On nuclear short-range correlations and the zero-energy eigenstates of the Schrodinger equation

TL;DR

This paper investigates the universal behavior of nuclear short-range correlations and their connection to zero-energy eigenstates, revealing that certain coupled-cluster amplitudes obey universal equations independent of nucleon number.

Contribution

It demonstrates the universality of high-momentum coupled-cluster amplitudes and their equivalence to the zero-energy Bloch-Horowitz operator, linking nuclear many-body theory with the contact formalism.

Findings

Coupled-cluster amplitudes obey universal equations at high momentum.

These amplitudes coincide with the zero-energy Bloch-Horowitz operator.

Results suggest a universal asymptotic form for nuclear correlations.

Abstract

We present a systematic analysis of the nuclear 2 and 3-body short range correlations, and their relations to the zero-energy eigenstates of the Schrodinger equation. To this end we analyze the doublet and triplet Coupled-Cluster amplitudes in the high momentum limit, and show that they obey universal equations independent of the number of nucleons and their state. Furthermore, we find that these Coupled-Cluster amplitudes coincide with the zero-energy Bloch-Horowitz operator. These results illuminate the relations between the nuclear many-body theory and the generalized contact formalism, introduced to describe the nuclear 2-body short range correlations, and it might also be helpful for general Coupled-Cluster computations as the asymptotic part of the amplitudes is given and shown to be universal.