IL NUOVO CIMENTO VOL. 3 A, N. 4 21 Giugno 1971

The 0 - - > 0 + Decay of 14~13r and the Pseudoscalar Interaction.

T. NAGARAJAN

Department o] ~uelear Physics, University o] Madras - Madras

]~[. X:~AVINDRANATH a n d K . V]~i~KATA ~=~EDDY

Laboratories ]or .~uclear Research, Andhra University - Waltair

(ricevuto il 17 Agosto 1970)

Summary. - - The shape factor result of Daniel on the 0- -+ 0 + tran- sition of l~4Pr is at variance with all earlier reports, requiring terms up to W 2. For 16SHe 0 - - + 0 + decay, Daniel et al. require terms up to W 3, whereas Beekhuis et al. who t rea t W o as a free parameter fit the experi- mental shape with a fewer number of terms. In view of these disagree- ments, i t is considered worth-while to perform an accurate analysis of the x4~Pr spectral shape with the present spectrometer, which is ideally suited for such high-energy transit ions as ~44pr, for which scattering is a serious problem in other spectrometers. Tile measured shape of 144Pr is C(W) = k { 1 - - (0.0975 • 0.013)/W}. An analysis employing the exact formulation of Bhalla and Rose yields Cp/C~ ~ 10 and a ratio of axial vector matr ix elements 2 = - 11. These results exclude the predictions of par t ia l ly conserved axial vector current theory in the form proposed by Tadic. The nonzero l imit of P-contr ibut ion may arise due to the inadequacy of the t rea tment of P-coupling by Rose and Osborne or the neglect of higher-order matr ix elements in the present analysis. The parameter obtained in the present work agrees with the theoretical pre- dictions of Ahrens and Feenberg, and Pursey and excludes those of Rose and Osborn, and Pearson.

1. - ~tltroduction.

The d i r e c t e x p e r i m e n t a l ev idence conc e rn ing t h e a b s e n c e of t h e p seudo-

sca l a r coup l ing in b e t a d e c a y is v e r y weak . A s u i t a b l e t r a n s i t i o n for t h e in-

v e s t i g a t i o n of t h e p s e u d o s c a l a r c o n t r i b u t i o n is t h e 0 - --> 0 + t r a n s i t i o n s t o wh ich

699

7 0 0 T. NAGA/CAJAI~, M. RAVINDRANATII a n d K. VF, NKATA REDDY

only two mat r ix elements contr ibute. These transit ions also offer a tes t of the par t ia l ly conserved axial vector current theory (1) according to which the 0 - - > 0 + transit ions must have almost allowed shapes. The ~44Pr transi t ion ( 0 - >0 +) has been invest igated by many workers (3-6). No good agreement exists between the results of the various workers on the above transition. I t is also difficult to analyse the causes of these discrepancies. For such high-

energy transit ions as in the 144Pr ( 0 - - > 0 +) case, scat ter ing in the spectro- mete r can be appreciable. One should also ascertain str ict l inear i ty b y using conversion standards up to 3 MeV. Apar t f rom the earlier confusion in inter- pret ing the results due to the fact t ha t the main interact ion was thought to be S - - T instead of V - - A , a complete analysis has been made only recent ly by DA_WI~L et al. (6) and the computat ions of these observables in te rms of the exact formulat ion of BHALLA and Rose (7). The decrease in thei r measured shape, about 7 % in (1.2 --3.0) lYIeV is large compared to tha t of previous workers and the shape factor plot is quite curved near the end-point. The necessity of fitt ing a shape with W 3 and W 8 terms arises when the shape factor curve is ve ry curved near the end-point. Before a t t empt ing to fit the exper imenta l shape factor with such higher powers of W, one should examine the shape factor near W0 by simply changing Wo in ve ry small steps. In the invest igat ion of :e6Ho and ~44Pr by DA~'IEL et al. (e), the above fact has been ignored and consequently they had to use in 166H0 terms up to W 3 to fit the shape, whereas

in the measurement of ~ H o BEE:~-t~S (8) t reats Wo as a free pa ramete r and fits the shape with a smaller number of terms. In view of the low log Jr value equal to 6.5, there may not be any cancellation among the axial vector mat r ix elements. For pure axial vector interaction, the shape C(W) and electron po l a r i z a t i on - -P / (v / c ) should be proport ional (o) to ( l • and (1-4-b/W) respectively. The shape of the ~44Pr ground-state t ransi t ion is measured in the present spect rometer (~0.~1) which has been optimized for shape measure- ments and whose l inear i ty (13) has been checked up to 3 McV. The inter-

(:) (3) (') (') (5) (6) H. C) C. (s) H. (9) W. (1o) T. 67, 77

D. T ~ I c : Phys. f~ett., 12, 116 (1964). R. L. GRAHAM, J. S. GEIGER and T. A. ]~ASTWOOD : Can. Journ. Phys., 36, 1084 (1958). M. J. LAUBITZ: Proc. Phys. Soc., 69A, 789 (1956). N. J. FRnEMA~: Proc. Phys. Sot., 73, 600 (1959). F. T. PORTER and R. P. DAr: Phys. t~ev., 114, 1286 (1959).

DANIEL and G. Tm KASCIIL: ~N'uel. Phys., 76, 97 (1966). P. B~ALLA and M. E. RosE: Phys. t~ev., 120, 1415 (1960). BnEKIIvIS: Thesis 1967, Rijksuniversiteit te Groningen. BUnRING: Nucl. Phys., 40, 472 (1963). ~'AGA-RAJAN, ~ . I;~AVINDRANATH and K. VE~KATA REDDY: N2/~Z. Instr. Meth., (1969).

(11) W. NAGARAJAN, M. RAVINDRANATII, K. VENKATA REDDY and S. JNANANANDA: Phys. Bey., 178, 1968 (1969). (12) T. NAGXaAJAW: Thesis (1968), Andhra University, Waltair.

THE 0 - - ~ 0 + DECAY OF mPr AND TItE PSEUDOSCALAR IlgTERACTION 701

mediate-image spectrometer , by v i r tue of its ant iscat ter ing proper ty , is best suited for the invest igat ion of this t ransi t ion of high end-point energy. In the present measurement a good fit could be obtained only for a form factor of the type C(W)= k(1--b/W). The available electron polarization measurements are not ve ry accurate and they differ widely (Table I / I ) . Hence i t is considered worth-while to analyse this decay using the shape factor of the prcsent work through the exact computat ions of BmU~LA and Rosn (s) and compare the results

with electron polarization measurements (13-1e).

2. - Experimental procedure.

The nucleus ~44pr (17 rain) is a convenient isotope for investigation. I t decays effectively with the half-life of its paren t nucleus 14~Ce whose maximum beta energy is only 300 keV. The ground-state t ransi t ion to 14~Nd has an ex- tensive energy range and therefore the disturbing effects of source thickness and back-scat ter ing are quite negligible. The transitions to the excited levels of 144Nd are feeble and can be subtracted with enough accuracy.

Carrier-free 144Ce-l"pr sources were obtained from Bhabha Atomic ICcsearch

Centre, Trombay, in the form of CeC]3 in HCI, in two different consignments.

Uniform sources were prepared on thin aluminized mylar backing. The source thicknesses ranged from 25 to 35 ~xg/cm ~. The measurements were done with a Sicgbahn-Slatis spect rometer (10-1~) equipped with a well-type plastic whose counting efficiency is un i ty down to 50 keV and whose back-scat ter ing effect is negligible.

3. - Measurement of the shape of the ground-state transition.

The decay scheme of 144Ce--~144Pr-~144Nd is fair ly well established (~7)

(Fig. 1), bu t the spin assignment to the gromld state of 14~Pr has been the subject of considerable controversy (is). However S~ag~- et al. (~s) have made a unique spin assignment of 0- to the ground state of '44pr. The shape of the 2.311 MeV beta group measured (~.5) in coincidence with the 691 keV gamma-

ray and the correlation of the cascade (2.311~-0.691y) are consistent with

(13) H. DANIEL and S. A. A. ZAIDI: Ann. de Phys., 17, 33 (1966). (14) H. FI'~AUENFELDEIt, A. 0. HA1,;SEN, N. LEVINE, A. U. R0ssI and G. DE PASQUALI: Phys. l~ev., 107, 643 (1957). (15) j . S. G>:IGER, G. T. EWA~, R. L. GRAIIA~ and D. R. U. McKEI~ZIE: Phys. Rev., 112, 1684 (1958). (16) W. A. W. 5IEIILI-IOr: Thesis, Wash. University St. Louis (1959). (1~) Nucl. Data Sheets, NRC 59-1-106. (18) R. M. SINGRU, R. S. RAGHAVAN and R. M. ST~F~'~: Phys. Lett., 6, 319 (1963).

7 0 2 T. I~AGARAJ&I~, M. RAVINDRA~ATH a n d K. VENKATA REDDY

key

822

2311

3002

~44p 59 FS~

k ' - . , .

% Log ft

I 6.3

1.3 8.0

97.1 6.5

g o

5 x 10 15y 144. 60Nd84

keY j n

2180 1-

1780 6*

1300 4 +

691 2 +

0 0 §

Fig. 1. - Decay sheme of x44Pr. The beta end-points are deduced from Q~ = 3002 keV of the present work.

48

40

36

24

~6

O-

e � 9

o � 9 O,

~ I lOOl l

, eo �9 ~ 1 4 9

m O U O D D O O B e I

I I I I I I 300 900 1500

E (keY)

* e e o * * ~

I 210~

3MeV " " ] e e e

e~ ~ e o e

2700

Fig. 2. - The Fermi-Kurie plot of beta spectrum of 144Ce-144pr decay.

THE 0 - - - ~ 0 § DECAY OF mPr AND THE FSEUDOSCALAR INTERACTION ~ 0 3

the ~ssignment of first forbidden unique c, hsrac ter to this group. The intensi ty

of this group is known sccurately (1.3 %) from the gamma- r sy intensi ty bal-

ances (~'). The spectrum of this group 2r with end-point Wo, is con- s tructed according the expression

(i) -~o/(Wo,- w),@.

I f A ' is the s res of the spectrum (1) constructed with k = 1 ~nd A is the

; 6

C(A/) l1 0 0 0 a .a---a n , I1 n - - I II Cl II O II II g .p - -O II u ~ - - I :

cz)

~6

15;~

800

i ~ I i a I I I l . t {

0 ~ 1 1 I : ) 1I II II

I I 1200

T

1600 20o0 2400 2800 E(keV)

Fig. 3. - Shape factor of the 3002 keV beta component of mPr. The Figure shows the behaviour of C(W) near Wo when W o is changed, a) Eo= 2995keV, b) Eo----

2997 keV, c) Eo = 2999 keV.

C(W)

15

14

! zr I I w '~.-~---.---,..--ID--,r _ a ~ ~ = . ,~ p - a ~ ,~ ! [ {

800 1200 1600 2000 2400 2800 E(keV)

Fig. 4. - Shape factor of mPr (3002 keV) for two different runs. The experimental points are fitted with C(W) = k(1 4- 1/W) by weighted least squares. The dashed line is the theoretical shape factor corresponding to 2 = - 10.9 and ~ = 5.2-10L a) Run 1, E o ~2997 keV, b= (--0.0854-0.004)moc~; b) run 2, Eo=3007keV, b= (--0.114-0.003)moo e.

704 T. NAGA_RAJAN, M. RAVINDICANATI~ and x. VENKATA REDDY

area of the gross s p e c t r u m of ~**Pr a f te r the s u b t r a c t i o n of t he ~4Ce c ompone n t s ,

(2) o.ot3A ( 9z, N 2 ( p ) d p - - A ' i>] q2+ Lo] (W~

The F e r m i p lo t of t he ~4Ce-~44Pr b e t a spec t ra is shown in Fig. 2.

Af t e r s u b t r a c t i n g fl 'om the gross s p e c t r u m the 2.311 MeV b e t a group

c o n s t r u c t e d us ing the express ion (2), t he r e su l t i ng s p e c t r u m was sub jec ted to

shape fac tor ana lys i s i n the reg ion (800 - -2900)keV. I t is n o t necessa ry to

cons ider t he smal l -o rder shape factor , if any , to the 2.311 MeV b e t a group

on accoun t of i ts v e r y feeble i n t e n s i t y . F o r each r u n , the p rope r e n d - p o i n t

was o b t a i n e d j u d g i n g f rom the effect of smal l changes in e n d - p o i n t on the

TABLE I. -- Shape ]actor constants of 14aPr.

Run No. E o (keV) b(mo e2) V'Z2/(,n~- n)

1 2997 • 2 --0.085 • 0.004 1.4,:ii

2 3007 :h 2 --0.1 l ~ 0.003 1.7~

Mean 3002 =j= 5 (') --0.0975:1= 0.0125 (')

( ' ) M e a n d e v i a t i o n of t h e t w o r u n s .

TABLE II. - Comparison o/ results o/ various authors on laq)r.

Authors Ins t rument C(W)/k E o (keV) Change in Parameters shape factor

LAu- Lens 1 - - 0.058W-- 2990 4- 10 Decreases Cp/C~ ~ 100 BITZ (a) spectr. - - 0.389/W by 21% m

6% resol. (640+2700) keV

GilA- Double 1 + 0.0146W 4- 2984 Increases i = 0, C~/C~ < 15 11AM (1) lens -4- 0.0283/W by 3% m ). = 200, Cp/C~ < 10

(500+2500) keV

FREE- Prolatc 1 - - 0.0135W - - 2992 Decreases 0 < ). < 10 MAN (~) spheroidal - - 0.721/W + by 3% 111

+ 0.0002W ~ (500+2500) keV

POR- Argon 1 + 0.028W + 2996 ~ 3 Decreases t = 5 -4- 2 TER (~) double -~- 0.091/W-- by 5% m

lens - - 0.0041W 2 ( 500 +2700) keV

DA- IIeidelberg 1 + 0 .03W-- 3000 • 4 Decreases ), : - - 16 NI:EL (6) double - - 0.118/W-- by 7% 111 ICe/Cal < 5

lens - - 0.008W 2 (1200+3000) keV

Present Intermed. 0.0975 5= 0.013 3002 i 5 Increases A = - - 10.9 work imago 1 - W by 2% m [Cp/CA[ = 9.5

(800+2800) keV

THE 0---~ 0 + ])ECAY OF l~l)r AND TIIE PSEUDOSCALAR INTERACTION 70~

shape factor (Fig. 3). The shape factors corresponding to these proper end- points are weighted-least-square fitted with the expression C(W) = k(1 + b/W) (Fig. 4). The shape factor coefficients of some of the works cited in Table I I were however obtained by an actual fit of their respective experimental shapes.

4. - Analysis of the shape of the 14~pr (0---> 0 +) beta transition.

According to V - - A theory of weak interactions, only axial vector matr ix elements c , fy 5 and C, f a . k contribute to 0 - - ~ 0 + transitions. B ~ A and I~osE (7) have caletflated the spectral form and longitudinal polarization as functions of Cr, the pscudoscalar coupling constant, making use of the Foldy- Wouthuysen transformation. They give expressions for the form factor and electron polarization respectively as

(3)

(4)

C(W; 2, ~) -= bo + bl2 ~ -'r- b.2 2 + b3~ 2 + (b, + b5).)~,

ao -t- al 2~ -~- a2).--a3~ 2 + (a4 + asX)~ p ( w ; ~, ~) = - - -

bo + bl), ~ + b~). + b3~ 2 + (b, + bs).)~

where 2=ifrs/f .k is the ratio of axial vector matr ix elements and ---- Cp/MC~. C~. and C~ are tile pseudoscalar and axial vector coupling con-

stants and M is the nucleon mass; a2s and bi's are energy-dependent combina- t ion of E R W F S tabulated by BttALLA and ROSE (7) for 144Pr and l~SHo. Their computations include finite size of the nucleus and the de Broglie wavelength effects.

The mean value of b quoted in Table I, namely --0.975 ~ 0.0125, is used in the following analysis. The ratio of experimental shape factors at two ener- gies can be reproduced for a set of (2, ~) values by the ratio of the theoretical expressions (3) at the same energies. This set generates a conic section in the (2, ~)-planc. When the experimental error is taken into account, each pair of energies determines a hyperbolic band for the permissible values of 2 and in the (2, ~)-plane. In this analysis, the hyperbolic bands corresponding to the two constraints C(2.693)/C(4.61)=0.9825• and C(6.577)/C(4.61)= ----1.0065 ~0 .0005 arc considered (Fig. 5). Two well-defined solutions satis- fying both the contraints are obtained: set I) ) , ~ = - - 1 0 . 9 , 5.2.10 -a and set II) ~, ~ = -- 14.2, - - 6.10 -s. Whereas both sets are equally good in fitt ing the entire experimental shape factor, set II) gives the electron polarization with the wrong sign, and hence is completely ruled out. The electron polariza- t ion values calculated from set I) (Table I I I ) are compatible with the meas- urements of F~L~E.~FELDER et al. (14), but they are lower than the values of DANIEL et al. (13). The electron polarization values of DANIEL et al. (13) suggest a still lower limit for ~ (~ = 2.10 -3) than the results of the present shape factor

46 - I I N u o v o O i m e n t o A .

~0~ T. NAGARAJAN, M. RAVINDRA~ATH a n d K. V~ENK~TA REDDY

16

12

8

4

• .0

-4

- - 8

-12

52)

2•r-.,----(-14.2 ,-6)

clw2) / ~/

I L I / V 1 I I I I - 2 0 -18 -16 -1,', -12 -10 - 8 j. - 6

Fig. 5. - Analysis of 144Pr (0--7 0 +) beta transition. The shape factors are normalized at W=4 .61~0 e2. C(2.693)/C(4.61)=0.9825=]=0.00205, C(6577)/C(4.61)=1.0065:j= 0.0005.

m e a s u r e m e n t . E v e n t h o u g h t h e a g r e e m e n t b e t w e e n t h e v a r i o u s r e p o r t e d r e su l t s

of e l e c t r o n p o l a r i z a t i o n m e a s u r e m e n t s is n o t v e r y good, t h e i n c r e a s i n g t r e n d

w i t h e n e r g y is e v i d e n t . On t h e o t h e r h a n d , t h e p o l a r i z a t i o n v~lues p r e d i c t e d

in t h e p r e s e n t ~n~lys is a n d t h a t of DANz~,~ show a d e c r e a s i n g t r e n d w i t h e ne rgy .

TABLE I I I . - Electron polarization o] 144pr (0--> 0+).

Energies P(W)I(-- v /c ) P(W)I(-- v /c) Methods Authors (MeV) for 2 = - - 10.9 measured

and ~ = 5.2.10 -a

0.4--1.1 0.77 :t: 0.21 Moller scat. FRAUENFELDBR (14)

1.2--3.0 1.08 ::= 0.26 Mollcr scat. FI{AUENFELDER (14)

0.3--3.0 0.9 ~ 0.22 Mollcr scat. G]~IezR (1~)

1.0--3.0 0.986 =h 0.03 Moiler scat. MEnLHOP (lS)

0.904 0.828 0.988 • 0.037 Eternal DANIEL (la)

1.215 0.801 1.012 =t= 0.029 brehm.

1.532 0.798 1.022 • 0.045

THE 0----> 0 + DECAY OF 144pr AND THE PSI,~UDOSCAL~R I-~TERACTION 707

5 . - C o n c l u s i o n .

The above analysis yields Cp/C a = 9.5 and ~ ---- - - 10 . 9 ; this is not incom-

pat ible wi th the resul ts of DAX~:L {Table I I ) . I t is significant to note t h a t the second solution of D ~ m L (6) as well as the p resen t work with ~ negat ive are not p e r m i t t e d b y electron polar izat ion data. According to GOLDBERGER and

TREI~A~" (xg) axial vector coupling induces a t e r m which simulates pseudo-

scalar interact ion. Bu t this pseudoscalar coupling is v e r y small in nuclear

be ta decay: C~/C a ~ 0.04. TXDIC (s0) discusses the consequence of the par t ia l ly

conserved axial vector cur ren t t heo ry for nuclear be ta decay and according

to h im all 0 - ~ 0 + t ransi t ions should have near ly allowed shapes and ), = - - 60

to - -100 . Bu t the resul ts of the p resen t work do not suppor t the va l id i ty of

the par t ia l ly conserved ~xial vector cur rent theory , a t least in the fo rm used

b y TADIC (20). I f the precision of shape m e a s u r e m e n t alone is considered, i t

implies u nonvanishing cont r ibut ion of pseudosealar interact ion, name ly C~/C~ ~-, 10. This nonzero l imit m a y arise due to the inadequacy of the special t heo ry of the P-coupl ing due to Ros]~ and OsBo]~_~ (~1). Or, i t m a y be caused

b y the neglect of higher-order m a t r i x elements . An analysis of this p rob lem

including higher-order m a t r i x e lements is being unde r t aken b y author. The

value of 2 = - - 1 1 obta ined in the p resen t work agrees wi th the theoret ical es t imates of A I ~ s and FEE~]3]~G (ss) and I%'~sEY (23) (2 = 0 to - - 1 5 ) and

disagrees wi th the predict ions of Ros]~ and Os]30~x (~) { ) , = - - 3 0 to - - 3 7 ) and PEAI~SO~ (25) ()~ = _ 2.5 to - - 9).

The authors are ex t r eme ly indeb ted to Emer i tu s Professor S. J~'A~A~ANDA for his k ind encouragement . One of us (T.BT.) t hanks the D e p a r t m e n t of Atomic Ene rgy for the ot~er of a Research ~ellowship. The services of CDC 3600 T I F R , Bombay , and the assistance of Mr. C. 5TA~ASTM~A RAO are acknowledged.

(19) M. L. GOLDBERGER and S. B. TI~]~I~A~: Phys. Rev., l l l , 354 (1958). (20) D. TADIC: Phys..5ett., 12, 116 (1964). (21) M. E. Ros~. and R. K. O'SBORNE: Phys. Rev., 93, 1315 (1954). (s2) T. AHR]~rS and E. FE~.NBERG: Phys. Rev., 86, 64 (1952). (s3) D. L. PURSe.Y: Phil. Mag., 42, 1193 (1951). (24) M. E. Ross and R. K. OSBO~N: Phys. Rev., 93, 1326 (1954). (es) j . M. PE~r Can. Journ. P. hys., 38, 148 (1960).

�9 R I A S S U N T O (*)

I1 risultato sul fattore di forma ottenuto da Daniel per la transizione 0 - ~ 0 + del x44pr 5 in contrasto con tutti i risul~ati preccdenti che richiedono tcrmini sino a W 2. Per il dccadimento 0--+ 0 + del 16qIo, Daniel et al. richiedono termini sino a W a, mentre

(*) Traduzione a eura della Redazione.

70~ T. NAGARAffAN, ~I. RAVINDRA]VATH and K. VENKATA REDDY

Beekhuis et al., che t r a t t ano W0 come pa rame t ro indipcndente , appross imano la form~ sper imenta le con un minor numcro di termini . Vis~e queste discorclanze, si 6 considera to oppor tuno esegtfire un '~ecura t~ analisi dell~ fo rma spet t ra le del lX~Pr con l ' a t t ua l e spe t t romet ro , chc b ideate per tal i t rans iz ione di a l ta energi~ come quelle del ~ P r . La forma mis~ra ta dcl ~4~pr 6 C ( W ) ~ k ( t - - ( 0 . 0 9 7 5 - - 0 . 0 1 3 ) / W } . Un 'ana l i s i csegui ta usando la formulazione esa~ta di Bhal la e Rose forniscc C p / C ~ 10 ed uu rappor to degli c lemcnt i eli mat r i ce ve t to r ia l i assiali 2 . . . . . 11. Quest i r i su l ta t i eselu~lono le prc- dizioni della tcor ia della corrente ve t to r ia lc assiale pa rz ia lmentc conserva tn nclla fo rma propos ta da Tadic. II l imi tc non nullo dcl con t r ibu to t ' pub sorgere da l l ' inadcguatczza della t ra~tazione de l l ' accoppiamento P f a t t a da Rose ed Osborne o da l l ' ave r t r~scura to e lement i di mat r iee di ordinc maggiore nclla presente analisi. I1 p a r a m e t r o o t t enu to in qucs ta analisi concorda con le predizioni teor iche di Ahrens e Fecnbe rg e eli Purscy ed esclude qucllc ~ti Rose ed O s b o r n e quclle eli Pearson.

Pacna~ 0 - ~ 0 + a a a ~44~pr H IlCeB~OCRILq[$1pHOe B3a~Mo~e~CTBHe.

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