Pre-equilibrium Calculations Research Articles

Residual two-body matrix elements for pre-equilibrium calculations

The effective matrix elements which appear in pre-equilibrium calculations in the rate expressions for the residual two-body interactions have been evaluated from analyses of emitted particle energy spectra. Probably because of details in the model formulation, the results are found to depend on the nature of the projectile. They are, however, of reasonable magnitude and show a mass number and excitation energy dependence consistent with predictions based on calculations of mean free paths in nuclear matter. The square of the empirical effective matrix element is found to approximately obey the relation M 2 = K a A −3 E −1 with the values of K a = 95 MeV 3 and 725 MeV 3 applying to proton and α-particle induced reactions respectively. The quantities A and E are the mass number and excitation energy of the system respectively.

Reaction Mechanisms in (p,p′) Reactions Exciting the High-Energy Continuum

The reaction mechanism in ($p,{p}^{\ensuremath{'}}$) reactions exciting states above about 3-MeV excitation energy has been studied in several nuclei in which ordinary compound-nucleus contributions have been shown to be unimportant. Up to 7 MeV in $^{64}\mathrm{Ni}$ and $^{124}\mathrm{Sn}$, there is strong structure in the energy spectra of emitted protons which is closely correlated with the structure in ($d,{d}^{\ensuremath{'}}$) reactions; this indicates that direct reactions exciting collective states are the dominant mechanism here. Distorted-wave Born-approximation calculations are used to show that there is an additional mechanism contributing low-energy protons. This mechanism is believed to be isospin-conserving reactions via ${T}_{>}$ states, but it is shown that the decay of these states cannot be treated with statistical theory in the Sn region. A reason for this is proposed, and supporting evidence is presented. The applicability of pre-equilibrium calculations to ($p,{p}^{\ensuremath{'}}$) reactions is discussed.