Spectroscopic factors and asymptotic normalization coefficients in mirror three-body systems

Abstract

Using a three-body model, we study the dependence of spectroscopic factors for the overlap integrals $\ensuremath{\langle}\mathrm{core}+N|\mathrm{core}+N+N\ensuremath{\rangle}$ on the binding energy of the core $+ N$ subsystem, considering as prototypes $^{6}\mathrm{He}$, $^{6}\mathrm{Be}$, $^{9}\mathrm{Li}$, $^{9}\mathrm{C}$, $^{18}\mathrm{O}$, and $^{18}\mathrm{Ne}$. We show that at small $N$-core binding energies these spectroscopic factors can be strongly influenced by the geometrical mismatch between the two-body $N$-core wave function that stretches into the classically forbidden region and the spatially confined three-body function. This mismatch comes from the strong two-body correlations between the nucleons outside the core and due to the core recoil effects. The mismatch leads to symmetry breaking in mirror spectroscopic factors that in some cases can be large enough to be observed in nucleon removal reactions. It is also responsible for deviations of the ratios of mirror asymptotic normalization coefficients (ANCs) from the simple model-independent analytical estimates. We discuss the influence of such mirror symmetry breaking on the prediction of direct stellar ($p,\ensuremath{\gamma}$) reactions from the measured mirror neutron ANCs.