Nucleon-nucleon interaction in the J-matrix inverse scattering approach and few-nucleon systems

The nucleon-nucleon interaction is constructed by means of the $J$-matrix version of inverse scattering theory. Ambiguities of the interaction are eliminated by postulating tridiagonal and quasi-tridiagonal forms of the potential matrix in the oscillator basis in uncoupled and coupled waves, respectively. The obtained interaction is very accurate in reproducing the $NN$ scattering data and deuteron properties. The interaction is used in the no-core shell model calculations of $^3$H and $^4$He nuclei. The resulting binding energies of $^3$H and $^4$He are very close to experimental values.