Asymptotic normalization of mirror states and the effect of couplings

Abstract

Assuming that the ratio between asymptotic normalization coefficients of mirror states is model independent, charge symmetry can be used to indirectly extract astrophysically relevant proton capture reactions on proton-rich nuclei based on information on stable isotopes. The assumption has been tested for light nuclei within the microscopic cluster model. In this work we explore the Hamiltonian independence of the ratio between asymptotic normalization coefficients of mirror states when deformation and core excitation is introduced in the system. For this purpose we consider a phenomenological rotor + N model where the valence nucleon is subject to a deformed mean field and the core is allowed to excite. We apply the model to 8 Li/ 8 B, 13 C/ 13 N, 17 O/ 17 F, 23 Ne/ 23 Al, and 27 Mg/ 27 P. Our results show that for most studied cases, the ratio between asymptotic normalization coefficients of mirror states is independent of the strength and multipolarity of the couplings induced. The exception is for cases in which there is an s-wave coupled to the ground state of the core, the proton system is loosely bound, and the states have large admixture with other configurations. We discuss the implications of our results for novae.

Mechanism of the $^{7}$Li($d,t$)$^{6}$Li Reaction at 25 MeV Energy of Deuterons, Values of Spectroscopic Factors and Asymptotic Normalization Coefficients for the $^{7}$Li $\rightarrow $ $^{6}$Li + $n$ Vertex

“…There is an active discussion in recent years concerning the accuracy of a strong correlation between them (see [27] and references therein). Indeed, if the spectroscopic factors of these states are equal, relation (3) implies:…”

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

“…An extensive analysis of proton and neutron ANCs for light mirror nuclei has been performed using SM and cluster model wave function and various effective N N interactions [1,[15][16][17][18]. It has been found that the ratio of proton and neutron ANCs for mirror nuclei,…”

“…9(d). It should be stressed that the large difference of mirror ANCs in 18 Ne and 18 O is due to the symmetry breaking in mirror spectroscopic factors and not due to the change of the ratio of β 2 ℓj for protons and neutrons. A similar conclusion has been drawn in Ref.…”

“…[1,[15][16][17][18] that the ratio R of ANCs for mirror pairs is both approach-independent and interactionindependent. To investigate the proposed link between proton and neutron mirror ANCs [1], we employ the framework of the nuclear Shell Model (SM) for open quantum systems (OQS), i.e., the continuum shell model (CSM) [19,20], which offers a realistic treatment of the configuration mixing in well-bound, weakly-bound, and unbound states.…”

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.…”