Multistep Compound Processes Research Articles

Preequilibrium models for 58Ni (n, xp) reaction in Neutrons at 8, 9, 9.4, 11 and 14.8 MeV using the EMPIRE and TALYS codes

In this study, the calculations of proton emission spectra produced by 58Ni (n, xp) reaction are used in the framework of preequilibrium models with the EMPIRE and TALYS codes. Exciton Model predictions combined with the Kalbach angular distributions systematics and statistical Multi-step Direct (MSD) with Multi-step Compound (MSC) processes preequilibrium models were used. Also, some necessary parameters as optical model, level density, level density a-parameter and single-particle level density parameter have been investigated for our calculations. The comparison with experimental data shows clear improvement over the Exciton and MSD with MSC models calculations.

Inclusive cross-sections of (p,xp) and (p,xα) reactions onFe56atEp=29.9MeV

In this paper, we present new experimental data measured at E{sub p}= 29.9 MeV for the inclusive reactions (p,xp) and (p,x{alpha}) on nucleus {sup 56}Fe. We investigate the adequacy of the theoretical models in explaining the measured experimental data, and we determine the contributions of multistep direct and multistep compound processes in the formation of the cross-sections. We show that the traditional frameworks are valid for the description of the new experimental data, and our measurements agree with previous measurements for the (p,xp) and (p,x{alpha}) reactions on the {sup 54}Fe nucleus. The only exception is within the energy region of E{sub p}= 15 and 25 MeV for both reactions, where the cross-section for the {sup 56}Fe nucleus is smaller than the cross-section for the {sup 54}Fe nucleus.

Inclusive spectra of(p,xp)and(p,xd)reactions on90,92Zrand92Monuclei atEp=30.3MeV

New experimental data for the inclusive reactions (p,xp) and (p,xd) on isotopes of the nuclei $^{90,92}$Zr and $^{92}$Mo, have been measured at E$_{p}$=30.3 MeV, which has not been investigated in detail so far. We show the extension of the pre-equilibrium reactions to this energy region and interpret the results of these experiments. Moreover, we display the mechanism of the reaction and the level of energy-dependence. The adequacy of the theoretical models in explaining the measured experimental data is also discussed. In our theoretical analysis, the contributions of multi-step direct and compound processes in the formation of cross-sections are determined and we assert that the traditional frameworks are valid for the description of the experimental data.

Effect of the preequilibrium process upon fast neutron fission spectra from238U

A preequilibrium process for the prefission neutron which is emitted before scission is calculated with the model of Feshbach, Kerman, and Koonin. A forward-peaked angular distribution of the neutron emission from ${}^{238}\mathrm{U}$ bombarded by 14 and 18 MeV neutrons is expressed with the statistical multistep compound process and the one-step direct process. The fission neutron energy spectra are calculated with the model of Madland and Nix, with some modifications by Ohsawa et al. The calculated total neutron emission spectra and their energy-angle distributions (double-differential cross sections) are compared with the experimental data, and a strength of the residual interaction ${V}_{0}$ is estimated. The comparisons of the calculations with the experimental data show that the 14 MeV data are well reproduced but the 18 MeV data are underestimated. Anisotropy is seen in the angle-differential fission spectra, and this is due to an existence of the prefission neutron.

Microscopic calculation of the multistep compound process

The Feshbach, Kerman, and Koonin [Ann. Phys. (N.Y.) 125, 429 (1980)] model of the statistical multistep compound (MSC) process is calculated microscopically, and comparisons of the microscopically calculated MSC process with a phenomenological phase-space model are made. The microscopic model gives a small particle emission probability in comparison with the constant wave function approximation, and a simple way to reconcile the difference is proposed. A $2p\ensuremath{-}1h$ doorway state formation cross section is calculated with the spherical Nilsson model, and a strength of the residual interaction ${V}_{0}$ is estimated from the doorway state formation cross section. The obtained ${V}_{0}$ is of the same magnitude as those derived in the previous multistep direct analyses. Comparisons of the microscopic MSC calculations with the experimental data show that the calculated particle emission spectra reproduce the measurements at backward angles.

Statistical calculations of the damping width of giant resonances

The damping widths of giant resonances is calculated using a scheme developed for multistep compound processes. The results were found to be reasonable and compare well to those indirectly extracted from data.

Multistep compound reaction calculations using the Feshbach-Kerman-Koonin theory

The cross sections of (n,n') and (n,p) reactions at 14 MeV on a range of nuclei are analysed using the theory of Feshbach, Kerman and Koonin. The contributions of the multistep compound and multistep direct processes are evaluated, and the strength of the effective nucleon-nucleon potential determined for both the zero-range and Yukawa potentials.

Neutron production from thick targets bombarded by alpha particles: Experiment and theoretical analysis of neutron energy spectra.

The neutron energy spectra and angular distributions have been measured for thick targets of $^{9}\mathrm{Be}$, $^{181}\mathrm{Ta}$, and $^{197}\mathrm{Au}$ bombarded by 40--60 MeV alpha particles. These data as well as those of other authors have been analyzed in terms of the extended exciton model formalism of nuclear reactions. The model takes into account the emission of neutrons through the single-step direct, multistep direct, multistep compound, and compound-nuclear evaporation processes.

The Angular Distribution of Light Particle Projectile Based on a Semi-Classical Model

A semi-classical model of multi-step direct and compound nuclear reactions is proposed to describe the angular distributions of the light particle projectiles from reaction processes induced by a nucleon with energies of several tens of MeV. The exact closed solution to the time-dependent master equation of the exciton model is applied. Based on the Fermi gas model, the scattering kernal between two-nucleon collision includes the influences of the Fermi motion and the Pauli exclusion principle, which give the significant improvement to rise of the backward distributions. The energy-angular correlation for the first few steps of the collision process (muli-step direct process) yields the further improvement of the angular distribution. The pick-up mechanism is employed to describe the composite particle emission. This reasonable physical picture reproduces the experimental data of the energy spectra of the composite particles satisfactorily. The angular distribution of the emitted composite particle is determined by an angular factor in terms of the momentum conservation of the nucleons forming the composite cluster. The generalized master equation is employed for the multi-step compound process. Thus a classical approach has been establised to calculate the double differential cross sections for all kinds of particles emitted in multi-step nucler reaction processes.

Transmission coefficients in the presence of multistep-direct reactions

Formal expressions for transmission coefficients governing the multistep-compound process and introduced in an earlier paper, are explicitly worked out, using the idea of a multistep-direct process populating the compound nucleus. A perturbative treatment of inelastic scattering, combined with a “never come back” and the sudden approximation, and a statistical average over exit channels lead to simple, intuitively appealing expressions which contain shell-model type matrix elements and partial level densities and are therefore amenable to numerical evaluation.

Statistical nuclear theory: Novel results and open questions

Two recent developments are reviewed: (i) irregular classical scattering, its semiclassical extension, and the relationship of both to compound-nucleus scattering in the Ericson regime, and (ii) weak versus strong coupling in the multistep-compound process, its relation to fluctuations in level spacings and to the localization problem, and its influence on level densities in precompound reactions.

Multistep compound processes in nuclear reactions from 9 to 18 MeV

The quantum mechanical reaction theory of Feshbach, Kerman and Koonin (1980) has been developed to include neutron and proton distinguishability in the nuclear cascade. The modified theory has been used to analyse the multistep compound emission spectra for (n,n'), (n,p) and (p,n) reactions for incident energies from 9 to 18 MeV. Good agreement with experiment is found in most cases, enabling the strength of the residual interaction to be determined.

Statistical multistep direct and compound processes below 30 MeV for 93-Nb

A simple model for SMC- and SMD-processes including quasiparticle and phonon excitations is presented. Emission spectra and angular distributions are calculated without free parameters for 93-Nb (n, n′), (n, p) and incidence energies between 5 and 26 MeV.

Statistical theory of precompound reactions: The multistep direct process

We complete the statistical framework for a theory of precompound reactions established in a recent paper relating to the multistep compound process, by considering here a statistical approach to multistep direct reactions. This approach applies when the number of open channels is sufficiently large, and the eigenfunctions of the residual nucleus are sufficiently complex, to call for a statistical treatment. We consider especially the one- and two-step processes in the sudden and the adiabatic approximation and investigate time scales to determine which approximation is the more reasonable one. We compare our results with those of other approaches.

Statistical theory of precompound reactions: The multistep compound process

Using a quantum-statistical framework, the method of the generating function involving both commuting and anticommuting variables, and the saddle-point approximation followed by the loop expansion, we derive a theoretical framework for multistep-compound reactions. Our statistical input distinguishes between several classes of states of increasing complexity; this distinction is possible only at the expense of relinquishing the orthogonal invariance of the distribution of Hamiltonian matrix elements usually required in compound-nucleus theories. Our result contains both the compound-nucleus scattering cross section and the theory of Agassi Weidenmüller, and Montzouranis ( Phys. Lett. C 22 (1975), 145.) developed earlier as special cases. It goes beyond this theory, and extends the framework of precompound theories in general, by allowing the couplings between classes, and to the channels, to be reasonably strong. A self-consistency condition embodied in the saddle-point equation implies in this case that the level densities used in precompound calculations must be modified. We investigate the modification in simple model cases. Our results suggest that the modification may be relevant for the high-energy tail of the spectrum of precompound particles.

Statistical theory of precompound reactions: The multistep compound process: H. Nishioka, J. J. M. Verbaarschot, and H. A. Weidenmüller. Max-Planck-Institut für Kernphysik, Heidelberg, Federal Republic of Germany; and S. Yoshida. Department of Physics, Tohoku University, Sendai, Japan

Statistical theory of precompound reactions: The multistep compound process: H. Nishioka, J. J. M. Verbaarschot, and H. A. Weidenmüller. Max-Planck-Institut für Kernphysik, Heidelberg, Federal Republic of Germany; and S. Yoshida. Department of Physics, Tohoku University, Sendai, Japan

Pre-equilibrium processes in nuclear reaction theory: the state of the art and beyond

We have made a detailed comparative study of many existing programs in order to assess their usefulness for the present purpose. We begin by summarizing the essential ideas of the exciton model and the various formalisms that have been developed to enable the preequilibrium cross-sections to be calculated. In the work we describe here we use the theory of Feshbach, Kerman, and Koonin (1980) because it is applicable to both multistep compound and multistep direct processes and has been developed to the stage of numerical calculations. This theory distinguishes between two types of pre-equilibrium reactions, the multistep compound and the multistep direct. In the multistep compound reactions there is at least one stage in the reaction when all particles are bound, whereas in the multistep direct there is always at least one particle in the continuum. Multistep compound reactions predominate at lower energies and are defined to give cross-sections symmetrical about 90/sup 0/, whereas multistep direct reactions become increasingly important as the energy increases and give cross-sections peaked in the forward direction. At the energies of interest here both the multistep compound and the multistep direct processes are important. The formalisms for these processes are described applied to analyse the inelastic scattering of neutrons by /sup 59/Co and /sup 93/Nb. The final section is devoted to a detailed comparison between the exciton and quantum-mechanical theories, and some conclusions are drawn concerning their application to data evaluation.

The average angular distribution of emitted particles in multi-step compound processes

A simple model for the differential cross section that describes the angular distribution of emitted particles in heavy-ion induced multi-step compound reactions, is constructed. It is suggested that a careful analysis of the deviations of the experimental data from the pure Hauser-Feshbach behaviour may shed light on the physical nature of the pre-compound, heavy-ion configuration.

Variance of Ericson fluctuations in multistep compound processes

It is pointed out that within the nested doorway model, the approximate Ericson's formula for the variance of cross section fluctuations is valid independently of the number of doorway classes present. Comparison is presented with the experimental values of the variance for the recently analyzed $^{3}\mathrm{He}$+$^{25}\mathrm{Mg}$ reactions, in which multistep compound processes have been found to be dominant.NUCLEAR REACTIONS $^{25}\mathrm{Mg}(^{3}\mathrm{He}, p)$, $^{25}\mathrm{Mg}(^{3}\mathrm{He}, \ensuremath{\alpha})$; multistep compound; Ericson fluctuations; extracted and calculated reduced variance.

Multistep compound processes in heavy-ion-induced reactions

We suggest the possible contribution of multistep compound processes to light heavyion reactions at above-barrier energies. The presence of several correlation widths that characterize the fluctuation in energy of the excitation functions for different incidentoutgoing channel combinations is indicated and demonstrated explicitly for the system $^{12}\mathrm{C}$($^{15}\mathrm{N}$, $\ensuremath{\alpha}$) at ${E}_{\mathrm{c}.\mathrm{m}.}=9.51\ensuremath{-}17.33$ MeV. The importance of multistep compound processes to heavy-ion fusion studies is pointed out.NUCLEAR REACTIONS Multistep compound processes in heavy ion reactions discussed.