Linear correlations between4He trimer and tetramer energies calculated with various realistic4He potentials

Abstract

In a previous work [Phys. Rev. A 85, 022502 (2012)] we calculated, with the use of the Gaussian expansion method for few-body systems, the energy levels and spatial structures of the ${}^{4}$He 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 currently most accurate ${}^{4}$He-${}^{4}$He potential [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 $\ensuremath{-}573.90\phantom{\rule{0.16em}{0ex}}(\ensuremath{-}132.70)$ mK are respectively $\ensuremath{-}4.13\phantom{\rule{0.16em}{0ex}}(\ensuremath{-}1.52)$ mK, $+9.37\phantom{\rule{0.16em}{0ex}}(+3.48)$ mK, $\ensuremath{-}1.20\phantom{\rule{0.16em}{0ex}}(\ensuremath{-}0.46)$ mK, and $+0.16\phantom{\rule{0.16em}{0ex}}(+0.07)$ mK. Further including other realistic ${}^{4}$He potentials, we calculated the binding energies of the trimer and tetramer ground and excited states, ${B}_{3}^{(0)},\phantom{\rule{0.16em}{0ex}}{B}_{3}^{(1)},\phantom{\rule{0.16em}{0ex}}{B}_{4}^{(0)}$, and ${B}_{4}^{(1)}$, respectively. We found that the four kinds of the binding energies for the different potentials exhibit perfect linear correlations between any two of them over the range of binding energies relevant for ${}^{4}$He atoms (namely, six types of the generalized Tjon lines are observed). The dimerlike-pair model for ${}^{4}$He clusters, proposed in the previous work, predicts a simple interaction-independent relation $\frac{{B}_{4}^{(1)}}{{B}_{2}}=\frac{{B}_{3}^{(0)}}{{B}_{2}}+\frac{2}{3}$, 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.