Cumulative and independent population of individual levels via the Ni 58 ( α , p γ ) Cu 61 and Ni 58 ( α , 2 p γ ) Ni 60 compound-nucleus reactions: A correlation between level cross sections and angular momenta

The cross sections for the cumulative and independent population of 21 levels in $^{61}\mathrm{Cu}$ and 7 levels in $^{60}\mathrm{Ni}$ via the $^{58}\mathrm{Ni}(\ensuremath{\alpha},p\ensuremath{\gamma})^{61}\mathrm{Cu}$ and $^{58}\mathrm{Ni}(\ensuremath{\alpha},2p\ensuremath{\gamma})^{60}\mathrm{Ni}$ reactions at 19.67-MeV bombardment energy were carefully measured in $p\ensuremath{\gamma}$-coincidence experiments with the protons detected at 90 and 157\ifmmode^\circ\else\textdegree\fi{} relative to the beam direction. Spectra of the coincident protons leading to each level via $\ensuremath{\gamma}$ cascades as well as energy-integrated cross sections were obtained. The angular distributions for the protons above 3.26 MeV of center-of-mass energy were measured at seven laboratory angles between 25 and 168\ifmmode^\circ\else\textdegree\fi{}. Larger anisotropies for the protons from the ($\ensuremath{\alpha},2p$) reaction were observed relative to the ($\ensuremath{\alpha},p$) reaction. Some of the levels in $^{60}\mathrm{Ni}$ were found to have large anisotropies with the maxima at the backward angles. When the cross sections for the cumulative and the independent population of levels of given angular momentum in $^{61}\mathrm{Cu}$ or $^{60}\mathrm{Ni}$ are plotted as a function of the level energy, they are found to decrease rapidly with level energy. The cross sections for cumulative and independent population increase with angular momentum at least for levels with ${J}^{\ensuremath{\pi}}$ values between ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$ and ${\frac{11}{2}}^{\ensuremath{-}}$. The variation of the level cross sections with level energy follows closely the predictions of the compound statistical model for both the ($\ensuremath{\alpha},p\ensuremath{\gamma}$) and ($\ensuremath{\alpha},2p\ensuremath{\gamma}$) reactions. The experimental cross-section distributions, cross sections for the formation of individual levels and total cross sections for the ($\ensuremath{\alpha},p$) and ($\ensuremath{\alpha},2p$) reactions are compared with detailed calculations based on the statistical theory for nuclear reactions, in which Fermi-gas-model level densities and shell-model combinatorial level densities are employed. The experimental level cross sections and proton evaporation spectra are very well reproduced with level spacing parameters $a$ of 6.56, 7.63, and 5.8 ${\mathrm{MeV}}^{\ensuremath{-}1}$ for $^{61}\mathrm{Cu}$, $^{61}\mathrm{Zn}$, and $^{58}\mathrm{Ni}$, respectively. By comparison with experimental level cross sections the energy dependence of the spin cutoff parameter ${\ensuremath{\sigma}}^{2}$ and the yrast line were determined for $^{61}\mathrm{Cu}$. The $B(E1)$, $B(M1)$ and $B(E2)$ values for transitions originating at 10 MeV of excitation in $^{61}\mathrm{Cu}$ that reproduce the ($\ensuremath{\alpha},p\ensuremath{\gamma}$) and ($\ensuremath{\alpha},2p\ensuremath{\gamma}$) level cross sections were found to be 0.055, 0.085, and 9.5 Weisskopf units, respectively.