A detailed feasibility study on deducing the high-lying single particle components (HLSPCs), which are important but used to be ignored, in the ground and low-lying excited states of even-even light nuclei is performed by analyses of $(p,d)$ reactions with ${}^{12}\mathrm{C}$, ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, and ${}^{40}\mathrm{Ca}$ targets at 51.93 MeV. Coupled reaction channel analyses have been made for $(p,d)$ transitions to the $j$-forbidden excited states in ${}^{11}\mathrm{C}$ (${\frac{5}{2}}^{-}$; 4.32 MeV), ${}^{23}\mathrm{Mg}$ (${\frac{7}{2}}^{+}$; 2.05 MeV), ${}^{27}\mathrm{Si}$ (${\frac{7}{2}}^{+}$; 2.16 MeV), and ${}^{39}\mathrm{Ca}$ (${\frac{9}{2}}^{-}$; 3.64 MeV), including the major allowed transition components together with direct components of HLSPCs. Spectroscopic amplitudes of the HLSPCs are deduced by fitting the angular distributions of the ground and the $j$-forbidden excited states simultaneously. The present analysis demonstrates for the first time that information about HLSPCs in atomic nuclei can be obtained from analysis of $(p,d)$ reactions.

• Received 5 July 2018

DOI:https://doi.org/10.1103/PhysRevC.98.044622