Faddeev calculations on lambda hypertriton with potentials from Gel’fand–Levitan–Marchenko theory

Abstract

Effective lambda-proton and lambda-neutron potentials, restored from theoretical scattering phases through Gel’fand–Levitan–Marchenko theory, are tested on a lambda hypertriton through three-body calculations. The lambda hypertriton is treated as a three-body system consisting of lambda-proton, lambda-neutron and proton–neutron subsystems. Binding energy and root mean square radius are computed for the ground state of lambda hypertriton ( ). In coordinate space, the dynamics of the system is described using a set of coupled hyperradial equations obtained from the differential Faddeev equations. By solving the eigenvalue problem derived from this set of coupled hyperradial equations, the binding energy and root mean square matter radius computed are found to be −2.462 MeV and 7.00 fm, respectively. The potentials are also shown to display a satisfactory convergence behaviour.

Fast cooling and internal heating in hyperon stars

“…We also neglect cross-species pairing for simplicity, i.e. the formation of mixed nucleon-hyperon superfluidity, noting that several works find attractive interaction potentials among baryons of different species (Zhou et al 2005;Nemura et al 2009;Meoto & Lekala 2020;Haidenbauer et al 2020).…”

“…However, as pointed out in Sedrakian & Clark (2019), Cooper pairs made of particles of different species may form in regions of the star where the Fermi surfaces of hyperons and nucleons are close. Several works find indeed an attractive interaction among nucleons and hyperons (Zhou et al 2005;Nemura et al 2009;Vidaña 2018;Meoto & Lekala 2020;Haidenbauer et al 2020), although the interaction potentials are difficult to fit experimentally. For simplicity, we neglect the formation of superfluid phases arising from the attractive interaction between nucleons and hyperons.…”

$ΛNN $ three-body problem within $s$-wave inverse scattering on theoretical data

“…These potentials were restored through the application of this method on sub-threshold theoretical s-wave scattering phases. Based on the spin multiplicities of the 1 S 0 and 3 S 1 ΛN states, effective potentials are constructed from one-quarter spin singlet and three-quarters spin triplet potentials from inverse scattering theory [15]:…”

“…In order to provide a new perspective on the ΛN force, inverse scattering theory has recently been applied on theoretical Λp and Λn scattering data [14]. Spin averages of the recovered Λp and Λn potentials (GLM-YN0) were tested in [15] by computing the binding energy and root-mean-square radius of Λnp (J π = 1/2 + ), using Malfliet-Tjon V potential for the NN interaction. The aim of this paper is to use GLM-YN0 potentials with the semi-realistic spin-dependent Malfliet-Tjon I/III NN potential that correctly binds the deuteron, in exploring the Λnp (J π = 1/2 + ) and Λnn (J π = 1/2 + ) three-body problems.…”