Applications of progenitor sum rules in nuclear theory

Abstract

The energy-weighted sum rules, obtained by taking matrix elements of double commutators with the nuclear Hamiltonian of appropriately defined densities, are didactically reviewed. Following a catalogue of applications such sum rules have found in theoretical nuclear physics, the progenitor sum rules (PSR's) are derived using standard commutator relations for second-quantized nucleon field operators. This leads to the extension of PSR's to coupled Fermi-Bose systems, and in particular, to a simple model of interacting mesons and nucleons. The effects of interactions are also discussed from the point of view of (static) exchange potentials. The relation of the dipole sum rule to nuclear photoabsorption is reviewed briefly. The application of PSR's to the calculation of longitudinal inelastic form factors, and the use of the “doorway hypothesis” is discussed in detail, together with the semiclassical collective-oscillation interpretation of these results proposed by Bertsch. Suzuki's very interesting applications of PSR to the evaluation of collective mass parameters, coupling constants, and polarization functions of the Bohr-Mottelson self-consistent mean-field theory are also given a detailed treatment. Certain miscellaneous applications of PSR to calculation of Coulombic isospin mixing, to energy shifts in isospin multiplets, and to induced moments and effective charges are collected and discussed in a unified manner. The review concludes with a discussion of the qualitative character of the nuclear photoabsorption strength below the meson production threshold, especially with regard to the question of to what extent the (γ, NN) reaction is sensitive to pair correlations in the nuclear ground state.