Nuclear Surface Oscillations

Abstract

The extreme shell model of the nucleus is extended by allowing the last odd nucleon to interact with collective modes of motion of the even-even nuclear core. The interaction between a nucleon and the surface oscillations of the core was given by Bohr and is employed here with a Fock space representation for the core excitation. Because of the interaction neither the nucleon nor the core conserve their angular momentum, but the total angular momentum is conserved. The problem is treated by the Tamm-Dancoff method. In terms of the Tamm-Dancoff wave function, formulas are derived for the magnetic moment and the quadrupole moment of an odd nucleus. The energy of excitation of the core is taken empirically from the first excited state of the corresponding even-even nucleus. With this procedure all the parameters of the theory are fixed. The magnetic moment deviations calculated in this manner agree with experiment for nuclei in which the total angular momentum is one half, but the agreement does not exist for higher angular momenta. It is also possible to obtain a qualitative fit for the large quadrupole moments of nuclei with odd numbers of nucleons between fifty and eighty-two. The problem of two equivalent nucleons outside a closed shell is treated in the same manner, and it is shown that the first and second excited states have spins 2 and 4 as usually observed. In addition there is a pairing energy binding effect in the ground state which is larger when the individual angular momenta of the two nucleons is larger. This is the pairing energy rule usually employed in shell model calculations.