Zero-point Divacancy Concentration in the Shadow Wave-Function Model for Solid 4He

TL;DR

This study calculates the zero-point vacancy and divacancy concentrations in solid 4He using the shadow wave-function model, revealing low clustering propensity and no phase separation tendency.

Contribution

It provides the first detailed analysis of divacancy concentrations considering both in-plane and out-of-plane configurations within this model.

Findings

Zero-point monovacancy concentration is approximately 2.03 x 10^{-3}.

Divacancy concentration is only 4-5 times higher than in absence of clustering.

No significant vacancy aggregation or phase separation expected in the ground state.

Abstract

We address the issue of interaction between zero-point vacancies in solid 4He as described within the shadow wave-function model. Applying the reversible-work method and taking into account finite-size effects, we obtain a zero-point monovacancy concentration of (2.03 +- 0.02) 10^{-3}, which is slightly higher than the result due to Reatto et al. for the same model. Utilizing the same methodology, we then consider the divacancy, taking into account both the in-plane as well as out-of-plane configurations with respect to the basal plane. We find no significant anisotropy between both conformation. Furthermore, although there is a small binding tendency, the expected divacancy concentration is only ~4-5 times larger than the value expected in the absence of any clustering propensity, 2.5 10^{-5}. This result suggests that, within the employed model description, no vacancy aggregation leading to phase separation is to be expected in the ground state.