Quadrupole collectivity in island-of-inversion nuclei28,30Neand34,36Mg

The quadrupole collectivity of neutron-rich even-even neon and magnesium nuclei around $N=20$, ${}^{28,30}\mathrm{Ne}$, and ${}^{32,34,36}$Mg, was studied via proton inelastic scattering on a liquid hydrogen target by in-beam $\ensuremath{\gamma}$-ray spectroscopy in inverse kinematics. The angle-integrated cross sections for the first ${2}^{+}$ states of these nuclei were determined by measuring de-excitation $\ensuremath{\gamma}$ rays. The deformation lengths were extracted from the angle-integrated cross sections using distorted-wave calculations. The deformation length of ${}^{30}$Ne (${\ensuremath{\delta}}_{(p,{p}^{\ensuremath{'}})}=1.{59}_{\ensuremath{-}0.09}^{+0.08}$ fm) is smaller than that of ${}^{32}$Mg ($1.{83}_{\ensuremath{-}0.11}^{+0.10}$ fm), which exhibits the largest quadrupole collectivity among the neutron-rich $N=20$ isotones. Along the magnesium isotopic chain, the deformation lengths of ${}^{34}$Mg and ${}^{36}$Mg were deduced to be $2.{30}_{\ensuremath{-}0.10}^{+0.09}$ fm and $1.{90}_{\ensuremath{-}0.17}^{+0.16}$ fm, respectively. The evolution of quadrupole deformation in the vicinity of ${}^{32}$Mg is discussed by comparing the present results with the theoretical calculations.