Relation between Proton and Neutron Asymptotic Normalization Coefficients for Light Mirror Nuclei and its Relevance to Nuclear Astrophysics

Abstract

We show how the charge symmetry of strong interactions can be used to relate the proton and neutron asymptotic normalization coefficients (ANCs) of the one nucleon overlap integrals for light mirror nuclei. This relation extends to the case of real proton decay where the mirror analog is a virtual neutron decay of a loosely bound state. In this case, a link is obtained between the proton width and the squared ANC of the mirror neutron state. The relation between mirror overlaps can be used to study astrophysically relevant proton capture reactions based on information obtained from transfer reactions with stable beams.PACS numbers: 24.50.+g,27.20.+n,27.30.+t The astrophysical S-factor associated with the peripheral proton capture reaction B(p, γ)A at stellar energies is well known[1] to be related to the Asymptotic Normalization Coefficient (ANC) of the virtual decay A → B+p. The same ANCs play a crucial role in other peripheral processes such as transfer reactions whose cross sections are significantly higher and therefore more easily measurable than those of the direct capture processes at astrophysically relevant energies [1]. The study of ANCs of astrophysical interest is a new and rapidly developing direction in modern experimental nuclear physics [2,3]. However, in order to exploit these ideas to determine the ANCs for light proton-rich nuclei of importance to nuclear astrophysics the corresponding transfer reactions often require the use of weak radioactive beams which generally involves more difficult and less accurate experiments than are possible with stable beams. The higher intensities of stable beams means that they can be used at energies below the Coulomb barrier where the sensitivity to optical potentials, which are the main uncertainty of ANCs determined from transfer reactions, is minimised. We point out here that the ANC of the virtual neutron decay of the nucleus mirror to A, which may be susceptible to study with stable beams, is related in a model independent way by the charge symmetry of nuclear forces to the ANC of the corresponding proton decay of A. We propose to exploit this new insight to predict peripheral reaction cross sections in stars.An asymptotic normalization coefficient (ANC) is one of the fundamental characteristics of the virtual decay of a nucleus into two clusters and is equivalent to the coupling constants in particle physics [4]. When multiplied by a trivial factor, it equals to the on-shell amplitude for the virtual decay into two clusters and it determines the large distance behaviour of the projection of the bound state wave function of the nucleus onto a binary channel.In earlier work [5,6], the ANCs for the one-nucleon virtual decays of the mirror pairs 8 B − 8 Li and 12 N − 12 B were studied in a microscopic approach. The calculated ANCs themselves depended strongly on the choice of the nucleon-nucleon (NN) force but the ratios of ANCs for mirror pairs were practically independent of the choice of the NN force. This observation is based so far entirely on the c...

Experimental study of bound states in12Be through low-energy11Be(d,p)Johansen1, Bildstein2, Borge3 et al. 2013Phys. Rev. C293180View full textAdd to dashboardCite

“…is often making use of continuum discretized coupled channel (CDCC) calculations; see [47][48][49] and references therein. The concept of a spectroscopic factor, often used earlier as the key quantity to be extracted from experiment, has also been questioned during the last decade-see Mukhamedzhanov [49] and Jennings [50] for recent overviews-asymptotic normalization coefficients (ANCs) [49,[51][52][53] have been used instead. A proper theoretical analysis of our data is beyond the scope of the present paper so we shall here just briefly indicate what can be learned from a standard approach to allow comparison with earlier experimental work [26].…”

Overlap functions, spectroscopic factors, and asymptotic normalization coefficients generated by a shell-model source term

“…According to the analytical formula from Ref. [37], the ratio R = (C p /C n ) 2 for mirror ANCs in 14 N should be equal to 1.39. However, the experimental ratio, R exp = 1.12 (30) …”

Neutron halos in the excited states of B12

“…of mirror nuclei was established in Refs. [32,33]. Thus the radii of 12 B in the halo states that will be presented in this paper are useful in estimating the radii of the nuclei with A = 12 determined by other methods.…”