Extrapolation of scattering data to the negative-energy region

Abstract

Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed into forms convenient for extrapolating to the negativeenergy region and obtaining the information about bound-state properties. Alternative ways of extrapolation are discussed. Analytic properties of separate terms entering these expressions for the effective-range function and the partial-wave scattering amplitude are investigated.

Effective two-body model for spectra of clusters of H2,H3,Fraser1, Massen-Hane2, Kadyrov3 et al. 2017Phys. Rev. CSelf Cite

“…We do not consider the states to be coupled by a spin-isospin changing interaction. The deuteron states are both of positive parity and the low excitation spectrum of 6 Li only has positive parity states so the dominant character of the interaction potentials is of positive parity. The results were obtained using V 0 = -64.775, V ll = 0.93, V lI = 1.97, and V + II = -2.0 (all in MeV) with a geometry of R 0 = 2.3 and a 0 = 0.43 fm.…”

“…None of the four nuclei forming the clusters have low lying excited states below nucleon breakup thresholds. However the compound systems formed, 6 Li, 7 Li, 7 Be, and 8 Be, do. We use a Sturmian expansion approach to solve Lippmann-Schwinger (LS) equations; an approach that provides a low energy spectrum (bound and continuum states) of the compound nucleus formed by each cluster considered, as well as giving the relevant S -matrices with which scattering cross sections can be evaluated.…”

“…Spectra of 7 Li and 7 Be have been found previously [8] by solving the coupled-channel problems of nucleons coupling to 6 He and 7 Be nuclei allowing for the nucleons to interact with low excitation states of the nuclei. The results agreed well with known states in the spectra.…”

“…In this investigation, we calculate the lowenergy elastic scattering cross section of the 4 He+ 2 H system and the low-energy spectrum of 6 Li from the same clusterisation, both using the same interaction potential. Investigation of the low-energy scattering of deuterons from 4 He dates back to experimental work in the 1930s [7].…”

“…An interesting method of analytic continuation of the elastic scattering data at positive energies to negative energies was investigated in Ref. [6], and applied to extract bound-1 state properties of the 2 H+ 4 He system.…”