Deuteron-equivalent and phase-equivalent interactions within light nuclei

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.

Figure 1

Large (a) and small (b) components of the $np$ scattering wave function at the laboratory energy $E_{\mathrm{lab}}=10$ MeV in the $sd$ coupled partial wave in the $K$-matrix formalism (see Ref. [11] for details and nomenclature) generated by JISP16 and $NN$ interactions obtained from JISP16 by means of DET-PET $0s2s1s3s^{\pm }$. The sign of $\det U^0$ is given in the legends in parenthesis after the value of rotation angle $\beta$.

Figure 2

Same as Fig. 1 but for DET-PET $0s1s0d1d^{\pm }$.

Figure 3

Same as Fig. 1 but for DET-PET $1s0d0s1d^{\pm }$.

Figure 4

Tjon line obtained with DET-PET $1s0d0s1d^{\pm }$ in comparison with results obtained with various $NN$ and $NN+NNN$ interaction models from Refs. [32, 34, 35].

Figure 5

Same as Fig. 4 but for DET-PET $0s1s0d1d^{\pm }$.

Figure 6

Same as Fig. 4 but for DET-PET $0s2s1s3s^{\pm }$.