S-matrix andR-matrix determination of the low-energy5He and

Attila Csótó

¹

,

Gerald M. Hale

²

Abstract

We study the low-energy 3/2 − and 1/2 − states of 5 He and 5 Li in a microscopic cluster model. The scattering phase shifts of Bond (α + n) and of Schwandt (α + p), respectively, are reproduced well. We determine the resonance parameters by localizing the poles of the analytically continued S-matrix at complex energies. Our results differ from conventional R-matrix resonance parameters, which were extracted from experimental data using the definition of a resonance based on the positions and widths of reaction cross section peaks. However, they nicely agree with the results of an extended R-matrix method which works at complex energies.

Calculation of Expectation Values of Operators in the Complex Scaling Method

“…It has been observed that even in the phenomenological R-matrix case, it is beneficial to perform a continuation of the S-matrix in the complex energy plane in order to determine more reliably resonance parameters [26]. At first glance the complex energy would seem unnatural since reactions take place on the real energy axis.…”

Ab initiono-core Gamow shell model calculations with realistic interactions

“…First, one could apply the conventional R-matrix approach on the real axis and use the Lane and Thomas prescription for the extraction of positions and widths of a state [81]. The second way is the extended R-matrix approach [82,83], which associates the resonance parameters with the complex poles of the S-matrix. According to [80,84], this is the recommended prescription, and it is also the most appropriate for comparison to the NCGSM results, since our complex eigenvalues correspond, indeed, to the location of the poles of the S-matrix, with the correct asymptotic behavior.…”

Ab InitioMany-Body Calculations of theH3(d,n)He4andNavrátil1, Quaglioni2 2012Phys. Rev. Lett.13851630View full textAdd to dashboardCite

“…Consensus on the physics mechanism behind this enhancement has not been reached yet [6], largely because of the difficulty of determining the absolute value of the bare cross section. Past theoretical investigations of these fusion reactions include various R-matrix analyses of experimental data at higher energies [7-10] as well as microscopic calculations with phenomenological interactions [11,12]. However, in view of remaining experimental challenges (some of which are described above) and the large role played by theory in extracting the astrophysically important information, it would be highly desirable to achieve a microscopic description of the 3 Hðd; nÞ 4 He and 3 Heðd; pÞ 4 He fusion reactions that encompasses the dynamic of all five nucleons and is based on the fundamental underlying physics: the realistic interactions among nucleons and the structure of the fusing nuclei.…”