Deuteron-equivalent and phase-equivalent interactions within light nuclei

Abstract

Background: Phase-equivalent transformations (PETs) are well known in quantum scattering and inverse-scattering theory. PETs do not affect scattering phase shifts and bound-state energies of a two-body system but are conventionally supposed to modify two-body bound-state observables such as the rms radius and electromagnetic moments.Purpose: In order to preserve all bound-state observables, we propose a new particular case of PETs, a deuteron-equivalent transformation (DET-PET), which leaves unchanged not only scattering phase shifts and bound-state (deuteron) binding energy but also the bound-state wave function.Methods: The construction of DET-PET is discussed; equations defining the simplest DET-PETs are derived. We apply these simplest DET-PETs to the JISP16 $NN$ interaction and use the transformed $NN$ interactions in calculations of ${}^{3}$H and ${}^{4}$He binding energies in the no-core full configuration (NCFC) approach based on extrapolations of the no-core shell model (NCSM) basis space results to the infinite basis space.Results: We demonstrate the DET-PET modification of the $np$ scattering wave functions and study the DET-PET manifestation in the binding energies of ${}^{3}$H and ${}^{4}$He nuclei and their correlation (Tjon line).Conclusions: It is shown that some DET-PETs generate modifications of the central component while the others modify the tensor component of the $NN$ interaction. DET-PETs are able to modify significantly the $np$ scattering wave functions and hence the off-shell properties of the $NN$ interaction. DET-PETs give rise to significant changes in the binding energies of ${}^{3}$H (in the range of approximately 1.5 MeV) and ${}^{4}$He (in the range of more than 9 MeV) and are able to modify the correlation patterns of binding energies of these nuclei.