$β^-$ decay of $T_z$ = +$\frac{11}{2}$ isotopes $\mathrm{^{37}Al}$ and $\mathrm{^{39}Si}$: Understanding Gamow-Teller strength distribution in neutron-rich nuclei
$β^-$ decay of $T_z$ = +$\frac{11}{2}$ nuclei $\mathrm{^{37}Al}$ and $\mathrm{^{39}Si}$ was studied to obtain information about excited states in the daughter and granddaughter nuclei. New information on excited states has been obtained for $\mathrm{^{37,39}P}$ whereas level schemes for $\mathrm{^{37}Si}$ and $\mathrm{^{37,39}S}$ were confirmed and expanded on as compared to the most recent investigations. For the nuclei studied, the valence proton and neutron occupy different major shells with opposite parities, hence, the $β^-$ decay preferentially and primarily populates core-excited $1p1h$ intruder states with a parity opposite to the ground state of the daughter nucleus. These low-lying intruder states shed light on the $N = 20$ shell gap and its evolution with neutron number. The $β^-$ decay of very neutron-rich nuclei also illustrates how the Gamow-Teller (GT) strength distribution changes with neutron excess. Comparing $β^-$ decay of $\mathrm{^{37,39}Si}$ presented here with $\mathrm{^{38,40}Si}$ from a previous study, we clearly see an even-odd effect in the GT strength distribution with the decay from even-even nuclei showing strong low-lying strength whereas for the odd $A$ being very fragmented. Finally, configuration interaction shell-model calculations with the state-of-art SDPFSDG-MU effective interaction were performed to understand the structure of the $1p1h$ states and explore the GT strength distribution.