Nuclear structure studies by the 62–64Ni(d, p) reaction

I 1.E.1: 2.G

I

Nuclear Physics A143 (1970) 641--651; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

NUCLEAR STRUCTURE STUDIES

BY THE 62-64Ni(d,

p) R E A C T I O N

I. M. TURKIEWICZ t, p. BEUZIT, J. DELAUNAY and J. P. FOUAN Service de Physique Nucl(aire d Basse Energie, Centre d'Etudes Nucldaires de Saclay, France Received 11 August 1969 (Revised 22 December 1969) Abstract: Levels of 63Ni and 6SNi below 5 MeV have been studied by observation of the energy and angtdar distribution of protons emitted in the 62-64Ni(d, p) reactions. For many levels, lvalues of the captured neutrons have been assigned by comparison of the angular distribution with calculations based on the DWBA. These comparisons yield the spectroscopic factors. A sum rule analysis is made and the results are compared with the predictions of the strong-pairing and shell models. The positions of the single quasiparticle states determined have been used as input for an IGE calculation to obtain the force parameters. NUCLEAR REACTIONS 62"64Ni(d, p), E = ! 1.5 MeV, measured o'(Ep, 0). 63,6SNi deduced levels, 1, ~r, S. Enriched targets.

1. Introduction T h e m o t i v a t i o n for the present e x p e r i m e n t was twofold: (i) T o study the o d d isot o p e s o f Ni, in o u r systematic study o f the closed shell Z = 28 [refs. 1-3)]. It was n o t necessary to r e p r o d u c e the 5s - 60Ni(d ' p ) reaction because these reactions were studied often with g o o d r e s o l u t i o n 4,5). O n the c o n t r a r y the 6 2 - 6 4 N i ( d , p ) reactions were studied only once 6) with a resolution o f 45 keV. T h u s we r e p r o d u c e d these experiments with o u r 25 keV r e s o l u t i o n telescope. (ii) These studies are u n d e r t a k e n with the a i m o f m a k i n g a c o m p a r i s o n with the I G E ( B C S ) 7) calculation to o b t a i n first the energy levels a n d later the transition probabilities.

2. Experimental procedure E x p e r i m e n t s were p e r f o r m e d using a 11.5 M e V d e u t e r o n b e a m f r o m the Saclay Van de G r a a f f accelerator. The scattering c h a m b e r is described in an earlier p a p e r 1). The targets, e v a p o r a t e d on 20 p g / c m 2 c a r b o n foils, were m a d e f r o m s e p a r a t e d isotopes (62Ni - 99.02 ~ , 6 4 N i - 97.64 ~ ) . Target thicknesses r a n g e d f r o m 100 to 200/~g/cm 2. E n e r g y spectra o f emitted or scattered c h a r g e d particles were o b t a i n e d as a function o f angle relative to the b e a m direction t h r o u g h the use o f a A E - E telescope ( A E = 65 ~/m thick Ortec surface b a r r i e r detector, E = 5 m m thick R a d i o t e c h n i q u e lithium drifted silicium d e t e c t o r ) for particle identification. t On leave from the Institute of Nuclear Research, Warsaw. 641

..... : -'.~-=:-L ~ I~3 .......

'="

7: c.

........ :-~'s3i',

4972

4s.~ 678

" ~ 1 - - ~ _ _ 4 .~_~c

O

. . . . . . . .

I " .... i .,..~,....

~,~4

.~-

~

m

4.43~,

245 4 194

....

'~:_: =, .,:0L~ . . . . . . 3~32

c.~-- ......... 3 736

3 555

~ - :

=- . -

.....

.3346

3 401

U1 --~

2785

~

%_z.

282~;

o

--k _ _ ~ o o 2 330 .,~L-~

2159 1915

-'2".

1.013

,-0.686

0 ~

0.31~

0.0

, 0.062

P

"l D l a Z D I A ~ a I " . ~ L c t l . "I~l "1

Z'J~9

62 - 6a-Ni(d' p) REACTION

643

The observed energy resolution, for the entire system, was measured as about 25-30 keV (fig. 1) F W H M of the proton peaks studied. Proton energy spectra were obtained for the (d, p) reactions on 62Ni and 64Ni as a function of lab angle from 15 ° to 50 ° and 15 ° to 60 ° respectively, in 5 ° steps. The forward angles cross sections were also measured for 6SNi at lab angles of 20 °, 15°, 10° and 5 °, with a Buechner type magnetic spectrograph. Position sensitive detectors (Nuclear Diodes) 50 x 14 mm of 450 and/or 600/~m thick are arrayed on its focal surface. A position spectrum for each detector is readily obtained on an analyser , Counts

64Ni (d,p)6s Ni 200

11.5 M eV

LAB.ANGLE15"

o~,. cO

o

I00

m

\,,~...~

A

o

80

90

100

110

120

130

550

360

370

380

590

...Channel ,400

Fig. 2. Parts o f t h e p r o t o n energy s p e c t r u m f r o m the 64Ni(d, p)eSNi at 15 ° obtained with t h e m a g netic spectrograph.

through the use of an analog dividing s) circuit delivering the Ef(x)/E signal and particle identification can be performed when necessary with the E signal in a two-parameter mode 9). The system resolution (0.5 mm) is compatible with the spectrograph dispersion and the intrinsic resolution can be obtained. The experimental resolution obtained here (see fig. 2) is mainly due to solid angle and target thickness effects. Absolute energies were assigned by kinematic laws. Absolute differential cross sections were measured by comparing the yield o f the various levels in the (d, p) reactions with the yield of deuterons elastically scattered on the same targets, normalizing at a forward angle with the data of Lee and Schiffer 1o), which are in good agreement with ours. 3. R ~

Angular distributions are shown in figs. 3 and 4 for a number of proton groups which were sufficiently well separated from neighbouring peaks and extended enough above background to make the extraction reliable. The data reduction was made with

P

Z

B

0

o

o"

E

(

N

i

]

i

.....

i

...--

~ I

--

r " "" °"

I

,°

o,

,

°

.

Y

I

8

RELATIVE

,o

/,

.~'~

_

-/,'

-,,-"

CROSS

SECTION

1. . . .

c~

o

1 .....

i

\\ . . . .

',~

':2~:!i/

'

9-

-

i

i

o=

_

~

-'~1~

-.." ...... "

o "-"

.~

o

o 0

.~-

,~,,

N

,

_

i

I

".,..-'"'"

T

r-II ~J

6 2 - 6 4 N i ( d , p ) REACTION

645

L=O

L=2

L=3

I0,

IIi

7 -

--~_j

\

IC

/

10C

,

1~

"

J

i X

,

' 2.823

"1.919

L=I

~\

1oo

I0C

i

~ ,\

• /r

10~

\ i

//

I \, I "

]

i " ~

~' z

'~ '~

1o

.~

",2.785

,

0.062 10

\

\

.

t ",,3401

10, I to

I

8

/

\

|

,\

- ' - , 0.309

ua I00 //""iX,

__i

~//

V

I0 0

, j-?,

~

"J

~ -

\ ~ \

~ ",4.196

\ L=4

,--i-, ',,/" ~."~

't

I ~

",,3.555

",

10'

t

\

t ~"--

• V" . It"

0.686 100

'L.'," :'\

x t'\

1.013

I

J •

I--

,

//

1415

\

i

.'\

i',

.;

"',,3.736

.

100

".. "..f':'!'},, f':'!'},,

10 /

2.330

\

~

f

I'~-- 2.139

.i ~ i

',3.902 !

15 °

30 °

415 °

60 °

115.

310* ~5"

' ° 60

Fig. 4. A n g u l a r d i s t r i b u t i o n s o f p r o t o n s f r o m 6*Ni(d, p)eSNi reaction.

L=4 L=3

I.M. TURKIEWICZ et al.

646

a code ll). The results for these transitions are listed in tables 2 and 3 for 62Ni(d, p) 63Ni and 64Ni(d, p)65Ni respectively. The position of levels assigned to final nuclei are within the experimental errors the same as those obtained in the high resolution study of Tee and Aspinall ~2). The agreement with the results of Fulmer and McCarthy 6) is satisfactory as can be seen in tables 2 and 3. The only state requiring special comment is reported as 2.794 MeV [ref. 6)] in 65Ni where we detect a doublet separated by 38 keV. TABLE 1 T h e optical-model parameters V

Entrance channel Exit channel

W

92 50

0 0

ro

ro~

1.15 1.25

1.15 1.25

a

0.81 0.65

V~.o.

0 8

Ws.o.

r' o

a"

W'

0 0

1.34 1.25

0.68 0.47

23.7 11.5

TABLE 2 ~3Ni levels E,x~

0.000 0.088 0.155 0.518 1.000 1.292 2.291 2.514 2.692 2.941 3.092 3.283 3.964 4.279 4.376 4.642 4.718

Present work o~c;]~~ (mb/sr)

1

3.46 1.00 3.58 1.49 3.52 1.91 7.49 0.86 0.65 3.00 a) 0.35 1.85 3.82 1.41 ~) 2.11 2.22 3.86 ~)

1 3 1 1 1 4 2 4 1 0 1 2 2 0 2 2 0

probable j~ ½-.]3-]-½~+ ~r+ ~-+ ½½+ ½~+ s+ ½+ .]+ ~+ ½+

Ref. 6) ( 2 j + 1)Sll

E,x~

0.85 3.40 1.15 0.32 0.82 6.72 1.99 2.58 0.10 0.23 0.04 0.43 0.81 0.10 0.40 0.41 0.30

0.000 0.088 0.158 0.526 1.008 1.306 2.302 2.529 2.701 2.960 3.100 3.291 3.959 4.279 4.415 4.636 4.717

1

1 3 1 1 1 4 2 4 ( 2 or 3 ) 0 1 2 2 0 2 2 0

( 2 j + 1)Sij

0.747 2.39 1.065 0.306 0.663 6.1 1.66 2.70 0.16 or 0.7 0.375 0.06 3.96 0.739 0.180 0.309 0.396 0.306

a) F o r these levels, the normalization o f the theoretical curves was m a d e at 15 ° c.m.

The estimated accuracy of the cross sections relative to each other is about 5 % for the strong groups. As absolute measurements, we have to combine our statistical errors with our normalization to the data of Lee and Schiffer 1o) given with 5 % error. So we estimate the accuracy'between 10 and 20 % depending on the peaks.

62-64Ni(d,

647

p ) REACTION

TABLE 3 6sNi levels Ref. ~)

Present work

0.000 0.062 0.309 0.686 1.013 1.415 1.915 2.139 2.330 2.785 2.823 3.346 3.401

1.02 7.28 0.98 4.15 2.58 0.95 6.80 0.86 0.32+0.41 3.36 2.50 1.58 2.33

probable

(2j+l)Sij

F~zo

!

~½~.~~+ ½~-+ ½~- +~-+ ~+ ½+ ~+ ½+

2.52 1.41 0.17 0.75 7.39 0.15 1.46 0.11 0.52+1.02 0.64 / 0.19 j 0.27 0.17

0.000 0.065 0.315 0.699 1.021 1.415 1.919 2.153 2.338

3 1 1 1 4 1 (2) (1)

1.49 1.23 0.173 0.615 8.31 0.140 1.3 0.099

2.794 3.350 3.401

2 2 0

0.742 0.266 0.267

j~

(mb/sr) 3 1 1 1 4 1 2 1 3 +4 2 0 2 0

(2j + 1) S~j

3.555

3.44

2

~+

0.58

3.558

2

0.523

3.736 3.902 4,194 4.408

1.86 3.44 3.60 2.76

2 2 0 2

~+ ,~+ ½+ t+

0.31 0.58 0.26 0.43

3.740 3.892 4.196 4.392

2 2 0 2

0.263 0.422 0.273 0.369

Jr,

0.~

-., 64Ni

1 e~

b 0.S

~'., 62Ni

0.1

200

I

i

400

60 °

"0" c m=

Fig. 5. Angular distributions o f deuterons elastically scattered from eZNi and 64Ni targets. The curves are DWBA fits using the tabulated parameters.

648

I . M . TURKIEWICZ el

al.

The measured angular distributions were analysed with the DWBA code JULIE i 3). The optical-model parameters used for the deuteron originate from the analysis of Percy and Percy 14) and were also used successfully by Jolly et al. 15) in their analysis of deuteron elastic and inelastic scattering by nickel isotopes. This set of parameters (table 1) gives a good description of the deuteron elastic scattering differential cross sections (fig. 5) measured by us simultaneously with the (d, p) reactions. It was impossible to study the proton elastic scattering of protons by the final nuclei 63-65Ni because they are both unstable. We have taken the proton optical parameters from Percy ~6). The surface absorption is taken in both channels. The neutron is assumed to be captured into a shell-model orbit using a binding energy equal to the separation energy. This orbit is taken to be an eigenstate in a potential well of Woods-Saxon shape. We assumed the same radius and diffuseness as tbr the proton optical potential. A spin-orbit coupling 25 times the strength of the Thomas term was included. The calculations were performed with and without a radial cut-off equal to the radius of the nuclei. The effects were found to be small (2 to 10 %) but the fits were in general better without cut-off, we thus decided not to use it. The comparison of the measured angular distributions with the results of DWBA calculations is shown on figs. 3 and 4. The agreement is good enough to enable a unique assignment of the orbital angular momentum transfer I for most of the transitions. In the case of the transitions involving I = 2 we have observed a systematic shift of the maxima. With the magnetic spectrograph, by the angular distribution (fig. 4) at very forward angles, we were able to assign l = 0 to the 2.823 MeV and 3.401 MeV levels of 6SNi. The level 2.823 MeV was not observed in the earlier work. For the 3.401 MeV level, Fulmer and McCarthy 6) also assigned 1 = 0. The values of the angular momentum transfers are given in tables 2 and 3 in comparison with the results from the ref. 6). One can observe a general agreement. The angular distribution for the state at 2.330 MeV cannot be described by one/-value. We have fitted this distribution by the mixture of I = 3 + 4 (fig. 4). This level has not an assigned/-value in ref. 6) but in the unpublished results of the MIT group cited in ref. 6) one finds a 2.340 MeV level with l = 3. Roussel 17) has reported the undistinguished states 2.37+2.51 with l = 4 excited in the reaction 64Ni(~, 3He)65Ni. In both reactions, we have also observed few angular distributions for which it was impossible to assign any /-value. Spectroscopic factors were extracted by scaling the cross section from the DWBA calculations to achieve the best fit to the data at the first maximum, as shown in figs. 3 and 4. The relationship used is: do"

max

max

exp = 1.48(2J+ l)St;ae, l (l, J),

w h e r e j = l_+½ is the total angular momentum of captured neutron, J is the spin of final state, since both 62Ni and 64Ni targets have 0 + ground states we have J = j.

62-6'*Ni(d, p) REACTf0N

649

The shape of the angular distributions are j-independent in the range of angles under study, and we have to take the spin value from other works. The transitions with l = 0, 3 and 4 are known to correspond t o j ~ = ½+, ~- and ~+ respectively in this nuclei region from simple shell-model considerations. We have taken the spins of p-levels for 63Ni from the comparison of (d, t) and (d, p) reaction cross sections made by Fulmer and Daehnick is). The first four I = 1 transitions for the 64Ni(d, p)6SNi reaction were studied by Lee and Schiffer 19) at backward angles and the spin assignment were done on the basis o f j dependence of angular distributions. TABLE 4 C o m p a r i s o n o f experimental and theoretical values j~

62Ni ej

X(2j-I- 1) S b i experiment

~-.~.½•:~+

0.234 0.088 0.669 1.631

64Ni

1.47 3.40 1.81 9.30

ej

pairing theory ~)

shell model

1.08 3.48 1.64 9.8

0 4 2 10

5"(2j-]- 1 )SIS i experiment

0.616 0.398 0.320 1.172

0.92 3.04 1.67 8.41

pairing theory a)

shell model

0.62 2.22 1.38 9.8

0 2 2 10

~) F r o m ref. 19). TABLE 5 T h e i n p u t data a n d the results o f the I G E m e t h o d applied to the nickel isotopes

E~ 2p]_ If,. ~aNi Vo = --26.17

2p.~

--26.14

1g~_

2p,. 1f~

6SNi Vo = -- 26.69

2p½

-- 27.60

lg-I.

A~

v~

e-2

1.57

1.42

0.84

--0.67

1.64

1.45

0.88

--0.85

1.50

1.32

0.86

--0.71

1.49

1.43

0.80

0.00

1.41

1.40

0.67

0.14

2.07

1.42

0.34

1.5

4.20

1.08

0.13

4.06

3.04

1.19

0.19

2.79

1.76

0.95

0.96

-- 1.48

2.03

1.15

0.95

-- 1.67

1.44

0.94

0.94

- - 1.09

1.81

1.26

0.92

--1.30

1.50

0.94

0.33

1.17

1.73

1.14

0.35

1.30

4.10

0.77

0.09

4.03

2.58

0.97

0.19

2.39

650

I . M . TtmIC~WlCZ e t al.

Having no indication of the spins for l = 2 transitions, we have accepted j = -~+ for all observed states accordingly to the consideration of shell model which suggests a spacing between d~ and dt of about 3 MeV. In the range of excitation energy studied here, there is a great probability of finding only d,~.. The ¢r~'~c(/,j) for these two spins differs only by 3.5 ~ , so the possible false assignment of spin has little influence on the values (2J+ 1)Stj. The (2j+ I)S,~ values are listed in tables 2 and 3. The experimental spectroscopic factors were normalized for each target to satisfy the sum rule Z~ (2j+ 1)S~ = number of holes in the target. This sum is taken over the orbits 2p.i., lf~, 2p~ and lg~. The normalization is useful because of the approximations made in DWBA calculations. It corrects also for the influence of the error in the normalization of the experimental cross sections. This normalization changes the value obtained directly by 5.5 ~ for 6SNi and 11.2 ~ for 63Ni. The values Z~ (2j+ 1)S~i for each final state are given in table 4 in comparison with the values predicted by shell model and pairing 21) theories. Table 4 contains also the positions of the single quasiparticle states in the final nuclei calculated as the centers of gravity Z (2j+ 1)S[jE~c E*= Z (2j+ 1)SIi i

These energy positions were used to perform the calculations of the force parameters for the nickel isotopes by the IGE method 7). In the classical method 23,24), 8j, the single-particle energy and the strength Vo of the two-body force entering the nuclear Hamiltonian, are parameters determined by fitting the experimental spectra. The calculations give the value of the gap A and 0 j2, (the probability for the shell-model levelj to be filled), but with long and dubious least squares fits with many variables and the solutions are often not unique. At the contrary, in the IGE method 7), the only parameter is E i and one obtains unique values of Vo, A and ej. The only hypothesis in this calculation is that the states which are most strongly excited in one-nucleon transfer experiment can be identified to be pure one-quasiparticle states. Gillet and co-authors 7) made calculations for Ni using as E i input, values from experiments when available or by reasonable guesses. We reproduced their calculations with the values of E~ obtained from our experiment to see the influence of these changes. The new calculations are underlined in table 5. Our calculation was performed in the same conditions than the earlier namely with a Gaussian force of range 1.7 fm and a triplet to singlet ratio a = -0.4. The greatest changes observed are for g = e =2. The IGE method allows to extract the force parameters from the odd nuclei, the even nuclei configurations can be deduced without any new assumption. We are preparing calculations with the Gillet's group 22) to see the influence of such changes on the spectra and on the B(E2).

~2-64Ni(d, to)

REACTION

651

The authors acknowledge the essential role of J. P. Passerieux who designed and constructed the 25 keV resolution telescope and participated actively to the experiment. M. Doury prepared the targets. We acknowledge the assistance of L. Bianchi in the measurement with the magnetic spectrograph. We thank V. Gillet and Mrs. Tichit for the IGE computer code and their help. One of us (I.M.T.) wishes to express her gratitude to Service de Physique Nucl6aire ~t Basse Energie, C.E.N. Saclay for the extended hospitality. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21)

R. Ballini, A. G. Blair, N. Cindro, J. Delaunay and J. P. Fouan, Nucl. Phys. A U l (1968) 147 P. Beuzit, J. Delaunay, J. P. Fouan and N. Cindro, Nuch Phys. A128 (1969) 594 P. Beuzit, J. Delaunay, J. P. Fouan and I-L Ronsin, Nucl. Phys. A137 (1969) 97 E. R. Cosman, Phys. Rev. 142 (1966) 673 E. R. Cosman, Phys. Rev. 163 (1967) 1134 R. I-L Fulrner and A. L. McCarthy, Phys. Rev. 131 (1963) 2133 V. Gillet, B. Giraud and M. Rho, Nucl. Phys. AI03 (1967) 257 G. Lemarchand et J. Quidort, Note CEA N-1032 (1968) L. Bianchi et J. Quidort, Note CEA N-1232, (1969) L. L. Lee and J. P. Schiffer, Phys. Rev. 134 (1964) B765 J. Picard, CEA Report R-3024 R. G. Tee and A. Aspinall, Nuel. Phys. A98 (1967) 417 R. H. Bassel, R. M. Drisko and G. R. Satchler, O R N L 3240 C. M. Perey and F. G. Perey, Phys. Rev. 132 (1963) 755 R. K. Jolly, M. D. Goldberg and A. K. Sengupta, Nucl. Phys. A123 (1969) 54 F. G. Perey, Phys. Rev. 131 (1963) 745 P. Roussel, Thesis, Orsay 1968 R. H. Fulmer and W. W. Daehnick, Phys. Rev. 139 (1965) B579 L. L. Lee and J. P. Schiffer, Phys. Rev. 154 (1966) 1097 M. I-L Macfarlane and J. B. French, Rev. Mod. Phys. 32 (1960) 567 L. S. Kisslinger and R. A. Sorensen, Rev. Mod. Phys. 35 (1963) 853; Mat. Fys. Medd. Dan. Vid. Selsk. 32 (1960) no. 9 22) V. Gillet, B. Giraud and A. Jaffrin, to be published 23) N. Auerbach, Phys. Key. 163 (1967) 1203 24) S. Cohen, R. D. Lawson, M. H. Macfarlane, S. P. Pandya and M. Soga, Phys. Rev. 160 (1967)903