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arXiv:nucl-th/0405069 · Kluwer Academic Publishers eBooks

J-Pairing Interractions of Fermions in a Single-J Shell

A. Arima

Published Dec 17, 2005• 0 citations
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Abstract

In this talk I shall introduce our recent works on general pairing interactions and pair truncation approximations for fermions in a single- j shell, including the spin zero dominance, and features of eigenvalues of fermion systems in a single- j shell interacting by a J -pairing interaction.
DOI
10.1007/1-4020-2634-x_2

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Progress of Theoretical Physics Supplement•May 16, 2013•1 citation
We investigate Hamiltonians with attractive interactions between pairs of fermions coupled to angular momentum JJJ. We show that pairs with spin JJJ are reasonable building blocks for the low-lying states. For systems with only a J=JmaxJ={J}_{max}J=Jmax​ pairing interaction, eigenvalues are found to be approximately integers for a large array of states, in particular, for those with total angular momenta $I\ensuremath{\leqslant}2j$. For I=0I=0I=0 eigenstates of four fermions in a single-jjj shell we show that there is only one nonzero eigenvalue. We address these observations using the nucleon pair approximation of the shell model and relate our results with a number of currently interesting problems.
In this talk I shall discuss some regularities of many‐body systems in the presence of random interactions and regularities of a single‐j shell for the J pairing interaction which works only when two particles are coupled to spin J. I shall first explain an empirical rule to predict the spin I ground state probability. Then I shall present some interesting results of a single‐j shell under the J pairing interaction. Last I shall discuss some preliminary results of binding energies in the presence of random two‐body interactions.
The validity of the essential ingredients of the microscopic formulation of the interacting boson model: (i) truncation of the shell-model or fermion space and (ii) the procedures for mapping the truncated fermion space on to the boson space, is tested over various (spherical, deformed and transitional) regions both in the simplistic single j-shell, identical boson systems and the more realistic multi j-shell, proton-neutron systems depending on the feasibility of such calculations. In the situations where the truncation and mapping procedures fail to reproduce the exact shell-model results, it is demonstrated that renormalization and higher order mapping procedures cure the associated problems, respectively and provide excellent agreements. In addition, a Hamiltonian of the interacting boson-fermion model which is relevant for a study of odd mass nuclei is derived for a single j-shell case in the shell-model framework, which yields results identical to those in the shell-model for the monopole pairing interaction.