Linear correlations between 4He trimer and tetramer energies calculated with various realistic 4He potentials

TL;DR

This study calculates and compares the energies of helium-4 trimer and tetramer systems using various realistic potentials, revealing linear correlations and universal relations among their binding energies.

Contribution

It introduces a comprehensive analysis of helium-4 cluster energies with multiple potentials, confirming linear correlations and a universal relation predicted by the dimerlike-pair model.

Findings

Linear correlations between different helium-4 cluster energies were observed.

The dimerlike-pair model's universal relation accurately explains the energy correlation.

Inclusion of relativistic and QED corrections slightly adjusts the energy values.

Abstract

In a previous work [Phys. Rev. A 85, 022502 (2012)] we calculated, with the use of our Gaussian expansion method for few-body systems, the energy levels and spatial structure of the 4He trimer and tetramer ground and excited states using the LM2M2 potential, which has a very strong short-range repulsion. In this work, we calculate the same quantities using the presently most accurate 4He-4He potential [M. Przybytek et al., Phys. Rev. Lett. 104, 183003 (2010)] that includes the adiabatic, relativistic, QED and residual retardation corrections. Contributions of the corrections to the tetramer ground-(excited-)state energy, -573.90 (-132.70) mK, are found to be, respectively, -4.13 (-1.52) mK, +9.37 (+3.48) mK, -1.20 (-0.46) mK and +0.16 (+0.07) mK. Further including other realistic 4He potentials, we calculated the binding energies of the trimer and tetramer ground and excited states, B_3^(0), B_3^(1), B_4^(0) and B_4^(1), respectively. We found that the four kinds of the energies for the different potentials exhibit perfect linear correlations between any two of them over the range of binding energies relevant for 4He atoms (namely, six types of the generalized Tjon lines are given). The dimerlike-pair model for 4He clusters, proposed in the previous work, predicts a simple universal relation B_4^(1)/B_2 =B_3^(0)/B_2 + 2/3, which precisely explains the correlation between the tetramer excited-state energy and the trimer ground-state energy, with B_2 being the dimer binding energy.