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 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.Comment: 10 pages, 3 figures, published version in Phys. Rev. A85, 062505 (2012), Figs. 2, 5, and 6 added, minor changes in the description of the dimerlike-pair mode

Modelling double charge exchange response function for tetraneutron system

This work is an attempt to model the $4n$ response function of a recent RIKEN experimental study of the double charge exchange $^4$He($^8$He,$^8$Be)$^4$n reaction in order to put in evidence an eventual enhancement mechanism of the zero energy cross section, including a near-threshold resonance. This resonance can indeed be reproduced only by adding to the standard nuclear Hamiltonian an unphysically large T=3/2 attractive 3n-force which destroys the neighboring nuclear chart. No other mechanisms like cusps or related structures were found

Constituent quark model for baryons with strong quark-pair correlations and non-leptonic weak transitions of hyperon

We study the roles of quark-pair correlations for baryon properties, in particular on non-leptonic weak decay of hyperons. We construct the quark wave function of baryons by solving the three body problem explicitly with confinement force and the short range attraction for a pair of quarks with their total spin being 0. We show that the existence of the strong quark-quark correlations enhances the non-leptonic transition amplitudes which is consistent with the data, while the baryon masses and radii are kept to the experiment.Comment: 4 pages, 2 figures, talk presented at KEK-Tanashi International Symposium on Physics of Hadrons and Nuclei, Tokyo, Japan, 14-17 Dec. 199

Four- and Five-Body Scattering Calculations

We study the five-quark system $uudd{\bar s}$ in the standard non-relativistic quark model by solving the scattering problem. Using the Gaussian Expansion Method (GEM), we perform the almost precise multi-quark calculations by treating a very large five-body modelspace including the NK scattering channel explicitly. Although a lot of pseudostates (discretized continuum states) with $J^\pi={1/2}^\pm$ and $J^\pi={3/2}^\pm$ are obtained within the bound-state approximation, all the states in $1.4-1.85$ GeV in mass around ${\rm {\rm \Theta}}^+(1540)$ melt into non-resonant continuum states through the coupling with the NK scattering state in the realistic case, i.e., there is no five-quark resonance below 1.85GeV. Instead, we predict a five-quark resonance state of $J^\pi={1/2}^-$ with the mass of about 1.9GeV and the width of $\Gamma \simeq$ 2.68MeV. Similar calculation is done for the four-quark system $c{\bar c}q{\bar q}$ ($q=u,d$) in connection with X$^0$(3872)