Quadrupole deformation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts/><mml:none/><mml:mn>16</mml:mn></mml:mmultiscripts></mml:math> studied by proton and deuteron inelastic scattering
Y. Jiang, J. L. Lou, Y. L. Ye, Y. Liu, Zhijing Tan, W. Liu, Baodong Yang, Liwen Tao, Kai Ma, Z. H. Li, Q. T. Li, X. F. Yang, J. Y. Xu, H. Z. Yu, Jiaxing Han, Shiwei Bai, S.W. Huang, G. Li, H. y. Wu, H. L. Zang, Jie Feng, Z. Q. Chen, Y. D. Chen, Qiong Yuan, J. G. Li, B. S. Hu, F. R. Xu, J. S. Wang, Y. Y. Yang, P. Ma, Q. Hu, Z. Bai, Zhihao Gao, F. F. Duan, Liyuan Hu, Junhao Tan, S. Q. Sun, Yi-Dan Song, H. J. Ong, D. T. Tran, D. Y. Pang, Cenxi Yuan
Abstract
New measurements of proton/deuteron elastic and inelastic scattering to the ${2}_{1}^{+}$ state of the neutron-rich nucleus $^{16}\mathrm{C}$ have been performed at Radioactive Ion Beam Line in Lanzhou (RIBLL) in inverse kinematics. The angular distributions of elastic scattering were well reproduced by the systematic optical potential with normalization factors for the depths of real and imaginary parts. The neutron and proton deformation lengths of ${\ensuremath{\delta}}_{n}=1.25\ifmmode\pm\else\textpm\fi{}0.30$ fm and ${\ensuremath{\delta}}_{p}=1.07\ifmmode\pm\else\textpm\fi{}0.26$ fm were extracted from the inelastic scattering data. The ratio of neutron and proton matrix element ${M}_{n}/{M}_{p}=1.95\ifmmode\pm\else\textpm\fi{}0.47$ was determined from the two different probes. Within error bar, this result is in fair agreement with the previous measurements, demonstrating that the combination of proton and deuteron inelastic scattering offers a useful method to extract ${M}_{n}/{M}_{p}$ for the even-even nuclei. Most of the theoretical predictions by the shell model using the MK, WBT, WBT*, and YSOX interactions in $p\ensuremath{-}sd$ model space and by the ab initio in-medium similarity renormalization group are close to these experimental results.