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

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 He-4 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 He-4-He-4 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 -573.90 (-132.70) mK are 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 He-4 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 binding energies for the different potentials exhibit perfect linear correlations between any two of them over the range of binding energies relevant for He-4 atoms (namely, six types of the generalized Tjon lines are observed). The dimerlike-pair model for He-4 clusters, proposed in the previous work, predicts a simple interaction-independent 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.