Deuteron-equivalent and phase-equivalent interactions within light nuclei

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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 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 ³H and ⁴He 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 ³H and ⁴He 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 ³H (in the range of approximately 1.5 MeV) and ⁴He (in the range of more than 9 MeV) and are able to modify the correlation patterns of binding energies of these nuclei.