Two-pole structure of the 3/2+resonance ofHe5

Abstract

By a realistic dynamical microscopic reaction approach to ^He we reproduce the empirical positions of the two 5-matrix poles associated with the | resonance, and unambiguously prove that it arises from the t-\-d channel. The picture is not coherent though, unless the presently adopted a-\-n phase shift, extracted partly from a-\-p scattering data, is assumed to be incorrect. It is pointed out that the analog resonance in ^Li behaves very differently because the shadow pole is located on another Riemann sheet.

S-matrix andR-matrix determination of the low-energy5He andCsótó1, Hale2 1997Phys. Rev. C

“…We mention here two examples: the large cross section of the t(d, n)α reaction and the problem of the soft dipole resonance in neutron halo nuclei. Only analyses at complex energies were able to reveal that the large reaction cross section is caused by a shadow pole of the scattering matrix in the former case [3,4], and that the soft dipole resonance does not exist in 6 He in the latter one [5]. It is an intriguing question whether or not the results of methods that are not confined to real energies agree with those of conventional analyses for the relatively broad resonances encountered in light systems.…”

“…However, for broad resonances the results coming from the two definitions may be different, because only the scattering theoretical quantities defined at complex energies (e.g., the S-matrix, the Fredholm determinant, and the Jost function on the multisheeted Riemann energy surface) contain the correct dynamical information. Even in the case of a narrow multichannel resonance the results coming from the two definitions can disagree, and studying the complex energy scattering quantities can give a much deeper insight into the dynamics of the problem [3,4].…”

Erratum: Search for excited states in3Hand3He[Phys. Rev. C59, 1207 (1999)]

“…[17], and their singularities are localized. As a test calculation we searched for the boundstate poles and found them at the same energies as in the bound-state calculations.…”

Use of supersymmetric isospectral formalism to realistic quantum many-body problems

“…With the radioactive ion beam facilities, the information about the ground and resonance states are already known experimentally. Although there are numerous theoretical studies of the ground state [3][4][5], the calculation of high-lying resonance states of such highly unstable nuclei is a difficult task. The shallow well can trap the system temporarily giving rise to a broad resonance.…”

“…Isospectral formalism [1] is a novel technique for the calculation of such high-lying resonance states of weakly bound systems [2][3][4][5]. Starting from an effective potential v(r), one can construct a family of isospectral potentialv(r, λ) (where {λ} represents a set of one or more continuously variable real parameters).…”