Variational Calculation of ⁴He Tetramer Ground and Excited States Using Realistic ⁴He-⁴He Potentials

We calculated binding energies and wave functions of the ⁴He tetramer ground and excited states employing various realistic ⁴He-⁴He potentials which includes the currently most accurate one with the adiabatic, relativistic, QED and residual retardation corrections. We used our Gaussian expansion method (GEM) for ab initio variational calculations of few-body systems. We found that precisely the same shape of the short-range correlation (r_ij < 4Å) in the dimer appear in the ground and excited states of trimer and tetramer. The four kinds of the binding energies of the trimer and tetramer ground and excited states, B₃⁽⁰⁾, B₃⁽¹⁾, B₄⁽⁰⁾ and B₄⁽⁰⁾, for the different potentials exhibit perfect linear correlations over the range of binding energies relevant for ⁴He atoms; namely, six types of the generalized atomic Tjon lines were observed.