LETTERV. AL ~UOVO CI~V.NTO VOL. 23, N. 4 23 Se t tombre 1978

Negative-Parity Levels in Even Nickel Isotopes.

RAM RAJ, B. B. ROY, O. P. RUSTGI and M. L. RUSTGI

Physics Department, State University o] New York - Bu]]alo, 2r Y. 14260

(r icevuto il 17 Lugl io 1978)

I n recent years several groups of exper imenta l i s t s h a v e s tudied the h igher exci ted s ta tes in even nickel isotopes. F o r example , BRUG~, C~AVM~AUX, D~ VRIES, and Men- RIseN (1) have s tudied levels in 5SNi up to 10 MeV exc i ta t ion energy th rough the (a, cr reac t ion . Their results are found to be in surprisingly good agreement wi th those obta ined f rom a-transfer react ions such as 54Fe(~e0, ~2C)SSNi and 5*Fe(TLi, t)SSNi. P rev ious ly elast ic and inelast ic scat ter ing of alpha-part icles and pro tons by ~SNi and ~~ had been r epor t ed by INcur. (2) and J~mvIs et al. (a). I t is found t h a t in bo th 5SNi and ~~ most of t he s ta tes below 5 MeV h a v e posi t ive pa r i ty whereas most of the states above 5 M e u h a v e nega t ive par i ty . There is some disagreement on the 5.582 MeV level in 5SNi, which BRVGE et al. (~) find to be a 2+ s ta te while JARVIS et al. (2) and I ~ o u ~ (3) have ind ica ted i t to be a 4 + s ta te or 4 + § 5- states, respect ive ly . The 4.47 MeV 3- level (a) in 5SNi decays essential ly by E1 t ransi t ion to the 2 + s tate . On the con t ra ry (5), bo th t he 3- s ta tes at 4.05 and 3.74 MeV in ~~ and 6~Ni, respect ively , decay to bo th the 2 + and 2+ levels of these nuclei . The t ransi t ion to the second 2+ levels in e4Ni again has no t been observed. The v a r y i n g modes of decay of the 3- level in Ni isotopes show the exis tence of differences in the i r s t ruc ture and will r evea l 1imitat ion of any m o d e l

A n u m b e r of calculat ions (e-~3) on Ni isotopes employ ing schemat ic forces or reac t ion m a t r i x e lements have been r epor t ed in l i terature . I n th is le t te r t he results of calcula- t ions on the nega t ive-par i ty s ta tes for the even Ni isotopes carried out wi thin t he f l ame-

(1) G. BRUGE, A. CHAE~IEAUX, R. DEVRIES a n d G. C. MORRIS0N: Phys . Rev. Lett., 29, 295 (1972). (a) ]VI. INOUE: Nuc l . Phys . , l l g A , 449 (1968). (a) O. •. JARVIS, B. G. HARVEY, D. L. HENDRIE, and J . ]WAHONEY: Nucl . Phys . , 102 A, 625 (1967). (4) P . BEUZIT, J . DELAUNAY a n d J . P. FOUAN: Nucl . Phys . , 128 A, 594 (1969). (a) P. F. HINRICHSEN, G. T. WOOD a n d S. M. SCHAFROTH: Nuc l . Phys . , 81, 449 (1966L (6) S. COHEN, R. D. LAWSON, M. H . MACFARLANE, S. P. PANDYA a n d M. SOGA: Phys . Rev. , 160, 903 (1967). (7) N. AUERBACtt: Nucl . Phys . , 76, 321 (1966). (8) L* S. HSU: Nucl . Phys . , 96 A, 652 (1967). (9) ]3. ]3. RoY, R. RAJ a n d M. L. RUSTGI: Phys . Rev. C, 1, 207, 1138 (1970). (10) R. P. SINEH, R. RAJ, M. L. I~USTGX a n d I t . W. KUNG: Phys . Rev. C, 2, 1715 (1970). (11) M. L. RUSTGI, ~[. W. KUNG, R. RAJ, R . 2k. I~IISLEY a n d M. H . HULL j r . : Phys . tCev. C, 4, 854 (1971). (lz) p . W. M. GLAUDEMANS, IVL J. A. DE VOIGT a n d E. F. M. STEFFENS: N~C7. Phys . , 198 A, 609 (1972). (la) j . E . K e e P s a n d P. W. M. GLAUDEMANS: Zeits. Phys . , 2 8 0 A , 181 (1977).

126

NEG A TI V E- PA RI TY LEVELS IN EVEN NICKEL ISOTOPES 127

work of the modified Tam-Dancoff approximation (MTDA) method are reported assuming a 5eNi core. The extra-core neutrons are considered to occupy the lp~, 0]i, lP�89 and 0g~, single-particle orbitals, and the unperturbed single-particle energies for these orbitals are taken to be 0.0, 0.78, 1.08 and 5 MeV, respectively. The two-body renormalized matr ix elements of the Hamada-Johnston (H J) and Tabakin potentials are used. The gap and the number equations are solved to obtain the single quasi-particle eneigies and the occupation and unoecupation probabilities in the various single-particle levels. These quantities are needed for the setting up of the energy matrix. The effect of the spurious 0 + two-quasi-particle states from the basis wave functions is eliminated using the procedure employed earlier (9-~) before the diagonalization of the energy matrix.

The results of the calculation for the first few negative-parity states are listed in tables I and II. The results for 58Ni are reported in the Tamm-Dancoff approximation

TABLE I. - Energies (in MeV) o] the negative-parity states o] SSNi in the Tamm-Danco]] approximatien for the Tabakin (Tab.) and Hamada-Johnston (H J) reaction matrix elements.

J:~ Tab. t t J Experimental

3- 4.35 4.75 4.47

3- 5.96 6.24 6.02

4- 4.85 5.67

5- 4.57 5.40

6- 5.00 5.85

TABLE II . - .Energies (in MeV) o] the negative-parity states o/ece~ Ni isotopes in the MTDA approximation for the Tabakin (Tab.) and Hamada-Joh~stou (H J) potential reaction matrix elements.

j~ 60Ni e~Ni edNi ~6Ni

Tab. H J Tab. I~J Tab. HJ Tab. HJ

17 4.82 7.05 4.66 7.07 4.75 7.25 5.06 7.63

17 5.24 7.65 4.96 7.57 5.04 7.59 5.47 8.45

2i- 3.91 5.78 3.81 5.69 3.95 5.64 4.16 5.61

2~" 4.96 7.20 4.72 6.97 4.61 6.89 4.77 7.13

3i- 3.73 4.76 3.38 4.59 3.12 4.46 3.07 4.38

3~ 3.97 5.63 3.56 5.27 3.52 5.01 3.50 4.83

4~- 3.81 5.08 3.31 4.77 3.12 4.51 2.96 4.14

4~ 4.16 5.70 3.76 5.20 3.53 4.70 3.24 4.50

57 3.79 4.90 3.35 4.64 3.17 4.44 2.98 4.02

5~- 3.98 5.38 3.60 4.93 3.38 4.49 3.15 4.41

6~- 3.87 5.35 3.22 4.99 2.93 4.67 2.82 4.43

6~- 4.30 5.71 4.05 5.40 3.89 5.24 3.85 5.16

7~- 3.63 5.30 3.37 5.08 3.29 4.88 3.28 4.70

7~- 4.81 7.14 4.45 6.97 4.43 6.94 4.64 7.19

~ 2 ~ RAM RAJ', B. B. :ROY, O. 1 ). :RUSTGI a n d ~ , L. R U S T G I

TABLn I I I . - Reduced transition rates i~ the MTDA .method ]or even Ni isotopes. The B(M1) values are ia un i t s of ~.~ and the B(E3) va lues arc in uni ts of e2/a ~, whe re r = Mw/h and ]ho = 41A-} MeV.

Trans i t i on ~~ 62Ni

Tab . H J Tab. I I J

B(E3 2+--~ 35) 1.12.10 -3 9.50.10 -3 1.36.10 -~ 4 .17.10 -4

B(E3 2+-+ 3~) 7.62.10 -5 1.92.10 -2 9.28.10 -3 1.90.10 -2

B(E3 2+--~ 35) 1.72.10 -3 5.30.10 -~ 7.89- 10 -3 1.13- 10 -2

B(E3 2+-~ 3~) 6.93- 10 -5 4.14.10 -a 3.86.1O -a 1.28.10 -3

B(M1 35-~ 25) 6.13- 10 -a 8.27.10 -3 4.18- 10 -1 5.04- 10 -~

B(MI 3~-+ 25) 9.29- 10 -a 6.30- 10 -1 1.23.10 -3 6.19.10 -1

B(M1 35--~ 2~) 5 .11.10 -a 3.76.10 -a 9.11- 10 -a 3.73.10 -a

B(M1 3~-+ 2~) 2.79- 10 -a 1.25-10 -a 2.97-10 -3 1.30.10 -~

Trans i t ion edNi 6eNi

Tab. H J Tab. H J

B(E3 2+-~ 35) 1.30.10 -3 3.32.10 .4 4.58- 10 -3 1.08. tO -3

B(E3 2~-~ 3~-) 1.68.10 .3 1.40.10 -3 1.81- 10 -5 1.08- 10 -2

B(E3 2+-~ 3~) 3 .32.10 -a 8.46.10 -3 7.60- 10 -3 3.95.10 -3

B(E3 2+-+ 3~) 1.73.10 -4 3.42. l0 -a 1.56.10 -3 1.28.10 -4

B(M1 35-~- 25) 3.73- 10 -1 2.52.10 -3 4.18.10 -1 8.52.10 -3

B(M1 3~-~ 2~') 1.01- 10 -1 6.16.10 -1 1.71- 10 -1 6.12- 10 -1

B(M1 35-~ 2~) 5.49- 10 -a 9.97.10 -~ 4.69- 10 -3 3.11.10 -3

B(M1 3~--~ 2~) 2 .23.10 -3 1.29-10 -2 1.38- 10 -~ 4 .55.10 -3

while t h e mix ing of two and four quas i .par t ic le subspaees is inc luded for t h e o the r i sotopes .

F o r 5sNi the calculat ions w i t h t h e H a m a d a - J o h n s t o n and Tabak in in te rac t ions p red ic t t h e 3- level at 4.75 and 6.24 a n d 4.35 and 5.96 lV[oV, respec t ive ly , in r easonab ly good a g r e e m e n t w i t h t he measu red va lues of 4.47 and 6.02 ~r In general t he p red ic t ions of t h e two sets of ma t r i x e l emen t s are no t in accord w i t h one another .

In e~ again, the ca lcula ted energies of t he first two 3- s ta tes are in good ag reemen t w i t h t h e observed values of 4.04 and 5.60 ~ e V for t h e H a m a d a - J o h n s t o n po ten t i a l .

I t is no t ed by B~UZIT et al. (4) t h a t t h e energy of t h e first 3- s ta te decreases f rom 4.04 MeV in 60Ni to 3.56 MeV in 64Ni. Such a decrease is seen theore t ica l ly also.

In view of th is agreement , i t will be desirable to m a k e measu remen t s on the t rans i - t ion r a t e s to compare w i t h t h e resul ts p resen ted in t ab le I I I .

The au thors are gra tefu l to Prof . G. BR~I~ for his in te res t in th is work .