Measurement ofFe(α, α′)Fe*Reactions Produced by 21-, 27.5-, and 47.9-MeV Alpha-Particle Bombardment: Statistical-Theory Analysis

Abstract

The energy and angular distributions of inelastically scattered $\ensuremath{\alpha}$ particles from Fe have been measured at bombarding energies of 21, 27.5, and 47.9 MeV. The spectra are corrected for effects due to the presence of impurities in the target foil and to the energy degradation suffered as the $\ensuremath{\alpha}$ particles emerge from the target and pass through the forward portion of the detector. The energy and angular distributions have been analyzed with the semiclassical compound-nucleus theory of Ericson and Strutinski. In the analysis of the 21-MeV data, all of the inelastically scattered $\ensuremath{\alpha}$ particles are assumed to be emitted from the original compound nucleus. The angular distributions produced by the 27.5- and 47.9-MeV $\ensuremath{\alpha}$-particle bombardment are found to be consistent with the nuclear moment of inertia determined from the 21-MeV data when multiple-particle-emission reactions such as $\mathrm{Fe}(\ensuremath{\alpha}, n\ensuremath{\alpha})\mathrm{Fe}$ or $\mathrm{Fe}(\ensuremath{\alpha}, p\ensuremath{\alpha})\mathrm{Mn}$ are included in the analysis. The inclusion of multiple-particle emissions in the statistical-theory analysis of the 27.5- and 47.9-MeV-induced reactions also significantly improves the agreement between experimental and theoretical energy distributions. In the statistical-theory analysis essentially two assumptions were made about the dependence of nuclear level density on nuclear spin and nuclear excitation energy. The first assumption was that the nuclear level density of a residual nucleus with spin $J$ and excitation energy $U$ is given by $\ensuremath{\rho}(U, J)=(\mathrm{const})(2J+1){(U\ensuremath{-}\ensuremath{\delta})}^{\ensuremath{-}2}\mathrm{exp}{2{[a(U\ensuremath{-}\ensuremath{\delta})]}^{\frac{1}{2}}}\mathrm{exp}(\ensuremath{-}\frac{{\ensuremath{\hbar}}^{2}{J}^{2}}{2\mathcal{I}T}),$ where $T\ensuremath{\cong}{(\frac{U}{a})}^{\frac{1}{2}}$ in the high-excitation-energy limit and $\mathcal{I}$ is the nuclear moment of inertia. The second assumption was that this equation is valid only when the excitation energy $U$ is greater than approximately 6 MeV. For excitation energies below 6 MeV the nuclear density was assumed to be $\ensuremath{\rho}(U, J)=(\mathrm{const})(2J+1)\mathrm{exp}[\frac{(U\ensuremath{-}\ensuremath{\delta})}{{T}_{c}}]\mathrm{exp}(\ensuremath{-}\frac{{\ensuremath{\hbar}}^{2}{J}^{2}}{2\mathcal{I}{T}_{c}}),$ where ${T}_{c}$, the nuclear temperature, is constant. The use of the second assumption involving a constant nuclear temperature in the excitation region below 6 MeV gave better over-all results than the use of the first assumption over the entire energy range. This second assumption is generally consistent with a nuclear phase transition, i.e., with the superconductor nuclear model.