Coriolis-coupling calculation of low-lying states in As isotopes

I

1.D.2 l!

Nuclear Physics A125 (1969) 626--636; (~) North-HollandPublishing Co., Amsterdam N o t to be reproduced by photoprint or microfilm without written permission from the publisher

CORIOLIS-COUPLING

CALCULATION

OF LOW-LYING

STATES

I N As I S O T O P E S N. IMANISHI t, M. SAKISAKA and F. FUKUZAWA Department of Nuclear Engineering, Kyoto University, Japan tt Received 26 November 1968 Abstract: The theoretical level spectra and electrical properties of arsenic isotopes are reported. They are obtained by considering a collective and an intrinsic degree of freedom, where the motion of an unpaired quasi-particle in Nilsson's deformed orbit is coupled by a Coriolis force with the rotational motion. The level energies are expressed by two parameters ~7and ~2/2J, the deformation parameter and the moment of inertia, respectively. For 7~As, a least-squares fitting procedure has been carried out and a satisfactory agreement obtained between the calculated and experimental spectra for odd-parity levels below 1 MeV excitation energy. Most B(E2) values calculated without introducing any effective charge agree with experimental data to within a factor of two. For 77As and 7SAs, tentative theoretical level schemes are presented. 1. Introduction M a n y e x p e r i m e n t a l d a t a 1) have been recently a c c u m u l a t e d on the p r o p e r t i e s o f excited states in nuclei with 32 < Z < 36. But m o d e l calculations o f level p o s i t i o n s a n d other p r o p e r t i e s for these isotopes have been m a d e b y only a few groups, e.g., b y Kisslinger a n d Sorensen 2), Scholz a n d M a l i k a), Kisslinger a n d K u m a r 4). The recent e x p e r i m e n t a l evidence 1) suggests t h a t the nuclei with 32 < Z < 36 are c o n s i d e r a b l y d e f o r m e d , t h o u g h they d o n o t show as clear r o t a t i o n a l spectra as d o nuclei s) in the n e i g h b o u r h o o d o f A = 24, in the regions o f A = 150-190 a n d A > 220. The a i m o f this r e p o r t is to describe the level spectra a n d the electrical p r o p e r t i e s o f the arsenic isotopes b y considering a collective a n d an intrinsic degree o f freedom, where the m o t i o n o f an u n p a i r e d quasi-particle m o v i n g in N i l s s o n ' s d e f o r m e d o r b i t 6) is c o u p l e d b y a Coriolis force 7) with the r o t a t i o n a l m o t i o n . The p a i r i n g correlation, which is also considered in this p a p e r , reduces the strength o f Coriolis coupling a n d compresses the low-energy intrinsic s p e c t r u m o f the i n d e p e n d e n t single-particle picture. 2. The model W e assume that the nucleus As is axially s y m m e t r i c a n d has a reflection s y m m e t r y with respect to a plane p e r p e n d i c u l a r to the s y m m e t r y axis. W e c a r r y o u t the calculation within the f r a m e - w o r k o f a simple n o n - a d i a b a t i c m o d e l , where the m o t i o n o f an t Present address: Institute of Engineering Research, Kyoto University, Japan. tt Work supported in part by the 1967 Scientific Expenditure of the Ministry of Education. 626

627

COLLECTIVE REPRESENTATION

unpaired quasi-particle m o v i n g in Nilsson's deformed orbit is coupled by the Coriolis force with the rotational motion. The zeroth order H a m i l t o n i a n for the system is then, hz Ho = - - i 2 + E E,(a+a,+fl+fl~), 2J

(1)

and the corresponding wave function is

[21+ 1'~~,-~ , IIMKv> = ~ 1 ~ - 2 ) [~MKIq = 1, v > + ( - 1 ) ' + K D ~ _ r I q

= 1, ~>].

(2)

Here I is the total angular m o m e n t u m q u a n t u m number, J the m o m e n t of inertia, Ev the excitation energy associated with quasi-particles ct+ and fl+. The abbreviation v means q u a n t u m numbers which characterize the intrinsic state. The D~tK are the usual rotational wave functions which are characterized by the q u a n t u m numbers 1, M and K, that is, the total angular m o m e n t u m , its projection on the space-fixed axis and its projection on the nuclear s y m m e t r y axis, respectively. The functions Iq = 1, v> and Iq = 1, ~> which represent the ground and the low-lying intrinsic excited states, are described by the equations Iq = 1, v> = "~+lq = 0>,

Iq = 1, f ) = fl~lq = 0),

(3)

where the function Iq = 0) is the well k n o w n BCS wave function s), and the notations q = 1 and q = 0 are used to denote the one quasi-particle state and the v a c u u m with respect to quasi-particles, respectively. The above two functions Iq = 1, v) and [q = 1, ~) c o m p o s e a conjugate pair and correspond to the single-particle Nilsson state rv) and 1~7), respectively. W i t h o u t the Coriolis coupling, the c o m p o n e n t f2 of the angular m o m e n t u m j of the unpaired particle on the nuclear s y m m e t r y axis, is a good q u a n t u m number. Therefore, we denote explicitly the intrinsic Nilsson states Iv) and I~) as

Iv> ~-1~2~>,

I~> ~ I-t2~>,

(4)

and represent corresponding quasi-particle states as ]q = 1, v) - ]q = 1, f2~), Iq = 1, ~) - [ q

= 1,-a~

).

(5)

Here the extra index ~ is introduced to distinguish between different intrinsic Nilsson states with the same O. Considering I2 = K, we also rewrite the wave function in eq. (2) as

[IMKv) =_ [IMK£2~) - - [ I M K ~ ) . The quasi-particle excitation energy Ev in eq. (1) is connected with the single-particle

N. |MANISHI et al.

628

Nilsson energy e~ by 8) (6)

Ev =

The two parameters 2 and A are the chemical potential and the gap parameter, respectively, and they must be obtained by solving the following two equations:

A = G Y, U~ Vv,

(7)

v

n = 2 • V2.

(8)

v

Here G is the strength parameter for the pairing force and n the true particle number in the system. As is well known, the meaning of V, and Uv is that V2 is the probability of the pair (v, 9) being found in the ground state, while U~ is the probability for nonoccupancy. Due to blocking 9), the 2 and A values for excited states differ from those for the ground state and consequently U~ and V~ need to be adjusted. In the present work, however, we calculate the values 2, A only for the ground state and use them for all the excited states considered, because in the region in which we calculate, the corrections arising from blocking are generally small and affect only slightly the final energy spectra. In addition to Ho, we now consider the Coriolis interaction of the form, ~2

H' -

I .j.

(9)

J This Coriolis term mixes rotational bands of IAKI = 1, and this effect would be of major importance for the present case because the levels with the same spin belonging to different quasi-particle states are located very close together. The Hamiltonian for the system is then H = Ho+H'.

(I0)

The diagonal element of the Hamiltonian (10) is expressed as h2 [I(I + 1 ) - 2K 2 + 6K~a ( - 1)t+ ½(I + ½)], (H)dla = Ev+ 3 ~

(11)

where the decoupling parameter a is given by a = - ~ ( - 1)s+~(j+½)lcs~l z,

(12)

J

in the jr2 representation of Nilsson wave functions 6). Off-diagonal elements of H between the states of different rotational bands with IAK[ = 1 (which do not vanish)

COLLECTIVE REPRESENTATION

629

are given by

(IMK± I~'[HJlMK~) = (IMK~[H]IMK+_ ~') --

h2 (UK±~e,UKe+Vr+.le,Vre)(O+I~'Ij±IO~)[(I+K+I)(I-T-K)] ½,

(13)

2~

where the matrix element for the particle state is evaluated as fellows: = ~

cjo±tcj~(-1)'-~[(j--TY2)(j+_Q+I)] ~.

(14)

Thus, the quasi-particle formalism leads to a reduction of the off-diagonal elements of H and a compression of the low-energy spectrum of the independent single-particle picture. When the Coriolis interaction included in the Hamiltonian (10) is treated as a perturbation, we may expand the total wave function as

[IM>= \1-~x2][2I+ 1~~ K ~

~

Cre[Dmr[ q t,

= 1, 12¢> + ( - - 1)'+KD~_~Iq = 1, --f2¢>],

(15)

where the mixing amplitudes C~e are determined by the Jacobi diagonalization procedure. Finally, we carry out a least-squares fitting to the experimental energy spectrum and obtain the total wave functions as well as the theoretical energy spectrum. 3. Modification of Nilsson level energy and wave function

The Nilsson Hamiltonian has fcur parameters O5o, to, p and q. Among them, a reasonable value for &0 has been obtained by taking the root mean square radius for all the nucleons to be equal to ~/~. 1.20 A ~- fro, which gives ha50 ~ 41 A -¢ MeV for all nuclei 6). The two parameters t¢ and p are fixed so as to reproduce the singleparticle level spectra of spherical nuclei and explain odd particle spectra, the moments of inertia and the ground state equilibrium deformations for deformed nuclei. These two parameters tc and /~ have been reasonably fixed 5) for the shell with N > 3, while fcr N = 3, there remains some arbitrariness in their choice. For As isotopes, the unpaired proton or hole is situated mainly in the no. 16, no. 19 or no. 20 Nilsson orbit. Therefore, it is necessary to determine accurately the level energy and the wave functions for the N = 3 shell. We determine them for the N = 3 shell in the present investigation by referring to the single particle level spectrum of 57Ni, a spherical nucleus composed of doubly magic core plus one neutron. Fig. 1 summarizes the 5VNi excitation energies determined in several experimental studies of the reactions 56Ni(p, d) and 58Ni(d, t). Cohen et al. ~o) have interpreted the ground, 0.78 and 1.08 MeV states of 57Ni as 2p~, lf~ and 2p½ single particle states, respectively and the level at 2.6 MeV as a lf~

N. IMANISHI et al.

630

single hole state. From these observed level positions, we determine t¢ and # as 0.0339 and 0.284, respectively. These values also account well for the observed energy spacing between 2p} and lf~ levels in 41Ca and 41Sc, whose energy spectra are shown in fig. 1.

4.9

2.6 Mev

7/2-1.947 M e v

Y2-- MeV J86 . . . .

3/2--

4.e

~ ~ & ~

4.'/'

\

ORBITAL NO..,fin 26 [ / 2 /155/2-

\

>_ 4 6

o

_..._/_....~>~------

n.

~

w

/

~'2~-~

L6 3 / 2 -'-'-----.---20I/2 --

4.5 1.08 0.78

l/2-5/2-

4.4 "- 17 1 / 2 -

"0

,st

3/2Ni

41

Sc

7/2-'

41o C

7/2--

Fig. 1. Observed low-lying states in 57Ni, ~lSc and 4~Ca.

I -6

-4

I

I

-2 0 2 4 DEFORMATION r[

I

I

1

6

Fig. 2. Modified Nilsson diagram calculated for # = 0.284 and x = 0.0339.

A part of the Nilsson diagram which corresponds to the present choice of ~: a n d / t is shown in fig. 2 as a function of deformation q. The determination of t/will be discussed in sect. 5. 4. D e t e r m i n a t i o n o f c h e m i c a l p o t e n t i a l and gap p a r a m e t e r

Kisslinger and Sorensen 1t) have predicted the odd-even mass difference for the single closed-shell nuclei and obtained a good agreement with the experimental data. Referring to their results, we take the strength parameter for the pairing force to be G = 19 MeV/A for arsenic isotopes. Inserting this value and the true particle number into eqs. (7) and (8), we obtain the parameters 2 and A. In this calculation, we sum thirty consecutive Nilsson states for the protons. Fig. 3 gives the determined values of 2 and A as a function of t/. 5. L e v e l e n e r g y and w a v e f u n c t i o n

The present model spectra are obtained by diagonalizing the Coriolis interaction with the rotational wave functions built on three intrinsic states. These states are attributed to the motion of single "quasi-proton" in no. 16, no. 19 and no. 20 orbits. In these calculations, we omit the neutron states because all neutrons form pairs in the ground state of arsenic isotopes and their excitation energies are so high that they do not contribute to the low-lying states below 1 MeV.

631

COLLECTIVE REPRESENTATION

In the well known deformed region, rotational constants h2/2J in odd-mass nuclei are ordinarily smaller than those for neighbouring even nuclei and the differences vary rather randomly 12). Therefore, in the present calculation, the rotational constant h2/2J is used as a parameter, which is chosen to be the same for all bands and for the strength of the Coriolis coupling in each nucleus. Again, Nilsson wave functions and level energies depend on ~/. Hence band head energies computed from eq. (11), are also a function of t/. Finally, we calculate the model energy spectra as a function of t / a n d h2/2J and then fit them to the experimental ones. The mixing amplitudes C/~¢ are obtained simultaneously. // /// / / /// ,~

//

~M~V/

//

// /~//

.-

?

:-- 2 . O r - -

MeV - - q.4.5

-

,~

-

~

-

/

.7

-- 44.0

/

y

....

1.5

LOI

I I

T I I 2 $ 4 DEFORMATION

I 5

I 6

%

Fig. 3. Chemical potential 2 and gap parameter A as a function of deformation parameter ~. The solid curves are for A and the dashed curves are for ~.. 5.1. THE NUCLEUS 75As Among the As isotopes, the 75As level scheme is well established by 75As Coulomb excitation 13) and 75Ge and 7SSe decays 14). The best agreement with experiment is obtained for r/ = 6 and h2/2J = 0.06 MeV. The experimental and the calculated energy levels are shown in fig. 4. Previous theoretical level spectra by other groups are shown in the same figure. One was calculated by Kisslinger and Sorensen 2), another by Scholz and Malik 3) and the third by Kisslinger and K u m a r ~). The simple shell model predicts the ground-state spin and parity to be ~ - , but the microwave measurement 1) has shown it to be -~-, which is well interpreted by the present model. Kisslinger and Sorensen have studied systematically and in detail the various nuclear properties using the pairing-plus-quadrupole force and obtained overall agreement for m a n y spherical nuclei. But they have pointed out that their model seems inadequate for the nuclei with 32 < Z < 36. In 7SAs, for example, they predict only four levels in the energy region below 1 MeV and the ground state to be ½. Considering the anharmonicity of the doubly even system, Kisslinger and K u m a r have recently modified Kisslinger and Sorensen's coupling scheme for odd-

632

N, IMANISHIe t

al.

mass nuclei a n d o b t a i n e d i m p r o v e d theoretical spectra for the nuclei near the 28 closed shell. By their calculation, the g r o u n d - s t a t e spin o f 75As is correctly p r e d i c t e d a n d m a n y states are depressed in energy when c o m p a r e d with ref. 2). 75As

912 3/2

"'

5/2-

--3/2-

7/20

keY 839

7•2-

9/2~ 1 / 2 --.5/2 --712-

-

7/2,3/2- 617.7

........ ~9/2+

1/2-

512

712312-

5 1 2 ~ I 1 2

KS

keY 821.8 '

312-

.E:¢,4

~512-

(1/2,3/2-} 651 596 (5/2,712-) 529

572.3

3/27/25/2-

468.8 5121712- 400.5 303.7 279.8~ 26~7 198.6

0/2-) 5/2(+) 912(÷) 5/2( - )

279

23~

512312:

(112-)

211

112-

312-

312(-)

312(-~

~I12KK

0

~

0 - - 3 1 2 -

EXP

PT

Fig. 4. Comparison of theoretical level energies in ~SAswith those obtained by experiment (marked EXP). Present theoretical level energies (marked PT) are obtained for B = 6 and h/2J = 0.06 MeV. Previous theoretical works done by Kisslinger and Sorensen ~), Scholz and Malik a) and Kisslinger and Kumar 4) are marked KS, SM and KK, respectively. The present t h e o r y r e p r o d u c e d r a t h e r well the spins a n d the l o c a t i o n o f the lowlying o d d - p a r i t y levels except the 468.8 keV ½- state. T h e theoretical 651 keV 3 - state is fitted to the e x p e r i m e n t a l 617.7 keV state in the least-squares fitting procedure. T a b l e 1 gives the wave functions for the calculated energy levels. I n sect. 6, these values are used to calculate the r e d u c e d t r a n s i t i o n p r o b a b i l i t y . TABLE 1 Energies, spins and amplitudes of the calculated 75As odd-parity levels for ~7 = 6 and h/2J = 0.06 MeV Energy (keV)

Spin Parity

0 211 238 279 529 596 651 839

3½~~3{~-{-

Eigenfunction 13~01) 0.97 0.26 0.93 --0.36 --0.67 0.05 0.73

13½10> --0.25 1 0.84 0.33 0.69 0.64 0.48 0.50

13~12> 0.08 --0.48 0.17 0.63 --0.38 0.88 --0.46

5.2. THE NUCLEI 71,Ta,77As Less e x p e r i m e n t a l i n f o r m a t i o n is available for the nuclei 7 3As a n d 77As. O f the o d d p a r i t y levels in 7 3As [ref. 15)], only three are assigned, the g r o u n d state spin a n d p a r i t y

633

COLLECTIVE REPRESENTATION

being {% the 66.9 keV level being -~- and the 75.7 keV level being k- or ~ - . In 7 7 A s [ref. 16)], the spin assignments made for the ground, 215 and 268 keV states are ~-, 3 - and { - , respectively. Therefore, we present here only the level position as a function of r/ and h2/2J instead of trying a least-squares fitting. These calculated level ~

~

.0.0 IBMeV

-O.06MeV

5/2-

keY I 1200

>-

5/2°

IOOO

0 or

uJ 8 0 0

"/'/2-

7/2

Z ILl

600

5/2

~

>

key 831 . . . . . .

7/2-

5/2427

4O0 1/2-

5/2-

200

(912 ~')

5/2-

~ ~ 3 / 2 1 / 2 _

. . . . . . . 75.7

I 2

.545

(I/2,a/2-) (5/2-1

&/2- 66'09

i 2-

6 I 2 54 DEFORMATION g,

5

6

{3/2-)

7:3AS

EXP.

Fig. 5. Experimental energy levels in VaAs and the calculated odd parity level spectra as a function of deformation r/ for different rotational constants. The spectrum calculated for ~7 = 2.7 and h212J = 0.06 M e V fits well to the experiment. ---O.06MeV 2~

key I20C

E-~ .0.1MeV

=0,14 MeV I . ~ ~-\~...~/7"/2-

WZj

-

_

.oo

.

i ~ - - ~

o1_, 'V~ I

-/

, P"-L_,

2 5 4 5 6

-

I 2 5 4 5 DEFORMATION

/2

473

(9/2"0

/2-

268 215

~v2(-) {3/2-)

"~•

0

3/2-~ =/2

6

I 2 "[

(5/2.T/2)

755--

\\

z~

200

keV J282 '195

3 4 5 6

5/27~s EXI~

Fig. 6. Experimental energy levels in ~TAs and the calculated odd parity level spectra as a function of deformation ~/ for different rotational constants. The spectrum calculated for ~ / = 3.5 and h z / 2 J = 0.14 M e V fits well to the experiment.

spectra of 7 3 A s and 7 7 A s a r e shown in figs. 5 and 6, respectively. For 7 3 A s ' we reproduce tentatively the position of the established levels at ~/ -- 2.7 and h 2 / 2 J - ~ 0.06 MeV. For 7 7 A s , the model spectrum calculated for t/ = 3.5 and h 2 / 2 j ~" = 0.14 MeV fits well the experimental data. Here the present theory predicts the ~ - and { - levels at 340 and 900 keV, respectively.

N. IMANISH'Iet aL

634

The ground state in 7tAs is known to be ~-, which suggests t/ smaller than 2.5 according to the present model. 6. Electrical properties

The reduced transition probability between states i and f whose spins are I i and If respectively, has the following form 17): B(E2, i -~ f) = 5e 2 {Qc+ .=Z-2 2 q(n)}2"

(16)

Here Qc represents the quadrupole moment generated by the collective motion of the nucleus and is given by Qc -- Qo Z 6v,vr(Ii K2OIIfK)Ct~, Ct~f•

(17)

The intrinsic moment Qo of the core is related to the well-known parameter 6 by 6) Qo = 0.8ZR26( 1 +:]6),

(18)

Ro = 1.2A + fm.

(19)

where R0 is radius of nucleus

The terms q(n), which are the contribution of quasi-particles to the quadrupole moment, are defined by 2h y, r x q(n) : ( - 1)"(le-½)(1 +Z/A2) MpO)o K~¢,¢~(u~i v ~ - v~, vv~)c~, c .

x[(IiKi2nllfKf) 2 (Nflf[r21Nil,) ( ~ ) ½ ( l i 0 2 0 l l f 0 ) ldf

X

E

\ 2 l f + 1/

6~:~at~a,a,,at(liAi2nllfAf)]+q'(n),

(20)

AIAf-Yi,~f

where g f = K i + n,

A t = A i + n.

The terms q'(n) in the expression (20) which vanish for K i + K f > 2, are defined by

q'(n) = ( - 1)'<'f-~)(1 +Z/A 2) 2h

X (V~l Uvf- Vv, Vvf)C~i Cvr

mp o)o Kt~i~f × [(/i Ki2nllfKf) ~'~ (NflflrZlNi li) / ~ ] ~ ( l i 0 2 0 l / e 0 ) lit~

×

\21f + 1/

X~ ~-~fz, atrafat~A~(liZi2nllfhf)], AiAfZi~f

where

Kf = - K i - n ,

At = -Ai-n.

(21)

635

COLLECTIVE REPRESENTATION

The factor (Uvi Uv~-Vv, V~r) in the above equations result from pairing effect and diminishes the contribution of quasi-particles. Using the wave functions obtained in sect. 5, we calculate the B(E2; i ~ f) values f o r 75As and the results are shown in table 2. An overall agreement with experiment [ref. 13)] is seen and this seems worth noting because the calculation is done without using effective charges. TABLE 2 Theoretical B(E2; i -+ f) in ~SAs compared with experiment Transition spin parity (energy keV) ½-(198.6) -- ,~-(0) -~-(264.6)--~-(0) ½-(279.5)--~-(0) ½-(468,5) --~-(0) :~--(572,1) -- ~-(0) ~-(572,1) --~-(0) ~-(617.7) --~-(0) ~-(821.8) --~-(0)

Experiment a) e2 • b a 0.034 0.0054 0.032 0.007 0.049 0.037 0.0017 0.037

Theory e~ • b ~ 0.006 0.005 0.062 0.009 0.029 0.002 0.008

a) Ref. 1).

For the 75As nucleus, the value of the intrinsic quadrupole moment Q0 for the deformation parameter q = 6 is evaluated using eq. (18) and is found to be 156 e.fm 2. This value is in accordance with the values for the neighbouring even nuclei. 74Ge and 76Se [ref. 1)], whose intrinsic quadrupole moments are known to be 178 fm 2 and 217 fm 2, respectively. The quadrupole moment Q, a = Z IC~l 2 3 K 2 - I ( I + 1) Q0, re (I + 1)(21 + 3)

(22)

is now calculated for the ground state of 75As and yields a value of 28 fm z, which agrees with the experimental value 1) of 29 fm 2. We are indebted to Professor T. Nishi for his continuous encouragement and valuable discussions. We would also like to acknowledge the helpful discussions with Drs. I. Fujiwara and H. Nakahara. References 1) W. B. Ewbank et al., Nuclear data sheets, Nuclear data B1-6-1 (1966); A. Artna, Nuclear data sheets, Nuclear data B1-4-1 (1966); P. H. Stelson and L. Grodzins, Nuclear data A1-1-21 (1965) 2) L. S. Kisslinger and R. A. Sorensen, Revs. Mod. Phys. 35 (1963) 853 3) W. Sholz and F. B. Malik, Bull. Am. Phys. Soc. 12 (1967) 66 4) L. S. Kisslinger and K. Kumar, Phys. Rev. Lett. 19 (1967) 1239 5) B. Mottelson and S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 1, No. 8 (1959) 6) S. G. Nilsson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 16 (1955) 7) A. K. Kerman, Mat. Fys. Medd. Dan. Vid. Selsk. 30, No. 6 (1956)

636

N. IMANISHI et al.

8) J. Bardeeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108 (1957) 1175; S. T. Beliaev, Mat. Fys. Medd. Dan. Vid. Selsk. 31, No. I1 (1959) 9) S. G. Nilsson, Nucl. Phys. 55 (1964) 97 10) S. Cohen, R. D. Lawson, M. H. Macfarlane, S. P. Pandya and M. Soga, Phys. Rev. 160 (1967) 903 11) L. S. Kisslinger and R. A. Sorensen, Mat. Fys. Medd. Dan. Vid. Selsk. 32, No. 9 (1960) 12) O. Nathan and S. G. Nilsson, in Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland, Amsterdam), p.601 13) R. C. Ritter, P. H. Stelson, F. K. McGowan and R. L. Robinson, Phys. Rev. 128 (1962) 2320; N. Imanishi, F. Fukuzawa, M. Sakisaka and Y. Uemura, Nucl. Phys. A101 (1967) 654 14) A. W. Schardt and J. P. Welker, Phys. Rev. 99 (1955) 810; H. J. van den Bold, H. C. Geijn and P. M. Endt, Physica 24 (1958) 23; P. V. Rao, D. K. McDaniels and B. Crasemann, Nucl. Phys. 81 (1966) 296 15) C. H. Johnson, C. C. Trail and A. Galonsky, Phys. Rev. 136 (1964) B1719 16) J. B. van der Kooi and H. J. van den Bold, Nucl. Phys. 70 (1965) 449 17) W. Scholz and F. B. Malik, Phys. Rev. 147 (1966) 836