Cross-shell configurations in $^{38}$Cl structure and the quest for a new shell model interaction.

$^{38}$Cl with Z = 17 and N = 21 has long been recognized as providing a window into the interactions between $\pi 0d_{3/2}$ and $\nu f_{7/2}$ nucleons. The availability of a $^{14}$C beam to occur a fusion evaporation reaction in conjunction with the $\gamma$-detector array at the John. D. Fox laboratory has allowed further exploration of the higher-spin structure of $^{38}$Cl to elucidate the role of excitations across the N = 20 shell gap. Comparison with microscopic structure models has proved very fruitful in the past in interpreting level schemes, but were limited by the need to adjust the N = 20 shell gap for cross-shell excitations for different nuclei. Therefore, we developed a microscopic effective interaction based on fitting the shell model cross-shell interaction matrix elements over a wide range of particle-hole states in nuclei across the $sd$ shell and beyond. The main focus was to tune the monopole terms across the shell gaps, N = 8 and N =20. The valence space of the new FSU interaction comprises the $spsdpf$ model space, compatible to the normal and intruder states of the $sd$ shell isotopes. The shell model calculations using FSU interaction have been performed in this work to better understand the structure of $^{38}$Cl and some nearby even A Cl isotopes.