Theory of the Anharmonicity in the Vibrational Motion of Even-Even Spherical Nuclei

Abstract

By extending a method developed recently for the electron gas problem to the case of even-even spherical nuclei, corrections to the random phase or harmonic description of the vibrational spectrum have been obtained. The calculation, which was based on the conventional pairing plus quadrupole force effective Hamiltonian, indicates a systematic sequence of higher approximations taking into account successively more complicated phonon-phonon and phonon-quasiparticle pair interactions. The approximation of this paper, which includes only the leading phonon-phonon interaction in its effect on the one and two phonon states, is in principle rich enough to allow all of the observed orderings of the two-phonon triplet. The case of ${\mathrm{Ni}}^{62}$ has been studied in detail, with all parameters except the strength of the quadrupole force taken directly from the work of Kisslinger and Sorensen and the latter constant readjusted so that the improved theory gives the energy of the first $2^{+}$ state. A parameter-free accord to the ordering ($0^{+}$, $2^{+}$, $4^{+}$) of the two-phonon state is obtained, though the energies are on the whole high. The main defects of the calculation are discussed.