The normal-ordered Holstein-Primakoff boson expansion method based on the Dyson boson Mapping

Peter Ring, Peter Schuck

Motoyuki Sato, Kosuke Takada

When the Holstein-Primakoff (Hermitian)-type boson expansion theory is applied for nuclear structure calculations, truncation at the fourth-order expansion of the boson Hamiltonian is often used. The Dyson-type boson mapping has no difficulty concerning boson expansion, since the Dyson boson Hamiltonian is written in up to sixth-order boson operators, and we do not have to make any truncation of the boson expansion. In the present work, we propose a new clear-cut method to obtain the normal-ordered Holstein-Primakoff boson expansion. Using this method, we test whether or not the truncation of the boson expansion is good approximation in various cases. We show that truncation at the fourth-order expansion of the normal-ordered Holstein-Primakoff boson Hamiltonian is a rather good approximation, but it is not sufficient for detailed analyses.

Kosuke Takada

F.J.W. Hahne

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.

Kosuke Takada

Eugene R. Marshalek

Boson expansion theory is extended so as to allow for the coupling of several fermion-like valence particles or holes to the collective vibrations of a closed shell, described in terms of boson degrees of freedom. The result is a faithful mapping of the original many-fermion problem into a certain boson-fermion subspace without redundant variables. Generalizations of the Dyson and Holstein-Primakoff representations are derived with the aid of algebraic techniques.