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 $\gamma$-ray spectroscopy in inverse kinematics. The angle-integrated cross sections for the first $2^{+}$ states of these nuclei were determined by measuring de-excitation $\gamma$ rays. The deformation lengths were extracted from the angle-integrated cross sections using distorted-wave calculations. The deformation length of ${}^{30}$Ne (${\delta }_{(p,p^{\prime })}=1.{59}_{-0.09}^{+0.08}$ fm) is smaller than that of ${}^{32}$Mg ($1.{83}_{-0.11}^{+0.10}$ 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 $2.{30}_{-0.10}^{+0.09}$ fm and $1.{90}_{-0.17}^{+0.16}$ fm, respectively. The evolution of quadrupole deformation in the vicinity of ${}^{32}$Mg is discussed by comparing the present results with the theoretical calculations.

• Received 15 October 2013
• Revised 10 April 2014

DOI:https://doi.org/10.1103/PhysRevC.89.054307