Indispensability of cross-shell contributions in neutron resonance spacing

Spin and parity dependent nuclear level densities (NLDs) are obtained for configuration interaction shell model using a numerically efficient spectral distribution method. The calculations are performed for $^{24}$Na, $^{25,26,27}$Mg nuclei using full $sd$-$pf$ model space that incorporates the cross-shell excitations from $sd$ to $pf$-shell. The NLDs so obtained are then employed to determine the s-wave neutron resonance spacing (D$_0$) which is one of the crucial inputs for the predictions of astrophysical reaction rates. Though the considered nuclei are not neutron-rich, the contributions from cross-shell excitations to $pf$-shell are indispensable to explain the experimental data for D$_0$ which otherwise are significantly overestimated.