Shell-Model Study of the ($p$, ${\pi }^{-}$) Reactions in the $f_{\frac{7}{2}}$-Shell Region

Relative cross sections for the ($p$, ${\pi }^{-}$) reaction for nuclei in the region $40<A<\mathrm{}56\mathrm{}$ are calculated with use of ${\left(1\mathrm{}{f}_{\frac{7}{2}}\right)}^n$ wave functions and a zero-range plane-wave approximation for this three-nucleon process. The results of the calculation for the low-lying discrete states are in excellent agreement with recent data and many detailed aspects of the spectra are understood for the first time.