Study of nuclear pairing with Configuration-Space Monte-Carlo approach

TL;DR

This paper introduces a novel Configuration-Space Monte-Carlo method for modeling nuclear pairing correlations, offering advantages like no fermionic sign problem and scalability to large systems, demonstrated through models and realistic examples.

Contribution

A new CSMC method for nuclear pairing that overcomes limitations of existing techniques, enabling large-scale and complex problem solving with controlled accuracy.

Findings

CSMC effectively models pairing in nuclei.

No fermionic sign problem in the approach.

Handles large configuration spaces and complex scenarios.

Abstract

Pairing correlations in nuclei play a decisive role in determining nuclear drip-lines, binding energies, and many collective properties. In this work a new Configuration-Space Monte-Carlo (CSMC) method for treating nuclear pairing correlations is developed, implemented, and demonstrated. In CSMC the Hamiltonian matrix is stochastically generated in Krylov subspace, resulting in the Monte-Carlo version of Lanczos-like diagonalization. The advantages of this approach over other techniques are discussed; the absence of the fermionic sign problem, probabilistic interpretation of quantum-mechanical amplitudes, and ability to handle truly large-scale problems with defined precision and error control, are noteworthy merits of CSMC. The features of our CSMC approach are shown using models and realistic examples. Special attention is given to difficult limits: situations with non-constant pairing strengths, cases with nearly degenerate excited states, limits when pairing correlations in finite systems are weak, and problems when the relevant configuration space is large.