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Journal of Physics G Nuclear Physics

Constrained variational results for the new Bethe homework problem

C Howes, J M Irvine, R. F. Bishop

Published Mar 1, 1978• 15 citations
Publisher

Abstract

Bethe (1973) has proposed two model N-N interactions, one containing a central plus sigma 1 . sigma 2 spin dependence and the other containing in addition a tensor force to study the convergence of various many-body techniques for calculating the bulk properties of many fermion fluids. Following the success of the authors' constrained variational calculations in describing the behaviour of the original Bethe homework problem involving a purely central interaction, they now present their results in neutron matter and nuclear matter for the new spin-dependent potentials.

DOI
10.1088/0305-4616/4/3/001

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Bethe (1973) has proposed two model N-N interactions, one containing a central plus sigma 1 . sigma 2 spin dependence and the other containing in addition a tensor force to study the convergence of various many-body techniques for calculating the bulk properties of many fermion fluids. Following the success of the authors' constrained variational calculations in describing the behaviour of the original Bethe homework problem involving a purely central interaction, they now present their results in neutron matter and nuclear matter for the new spin-dependent potentials.
The Fermi-hypernetted-chain method for quantum many-body calculations is studied and investigated in some detail by calculations of the ground-state energy for neutron matter. The calculations are done for five different two-body potentials and results are compared with other theoretical results. Our Fermi-hypernetted-chain results are rather close to results obtained by lowest-order constrained variation calculations, and the results are quite dependent on the chosen potential, especially at high densities.
A perturbation scheme based not on the ideal gas but on a system of purely repulsive cores is applied to a typical fully interacting fermion gas. This is ``neutron matter'' interacting via (a) the repulsive ``Bethe homework-problem'' potential, (b) a hard-core--plus--square-well potential, and (c) the Baker-Hind-Kahane modification of the latter, suitable for describing a more accurate two-nucleon potential. Pad\'e extrapolation techniques and generalizations thereof are employed to represent both the density dependence as well as the attractive coupling dependence of the perturbation expansion. Equations of state are constructed and compared with Jastrow--Monte Carlo calculations as well as expectations based on semiempirical mass formulas. Excellent agreement is found with the latter.