Variational calculation of 4He tetramer ground and excited states using a realistic pair potential

TL;DR

This paper employs a Gaussian expansion method to accurately calculate the ground and excited states of 4He tetramers and trimers, providing detailed energy values and a predictive model based on dimer binding energy.

Contribution

It introduces a variational Gaussian expansion approach for four-body helium systems and proposes a simple N/2(N-1) model for excited state energies based on dimer data.

Findings

Calculated tetramer and trimer energies agree with existing literature.

Identified similar short-range correlations in dimers, trimers, and tetramers.

Proposed a predictive model for excited state energies using dimer binding energy.

Abstract

We calculated the 4He trimer and tetramer ground and excited states with the LM2M2 potential using our Gaussian expansion method (GEM) for ab initio variational calculations of few-body systems. The method has extensively been used for a variety of three-, four- and five-body systems in nuclear physics and exotic atomic/molecular physics. The trimer (tetramer) wave function is expanded in terms of symmetric three-(four-)body Gaussian basis functions, ranging from very compact to very diffuse, without assuming any pair correlation function. Calculated results of the trimer ground and excited states are in excellent agreement with the literature. Binding energies of the tetramer ground and excited states are obtained to be 558.98 mK and 127.33 mK (0.93 mK below the trimer ground state), respectively. Precisely the same shape of the short-range correlation (r_ij < 4 \AA) in the dimer appear in the ground and excited states of the trimer and tetramer. Analyzing the asymptotic wave functions (accurate up to 1000 \AA) of those excited states, we propose a model which predicts the binding energy of the first excited state of 4He_N measured from the 4He_{N-1} ground state to be N/2(N-1)xB_2 using dimer binding energy B_2 only; fit in N=3 and 4 is excellent.