Spin of the first excited state of B12

Nuclear Physz~s

1 5 (1960) 254--260 ; (~)

North-Holland Pubhshsng Co, Amsterdam

Not to be reproduced by photopnnt or mtcrohlm without written permission from the pubhsher

S P I N OF T H E F I R S T E X C I T E D S T A T E OF B s2 E

K O N D A I A H and C B A D R I N A T H A h Y

Tara Instztute o/ Fundamental Research, Colaba, Bombay-5 Received 22 O c t o b e r 1959 A n g u l a r d i s t r i b u t i o n of g a m m a r a y s arising from t h e 0 95 MeV level of B ts in the reaction Bii(d, 10)/3it h a s been studied a t a d e u t e r o n e n e r g y of 0 8 MeV. I t h a s been found t h a t t h e g a m m a a n g u l a r d m t r i b u t l o n is deflmtely non-lsotoroplc a n d has a m i n i m u m a t a n angle of 45 ° to t h e incident d e u t e r o n b e a m . This leads to t h e exclusion of 04", 1- a n d 2a s s i g n m e n t s to t h e 0.95 MeV l e v e l m B it l e a v i n g t h e possible a s s i g n m e n t s 2+ or 3 +

Abstract:

1. Introduction The Bn(d, p)B x* reaction is known to lead to the ground state as well as excited states an B 1. 1). The ground state Q-value for this reaction is 1.136 MeV and accordingly, at a deuteron energy of 0.8 MeV, only the ground state and the first excited state of B 12 are reached favourably. Holt and Marsham 2) studied the angular distribution of protons in this reaction using 8 MeV deuterons. The ol~served angular distributions of protons leading to ground and first excited sta~es of B 12 fitted very well with l. = 1 curves based on stripping theory. The ground state of B n is known to be a { - state. Hence, the ground state as well as the first excited state of B 12 should have even parity and a spin of 0, 1, 2 or 3. The ground state of B 12 is known to be a 1+ state. 2. Theoretical g a m m a A n g u l a r D i s t r i b u t i o n s Accorchng to Satchler 8), the angular distribution of a gamma ray observed in coincidence with the outgoing nucleon in a (d, p) or (d, n) reaction can be calculated from

W(O) = ~ B(i)B(I' ) C(L) C(L') ~Tv(Tl'JtJe)a,(LL'JtJe) Pv(cos 0), yJJ"L" L

where 0 is the angle that the gamma ray makes with the recoil axis (see fig. 1), B(1 ) and C(L) are proportional to the (real) reduced matrix elements for the capture of the nucleon and the emission of the gamma ray respectively so that />2(/') is the fraction captured with j, and so on; J t is the spin of the target nucleus, J e the spin of the excited state emitting the gamma ray, Jr the spin of the final state to which the gamma ray is emitted; I is the total angular momentum of the captured nucleon; L as the multipole order of the gamma ray 254

SPIN OF THE FIRST EXCITED STATK OF B lz

9-55

takes values consistent with J l and Je, whereas L takes values consistent with J t and J e . One has to sum over all values of i and L consistent with J l , J e and J r . Values of the reduced matrix elements B(i) and C(L) are not actually known and are taken out as constants which m a y be evaluated b y fitting the theoretical distribution to the experimentally observed distribution in suitable cases. The function P~ (cos O) is the Legendre polynomial of v th order; v takes all even values consistent with I", L and J e with the condition that v =< (1+/'),

(L+L'), or 2Je.

D

B'II

D ~ Deuteron

F i g 1 S c h e m a t i c d i a g r a m o f BlX(d. p ) B x~ r e a c t i o n b e a m , bl = R e c o i l i n g n u c l e u s , P ~ P r o t o n , ~, ~ G a . m m a - r a y

Satchler s) has tabulated values of ~ and ~ for certain values and has given methods of calculating these factors for other values. Using these methods, the gamma angular distribution has been evaluated for the B 11(d, F / ) B 1~ reaction for J ~ 0:~, 1±, 2~ and 3 + for both electric and magnetic multlpole order gamma rays. Table 1 gives these theoretical gamma ray angular distributions. For l~ -~ l, the value Je -- o± gives uniform angular distribution, as Je--- 0 and Po(cos 0) ~ 1. The values J e = 1 - or 2 - also gave uniform angular distribution if one considers only l~ = 0 (that is s-wave neutron capture), as <0+f) le- 0. The value Je = 1+ gives a distribution peaked at 0 = 90 ° (see fig. 3 (n)), as the constants b and/~ in the expression for W(O)happen to be both positive *. For this case, b = y ~ l ( A + 0 112 B+B~/A) and fi = y~ (0.335 B+O.3B~/A), where ~,I~----C(1)C(1), A = BZ({), B = B({)B({) and B~/A = B~({); as all these are positive, the constants b and p are positive If only p-wave (l~ = 1) neutron absorption is considered, Je ~-3+ gives an angular distribution ? T h e s a m e is t r u e f o r J e = 2+ d o n l y M 1 g a m m a s a r e c o n s i d e r e d , i n t h i s ca~e, b = y z l ( A + 0 3 5 and ~ = 1 05 BFI 1

B+BZ/A)

")'~6

E. KOND~kI.~H AND C

BADRINATHAN

W(O) =k(0.8167+0.5499 cos~O), where k-=7~2BS(]), 7s~ standing for C(2)C(2). If this is the case actually holding, one can obtain the value of k and thereby the value of reduced matrix elements by fitting the theoretical angular distribution to the observed distribution. TABLE 1

Theoretmal angular dmtnbutaons of B11+d--p $

~

BlX(d,

p~)B xl reactmn

P

1' = ~ - Q = i 136 Me V 0 95 MeV -~ 0

Je

] I,

0 1+ 1-, 2-

[ 1 2

I1÷ ''2+

I 1.8!

!2+ 3+

I 1

I

]or/'

LorL'

~ 7 Bxs

~

0

consent

t

o

consent

[ ½. ~a

I

O. 2

(b--~cos'O)

I ~' j' j

1

0, 2

(b+/~ cosSO)

1

Jt ~

1÷

W(O)

{

[ ½,~

Je

(b+pcos,O)

1, 2

9, 2

(b+/~ cos'O) t

i 1.3 I ½' ~' ~' ]

1. 2

O. 2. 4

(b+fl cos'O+p cos'O)

[ 1

2

O, 2, 4

k(O 8167+0 6499 cos'O)

[ t

t, |, ~ 2 0, 2, 4 (b+,8 c o s ~ + p cos~0) I " l t For tins case, if pure M1 gammas are consadered we get

W(O) ~ k ' - - l . O S k " c o s ~

k'

and

k " are

where

both posatlve and hence a peak at 0 ~ 90 ° wall be obtained as shown m fig. 3 01).

For the other cases which take into account higher order orbital angular momenta of the captured neutron, the forms of gamma angular distribution are given under W(O)in the last column of table 1. The values of b, fl a n d p occurring in the expressions for W(O)given in the last column of table 1 differ from case to case and they can in general be positive or negative independently. Fig. 3 gives the shapes of gamma angular distributions to be expected in the Bit(d, pT)B 1~ reaction considering only the lowest possible orbital angular momentum of captured neutron consistent with parity. 3. Experiment

and

Results

An isotopically separated B vt target was obtained from A.E.R.E. Harwell. The thickness of the target was 100 pg/cm ~. The gamma detector was a 2" diameter, 2" long NaI (T1) crystal. A 800 keV deuteron beam was obtained from

SPIN

OF

THE

FIRST

EXCITED

OF

STATE

B z2

~7

the 1 MeV cascade accelerator of this Institute. A typical gamma spectrum taken at 0 ° to the incident deuteron beam is given in fig. 2. The 511 keV peak is due to the Cl~(d, n)NZa~ +) reaction; Cz~ contamination arose from the oil diffusion pump of the accelerator The 661 keV peak zs due to a Csla~ gamma source purposely kept for cahbration. The peak at (900±50) keV agrees with the energy of the gamma ray expected from the 0.95 MeV level in B lz due to the BU(d, p)B 1= reaction

(Nt3}

OB,d • T.d

,

l

z

/

661 ~eV (cs )

~

900 ~: 50 key

(e~)

.,.,.,,.,°.-o.,-., .. , . , j ENERGY

°.°,, ~ , , . , . . ~ ° .

I

,

-SPECTRUM

Fig 2 y-spectrum

The BU(d, n)C 1~-reaction which occurs simultaneously with the Bn(d, p)B Iz reaction, m a y also give rise to gamma rays around 900 keV due to neutron interactions with the gamma detector as well as surrounchng materials hke the target tube etc. B lz (d, n)C 1= neutrons are polyergic with a maximum energy up to 13.4 MeV at 800 keV incident deuteron energy. Accordingly, a study of the gamma spectrum was undertaken using a T(d, n) source giving fast neutrons. The T(d, n) source was operated to give the same number of neutrons as the BU(d, n) source using a neutron monitor. This gamma spectrum is also given in fig. 2. It can be seen that there is no peak around 900 keV gamma energy in the T(d, n) case a¢ the same level of neutron intensity as for BU(d, n). The general counting rate in this region of the gamma spectrum zs about 10 to 15 times less m the case of T(d, n) source than in the case of the ( B U + d ) source. Hence,

258

E. K O N D A I A H

AND

C

BADRINATHAN

the peak at 900 keV in fig. 2 can safely be taken as due to the Bn(d, p)B 1. reaction and not to a n y second order effects of neutrons arising from the Bn(d, n)C u reaction. While studying the angular distribution of these gamma rays, the 900 keV

bJ

w(e)

w(e) ~,.o*,,~2-

(b-l~) "1 Je~l + . In~l, o r

In m 0

Je=2+, In== 1, (Mr)

o

0

180

{I) W(e)== CONSTANT

910

e

180

(.)w(e)=(b-.~ cos' 8)

w(e) 6 1 ~=2+. i.ffil oJ o 9'o e 0,,)w(e).(b+J~cos'e)

180

0

Je= S+An= 1 glO

180

e Ov)w((~=k(0.82+055 cos~e)

Fig. 3 Theoretical gamma angular distributions

gamma rays emitted at 0 ° to the deuteron beam were used as momtor, whereas the movable gamma detector was moved around the target as centre. Each of the points in the gamma spectra recorded by the movable detector was calculated for a fixed number of counts in the monitor. Statistical acuracy of each of the points in all the spectra taken at different angles is better than 2 %. The angular aperture of the movable gamma detector was 10 ° at all the angles.

S P I N OF T H E F I R S T E X C I T E D STATE OF B t=

259

Gamma spectra were recorded at 15° intervals in the region 0 ° to 135° with respect to the incident deuteron beam. Observations at each angle were repeated at least twice and intensities of the 900 keV gamma rays at each angle agree within the errors shown in fig. 4 which gives the observed angular distribution.

B tl (d,p ~')B ~

t

z okU Ld

U

Z Ld elf

t~

*~"

o' Fig

4

Experimental

13b,

~o" gamma

angular

distribution

The errors given in fig 4 refer to self consistency of the intensities observed in different runs at each angle. The gamma angular distribution is definitely nonisotropic and has a minimum at an angle of 45 ° to the incident deuteron beam.

4. D i s c u s s i o n The theoretical angular distributions given in table 1 and fig. 3 are for coincidence distributions whereas the observed gamma angular distribution given in fig. 4 is for gamma rays only. Observation of P---9' coincidences fixing the proton detector enables one to locate the axis of recoil and hence the actual position of maxima or minima m the angular distribution. From mere observation of gamma angular distributions in a (d,p) or (d, n) reaction, it is not possible to locate the angular positions of the maxima or minima with respect to the recoil axis since the direction of the captured nucleon is no longer fixed. However, the gamma angular distribution should have the same general shape as the (P--9') coincidence angular distribution irrespective of the angular positions of the maxima and minima Thus, for different values of Je, the general shape of gamma angular distributions should be similar to the ones shown in fig. 3.

~60

E

KONDAIAH

AND

C

B.~DRINATHA.N

As the observed gamma angular distribution is definitely non-uniform (see fig. 4), Are = 0~ as well as J e -~ 1-, 2- (if s-wave neutron absorption only is considered) can be ruled out. As J e -- 1+ (In = 1) should give a peak (see fig. 3 (ii)) and not a trough as seen in fig. 4, it can also be ruled out, on the assumption that only p-wave neutrons take part, which is found to be true even at 8 MeV deuteron energy 2). Thus, the 0.95 MeV level of B is is most probably a 2+ or 3+ state. The (p---~) coincidence angular distribution in this reaction, which m a y throw further hght on the spin of this level, is at present under s t u d y in our laboratory. Messrs M. D. Deshpande and M. S. K a m a t h have given technical assistance during the course of this work. r

References I) F. Ajzenberg and T Laurtmen, Nuclear Physzcs II (1959) 1 2) J R Holt and T. N. Marsham, Proc Phy Soc A 66 (1963) 1032 3) G. R Satchler, Proc Phys Soc. A 66 (1953) 1081