Application of spectral averaging theory in large shell model spaces: Analysis of level density data of fp-shell nuclei

Abstract

Abstract In the spectral averaging theory extended to large shell model spaces (i) using a significant unitary group decomposition under which a one-plus two-body nuclear hamiltonian H decomposes into an orthogonal effective one-body part h and an irreducible two-body part V(H → h+V), (ii) applying the Central Limit Theorems locally and (iii) decomposing the shell model space into distant non-interacting S-subspaces (for light nuclei S denotes hω excitation), the state densities IH(E) take convolution form, IH(E) = ∑SIh,S ⊗ ϱGV,S[E], where Ih is the renormalized non-interacting particle state density and ϱG is a normalized spreading Gaussian due to V. A similar convolution form is available for spin-cutoff densities that give spin-cutoff factors. For a first systematic analysis, using the extended spectral averaging theory, of experimental level density data in a given region of the periodic table, fp-shell nuclei are chosen as an example. Calculations, using surface delta interaction, are carried out by including configurations up to 2hω excitations and by employing eight spherical orbits (ds, fp, 1g 9 2 ) for the five nuclei 55Mn, 56Fe, 59Co, 60Co and 60Ni and by extending for obvious reasons to ten spherical orbits (ds, fp, 1g 9 2 , 2d 5 2 , 1g 7 2 ) for the three A > 60 nuclei 62Ni, 63Cu and 65Cu. In general, spectral averaging theory is seen to provide a good representation of the observed total level densities and spin-cutoff factors.