthe University of Tokyo. In 1964, hejoined the Department of Physics, Toya-ma University, Toyama, Japan, where he

g . Q s is at present a professor of physics. Heheld postdoctral positions from 1968 to1969 and in 1974 in the Department ofChemistry at Rice University, Houston.His research interests include laser spec-troscopy and microwave spectroscopy ofmolecules and spectroscopy of interstel-

lar molecules. He is a member of the Physical Society of Japan andthe International Astronomical Union.

Katsumi Itoh

y IFP~ 0 S t Katsumi Itoh received the B.S. degree in1981 and the M.S. degree in 1983, both inphysics, from Toyama University, Toya-ma, Japan. In 1984 he joined SUNXCompany, Ltd., where he is currently en-gaged in the quality control of hybridintegrated circuits in the R&D Center ofSUNX in Tokyo. He is a member of thePhysical Society of Japan.

Shoichi Tanimur;

Eiji Miura received the B.S. degree inphysics from Shinshu University, Na-gano, Japan, in 1979. He received theM.S. degree in physics from ToyamaUniversity in 1983. Since 1983 he hasbeen at the Engineering Section of San-kyo Seiki Manufacturing Company, Ltd.,Komagane, Japan, where he is now en-gaged in the design of floppy disk drives.

a

Shoichi Tanimura received the B.S. de-gree in 1982 and the M.S. degree in 1984,both in physics, from Toyama Universi-ty. In 1984 he joined the MatsushitaElectric Industrial Company, Ltd., wherehe is currently engaged in the develop-ment of photochemical vapor depositiontechnology for very-large-scale-integra-tion devices in Semiconductor ResearchCenter of Matsushita, Moriguchi, Japan.He is a member of the Physical Society ofJapan and the Japan Society of AppliedPhysics.

0

0

a.)Ac;

cd

Takagi et al.

laser stark spectroscopy of phosphine

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