Variational Theory and Parquet Diagrams for Nuclear Systems: A Comprehensive Study of Neutron Matter

TL;DR

This paper combines variational and parquet diagram techniques to study neutron matter, revealing significant short-range non-parquet corrections and their impact on many-body properties, including pairing and spin-orbit interactions.

Contribution

It introduces a combined variational and parquet diagram approach to analyze realistic nuclear interactions, emphasizing the importance of non-parquet diagrams at short distances.

Findings

Non-parquet contributions are dominant at short distances.

Many-body correlations reduce the spin-orbit interaction.

Pairing gaps vary significantly with the potential model.

Abstract

To deal with the problem of realistic nuclear interactions we have combined techniques of the Jastrow-Feenberg variational method and the local parquet-diagram theory. In the language of diagrammatic perturbation theory, ``commutator diagrams'' can be identified with non-parquet diagrams. We examine the physical processes described by these terms and include the relevant diagrams in a way that is suggested by the Jastrow-Feenberg approach. We show that the corrections from non-parquet contributions are, at short distances, larger than all other many-body effects. We examine here neutron matter as a prototype of systems with state-dependent interactions. Calculations are carried out for neutrons interacting via the so-called $v_8$ version of four popular interactions. We determine the structure and effective interactions and apply the method to the calculation of the energetics, structure and dynamic properties such as the single-particle self-energy and the dynamic response functions as well as BCS pairing in both singlet and triplet states. We find that many-body correlations lead to a strong reduction of the spin-orbit interaction, and, therefore, to a suppression of the $^3P_2$ and $^3P_2$-$^3F_2$ gaps. We also find pairing in $^3P_0$ states; the strength of the pairing gap depends sensitively on the potential model employed.