Pre-equilibrium Contribution Research Articles

Preequilibrium neutron emission in109Ag(3He,xn) and111Cd(p, xn) reactions

Excitation functions of the reactions109Ag(3He,xn) and111Cd(p, xn) have been measured with stacked foil techniques for projectile energies E≦45 MeV and multiplicitiesx≦4 populating ground and spin isomeric states in112−xIn. Preequilibrium (PE) contributions are more pronounced for thep than for the3He entrance channel and for low multiplicitiesx and can be reproduced with the (geometry dependent) hybrid model. The observed isomeric cross section ratios require a reduced population for the high spin state (as compared with the expectation for equilibrated systems) whenever PE emission contributes significantly. Calculations for a full statistical model with a PE decay mode and approximate angular momentum conservation indicate PE neutron emission to be stretched in angular momentum space. For the (p, xn) reactions a more detailed coupling scheme is imperative whereas the (3He,xn) data suggest the competitive PE emission of complex particles.

Pre-equilibrium effect in (n, xn) reactions

A method has been developed to calculate (n, xn) cross-sections (x=2, 3, 4), taking into account pre-equilibrium emission of the first particle. Emission of subsequent particles is considered to be entirely due to the equilibrium mode. Based on this model the cross-sections have been calculated and compared for a number of nuclei in the mass regionA=89 to 238 for incident energies from threshold to 28 MeV. Using the squared matrix element of Kalbach we found that the preequilibrium contribution was considerable at incident energy higher than 16 MeV. In general, agreement between the measured and the calculated cross-sections is within 10 to 15%. Cross-section for (n, 4n) reaction is also calculated and compared with the available data. The method developed here may be used to calculate (n, xn) cross sections for unstable nuclei for which a direct measurement is not possible.

Exclusive (α, 2nγ) neutron spectra and the pre-equilibrium exciton model

The pre-equilibrium (exciton) model reproduces qualitatively the structure observed in the neutron energy spectra of the exclusive (α, 2nγ) reactions. For this, the pre-equilibrium contribution is necessary, and the influence of the binding energies is essential.

Experimental and theoretical study of continuous proton spectra from high-energy deuteron induced reactions

Inclusive proton spectra were measured from 80 MeV deuteron-induced reactions on 27Al, 93Nb and 197Au targets. At forward angles the spectra exhibit broad deuteron break-up peaks centered around one-half of the incident deuteron energy for all the nuclei studied. Double-differential as well as angle-integrated cross sections in the bump region are well reproduced by calculations in the framework of the DWBA approach to break-up taking elastic and inelastic reactions of the neutron with the target nucleus into account. Like the observation made in case of low-energy deuteron break-up as well as in high-energy alpha break-up, the inelastic break-up is found to be a dominant reaction mode at this higher deuteron energy also. The preequilibrium contributions to the outgoing proton spectra have also been calculated. The analysis of the experimental data has been discussed in the light of these two different reaction mechanisms. It is found that these two reaction mechanisms put together provide a good overall description of the experimental proton spectra.

Inclusive proton spectra from deuteron break-up: Theory and experiment

Abstract Two silicon detector telescopes were used to measure continuous proton spectra at lab angles from 20° to 160° resulting from deuteron-induced reactions on targets of 27 Al, 62 Ni, 93 Nb, 119 Sn and 181 Ta at 25.5 MeV bombarding energy. The spectra show a prominent bump at around 15 MeV which is strongly rising at forward angles. Doubly differential cross sections, angle-integrated spectra and energy-integrated yields are compared with a new DWBA approach to deuteron break-up taking elastic and inelastic reactions of the break-up neutron with the target nucleus into account. The inelastic mode has a finite cross section at the maximum proton energy from break-up (zero neutron energy) and is generally stronger that the elastic one. The mass dependence of the experimental break-up yield corrected for equilibrium and preequilibrium contributions is discussed in connection with the limits of the present theory.

Evidence for pre-equilibrium contributions to the reaction209Bi(n,2n)208Bi

Coincident neutron emission from the reaction 209Bi(n,2n)208Bi at En0=14.1 MeV has been measured in a kinematically complete experiment providing direct evidence for pre-equilibrium contributions. The outgoing neutrons were observed at several angles with two time-of-flight detectors. Neutron yields and energy spectra are interpreted with statistical-model calculations including pre-equilibrium decay modes.

Excited analogs inNi62andCu63(p, n)and the weak-coupling model

The ground- and ${2}^{+}$ excited-state analog cross sections in $^{62}\mathrm{Ni}(p, n)$ have been measured at bombarding energies of 16, 19, and 22 MeV. The measurements at 19 and 22 MeV confirm the weak coupling and Thankappan-True prediction of \ensuremath{\sim} 0.4 for the fractionation of the ${2}^{+}$ strength into the ${\frac{7}{2}}^{\ensuremath{-}}$ excited analog transition in $^{63}\mathrm{Cu}(p, n)$. At 16 MeV, agreement with the weak-coupling model is poor. The discrepancy is possibly due to a preequilibrium contribution to the ${\frac{7}{2}}^{\ensuremath{-}}$ excited analog transition in $^{63}\mathrm{Cu}(p, n)$.NUCLEAR REACTIONS $^{62}\mathrm{Ni}(p, n)$, $E=16, 19, 22$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$ ground-state and ${2}^{+}$ excited-state analog; calculated $\ensuremath{\sigma}(\ensuremath{\theta})$ ${2}^{+}$ using weak-coupling model.

Excitation functions of51V,56Fe,65Cu(p, n) reactions between 10 and 45 MeV

The (p, n) reaction cross-sections of51V,56Fe and65Cu have been measured, for incident-proton energies ranging from 10 to 45 MeV, in steps of 2 MeV. The excitation curves exhibit the usual changes in slope consistent with the expectation that the high-energy tails are mainly due to pre-equilibrium neutron emission. These changes occur for proton energies around 20 MeV, a value in accord with the result previously obtained for reactions of the same type in heavier nuclei. A detailed analysis of the excitation curves has been performed under the hypothesis of incoherent addition of the contributions from compound-nucleus evaporation and pre-equilibrium emission. It is concluded that calculations, based, for the pre-equilibrium contribution, on the exciton model, can give results in satisfactory agreement with the experiment even for nuclei with mass numbers as low asA≃50.