Statistical Theory Predictions for 5- to 11-MeV ($p, n$) and ($p, p^{\prime }$) Nuclear Reactions in ${\mathrm{V}}^{51}$, ${\mathrm{Co}}^{59}$, ${\mathrm{Cu}}^{63}$, ${\mathrm{Cu}}^{65}$, and ${\mathrm{Rh}}^{103}$

Absolute ($p, n$) cross sections for proton energies between 5 and 11 MeV have been measured for ${\mathrm{V}}^{51}$, ${\mathrm{Co}}^{59}$, ${\mathrm{Cu}}^{63}$, ${\mathrm{Cu}}^{65}$, and ${\mathrm{Rh}}^{13}$ using a "long counter." The experimental values are compared with the predictions of the statistical theory. An analysis is made of the use of different level density functions in the calculations of the cross sections. The choice of parameters—the nuclear radius $r_0$, the level density parameter $a$, and pairing energies, $P(Z, N)$—has been made with the idea of fitting not only these measured ($p, n$) cross sections but also other available experimental information such as the proton-reaction cross section, $\sigma (p, p^{\prime })$, the differential energy spectrum of the neutrons resulting from these proton reactions, and some of the proton spectra from the ($p, p^{\prime }$) reaction for the copper isotopes. It is shown that the "measured" value of $a$ changes drastically from approximately $\frac{A}{20}$ or $\frac{A}{30}$ to approximately $\frac{A}{8}$ to $\frac{A}{6}$ depending upon whether $\exp \left\{2\mathrm{}{\left[a\right(U+P(Z, N)\left)\right]}^{\frac{1}{2}}\right\}$ or ${[U+P(Z, N\left)\right]}^{-2\mathrm{}}\exp \left\{2\mathrm{}{\left[a\right(U+P(Z, N)\left)\right]}^{\frac{1}{2}}\right\}$ is used for the level density. However, the ($p, n$) and ($p, p^{\prime }$) cross sections obtained with these level density functions when the correspondence $a$ is introduced are quite close. In most of the cases it is not possible to make a definite choice if the accuracy of the measured cross sections is not better than 5%.