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Monte-Carlo Study of Bound States in a Few-Nucleon System: Method of Continued Fractions

Masui, H, Sato, T

Published Jan 1, 1998• 1 citation
OpenAlex

Abstract

We propose a new type of Monte-Carlo method which enables us to study the excited state of many-body systems.

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The method of coherent correlated pairs is applied with a realistic effective Hamiltonian to the four-nucleon system. Three methods of solution are compared for ease of implementation and convergence rates. A Monte Carlo method yields the best upper bound within the coherent correlated pair space. The full variational treatment of the four-nucleon coherent correlated pair problem yields equations which have poor stability properties. An ansatz variational method proves to be rapidly convergent and yields results very close to those of the Monte Carlo method. The results for binding energy and the one body density distribution are compared with Hartree-Fock results using the same effective Hamiltonian in the same model space. As in previous soluble model applications the coherent correlated pair method provides a superior upper bound to the ground state energy.
Recently, a realistic nucleon-nucleon potential has been developed with the goal of accurately reproducing isospin symmetry breaking effects in the nuclear interaction. We briefly discuss the motivation for this potential, called Argonne $v\sb{18},$ as well as the Urbana models of three-nucleon interactions. Our approach for modeling the ground states of nuclear systems begins with the development of a variational wave function. We discuss the basis for our variational wave functions and the Monte Carlo techniques used to evaluate expectation values with these wave functions. To determine the exact ground state, Green's function Monte Carlo (GFMC) techniques are used. We review the method of GFMC in general and then discuss its application to the problem of nuclear ground states in some detail.