Proton Strength Functions from (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mi>n</mml:mi></mml:math>) Cross Sections

Abstract

To an accuracy of \ifmmode\pm\else\textpm\fi{}10%, ($p, n$) total cross sections averaged over resonances have been measured from threshold to about 500 kev above threshold for 12 nuclei from ${\mathrm{Cl}}^{37}$ to ${\mathrm{Nb}}^{93}$. For each nucleus the excitation function of the average cross section is a monotonically increasing function of proton energy. At 500 kev above threshold the cross sections vary from 40 mb for ${\mathrm{Cl}}^{37}$ to 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ mb for ${\mathrm{Nb}}^{93}$. One new threshold, that for ${\mathrm{Se}}^{77}(p, n){\mathrm{Br}}^{77}$, was found to be 2.175\ifmmode\pm\else\textpm\fi{}0.004 Mev. In the course of calibrating the neutron detector with an Sb-Be source, a new determination was made of the ${\mathrm{Sb}}^{124}$ half-life: 59.9\ifmmode\pm\else\textpm\fi{}0.5 days.A black-nucleus square-well model was used to compute the cross sections for formation of the compound system. The Coulomb penetrabilities that appear in this calculation qualitatively account for the very large range of cross sections observed. In a more detailed comparison compound-nucleus formation was assumed, and the Hauser-Feshbach formalism was used to include the effects of proton and, especially, $\ensuremath{\gamma}$-ray emission from the compound nucleus. In general, there is agreement with the shapes of the excitation functions but not always with the magnitudes. The ratio of observed to black-nucleus cross-section peaks up by about a factor of 2 between ${\mathrm{Cu}}^{65}$ and ${\mathrm{Se}}^{82}$. The maximum in the peak is between masses 70 and 75. This peak may be correlated (by a complex-potential model) with a peak in the strength function for $s$-wave protons and, to a lesser extent, with a peak in the strength function for $d$-wave protons. Proton strength functions were calculated for a complex square-well of radius $R=1.45{A}^{\frac{1}{3}}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$ cm with the approximation of a Coulomb potential constant inside the well and equal to $(\frac{4}{3})(\frac{Z{e}^{2}}{R})$. In order to fit the observed position of the peak, $A\ensuremath{\sim}70 \mathrm{to} 75$, the depth of the specifically nuclear part of the well was required to be 46 Mev, 4 Mev deeper than the neutron well of Feshbach, Porter, and Weisskopf.