A comparison between the finite Dyson-type and the infinite Holstein-Primakoff-type boson expansion is presented, considering both particle-hole and pairing type excitations. The significance of truncating to the truly collective branches is emphasized, and the convergence of the Holstein-Primakoff expansion is discussed. It is shown that in both expansions there is no need to construct physical basis states. Complete equivalence between the two types of expansion is exhibited by treating these excitations within models which are schematic but not totally unrealistic.NUCLEAR STRUCTURE Boson expansion theory, convergence, comparison of different methods, finite Dyson expansion, infinite Holstein-Primakoff expansion, pairing and particle-hole collective motions.
Abstract This chapter discusses the significance of two body interactions to many-body properties, beginning with a schematic model showing the relevance of short-range correlations beyond those of the Fermi gas. These correlations are studied within Brueckner theory and the help of the Bethe-Goldstone equation, mainly for nuclear matter proper but extensions to finite temperature are presented. Effective forces of Skyrme type are derived through an expansion of the G-matrix to small relative momenta. This scheme hinges essentially on the Brueckner-Hartree-Fock approximation, for which results for binding energy and equilibrium density are presented. An alternative variational method based on Jastrow functions is sketched, which demonstrates the necessity for considering effective three body forces. The concept of the nuclear equation of state is presented and parameterized by Skyrme forces with density dependent parameters. Finally, a semi-classical transport theory is presented which accounts for statistical collisions of the nucleons.
Based on the relativistic Hartree-Bogoliubov theory, the influence of the pairing interaction strength on the dineutron correlations and the crossover from superfluidity of neutron Cooper pairs in the
1S0 channel to Bose-Einstein condensation of dineutron pairs is systematically investigated in the nuclear matter. The bare nucleon-nucleon interaction Bonn-B is taken in the particle-particle channel with an effective factor to simulate the medium effects and take into account the possible ambiguity of pairing force, and the effective interaction PK1 is used in the particle-hole channel. If the effective factor is larger than
1.10, a dineutron Bose-Einstein condensation (BEC) state appears in the low-density limit, and if it is smaller than
0.85, the neutron Cooper pairs are found totally in the weak coupling Bardeen-Cooper-Schrieffer (BCS) region. The reference values of several characteristic quantities which characterize the BCS-BEC crossover are obtained, respectively, from the dimensionless parameter
1/(kFna) with
a the scattering length and
kFn the neutron Fermi momentum, the zero-momentum transfer density correlation function
D(0), and the effective chemical potential ${\ensuremath{\nu}}_{\mathrm{n}}$.