Differential cross sections for charged-particle emission in reactions of 58-MeVαparticles withC12,O16, andFe54: Comparison with the exciton model of pre-equilibrium particle emission

Abstract

Cross sections differential in energy and angle are presented for the proton, deuteron, triton, and $\alpha$ particles from reactions of 58-MeV $\alpha$ particles on C, O, and ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, and the angle-integrated differential spectra are compared with the predictions of an extended exciton model of pre-equilibrium reactions. The experimental results were obtained with a semiconductor telescope and cover the whole energy range above a few MeV. Except for oxygen, the results are given with uncertainties of 5-10%; for oxygen, relative intensities are valid at a given angle, but the absolute uncertainty is about 50%. The high-energy segment of the spectrum is highly anisotropic for all emitted particles, but for low energies the evaporation mechanism may be important for proton and perhaps $\alpha$-particle emission. The inelastic $\alpha$ spectra from ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$ are more similar in shape to previous observations of the ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}\mathrm{}(p,xp)\mathrm{}$ spectra than to the presently reported ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\alpha ,x\alpha )$ results. Comparisons are made between the data and the exciton model assuming an initial configuration of four particles. The model was extended to recognize that for reactions of incident $\alpha$ particles, emitted $\alpha$ particles and even deuteron, triton, and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ particles may contribute a significant fraction of the pre-equilibrium emission. The empirical internormalization factor for the relative intensity of various exit particles (mass number $p_{\beta }$) is found to be consistent with the ($p_{\beta } !$) value deduced previously from results with incident protons. Using matrix elements deduced from systematics, the predictions for ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ yield qualitatively correct shapes with normalization for the various particle types correct to within a factor of 6. For ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, the magnitude and shape of the predicted integral spectra are good for secondary protons and deuterons, but the predicted spectra fall off far too rapidly at high energies for tritons and $\alpha$ particles.