Measurement of deep hole states in $^{39}$K by $^{40}$Ca$(\overrightarrow{p},2p)$ reaction at 392~MeV

The spectroscopic factor and the width of 1s$_{1/2}$ state in $^{40}$Ca have been deduced from $^{40}$Ca($p,2p$) reaction experiment. In the experiment the cross sections and analyzing powers of the $^{40}$Ca($\overrightarrow{p},2p$) reaction at $392$~MeV have been measured. The strength distributions of the single-hole states in $^{39}$K were successfully obtained by multipole decomposition analysis on the basis of the angular momentum $L$. The central value and the width (FWHM) of the obtained strength distribution of 1s$_{1/2}$ are 52~MeV and 22~MeV. The obtained spectroscopic factor of 1s$_{1/2}$ state is about 60\% of the $2J+1$. This value will be compared with the theoretical calculations that include short-range correlations and tensor correlations.