Toward a New Theory of Spherical Nuclei. I
Abstract
A tentative theory of the quadrupole moment Q_{2}^{+} of the first 2^{+} excited state of spherical nuclei is developed as a logical extension of the methods used in the usual theory based on pairing plus quadrupolequadrupole interaction. In the latter, in which the quasiparticle occupation amplitudes in the ground state are taken to be of zero order and the offdiagonal amplitudes connecting the ground state with the 2^{+} state to be of first order (and described by the randomphase approximation), Q_{2}^{+} is nominally of second order. We find that, in a consistent calculation, the quadrupole deformation is driven by the offdiagonal amplitudes, but that there is also the possibility of a selfsustained deformation for sufficiently large quadrupole coupling constants. Numerically, one finds ranges of the latter, all in accord with the excitation energy and the E2 transition probability, for which Q_{2}^{+} shows extremely rapid variations, and in particular, also assumes values sufficiently large to contradict the whole basis of the calculation. The need for a selfconsistent intermediate coupling calculation is indicated.
 Publication:

Physical Review
 Pub Date:
 April 1967
 DOI:
 10.1103/PhysRev.156.1159
 Bibcode:
 1967PhRv..156.1159D