  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 \nuc{12}{C}, \nuc{24}{Mg}, \nuc{28}{Si}, and
\nuc{40}{Ca} targets at 51.93 MeV. Coupled reaction channels (CRC) analyses
have been made for $(p,d)$ transitions to the $j$-forbidden excited states in
\nuc{11}{C} (${\tfrac{5}{2}}^-$, 4.32 MeV), \nuc{23}{Mg} (${\tfrac{7}{2}}^+$,
2.05 MeV), \nuc{27}{Si} (${\tfrac{7}{2}}^+$, 2.16 MeV) and \nuc{39}{Ca}
(${\tfrac{9}{2}}^-$, 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.
