Coulomb renormalization and ratio of proton and neutron asymptotic normalization coefficients for mirror nuclei

Abstract

Asymptotic normalization coefficients (ANCs) are fundamental nuclear constants playing important role in nuclear reactions, nuclear structure and nuclear astrophysics. In this paper the physical reasons of the Coulomb renormalization of the ANC are addressed. Using Pinkston-Satchler equation the ratio for the proton and neutron ANCs of mirror nuclei is obtained in terms of the Wronskians from the radial overlap functions and regular solutions of the two-body Schrödinger equation with the short-range interaction excluded. This ratio allows one to use microscopic overlap functions for mirror nuclei in the internal region, where they are the most accurate, to correctly predict the ratio of the ANCs for mirror nuclei, which determine the amplitudes of the tails of the overlap functions. Calculations presented for different nuclei demonstrate the Coulomb renormalization effects and independence of the ratio of the nucleon ANCs for mirror nuclei on the channel radius. This ratio is valid both for bound states and resonances. One of the goals of this paper is to draw attention on the possibility to use the Coulomb renormalized ANCs rather than the standard ones especially when the standard ANCs are too large.

Updated evidence of the Trojan horse particle invariance for the2H(d,p)3H reaction

“…• l l is the orbital angular momentum of particles s and x in the entry channel of the binary subreaction and L l l is a function of relative momentum and kinetic energy in the entry channel of the binary subreaction as defined in [25];…”

Ab initiono-core Gamow shell model calculations with realistic interactions

“…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].…”

Asymptotic normalization coefficients and radiative widths

“…The internal radial scattering wave function (r ≤ r 0 , r is the distance between the particles a and A, r 0 is the channel radius) in the single-channel R-matrix approach in the case of an isolated narrow resonance takes the form [3,6] …”

“…The ANC plays an important role in nuclear reaction and structure theory and in nuclear astrophysics [1][2][3][4]. By definition, the ANC is the amplitude of the tail of the overlap function.…”