Study of the mechanisms of pre-equilibrium nuclear reactions in the microscopic approach

The mechanisms of pre-equilibrium nuclear reactions are investigated within the Statistical Multistep Direct Process (SMDP) + Statistical Multistep Compound Process (SMCP) formalism. It has been shown that from an analysis of linear part in such dependences as $$\ln \left[ {{{\frac{{d^2 \sigma }}{{d\varepsilon _b d\Omega _b }}} \mathord{\left/ {\vphantom {{\frac{{d^2 \sigma }}{{d\varepsilon _b d\Omega _b }}} {\varepsilon _b^{1/2} }}} \right. \kern-\nulldelimiterspace} {\varepsilon _b^{1/2} }}} \right]upon\varepsilon _b $$ and $$\ln \left[ {{{\frac{{d\sigma ^{SMDP \to SMCP} }}{{d\varepsilon _b }}} \mathord{\left/ {\vphantom {{\frac{{d\sigma ^{SMDP \to SMCP} }}{{d\varepsilon _b }}} {\frac{{d\sigma ^{SMDP} }}{{d\varepsilon _b }}}}} \right. \kern-\nulldelimiterspace} {\frac{{d\sigma ^{SMDP} }}{{d\varepsilon _b }}}}} \right]upon{{U_B } \mathord{\left/ {\vphantom {{U_B } {\left( {E_a - B_b } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {E_a - B_b } \right)}}$$ one can extract information about the type of mechanism (SMDP, SMCP, SMDP→SMCP) and the number of stages of the multistep emission of secondary particles. In the above approach, we have discussed the experimental data for a broad class of reactions in various entrance and exit channels.     

Angular distributions in pre-equilibrium reactions

A new model is proposed for calculating angular distributions in preequilibrium reactions. In this model, as in the model of Feshbach et al. the system consisting of target plus projectile initially branches into two sets of states with either no particle in the continuum (multistep compound states) or with at least one particle in the continuum (multistep direct states). The multistep compound emission is assumed to be isotropic while the angular distribution of the multistep direct emission is described using the fast particle model of Mantzouranis et al. A similar master equation is used for both chains of states differing only in the angular dependence of the emission rates. The two chains of states are treated independantly neglecting inter-branch transitions. The angular distributions for 14.6 MeV neutrons calculated using this model are found to be in better agreement with the data than the fast particle model.     

Analysis of intermediate structures of spectral emission in pre-equilibrium nuclear reactions in the microscopic approach

The quasi-particle-phonon model of pre-equilibrium decay (QP Ph M PED) is proposed. Within this model, intermediate states are specified by the number of quasi-particles, quasi-holes and phonons. In describing nuclear relaxation we consider two types of internuclear transitions with the change in exciton number byN _ex=0, ±2 and number of phononN _ph=±1. The mixed densities of intermediate states(N _ex,N _ph,E) have been determined. An analysis has been made of the structure of the hard part of the emission spectrum in the⁶⁰Ni(p,p) and¹²⁰Sn(p,p) reaction at _p=62 MeV. This analysis suggests the importance of taking into account the transitions withN _ph=+1, along with the transitions withN _ex= +2.     

Studies of nuclear second moments for pre-equilibrium nuclear reaction theories

The nuclear second moments, important inputs to pre-equilibrium reaction theories, are evaluated by assuming a simple model. The positive definite nature of the second moments is examined, and the nuclear level densities are calculated using positive definite second moments.     

Effect of pre-equilibrium emission on probing postsaddle nuclear dissipation with neutrons

Using the stochastic Langevin model coupled with a statistical decay model, we study the influence of pre-equilibrium(PE) emission on probing postsaddle friction(β) with neutrons. A postsaddle friction value of(14-16.5) ×10~(21)s~(-1) and(11-13) ×10~(21)s~(-1) is obtained from comparing calculated and measured prescission neutron multiplicities of heavy fissioning systems248 Fm and256Fm in the absence and presence of the deformation factor.Moreover, it is found that a larger β is required to fit multiplicity data after the PE effect is accounted for, and that the effect becomes stronger when more energy is removed by PE particles. Our findings suggest that, to more accurately determine the postsaddle friction strength through the measurement of prescission neutrons, in addition to incorporating the contribution of PE evaporation source into the experimental multi-source analysis for particle energy spectra in coincidence with fission fragments, on the theoretical side, it is very important to make a precise evaluation of the energy that PE emission carries away from excited compound systems produced in heavy-ion fusion reactions.     

Energetic particles emitted from energetic nuclear reactions

Protons and pions emitted with extreme momenta from energetic proton and heavy ion induced nuclear reactions are analysed in terms of two simple phenomenological models: the nuclear phase space model and a simplified multiple collision model. The systematic analysis of the observed spectra over many orders of magnitude for a variety of projectile and target combinations in the beam-energy range of 0.08 to 2 Gev/nucl shows the importance of multiple collision contributions and the neccessity of off-shell scattering effects.     

Neutron skin effect of some Mo isotopes in pre-equilibrium reactions

The neutron skin effect has been investigated for even isotopes of molybdenum at 25.6 MeV ^{94 − 100}Mo(p, xn) reaction using the geometry-dependent hybrid model of pre-equilibrium nuclear reactions. Here the initial neutron/proton exciton numbers were calculated from the neutron/ proton densities obtained from an effective nucleon–nucleon interaction of the Skyrme type. Initial exciton numbers from different radii of even Mo isotopes were used to obtain the corresponding neutron emission spectra. In this investigation the calculated results are compared with the experimental data as also with each other. The results using central densities in the geometry-dependent hybrid model are in better agreement with the experimental data.     

Pickup mechanism in (p, α) pre-equilibrium reactions

The contribution of the one-step triton pickup to the continuous spectra of (p, α) reactions is analyzed in terms of the DWBA theory. The formalism is succesfully applied to ⁹³Nb(p, α)⁹⁰Zr and ¹¹⁸Sn(p, α)¹¹⁵In reactions at two incident proton energies.     

Double-differential spectra of the secondary particles in the frame of pre-equilibrium model

An approach was developed to describe the double-differential spectra of secondary particles formed in heavy-ion reactions. Griffin model of nonequilibrium processes was used to account for the nonequilibrium stage of the compound system formation. Simulation of de-excitation of the compound system was carried out using the Monte-Carlo method. Analysis of the probability of neutron, proton, and α-particle emission was performed both in equilibrium, and in the pre-equilibrium stages of the process. Fission and γ-ray emission were also considered after equilibration. The analysis of the experimental data on the double-differential cross sections of p, α particles for the ¹⁶O + ¹¹⁶Sn reaction at the oxygen energy E = 130 and 250 MeV were performed.     

Intermediate mass fragment emission in Boltzmann master equation theory of pre-equilibrium reactions

A coalescence model originally proposed to account for the emission of nucleons and light particles in nuclear reactions is extended to account for intermediate mass fragment (IMF) emission. This theory uses a set of Boltzmann master equations to evaluate the time evolution of the occupation probability of nucleon states in the course of the de-excitation cascade during which the IMF are emitted. The internal structure of the IMF and the depletion of nucleon states due to IMF emission are explicitly considered. The theoretical predictions reproduce satisfactorily the experimental multiplicity spectra measured in central collisions of³⁶Ar ions with¹⁹⁷Au at incident energies of 35 MeV/nucleon.     

A program for simulation experiments to study reactions with three particles in the final state

The results from the kinematic simulation of experiments to study two-stage A + B → C + D* → C + (E + F) reactions that proceed through a decaying intermediate state D* with three particles in the final state are presented, and the program used in this modeling is described. The program allows us to determine an experiment’s geometry, calculate the time-of-flight times and energies for all secondary particles within the chosen geometry, and optimize the setup parameters (detector size and time and energy resolution) so as to obtain the proper excitation energy resolution of intermediate state D*. The results obtained in simulating an experiment to study the d + ³H → ³He + ²n, ²n → n + n reaction are detailed.     

α-Emission by pre-equilibrium processes in (n,α) reactions

The existence of a pre-equilibrium emission mechanism in the (n, α) reaction on nuclei with A > 90 is shown. Both the α-spectrum shape and excitation function can be fitted by considering a contribution from this reaction mechanism and, in lighter nuclei, from statistical evaporation. From a fitting of the absolute values of the cross sections a parameter ? is extracted, having the physical meaning of the probability for the incoming particle to strike a preformed α-cluster.     

Low-energy nuclear reactions with double-solenoid-based radioactive nuclear beam

The University of Notre Dame, USA (Becchetti et al, Nucl. Instrum. Methods Res. A505, 377 (2003) and later the University of São Paulo, Brazil (Lichtenthaler et al, Eur. Phys. J. A25, S-01, 733 (2005)) adopted a system based on superconducting solenoids to produce low-energy radioactive nuclear beams. In these systems the solenoids act as thick lenses to collect, select, and focus the secondary beam into a scattering chamber. Many experiments with radioactive light particle beams (RNB) such as ⁶He, ⁷Be, ⁸Li, ⁸B have been performed at these two facilities. These low-energy RNB have been used to investigate low-energy reactions such as elastic scattering, transfer and breakup, providing useful information on the structure of light nuclei near the drip line and on astrophysics. Total reaction cross-sections, derived from elastic scattering analysis, have also been investigated for light system as a function of energy and the role of breakup of weakly bound or exotic nuclei is discussed.     

Special features of isomeric ratios in nuclear reactions induced by various projectile particles

Calculations for (p, n) and (α, p3n) reactions were performed with the aid of the TALYS-1.4 code. Reactions in which the mass numbers of target and product nuclei were identical were examined in the range of A = 44–124. Excitation functions were obtained for product nuclei in ground and isomeric states, and isomeric ratios were calculated. The calculated data reflect well the dependence of the isomeric ratios on the projectile type. A comparison of the calculated and experimental data reveals, that, for some nuclei in a high-spin state, the calculated data fall greatly short of their experimental counterparts. These discrepancies may be due to the presence of high-spin yrast states and rotational bands in these nuclei. Calculations involving various level-density models included in the TALYS-1.4 code with allowance for the enhancement of collective effects do not remove the discrepancies in the majority of cases.     

Polymer-inorganic composite with ultradisperse gadolinium particles

The objects of investigation are polystyrene-based composites with ultradisperse particles (including nanoparticles) of metallic Gd and SiO₂. The composites prepared by milling starting materials in a barrel mill at room temperature are studied by the ferromagnetic resonance method, transmission electron microscopy (TEM), and reflection X-ray diffraction (RXD). It is found that the magnetic subsystem of the composites is formed by magnetic nanoclusters, Gd crystallites 30 ± 10 nm across, which possess volume and surface magnetic anisotropy and pass into the superparamagnetic state at 210 ± 10 K. It is also found that the Landau-Lifshitz equation with the damping term in the Landau-Lifshitz form provides the best quantitative fit to experimental data for the ferromagnetic resonance of superparamagnetic metal nanoparticles.     

A generator coordinate theory of nuclear reactions

The generator coordinate formalism is generalized to incorporate optical potentials, coupled waves, and a distorted-wave approximation. An estimate of the importance of recoil is proposed. An analytical illustrative example related to the generator coordinate DWBA is given.     

Nuclear surface,mean field and isospin effects in Boltzmann master equation theory of pre-equilibrium reactions

Pre-equilibrium emission of nucleons and light charged particles is investigated in central collisions leading to the complete fusion of two heavy ions, within the Boltzmann master equation approach. Realistic nucleon momentum density distributions for both projectile and target nuclei are used and mean field effects are schematically introduced in the early stage of the reaction process. The isospin dependence of the calculation parameters is also discussed. Theoretical predictions of the spectra of the particles emitted both in symmetric and asymmetric interactions at incident energies of a few ten MeV/nucleon are in satisfactory agreement with the experimental findings.     

Experimental study of nuclear fusion reactions in muonic molecular systems

Since the pioneering discovery of the muon catalysis by Alvarez [L. W. Alvarez, K. Brander, F. S. Crawford, et al., Phys. Rev. 105, 1127 (1957)], considerable efforts were aimed at observation of various fusion processes. Results of these studies facilitated understanding the properties of lightest nuclei and dynamics of low-energy fusion reactions. There still remain unsolved theoretical and experimental problems, especially in case of pt fusion.