A modified Tamm-Dancoff approximation, developed in a previous paper, has been applied to even Ni and Sn isotopes. Detailed spectra, £2 transition strengths connecting various levels, and the quadrupole moment of the first excited 2 + level have been calculated and the trends of the results compared with experimental values. The method appears to be fairly satisfactory. It points to the necessity of more reliable information on the effective interaction, active single-particle orbitals, and single-particle radial functions in order that a dependable quantitative fit to the data can be achieved.
Expressions are derived in the modified Tamm-Dancoff (TD) approximation which take into account the mixing of zero-, two-, and four-quasiparticle states for the description of the collective vibrational states of spherical nuclei. The proposed method is free from two very important defects inherent in the higher randomphase approximation (HRPA), namely, nonorthonormality and redunancy of the four-quasiparticle basic states. The relative merits of the present method over the existing one (HRPA) are discussed. [A(abJM),JV(cdJ'M')l=P(abJ)Z_ (-lV" +M '-M X(abcd; JJ'J")A{adJ", M'-M), where the operator P(abJ) = 1-(-\) a+b~J P{a <-> b) and the operator P(a «-»b) interchanges a and b. The symbol X(abcd; J J'J") is given by X(abcd; J J'J") = S bc (LJJ"J) ll2 W(JaJ' J J" J' • -M M'-M M'.where we have used the notation [//"]= (2/+l)(27"+l). Using (3.9), the commutators of B 0 +H int with the 'd;bJ")\\ LI ;]•
Exact configuration-mixing calculations have been done for Ni 68 and Ni 60 , which have two and four neutrons, respectively, in unfilled shell-model orbitals. Several different types of effective potentials have been used; they are: (1) the surface-delta interaction, (2) Serber exchange, (3) a potential similar to the Rosenfeld mixture, (4) an approximate reaction matrix calculated with the Hamada-Johnston two-nucleon potential, and (5) Tabakin's nonlocal separable two-nucleon potential. These results are compared with those obtained by using the two-body matrix elements given by Cohen et al. (EIC) and by Auerbach (EIA). The overlap of the BCS projected wave function with the exact shell-model ground-state wave function is calculated. The odd-even mass difference obtained from pairing theory using these potentials is compared with the experimental values. It is found that the first three potentials give nearly the same quantitative results as that calculated with EIC and EIA, while the Hamada-Johnston and Tabakin potentials are rather weak.
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