Asymptotic normalization coefficients and continuum coupling in mirror nuclei

Abstract

Background: An asymptotic normalization coefficient (ANC) characterizes the asymptotic form of a one-nucleon overlap integral required for description of nucleon-removal reactions.Purpose: We investigate the impact of the particle continuum on proton and neutron ANCs for mirror systems from p-and sd-shell regions. Method:We use the real-energy and complex-energy continuum shell model approaches.Results: We studied the general structure of the single-particle ANCs as a function of the binding energy and orbital angular momentum. We computed ANCs in mirror nuclei for different physical situations, including capture reactions to weakly-bound and unbound states. Conclusions:We demonstrated that the single-particle ANCs exhibit generic behavior that is different for charged and neutral particles. We verified the previously proposed relation [1] between proton and neutron mirror ANCs. We find minor modifications if the spectroscopic strength is either localized in a single state or broadly distributed. For cases when several states couple strongly to the decay channel, these modifications may reach 30%.

Ab initiono-core Gamow shell model calculations with realistic interactions

“…We then find a width Γ ANC = 311 keV and Γ ANC = 570 for Λ = 1.9 fm −1 and 2.1 fm −1 respectively, which is consistent with the width obtained in NCGSM/DMRG (or NCGSM/4p4h). As we said, relation (25) is mainly valid for narrow resonances, which is known for calculations on the real-axis [99] and it was also proved in [96] for an unbound state in the complex plane. The approximation is that the real part of the linear momentum k = 2mS1n 2 is considered.…”

“…Experimentally, ANCs have been measured for s-shell and p-shell nuclei and for a detailed list of references we refer the reader to [94]. Recently, theoretical calculations of ANCs have been performed in the framework of the HH approach [95], the GSM and SMEC [96], the GFMC [47,94,97] and also [98].…”

“…Indeed, the width and ANC are related via the relation (see Ref. [47,96] and references cited therein)…”

Constraint of the AstrophysicalAl26g(p,γ)SiPain1, Bardayan2, Blackmon3 et al. 2015Phys. Rev. Lett.Self Cite312290View full textAdd to dashboardCite

“…In order to determine the proton spectroscopic factors for the mirror states in 27 Si, calculations of spectroscopic factors were performed for states in 27 Al and 27 Si within the Shell Model Embedded in the Continuum (SMEC) formalism [37], using the USD-b effective interaction and a continuum coupling constant of −650 MeV fm 3 (found in previous studies to be typical for this mass region [38]). The ratio of the theoretical spectroscopic factors (C 2 S th π for 27 Si to C 2 S th ν for 27 Al, for the same shell model state) is used to scale the experimentallydetermined neutron spectroscopic factor C 2 S exp ν for 27 Al to calculate the proton spectroscopic factor C 2 S π for the mirror state in 27 Si.…”

Spectroscopic study of the exotic nucleusP25

“…Similar uncertainties compared to those introduced by the use of Eq. (2), i.e., in the range 10%-30% or exceptionally up to 50%, were found in other microscopic approaches [40,41] and in the coupled-channel calculations [42]. They are partially associated with the different radial extent of the mirror proton and neutron overlap integrals at large r caused by the absence or presence of the Coulomb interaction for neutron or proton, respectively.…”