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.

20 pages, 14 figures

References in corpus (6)

• Ab Initio Many-Body Calculations of n-3H, n-4He, p-{3,4}He, and n-10Be Scattering
• Quantum Monte Carlo calculations of neutron-alpha scattering
• Asymptotic normalization coefficients from ab initio calculations
• {Once more about astrophysical $S$ factor for the $\alpha +d\to {}^6\mathrm{Li}+\gamma$ reaction
• Unitary correlation in nuclear reaction theory
• Astrophysical S factor for the radiative capture 12N(p,gamma)13O determined from the 14N(12N,13O)13C proton transfer reaction

Cited by in corpus (8)

• Ab-initio No-Core Gamow Shell Model calculations with realistic interactions
• Concurrent application of ANC and THM to assess the ${}^{13}\mathrm{C}(\alpha ,n{)}^{16}\mathrm{O}$ absolute cross section at astrophysical energies and possible consequences for neutron production in low-mass AGB stars
• Subthreshold resonances and resonances in the $R$-matrix method for binary reactions and in the Trojan Horse method
• Extrapolation of scattering data to the negative-energy region. Application to the $p{-}^{16}$O system
• Connection between asymptotic normalization coefficients and resonance widths of mirror states
• Trojan horse method as surrogate indirect approach to study resonant reactions in nuclear astrophysics
• New method of analytic continuation of elastic-scattering data to the negative-energy region and asymptotic normalization coefficients for ${}^{17}$O and ${}^{13}$C
• A Cautionary Tale: The Coulomb Modified ANC for the $1/2_2^{+}$ State in ${}^{17}$O