Cross-shell excited configurations in the structure of 34Si

The cross-shell excited states of $^{34}$Si have been investigated via $\beta$-decays of the $4^-$ ground state and the $1^+$ isomeric state of $^{34}$Al. Since the valence protons and valence neutrons occupy different major shells in the ground state as well as the intruder $1^+$ isomeric state of $^{34}$Al, intruder levels of $^{34}$Si are populated via allowed $\beta$ decays. Spin assignments to such intruder levels of $^{34}$Si were established through $\gamma$-$\gamma$ angular correlation analysis for the negative parity states with dominant configurations $(\nu d_{3/2})^{-1} \otimes (\nu f_{7/2})^{1}$ as well as the positive parity states with dominant configurations $(\nu sd)^{-2} \otimes (\nu f_{7/2}p_{3/2})^2$. The configurations of such intruder states play crucial roles in our understanding of the $N=20$ shell gap evolution. A configuration interaction model derived from the FSU Hamiltonian was utilized in order to interpret the intruder states in $^{34}$Si. Shell model interaction derived from a more fundamental theory with the Valence Space In Medium Similarity Renormalization Group (VS-IMSRG) method was also employed to interpret the structure of $^{34}$Si.