Creation of neutron spinless pairs in a superfluid liquid $^4$He and a neutron gas mixture

TL;DR

This paper predicts the formation of neutron spinless pairs in a superfluid helium-4 and neutron gas mixture, using an extended Bose gas model to explain the interactions leading to bound neutron pairs.

Contribution

It introduces an exact solution to a dilute Bose gas model with variable condensate fraction, extending the Bogoliubov model, to describe neutron pair formation in superfluid helium-4.

Findings

Prediction of free neutron spinless pairs in the mixture.

Condensate atoms suppress collective modes and promote single-particle excitations.

Interaction between excitations mediates attractive forces leading to neutron pairing.

Abstract

First, the creation of a free neutron spinless pairs is predicted in a superfluid liquid $^4$He and a neutron gas mixture. For solving the given problem, it is presented an exact solution to the model of dilute Bose gas as an extension of the Bogoliubov model, at quantity of the condensate fraction varying in the state $0\leq\frac{N_0}{N}\leq 1$, which in turn might be useful for a description of the superfluid liquid $^4$He. Due to an application of presented new model of dilute Bose gas, we prove that an appearance of atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms of the interaction between the Bogoliubov excitations (Bogoliubov phonon-roton modes) and the density modes of the neutron meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair.