Nuclear moments of the low-lying isomeric 1$^+$ state of $^{34}$Al: Investigation on the neutron 1$p$1$h$ excitation across $N=20$ in the island of inversion

The nuclear $g$ factor and quadrupole moment ($Q_s$) have been measured for the low-lying isomeric $1^+$ state of $^{34}$Al, using the $\beta$-detected nuclear magnetic resonance ($\beta$-NMR) and quadrupole resonance ($\beta$-NQR) methods. Spin-polarized $^{34}$Al isotopes were produced in a one-neutron pickup reaction induced by a $^{36}$S beam on a $^9$Be target at a kinetic energy of 77.5 MeV/nucleon, and were collected with the LISE fragment separator at GANIL. The measured $g$ factor ($\lvert g \rvert$ in a range of $1.757 \pm 0.014$) and quadrupole moment ($\lvert Q_s \rvert =38(5)$ mb) are in good agreement with shell-model calculations using effective interactions. The similarity between the $g$ factor of $^{34m}$Al and that of $^{32}$ Al confirms a dominant neutron $2p1h$ configuration $\pi (d_{5/2})^{-1} \otimes \nu(d_{3/2})^{−1}(f_{7/2})^2$ of $^{34m}$Al. In addition, the enhanced quadrupole moment of $^{34m}$Al relative to that of $^{32}$Al suggests that the neutron $1p1h$ excitation across the $N=20$ shell gap introduces extra nucleon–nucleon correlation and deformation.