Small-order deviations of90Y and32P

IL NUOVO CIMENTO VOL. 2 A, N. 3 1 Aprile 1971

Small-Order Deviations of ~oy and 3~p.

T. I~-AGARAJAiN

A. C. College o] Technology, University o] Madras - Madras

M. RAVINDI%ANATII a n d K. VENKATA ]:~EDDY

Laboratories ]or Nuclear Research, Andhra University - Waltair

(ricevuto il 6 Aprile 1970)

S u m m a r y . - - The shape of 9oy is studied as an overall check of the spectrometer response. The measured form factor of 9oy, viz. (q2+ 9L1/Lo ). • {1 - - (0 .001~ 0.003) W} indicates tha t the spectrometer is free from any distorting effect to within 0.3~o per moe% This agrees very well with the conclusion arrived at by a direct s tudy of the instrumental effects. The large hyperbolic terms reported for 9oy and a few other allowed and 1st unique spectra are characteristic of only 180 ° spectrometers whose line-shapes are highly asymmetrical . The shape deviation of asp for optimal base position is found to be small (a = --0.006 ± 0.005) in spite of its large log ]t value. Wrong positioning of the entrance base resulted in large hyperbolic deviation and shape with double slopes. These anomalies resembled some of the results reported in the literature. The two prevailing approaches, viz. l-forbiddenness and cancellation effect in allowed matr ix elements to explain the large log ]t value, small linear- shape deviation and longitudinal polarization of ( - -p /W) are only quali tat ively successful.

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

T h e shapes of a l l owed s p e c t r a m u s t be e n e r g y - i n d e p e n d e n t un less second-

o rde r t e r m s c o n t r i b u t e s ign i f i can t ly . These s econd-o rde r t e r m s are a) r e g u l a r

t w i c e - f o r b i d d e n c o n t r i b u t i o n s a n d b) (~ w e a k m a g n e t i s m >> effects. I n t he case

of u n i q u e spec t r a , one expec t s a (( t m i q u e ~> shape un less t h e r e a re cons ide ra -

b l e a) r e g u l a r t h i r d - f o r b i d d e n c o n t r i b u t i o n s a n d b) w e a k m a g n e t i s m effects.

T h e e n e r g y d e p e n d e n c e i n t r o d u c e d b y (< w e a k m a g n e t i s m ~> effects h a v e b e e n

662

SMALL-ORDER DEVIATIONS OF 9oy AND a2p 663

deduced (1,2). The measu red (3,4) shape fac tor of ~2B and ~1~ are of the f o r m

C(W) = 1 :k 0 .003W for e v decays. This f inding fu l ly agrees wi th the predic-

t ions concern ing we~k magne t i sm. The effects of weak m a g n e t i s m are ve ry

smal l in the low-energy beta- t runs i t ions , ~n4 become detee t~ble on ly for

Wo> 7moC ~. B u t for the smal l -order devia t ions of bo th a l lowed and un ique

t rans i t ions r epor ted in the l i t e ra ture the shupe fac tor coefficient a is nega t ive

for b o t h e ± deeuys.

The exper imenta l s i tua t ion in the smal l -order deviut ions of a l lowed and

f i rs t - forbidden un ique spect ra is no t sa t isfactory. The Heide lberg g roup employ-

ing ~ double-lens spec t romete r repor ts no dev ia t ion f rom the t h e o r y for a n u m -

ber of a l lowed and un ique be ta spect ra (~-12). Similur results were o b t a i n e d b y

o the r g roups (~322) us ing lens spect rometers . B u t the s t r ik ing shape fac to r

a n o m a l y t e r m e d as <( smull-order devia t ions )> of be t a spect ra was first r epor ted

b y the I n d i a n group, who measured a n u m b e r of be t a spec t ra (23-29) in the i r

(1) M. (2) j . (3) T. (4) y . (5) H. Meth., (e) H. (7) H. (8) H. (9) H. (lO) D.

CvELL-MANN: Phys. Rev., 111, 362 (1958). ]~. DREITLEIN: Phys. Rev., 116, 1604 (1959). MAYER-KucKUK and F. C. MICHEL: Phys. Rev., 127, 545 (1962). K. LEE, L. W. Mo and C. S. Wu: Phys. Rev. Lett., 10, 253 (1963). DANIEL: Nucl. Phys., 8, 191 (1958); D. FEHRENTZ and H. DANIEL: -Yucl. Inst. 10, 185 (1961). DANIEL and U. SCHMIDT-ROtlR: Nucl. Phys., 7, 516 (1958). LEUTZ: Zeits. Phys., 164, 78 (1961). DANIEL and PH. PANUSSI: Zeits. Phys., 164, 303 (1961). DANIEL, 0. MEIILING and D. SCHOTTE: Zeits. Phys., 172, 202 (1963). SCHOTTE: Dipl. Heidelberg, 1963 (unpublished).

(11) H. DANIEL, 0. MEHLING, P. SCHMIDLIN, D. SCHOTTE and E. THUMMERNICHT: Zeits. Phys., 179, 62 (1864). (12) H. DANIEL, G. TH. KACHL, H. SCHMITT t~nd K. SPRINGER: Phys. Rev., 136, B 1240 (1964). (13) F. (14) 1~. (15) p.

T. PORTER, F. WAGNER jr. and M. S. FREEDMAN: Phys. Rev., 1{}7, 135 (1957). T. NICHOLS, R. E. MCADAMS ~nd E. N. JENSEN: Phys. Rev., 122, 172 (1961). DEPOMMIER ~nd M. CHABER: Journ. Phys. Rad., 22, 656 (1961).

(16) F. BONIIOEFFER: Zeits. Phys., 154, 62 (1959). (17) I. HOFMAN: SGAE-PH. 13, Seibersdorf 1963 (1963). (i8) H. PAUL, F. P. VIEHBOCK, P. SKAREK, H. BAIER, I. HOFMAN and H. WOTKE: Acta Phys. Austriaca, 16, 278 (1963). (19) T. YUASA, J. LABERRIGUE-FROLOW and L. FEUVRAIS: Journ. Phys. Rad., 18, 559 (1957). (20) K. EGELKRANT and H. LEUTZ: Zeits. Phys., 160, 74 (1960). (21) p. RIEHS: Nucl. Phys., 75, 381 (1966). (22) S. ANDRE and P. DEPOMMIER: Journ. de Phys., 25, 673 (1964). (23) 0. E. JOHNSON, R. G. JOHNSON and L. M. LANGER: Phys. Rev., 112, 2004 (1958). (24) J. H. HAMILTON and L. M. LANGER: Phys. Rev., 112, 2010 (1958); J. H. HAMILTON, L. M. LANGER and D. R. SMITH: Phys. Rev., 119, 772 (1960). (25) J . H. HAMILTON, L. M. LANGER ~nd D. R. SMITH: Phys. Rev., 123, 189 (1961). (2e) D. C. CAMP and L. M. LANGER: Phys. Bey., 129, 1782 (1963). (27) D. ]~. WORTMAN ~nd L. M. LANGER: Phys. ]~ev., 131, 325 (1963).

~4 T. NAGARAJAN, M. RAVINDRANATH a n d K. VENK&TA REDDY

180 ° inhomogeneous spectrometer , which can be fit ted wi th the empirical shape factor C ( W ) = 1 +rb/W. They obta ined b-values around 0.3. Such large

deviat ions were also repor ted by others (3o,31) using fiat spectrometers.

Whenever the It value is high, indicating tha t the t ransi t ion ra te is consid- erably slower than what is normal ly the case for an allowed beta-decay, one would suspect tha t higher-order terms, which usually can be neglected in al-

lowed transit ions, m a y have an observable effect. Such second-order effects are expected to contr ibute to b e t a - g a m m a correlation and electron polariza- t ion as we]l. FISCH]~ECK et al. (3~) per formed the angular correlation of (2.86~-0.845y) cascade of 56Mn and they found a very small negat ive corre-

la t ion which cannot be reconciled wi th the large value of b ~--0.3 repor ted b y the Langer group (33). They concluded tha t i t is quite unl ikely t ha t a large

b/W t e rm for the shape factor of the allowed transi t ion could be caused b y

higher-order effects unless this phenomenon is accompanied b y a large ani- sot ropy in the b e t a - g a m m a angular correlation. F rom the observed small anisotropy, FISCHBECK et al. (32 deduced the magni tude of the coefficient a

to be very small. BHALLA (34,3~) a t t e m p t e d to explain the results of LAiNGEt¢ et al. (23) for 1~dIn by considering interference f rom second-forbidden m a t r i x

elements to the Gamow-Teller ma t r ix element but anomalously large values of the second-forbidden ma t r ix elements had to be adopted. I t is interest ing to note in this connection t ha t I~ICHOLS (14), ANDtCE (~2) and DANIEL (s.12)

repor t negligible deviations f rom the allowed shape for =L 144In.

I f the higher-order contr ibut ion is appreciable, then deviations of electron longitudinal polar izat ion f rom (-- v/c) must correspond to definite deviations of be ta spec t rum f rom stat is t ical shape (36). BUHRING (37) and also EMAN et al. (3s) showed tha t the be ta polarizat ion need not deviate f rom uni ty even if a shape

factor ( 1 - - a W ) enters the spectral distribution. This is, however, not t rue for a shape factor (1 + b/W). I n this case, the be ta polarizat ion mus t also be affected by a factor ( 1 - b/W). I n view of the fact t ha t the measured

(2s) L. M. LANGE~, E. H. SPEJEWESKI and D. E. WORTMAN: Phys. Rev., 133, B 1145 (1964). (29) L. M. LANGER, E. H. ~PEJEWEJKI and D. E. WO~TMAN: Phys. Bey., 135, B 581 (1964). (30) J. I. RHODE and 0. E. JOHNSON: Phys. Rev., 131, 1227 (1963). (31) W. H. BRANTLY, W. B. NEWEOLT and J. H. HAMILTON: Bull. Am. Phys. Soc., 9, 348 (1964). (32) ILl. J . FISCHBECK: Phys. Rev., 145, 907 (1966). (33) D. A. HowE, L. M. LANGER, E. H. SPEJEWESKI and D. A. WORTMAN: Phys. Rev., 128, 2748 (1962). (st) C. P. BHALLA: Phys. Rev., 129, 2130 (1963). (35) C. P. BHALLA: Nucl. Phys., 67, 353 (1965). (ae) W. BUHRING: Nucl. Phys., 40, 472 (1963). (37) G. SCHATZ, H. REBEL and W. BUHRING: Zeits. Phys., 177, 495 (1964). (ss) B. EMAN and D. TADIC: Glas. Mat. Fiz. i. Astr., l , 2 (1961).

SMALL-ORDER DEVIATIONS OF 90y AND 32p 665

be ta longitudinal polar izat ion for a2p (39) and 90y (4o) is uni ty , a shape factor

of the form (1 ÷ b/W) with large b-values as repor ted b y LAI~GER and co- workers should be in error.

The large b/W fo rm repor ted b y LARGER and co-workers m a y arise f rom the inherent distort ing p rope r ty of the inhomogeneous spect rometer used by

them. This should evident ly be the reason, because two other groups (30.a~)

using the same ins t rument obta in the same anomaly, whereas lens spect rometer da ta do not support such large hyperbol ic energy dependence. The distort ing propert ies of the f la t - type spect rometers have been discussed elsewhere (4~).

2. - Experimental procedure.

The dependence of the decay electron energy distr ibution on the beta moments occurs only in a t e rm called (~ the shape factor ~) and it is the careful

measurement and analysis of this (( shape factor )) which m a y yield informa-

tion about the be ta moments as well as the nuclear spin and pa r i ty changes

tha t have t aken place during the transit ion. The be ta moments p lay only a

pe r tu rba t ion role in the de terminat ion of the electron distr ibution and the sub- tleties of the be ta shape m a y often be lost of sight, since the exper imenta l shape is ex t remely sensitive to distortions in the data. I n an a t t e m p t to arrive a t the genuine spectral shape, the following causes which are main ly responsible for shape distortion have been analysed by the authors:

1) Source and foil thickness effects (4I).

2) I n s t r u m e n t a l distortion. I t has been proved by the authors (4_~) tha t , of all ins t ruments , the Slat is-Siegbatm spect rometer has m in imum distortion. A Slatis-Siegbahn spect rometer equipped with well- type plast ic is used in the

present work. Addit ion of a scint i l lator enables discrimination between electrons of selected m o m e n t u m and scat tered electrons.

3) Detector problems (,2.43); efficiency and backscat ter ing. Most lens spectrometers employ flat an thracene or plast ic phosphors. A well- type detector is not in vogue, because of the oblique incidence of be ta- rays and

spherical aberra t ion of the image in a lens. Even in a spect rometer of fixed

trajectories energy-dependent t ransmission will result, if the detector orifice

(30) H. W~NNINGJdR, J. STIEWI~;, H. MUUSZ and It. LEUTZ: Nucl. -Phys., 96 A, 177 (1967). (40) Nuclear Data Sheets, NRC 60-4-34. (41) T. NAGARAJAN: Thesis (1968), Andhra University, Walt~ir. (42) T. NAGARA.IAN, M. RAVINDRANATH and K. VENKATA REDDY: Nucl. Instr. Meth., 67, 77 (1969). (4a) W. NAGARAJAN, M. RAVINDRANATH and K. VENKATA REDDY: Phys. Rev., 178, 1968 (1969).

6 6 6 T. NAGARAJAN~ M. I~AVINDRANATtt a n d K. VENKATA REDDY

is not of appropriate size. We have used a I~IE102 plastic well of suitable geom- e t ry (4~)whose backscattering und detector noise are negligible compared

to an anthracene or a semiconductor detector. The plastic is coupled to a high-gain photomultiplier, namely 6810A, outside the pole-piece, by a short lucite pipe. For the discrimination levels used in the present work, the backscattering correction amounted to 0.2 ~o at 80 keV and the counting efficiency

to uni ty down to 50 keV.

4) Interpolat ion linear or otherwise of the spectrometer background (4~). The L K B Slatis-Siegbahn spectrometer has the advantage tha t its annular slit can be closed from outside and reproduced at will. This enabled us to determine the source-dependent background at every measurement point. In most reported l i terature, the background spectrum is constructed from the count ra te at zero field and the spectrometer current setting beyond the end point. This procedure is ambiguous, because the source-dependent background

varies with current setting.

5) The sensitive dependence of shape factor on end point. The mode of analysis of the shape factor has been highly controversial. The correctness of the present analysis has been discussed elsewhere (44).

6) We found tha t the scatter of points in the shape factor plot is more than could be warranted by mere counting statistics and is due to the l imited precision of the current-measuring device. In the present work we employ a high-precision Leeds and l~orthrup K- type potent iometer whose l ineari ty has

been carefully checked.

7) The use (43) of different Fermi functions and screening corrections

can lead to different shape coefficients through a slight change in Wo.

8) Assumption of line shapes and approximations involved in the ap-

pl icat ion of resolution correction (~2).

9°Sr-9°Y: The isotope of 9°Sr is a fission product which decays by ~ emission to 9oy. I t s half-life is 28 years. A single beta group of maximum energy 54~keV is associated with its decay. The features of the decay of 9°Sr-9°Y are shown in

Fig. 1. 9°Sr-~°Y is obtained from Bhabha Atomic Research Centre, Trombay, as

carrier-free solution. The sources were vacuum-evaporated on A1 foils of 180 ~g/cm ~. One liquid-deposited source on aluminized mylar foil of 900 ~g/cm ~ was used. Insulin was used to help uniform spreading of the source and to define source area. Measurements were taken roughly in steps of 25 keV. The

background was taken at every measurement point by closing the central baffle.

(44) T. NAGARAJAN and K. V]~NKATA REDI)Y: .~ucl. Inst. Meth., 80, 217 (1970).

8MALL-ORDER DEVIATIONS OF 90"~ AND ~ P 667

t • ~ '5. ~y ~,°,s~ o*

. ~ ~ <o.~ o.o,./o ~.~)~

!~ ~" -"*,~ 8 " ~ o o + "--a, 24 ""o., A) o.., °o,, ........ oO

0 ~ 200 600 1000 1400 1800 2200

E(keV)

Fig. 1. - Fe rmi -Kur i e analysis of the composi te spec t rum of 9°Sr*°Y. A) is the to ta l spec t rum; B) is the par t of the spec t rum due to 9oy l inearized wi th the shape factor ( q e ÷ 9 L 1 / L o ) ( 1 - 0.0086 W); C) is the F - K curve of ~°Sr, resul t ing after the subtract ion of B) from A).

5o D

~%52

56

S4

52

50

48

{g

I _ L ~ _ l 1 ...... A_ ..... I i 1 I~i-x~)

600 I000 1400 1800 2200 EikeV)

Fig. 2. - Small-order devia t ion of the 90y plot corrected for un ique shape. A strong source is used to de te rmine the correct end-point energy from the beh~viour of small-order shape near Wo, when W 0 is va r ied in steps of 2 keV. Source thickness 190 t~g/cm 2. C -- q2 ~_ 9L1/Lo" A ) E o ~ 2280 keV; B) E o -- 2282 keV, a = (--0.0086 ~= 0.001)(~%c2)-1; C) E o = 2284 keV.

~68 T. NAGARAJAN, M. RAVINDRANATH a d d K. VENKATA REDDY

The background-subtracted count rates we reeorreeted for backseattering and

finite resolution. The program F E R M K U R I interpolates the t~bles of BttALLA

und ROSE (4~) and draws the F.K. plot (Fig. 1).

The program B E T A S H A P draws the shape factor plot (hT/PICu(Wo--W)2)

vs. energy for various values of Wo (Fig. 2). The function 9L1/Lo in C~----

= q2+ 9LI/Lo is corrected for screening from the tables of BUHRI~G (4~). I n

Fig. 3 is shown the shape factor of a thin vacuum-evaporated source

(~ 15 9g/em2). The thick source (190 ~g/em 2) of Fig. 2 is presented mainly to

bring out the source thickness effects. The coefficient a obtained by a

weighted least-square fit, namely, - - 0.001 =L 0.003 and - - 0.0086 ± 0.001 are

small when compared to those of LAiNGER and co-workers. Hence source thick-

ness effect cannot account for the disagreement. Table I summarizes the re-

sults of different workers. I t is evident tha t the data with 180 ° inhomogeneous

spectrometers a yield large hyperbolic term for the 9oy shape. Incidental ly the

shape of the ~°Sr beta group is also analysed (Fig. 4) after subtraction of the

linearized 90y beta group (Fig. 1). The shape of the 9°Sr beta group is again

TABLE I . - - Small-order shape ]actor o] 90y due to di]]erent authors.

Authors Instrument E o (keV) a(moc2) -1 b(mo c2)

JOHNSON (23) 180 ° inhomog. 2261± 3 0.2 ~ b ~ 0.3

YUASA (19) double lens 2265! 5 0.025

POHM (47) thin lens interm, image 2275± 10 0 0

NICHOLS (14) interm, image 2271± 2 --0.0047±0.0008

ANDRE (22) interm, image 2268± 2 0.26±0.03

LANGER(29) 180 ° inhomog. 2273=~ 5 0 . 3 < b ~ 0 . 4

DANIEL (12) double lens 2284± 5 --0.0072±0.0032

RIEHS (~1) interm, image 2280± 5 1--(0.0064±0.0016) W+ +(0.048±0.008) W

Present work interm, image 2288i 3 --0.001 ±0.003

(45) C. P. BHALLA and M. E. ROSE: 0RNL 3207 (1962). (46) W. BUHRING: N~tcl. Phys., 61, 110 (1965). (47) A. V. POHM: Ph. D. thesis, Ames, Iowa State University (1954).

SMALL-ORDER DEVIATIONS OF o o y AND 32F 669

l i n e a r a n d is g i v e n b y C(W) = C~{1 - - (0.022 4- 0.001) W} a n d i t s e n d p o i n t is

584 keV. T h e p r e s e n t r e s u l t s of t h e a c c u r a t e d e t e r m i n a t i o n s of e n d p o i n t s a re

i n c o r p o r a t e d i n F ig . 1.

lOZ~

102

IOO

E 98

Y. %

9a

92 600

r 0 I I I I I 1 22100 I O0 1400 1800

E (keY)

Fig. 3. - Small-order shape factor of 9oy obta ined with th in source. Evapora ted source < 15 ~xg/cm% ] = (]~-1 + g2-~)/2; E0 = 2288 keV; a = (-- 0.001 ~= 0.003)(moC2)-~; C = q~ =t= + 9L1/Lo; Ful l curve: weighted least-square /it.

~6

17 I I I I ~ I I I ' 200 280 3 0 La0 520

E(keV)

Fig. 4. - SmMl-order devia t ion of 9°Sr. The 9°St beta group is obta ined from the com- posite 9°Sr-9°Y spectrum, after subt rac t ion of the 9oy corrected with un ique as well as a small-order shape factor (1- -0 .0086 W). Source thickness 190 ~g/em 2. E o = 548keV; a - - ( 0.022 ~ 0.001)(mo c2) 1.

3. - M e a s u r e m e n t o f the 32p spectrum.

3"1. I n t r o d u c t i o n . - The beta spectrum of 3~p has been quite extensively studied. The end-point energy of 1.712 MeV is sufficiently high to permi t accurate measurements over much of the spectrum and the hMf-life of 14.31

days is conveniently long. I t decays by a single beta group to 3~S (decay scheme Fig. 5) wi thout any accompanying gamma-rays. The large log# value of

7.9 led the early workers to classify the spectrum as first- or even second-forbidden. The strongly energy-dependent matr ix elements of second-forbidden transit ion could never be fitted to ~ decay exhibit ing a small shape deviation. Fur thermore , the spin of 3~p has been measured to be one (48). Since

(ds) CT. FEHER, C. S. FULLER and E. A. (~-ERE: Phys. Rev., 11}7, 1462 (1957).

~ 7 0 T. N A G A R A J A N , M. R A V I N D R A N A T t t and K. V E N K A T A R E D D Y

the measured spin of ~2S is zero, the decay cannot be second-forbidden. The decay cannot be even first-forbidden obeying ~-approximation, since such a t ransi t ion would require a change of pa r i t y between the init ial and final s tates

75

60

45

30

15

*°. <24.6 keV (33p beta g#oup)

1ooo/o

"*~ "% * - . - - 7 - - °+

i • i L i • i L J_ 300 600 900 1200 1500

E(keV)

60

45

30

15

Fig. 5. - Fermi-Km'ie plot of 3~p for optimum positions of entrance baffle and source. A) Uncorrected Fermi-Kurie plot; B) corrected with C ( W ) = # I1 - - 0.006 W]. Vacuum- evaporated source (< 15~g/cm2); source backing 180~g/cm 2 A1; source diameter 2 m m ; x = 2 0 0 m m ; y = 7 m m ; annular-slit width 3ram.

of the nucleus. The nuclear shell model predicts posi t ive pari t ies for both of these states and the measured pari t ies have always confirmed the predic- tions of the shell model in this mass region. This leads to the conclusion

tha t the decay is allowed in spite of its high I t value.

Even though the spec t rum is a very convenient one to work with experi-

men ta l ly and several studies have been carried out wi th high statistical preci-

sion, there still remains wide dispar i ty among the exper imenta l results. T h e

most thoroughgoing works seem to be t ha t of the Argonne group (13) as well

as the extensive measurements b y the Ames group (47) and the superior statis-

t ical analysis of the la t te r by HENTON and CARLSON (49). Both the groups

detected a definite deviat ion f rom statist ical shape with a l inear shape factor decreasing b y about three percent over the energy range measured. In ad-

di t ion ttENTON and CARLSOS (~") confirmed tha t the in termedia te- image da ta

are more sensitive to the curvature of the shape factor than the thin-lens spee-

(49) G. ]3. HENTON and B. C. CARLSON: U.S. AEC Report ISC-1006 (1957).

8MALL-ORDER DEVIATIONS OF ~oy AND a2F 671

t rometer . Some authors repor t s tr ict ly stat ist ical shape (50,51) whereas m a n y

authors (5,~5,~3) repor t l inear and hyperbol ic shape factors decreasing by 4 to 8 %

in the in terval (250 -1600 )keV. The s i tuat ion is made more complex b y LEItMA~ (5~) repor t ing a discontinuous shape for 3~p.

In most of the earlier methods a imed at determining the extent of the Fierz interference, the authors fitted the higher-energy points to a s t ra ight

line and then examined the deviations f rom this line in the lower-energy pa r t of the spectrum. Some authors fit the F .K. plot of the entire spec t rum by

least squ~res in order to obta in the end point . For ~ t ransi t ion character ized

b y negat ive slope for the shape f~ctor, this method will yield a lower value

for the end point. The me thod employed in the present work el iminates the

above anomalies. The 4~-semiconductor a r rangement of PERSSObT and REYNOLDS (5o) who

repor t a stat ist ical shape for 3~p is not superior to tha t of SPEJEWSKI (~3). Bu t the precision tha t can be obta ined with the a r rangement of SPEJEWSKI is tOO lOW (41). In Persson and Reynolds ' a r rangemen L the two detectors were sepa-

ra ted b y a finite distance and the spec t rum corresponding to zero separat ion was obtained by extrapolat ion. In addition, the slope of the shape factor to- wards the end point varies wi th different depths corresponding to the different

detector biases. Since the end point was to be determined f rom the high-energy

port ion of the spectrum, such a dependence of shape factor on sensitive depths

is a handicap. The energy dependence of detector efficiency par t icular ly a t

low energies should be given careful consideration when the detectors are separa ted by a finite distance.

3"2. Experimental procedure. - The 32p source is obta ined f rom Bhabha A- tomic Research Centre, Trombay. Volatilized sources on 180 ~g/cm 2 A1 backing had very small thicknesses ( ~ 15 ~g/cm2). Sources were also prepared by slow evapora t ion in va cuum of a drop of ortho-phosphoric acid in dilute HC1 on thin conducting foils of mylar . Insul in was used to define the source area and help

uni form spreading. The various consignments of sources contained roughly 2 °/o of 33p con taminant which has a half-life of 25d and decays with a single

be ta group of end point 246 keV.

The measurement procedure is the same as before. The analysis also in-

cludes half-life correction. Runs 1 and 2 were t aken respect ively with a very

strong source (180 ~g/cm 2 on m y l a r foil of 900 ~g/cm 2) and a thin vacuum-

evapora ted source ( ~ 15 ~g/cm2). In runs 1 and 2, the entrance baffle was

kep t a t op t im um position. The shupe fuctor plots were drawn by changing the

(so} B. PERSSON and J. REYNOLDS: Nucl. Phys., 66, 439 (1965). (51) M. J. CANTY, W. F. DAVIDSON ~nd R. D. CONNOR: Nucl. Phys., 85, 317 (1966). (52) j . LEHMAN: ~ucl. Phys., 68, 141 (1965). {53) E° H. SPEJEWSKI: Nucl. Phys., 82, 481 (1966).

6 7 2 T . N A G A R A J A N , M . R A V I N D R A N A _ T I t and K . V E N K A T A R E D D Y

e n d p o i n t s in s t eps of 2 k e V (Fig. 6). F o r e i t h e r a too low or h igh v a l u e of Wo, t h e p o i n t s n e a r Wo curve up or down. The cor rec t e n d p o i n t is d e t e r m i n e d

in th i s w a y for each run . The shape f ac to r of r u n 1 was w e i g h t e d l e a s t - s q u a r e

f i t t e d w i t h b o t h l i n e a r a n d h y p e r b o l i c t e r m s , n a m e l y C(W)= k(1 ÷ aW) a n d

C(W) = k(1 ~ - b / W ) (Fig . 7). I t is seen t h a t t h e curve for w h i c h C(W)=- - - - - 1 - - 0 . 0 1 5 W is c l ea r ly ou t s ide t h e r a n g e of e x p e r i m e n t a l po in t s .

The fit of r u n 2 w i t h d i f ferent f o rm fac to rs (shown in F ig . 7) y i e l d e d

C(W) = 1 - - (0.023 ± 0.001) W a n d C(W) = 1 ~- (0.23 ~= 0.005)/W. R u n s 3 a n d 4

a r e t a k e n w i t h t h e e n t r a n c e baff le 2 m m f rom t h e o p t i m u m p o s i t i o n n e a r e r

5°I ~c) 4.9

/,8

z+7

26

25

39

38

3"7

36

35

I

400

B)

F A )

!

c)

3)

~ ~ ~ + , . A)

4)

I I J I I I I I 700 1000 1300 1600

E(keV)

Fig. 6. - Shape factor of 32p. For each run the end-point energy is determined as shown in the Figure. a = ( - - 0.024 ± 0.001)(moC2) -1. A) E o = 1716 keV; B) E o = 1718 keV; C) E o = 1720 keV.

S M A L L - O R D E R D E V I A T I O N S O7c " 9 o y A N D ~2]~ 6 7 3

a n d a w a y f rom t h e source. I t is e v i d e n t f rom F ig . 6 t h a t t h e shape f ac to r

cu rves a re d i s to r t ed . I n c i d e n t a l l y r u n 3 s i m u l a t e s t h e d o u b l e s lope r e p o r t e d

b y LEHMAN (52) where~s r u n 4 is i d e n t i c a l w i t h t h e h y p e r b o l i c shape f ac to r

48..~~ ~

48 i ~so ~

42 )

I [ I i I I I ~ 400 700 1000 1300 1600

E (keY)

Fig. 7. - Shape factor plot of 32p under different baffle conditions. Run 1: Vacuum- evaporated source (< 15 ~g/cm 2) with entrance baffle at opt imum position. Runs 2, 3 and 4 are taken with a strong source with baffle at opt imum position and at 2 mm from the optimM position nearer and away from the source respectively. The various continuous lines are identified by their coefficients which are obtained by a weighted least-square fit of the data. The end-point energy also changes with baffle position, thereby indicating the change of calibration constant. 1) E o = 1714keV, A ) a = =--0.015(moce) -1, B) b:(O.O33~O.OO1)(moc2), C) a = (--0.006±0.005)(moc2)-t 2) E o = 1718keV, A) b=(O.23=hO.OOS)(moC2), B) a = - - 0.023 =k 0.001. 3) E o = 1 7 1 2 k e V , A) b=(0.24~=0.003)(~oC~), B) a = - - .009 ~ 0.001; C) a=( - -0 .001 ±0.001)(moc2)-< 4) Eo=1720keV, A) b=(0.18±0.002)(moc2).

r e p o r t e d b y JOHNSOn" et al. (23). These effects a r e r e l a t e d to t h e fac t t h a t a t

w r o n g baff le p o s i t i o n s e l ec t rons h a v i n g too ]ow or l a rge emis s ion ang les a re

a d m i t t e d a n d as such t h e r e sponse f u n c t i o n of t h e s p e c t r o m e t e r d e v i a t e s f r o m

s y m m e t r i c a l f o rm a n d also t h e c a l i b r a t i o n c o n s t a n t changes .

43 - I I Nuovo Cimento A .

67~ T. NAGARAJAN, M. I~AVINDRANATH and K. VENKATA REDDY

T h e a c c u r a t e end p o i n t o b t a i n e d in th i s w o r k co r r e sponds to r u n 1, viz.

(1714 ± 3) keV. The e n d p o i n t o b t a i n e d in r u n 2 is h ighe r b y 4 keV. The source

u sed in r u n 2 was s l i g h t l y b r o a d e r t h a n those u sed in c a l i b r a t i o n runs . I n a l l

o t h e r m e a s u r e m e n t s p e r f o r m e d in th i s work , a source d i a m e t e r of 2 m m was

s t r i c t l y a d h e r e d to. The s h a p e - c o r r e c t e d F . K . p l o t of r u n i is shown in F ig . 5.

3"3. Results and discussion. - T h e r e c e n t abso lu t e m e a s u r e m e n t of po la r i z -

a t i o n b y seve ra l au tho r s (39.s~.ss) i n d i c a t e t h a t t h e p o l a r i z a t i o n of 32p fol lows

(-- v/c). WENIiNGER et al. (39) d e d u c e d a n u p p e r l i m i t for b in t h e expres -

TABLE I I . - Shape /actor results o/ various authors on 32p.

Authors Ins t rument E o (keV) a b

POHM (4~)(*) interm, image 1714.4±0.5 --0 .0035±0.0017 1713.4±0.5 0.033:~0.01

POHM (47)(*) tMn lens 1 7 1 3 . 7 i l --0.0039~-0.0028 1713.5±0.9 0.02810.018

PORTER (1~) double lens 1711 0.05 < b < 0.093

DANIEL (~) double lens 1705 =L4 --0.041 =t=0.013

GRAHAM (5~) double lens - - 0.02

JOHNSON(2a) 180 ° inhomog. 1711 ± 3 0.2 < b < 0 . 4

(*) The data of these authors as analysed by HENTON and CARl.SON (~9) are quoted here.

(54) A. R. BROSI, A. I. GALONSKY, B. H. KETELLE and H. B. WILLARD: Nuel. Phys., 33, 353 (1962). (ss) j . D. ULLMAN, H. FRAVNFELDER, H. J. Ln'KIN and A. RossI : Phys. Rev., 122, 536 (1961). (s6) R. L. GRAHAM, J. S. GEIGER and T. A. ]~ASTWOOD: Can. Journ. Phys., 36, 1084 (1958).

SMALL-ORDER DEVIATIONS OF 9oy AND 32p

TABLE II (continued).

675

BRABEC (5~) i n t e r m , i m a g e 1 ±0.35 W+4.9 /W

NICHOLS (14) interm, image 1707.6±0.9 --0.0133±0.0011

DEPOMMIER (15) interm, image 1706 --0.03

CHING-CHENG (58) double focus (0.025± ±0.007) w+o.12/w or 1+0.195/W

SHARMA (59) interm, image 1700 --0.025

QuivY (~o) double lens

PERSSON (50) semi 4z - - 0 . 0 1 ~ a ~ 0 . 0 1

LEHMAN (52) interm, image 1706 ~ 5 a ~ - - 0.09 (300 to 600keV) a = --0.01 (600 to 1650 keV)

CANTY (51) interm, image 1697 -L2 0

Present work interm, image 1714 ± 3 --0 .006±0.005

(57) V. ~BRABEC and M. YINDUSKA: Czech. Journ. Phys., 10 B, 614 (1960). (ss) CHING-CHENt;-JvI and L. S. NovIKov: Soy. Phys. (JETP), 15, 252 (1962). (59) R. P. SIIAnMA, S. H. DEVARE and B. SARA~: Phys. Rev., 125, 2071 (1962). (60) R. QuIvY: Cong. Inst. de Phys. Nucl. Paris (1964).

676 T. NAGARAJAN, M. RAVIN'DRANATH a n d K. ¥ E N K A T A R E D D Y

sion for - - P/(v /c) -~ 1 ~- b / W as b = (0.8 ± 2.5)10 ~mo c2. This l imit is lower than tha t obtained in the fit of da ta of run 1, which gives b -- 0.033 ~ 0.01. I t is no tewor thy tha t even though higher-order contributions are expected to be present for ~2p, the hyperbolic l imit obtained in the present work is an order of magni tude smaller than the limit obtained by MAH~IOUD and Ko~oPINS~r (GI), who analysed a number of faster and super-allowed transitions. The results of various authors are summarised in Tuble II . I t is remarkable tha t the present results are in good agreement with those of PoH~t et al. (4~) and these exclude all other results. The statistical shape obtained by CATTY et al. (5~)

is due to the low end-point energy (1697 keV) adopted by them and this value of end point disagrees with these of all other workers.

I t can be concluded from the above analysis tha t the shape of 32p deviates f rom statistical shape by about 2 ~o in the investigated energy range. For such small-order deviations, the statistical precision of the present work is not good enough to distinguish between 1 - - a W and 1 ~- b / W forms. Pohm's results give Z 2 = 33 for linear fit and ; / ~ 39 for hyperbolic fit. Thus a linear shape factor C( W) ~-- k ( 1 - - 0 .01W) will be consistent with the present result as well as those of the Argonne (is) group and the Ames (49) group.

Despite the small deviation from statistical shape and the large log It value, the polarization - - P/(v/c) is practically uni ty. The initial- and final-state configurations of this transit ion are [(us½)l(vd~)']j_~ and [(ns½)~]j:o. Thus the beta t ransi t ion involves a change of the dt neutron into a s½ proton, thus making closed-shell configuration. The G.T. matr ix element f a cunnot connect two states involving a change of two units of orbital angular momentum. Only a tensor of second rank can connect such states and as such second-forbidden mat r ix elements would be expected to occur. The shape and log/t value however indicate tha t f a must also contr ibute to this transition. This situation m ay arise when there are contributions from other nucleon configurations for which the mat r ix element ~ is not forbidden. Near a closed subshell configura- t ion such as 32S, the amount of configuration mixing should be generally smull. The large log It value of this transit ion also indicates tha t any mixing from permissible configuration should be small, in which c~se f a is appreciably smaller than for allowed decay~ while the second-forbidden matr ix elements are of normal size. An interference between (~ and second-forbidden matr ix elements can give a shape factor having a linear deviation. This possibility has been investigated by HE~TO~ and CARLSO~ (~9) and BUHRI~G (62). According to BUgRI~G, the spectrum shape and polarization are given by

,~/Lo = 1 + al W ÷ b _ l / W ,

- - P / ( v / c ) -~ 1 + bo + b _ l l W .

(61) H. M. MAItMOUD and E. H. KONOPINSKI: Phys. Rev., 88, 1266 (1952). (6~) W. BUHRI~G: Zeits. Phys., 177, 495 (1964).

S M A L L - O R D E R D E V I A T I O N S OF 9 o y A N D 32p 677

is a funct ion of f ( a . r ) r , al is a funct ion of ( ( a ' r ) r and ( o r × r , whereas bo is a funct ion of three ma t r ix elements f ( a ' r ) r , (o t×r and ~iTsr. As the b_l

contr ibut ion f rom the relat ivist ic ma t r ix elements is small. BuImI~G is able to show tha t bo ~nd b-1 are very small. I n such a case, polar izat ion will not show noticeable deviat ion f rom uni ty. HENTON and CAI~LSON have calculated the value of a, based on infinite-square-well wave function. They obtain

the value a~ ~ - - 0 . 0 4 which is large compared to the experimentu] value

a I ~ - - 0 . 0 1 .

l~ecent work (63) on the energy levels of all nuclei be tween 28Si and 40Ca

indicate strong configuration mixing for the ground s ta te of 32p and 32S.

C0VSSEMENT (64) has made an a t t e m p t to explain the high log it and spec-

t r u m shape purely on the basis of configuration mixing and cancellation effect in the allowed mat r ix element, wi thout the help of l-forbiddeness. This s i tuat ion also looks quite probublc, since the s½ and d~ orbitals are avai lable

for bo th the init ial and final s tates of the t ransforming nucleon and the con-

t r ibut ion of ma t r ix elements (s½ II ~'I0(O')J[8+} and (d] iJ T~o(a)iJ d~} are of opposite signs for the transi t ions generally classified as /-forbidden. I n the above t reat - men t COUSSEMENT (64) has fi t ted only the double slope repor ted by LEHMAN (52)

and he has not t r ied a fit with the simple l inear deviat ion and longitudinal polar izat ion data. I t also follows f rom the t r ea tmen t of COUSSEMENT (64) tha t

the ma t r ix elements which can be neglected on the basis of /-forbiddenness cannot be considered so when cancellation effect is impor tan t . There have been other (~5.~6) theoret ical a t t empt s to explain the large log]t value, but

the s i tuat ion is not well-established as far as the spectral shape and longitudinal polar izat ion of ~2p are concerned.

The authors are grea t ly indebted to Emer i tus Prof. S. JNAI~ANANDA for

his encouragement . One of us (T.SL) is thankful to the D e p a r t m e n t of Atomic Energy for the award of a research fellowship. The services of CDC 3600,

T I F R , Bombay , are acknowledged.

(63) p, W. M. G L A U D E M A N S , G. WIECttERS and P. J. BRUSSARD: Nucl. Phys., 56, 529 (1964). (64) t~. COUSSEMENT: ~7~ucl. Phys., 75, 1 (1966). (65) ]3. L. BIRBRAIR: Phys. Lett., 12, 20 (1964). (66) M. VAKSELJ: Nucl. Phys., 31, 525 (1962).

0 R I A S S U N T O (*)

Si studia la forma del 90y come un completo controllo della risposta dello spettrometro. ll fattore di forma del 9oy misurato, cio~ (q2 + 9L1/Lo ) . { l _ (0.001 ± 0.003) W} indica che lo spettrolnetro 5 privo di ogni effetto distoreente entro 0.3% per mo c~. Cib con-

(*) Traduzione a cura della Redazione.

6 7 8 T. NAGARAJAN, M. RAVINDRAlgATH a n d K. V]~NKATA REDDY

corda mol to bene con la conclus ione r a g g i u n t a con uno s tudio d i r e t t o degli effet t i s t ru - ment~l i . I g r a n d i t e r m i n i iperbol ie i r i p o r t a t i pe r il 90y e per poch i a l t r i spe t t r i pe rmess i e p r i m i unic i sono c~ra t t e r i s t i c i dei soli s p e t t r o m e t r i a 180 ° in cui le fo rme delle l inee sono mol to as i inmet r i che . Si t r o v a e h e l a dev iaz ione della fo rma pe r il a-'P pe r posizione dell~ b~se o t t im~le ~ piccoI~ ( a = - - O . O 0 6 ± 0.005) m~ lgmdo il suo g r~nde va lore di log It. U n pos i z ionamen to seor re t to del la base di e n t r a t a ebbe come r i su l t~ to u n a g r a n d e dev iaz ione iperbo l ica ed u n a f o r m a con doppie pendenze . Queste anomal i e somig l i avano ad ~lcuni r i su l t a t i r i p o r t a t i in ~l t r i ar t ieol i . I due approec i p r eva l en t i , cio5 la p ro ib iz ione di 1 e l ' e f fe t to di canee l laz ione negli e l emen t i di ma t r i c e permessi , p e r spiegare il g r a n d e va lore di log ft, la pieeola dev iaz ione dal la f o r m a l iueare e la po la r izzaz ione long i tud ina l e di ( p/W) sono efficaci solo q u a l i t a t i v a m e n t e .

OTKJIOHeHI451 MaJIOFO nopl[~ga ~IAS 9oy n 32p.

Pe3IoMe (*). - - I4ccne)lyeTcn qbopna 90y, KaK n r o r o a a f l npoBep~a qyBCTBnTe~bttOCTH crIeKrpoMerpa. I/IaMepertHb~ qbOpM-~aaKTop ~0y, paaab t~ (q~" ,L91q/bo)(1--(O.O01± ±0 .003)W}, yKa3blaaeT, qTO cne~TpOMeTp cao60~len OT raKnx-HH6O nc~a~amt t tnx )leqbeK- TOB B npezlenax 0 .3% Ha mo e2. ~XO oqeHb xopoIllO cor~acyexc~ c pe3yJ~bTaTaMn, nony- tIeHHbIMH B pe3yHbTaTe HelIOCpe~CTBeHHOFO llCCJle)IOBaHllIt NHCTpyMeHTaJ1bHbIX 3~)qbeKTOB.

~OYlblIII4e rHrlepSoJarlqecrrle qHeHbI, IIOJlyqeHHbIe )2~lfl 90y, H HecKOYlbKO )Ipyrrlx p a 3 p e m e a -

HblX q.lleHOB I4 rlepBb/e O)2Ho3HaqHble CHeKTpbl flBH~tOTCfl xapaKreprtcTriqecK~tMrt TOfIbKO ~H~t 180°-CrleKTpOMeTpOB, qbOpMbI JIHHI4~ KOTOpbIX oqeHb aCHMMeTpl4qHble, l-[o~iyqaeTcfl, xiTO OTKHOHeHl4e qbOpMb[ zzp ~ylfl OIITHMaYlbHOFO noJao~KeHn~ ~eqbHeKTOpa ~IBYlfleTC~I Mam, IM (a = - - 0 . 0 0 6 ± 0.005), HeCMOTp~ Ha 6osmmyro BenrlqrlHy log ]t. HenpaBruibnoe pacr lono~eHne BXO)XHOFO lleqbHeKTOpa npnBe:Io r 60.rlblIIriM rnnep6oHHqecKnM OTKYlO- HeHl4~lM 14 dpopMe C ~BO~HbIMI4 CKYlOHaM[4. (~)TI, I aHoMamtrI COOTBeTCTBytOT HeKOTOpblM

pe3y.qbTaTaM, HMeIOIJXrIMC~I B HriTepaType. ~ a a pacrlpocTpaHeHHr~lx no)lxo~la, a nMeHHO, /-3aHpelJXeHHOCTb H 3qbqbeKT B3aI4MHOFO yHI4qTOTKeHI4~l B pa3pellIeHHbIX MaTpl4qHblX 3He- MeHTaX, TOJIbKO KaqecTBeHHO O6"bll:lCHfltOT 6OJ1bLtIOe 3HaqeHHe log It, MaHOe HIqHe~Hoe OTI~YlOHeHI4e qbOpMbI n npo,aonbHym n o n n p n a a I m m (--p/W).

(*) Hepeeec)eno peOaKque~.

Documents

Small-order deviations of90Y and32P