Inelastic Heavy-ion Collisions Research Articles

Analysis of multinucleon transfer reactions with spherical and statically deformed nuclei using a Langevin-type approach

An increasing interest in multinucleon transfer processes in low-energy deep inelastic (damped) collisions of heavy ions appeared in recent years is due, in part, to by the possibility of using them as a method of production of heavy neutron-enriched nuclei. Possible promising projectile-target combinations include nuclei deformed in the ground state (e.g., actinides). Mutual orientations of such the nuclei in the entrance channel of the reaction may significantly influence the reaction dynamics. Available experimental data on multinucleon transfer reactions with statically deformed as well as spherical heavy nuclei 144Sm + 144Sm, 154Sm + 154Sm, 160Gd + 186W, and 208Pb + 208Pb/238U have been analyzed within the developed model. A good agreement of the calculated quantities with the corresponding experimental data is reached. Special attention in the paper is paid to analysis of production possibility of the neutron-enriched isotopes of heavy and superheavy elements in multinucleon transfer processes in the 238U + 238U/248Cm/254Es collisions.

Study of deep inelastic collisions within multidimensional dynamical model

Energy, angle, and charge distributions of binary products of the deep inelastic collisions of heavy ions are studied in the framework of a multidimensional dynamical model of nucleus-nucleus collisions based on the Langevin equations. The model is verified on the example of the 136Xe + 209Bi system at several above barrier energies.

Modeling near-barrier collisions of heavy ions based on a Langevin-type approach

Background: Multinucleon transfer in low-energy nucleus-nucleus collisions is proposed as a method of production of yet-unknown neutron-rich nuclei hardly reachable by other methods.Purpose: Modeling of dynamics of nuclear reactions induced by heavy ions in their full complexity of competing reaction channels remains to be a challenging task. The work is aimed at development of such a model and its application to the analysis of multinucleon transfer in deep inelastic collisions of heavy ions leading, in particular, to formation of neutron-rich isotopes in the vicinity of the $N=126$ shell closure.Method: Multidimensional dynamical model of nucleus-nucleus collisions based on the Langevin equations has been proposed. It is combined with a statistical model for simulation of de-excitation of primary reaction fragments. The model provides a continuous description of the system evolution starting from the well-separated target and projectile in the entrance channel of the reaction up to the formation of final reaction products.Results: A rather complete set of experimental data available for reactions $^{136}\mathrm{Xe}+^{198}\mathrm{Pt},^{208}\mathrm{Pb},^{209}\mathrm{Bi}$ was analyzed within the developed model. The model parameters have been determined. The calculated energy, mass, charge, and angular distributions of reaction products, their various correlations as well as cross sections for production of specific isotopes agree well with the data. On this basis, optimal experimental conditions for synthesizing the neutron-rich nuclei in the vicinity of the $N=126$ shell were formulated and the corresponding cross sections were predicted.Conclusions: The production yields of neutron-rich nuclei with $N=126$ weakly depend on the incident energy. At the same time, the corresponding angular distributions are strongly energy dependent. They are peaked at grazing angles for larger energies and extend up to the forward angles at low near-barrier collision energies. The corresponding cross sections exceed 100 nb for the nuclei located at the border of the known region, which is nearly five orders of magnitude larger than can be reached in the fragmentation reactions.

Deformation relaxation in heavy-ion collisions

In deeply inelastic heavy-ion collisions, the quadrupole deformations of both fragments are taken as stochastic independent dynamical variables governed by the Fokker–Planck equation (FPE) under the corresponding driving potential. The mean values, variances and covariance of the fragments are analytically expressed by solving the FPE in head on collisions. The characteristics and mechanism of the deformation are discussed. It is found that both the internal structures and interactions of the colliding partners are critical for the deformation relaxation in deeply inelastic collisions.

Estimation of the spatial decoherence time in circular quantum dots

We propose a simple phenomenological model to estimate the spatial decoherence time in quantum dots. The dissipative phase-space dynamics is described in terms of the density matrix and the corresponding Wigner function, which are derived from a master equation with Lindblad operators linear in the canonical variables. The formalism was initially developed to describe diffusion and dissipation in deep inelastic heavy-ion collisions, but an application to quantum dots is also possible. It allows us to study the dependence of the decoherence rate on the dissipation strength, the temperature, and an external magnetic field, which is demonstrated in illustrative calculations on a circular GaAs one-electron quantum dot.

Description of deep inelastic transfer reactions at the Fermi energy within transport models

The possibility of studying the dissipative processes near the Fermi energy using the transport equations arising within the Boltzmann-Nordheim-Vlasov approach is discussed. It is shown that this approach makes it possible to reproduce all the main features of deep inelastic collisions of heavy ions: specifically, the deviation curves for reaction fragments and their Coulomb and nuclear rainbows and the strong correlation between the fragment exit angle and kinetic energy loss. The theoretical results are compared with the experimentally obtained data on the isotopic and velocity distributions of light fragments escaping at small angles in the 18O + 181Ta and 18O + 9Be reactions at an energy of 35 MeV/nucleon. It is established that the experimental velocity distributions contain two components: dissipative (with a velocity smaller than that of the projectile ion) and direct (having a maximum at the particle beam velocity). It is shown that the transport equations describe well the dissipative part of the reaction, which is about 30% of the total output. The direct component arises during fission of the projectile ion nucleus and is described well within the Goldhaber model.

Multi-Neutron and Proton Transfer Reactions in Deep Inelastic Heavy-Ion Collisions

Multi-Neutron and Proton Transfer Reactions in Deep Inelastic Heavy-Ion Collisions

Optical study of MeV energy heavy ion-induced effects in crystalline germanium and silicon

An optical study of Ni-ion (60 and 75 MeV) bombarded polished single crystals of Ge (〈111〉), Sb-doped, 1 Ω cm) and Si (〈111〉, intrinsic) at room temperature with fluence ranging from 1 × 10 13 to 1 × 10 15 ions/cm 2 has been carried out in the spectral regions of the fundamental optical absorption edge and interband transition. The damage inflicted by the MeV energy ion on the surface and deep inside the bulk of the semiconductors has been monitored by determining the dose dependence of optical constants α, R and n in the spectral range 200–2500 nm. Analysis of the results reveals that electronic energy loss arising out of the inelastic ionising collisions of swift heavy ions, in addition to the nuclear energy loss, influence the surface and the bulk properties of the bombarded semiconductors. Formation of divacancies in the bombarded Si is supported by the appearance of an absorption band at around 0.7 eV. The surface effects of ion-implantation at MeV energy are quite different from those at keV energy.

Partition of excitation energy between reaction products in heavy ion collisions

In the single-particle approach a partition of the excitation energy between the reaction products in deep inelastic collisions of heavy ions are investigated. The role of the particle-hole excitations and the nucleon exchange is considered. The ratio of the projectile excitation energy to the total excitation energy for the reactions238U(1468 MeV)+124Sn,238U(1398 MeV)+110Pd,56Fe(505MeV)+165Ho,74Ge (629 MeV)+165Ho and68Ni(880 MeV)+197Au is calculated. The results of calculations are in good agreement with the experimental data.

Gamma-ray studies of 119, 121, 123Sn isomers formed in deep inelastic heavy ion collisions

Yrast isomers in 119Sn, 121Sn and 123Sn have been identified among products of heavy ion collisions with 124Sn targets 10–15% above the Coloumb barrier. Isomeric decay schemes are reported, and further evidence for half-filling of the ν h 11 2 subshell at N = 73 is presented. For ( ν h 11 2 n seniority-3 states, observed level energies agree well with results of fractional parentage calculations.

Gamma-ray studies of 119, 121, 123Sn isomers formed in deep inelastic heavy ion collisions

Gamma-ray studies of 119, 121, 123Sn isomers formed in deep inelastic heavy ion collisions

Density matrix for the damped harmonic oscillator within the Lindblad theory

The time evolution of the density matrix of the damped harmonic oscillator is studied within the Lindblad theory for open quantum systems. The density matrix is represented via a generating function, which is obtained by solving a time-dependent linear partial differential equation derived from the master equation of the damped harmonic oscillator. Illustrative examples for specific initial conditions of the density matrix are provided. It is also shown that various master equations for the damped quantum oscillator, for damped collective modes in deep inelastic collisions of heavy ions and in different models of quantum optics are particular cases of the Lindblad equation and that only some of these equations satisfy the quantum mechanical constraints on the diffusion coefficients.

Microscopic analysis of deeply inelastic heavy-ion collisions

Deeply inelastic heavy-ion collisions from 14 to 25 MeV/u are investigated within a microscopic transport approach of the VUU type where the time-dependent mean field and the in-medium cross section are based on the same parametrization of the G-matrix. The transfer of energy and angular momentum from the relative motion to the internal degrees of freedom is studied in detail as a function of impact parameter and found to be dominated by nucleon exchange. The fluctuation in mass, furthermore, can also be ascribed to the random nucleon transfer mechanism. We calculate double-differential spectra with respect to total kinetic energy loss (TKEL) and mass as well as with respect to TKEL and scattering angle. Furthermore, the exclusive production of hard photons in Mo + Mo reactions at 19.5 MeV/u is found to be well described by incoherent proton-neutron bremsstrahlung as evaluated from the same parametrization of the G-matrix.

Time evolution of the mass exchange in grazing heavy-ion collisions

On the basis of a macroscopical approach to the description of two interpenetrating quantal objects, the equations of two-fluid hydrodynamics for the cohesion stage of deeply inelastic heavy-ion collisions are formulated. The elasticity of the ions is analyzed in peripheral mass exchange reactions at intermediate energies. The system of closed equations of Newtonian mechanics, which simultaneously describes the motion of the ions along classical trajectories as well as the mass time evolution during the interaction period are derived and solved. The role of mass exchange in the friction force is discussed.

Heat partition in damped reactions.

The effect of driving force on the division of excitation energy between the asymmetric colliding partners in deep inelastic heavy-ion collisions is studied in the nucleon-exchange model. For this purpose an event-by-event analysis using Monte Carlo simulation technique is performed. It is seen that the fraction of the total excitation energy carried by the projectile-like fragment is sensitive to the mass drift. The model is also applied to analyze the correlation between fragment mass and excitation energy for a given total energy loss and significant correlation is found. The reactions induced by $^{56}\mathrm{Fe}$ at 9 MeV/nucleon and $^{74}\mathrm{Ge}$ at 8.5 MeV/nucleon on $^{165}\mathrm{Ho}$ are considered in our analysis and the calculated correlations are in good agreement with the results obtained from the kinematic coincidence experiments.

Semiclassical theory of direct and deep inelastic heavy ion collisions

A sufficiently simple approach is formulated for the quantitative description of direct and multi-step processes in heavy ion collisions with arbitrary (not only small) mass, energy, and angular momentum transfer. The simplification is achieved owing to the use of semiclassical description of the colliding particles relative motion. The semiclassical approximation is used for the three-dimensional (not partial) distorted waves with accounting of all caustic properties, and the channel coupling is simulated by the dissipative forces. The transition amplitude is reduced to the one-dimensional integral along the so-called “transition lines” where the inelastic process is localized. The comparison is done with the experimental data and with exact calculations of some direct reaction cross sections. Heavy-ion-induced multi-step (quasidirect) massive transfer processes with the fast light particle formation are analyzed.

Effect of trajectory fluctuations on nucleon drift and diffusion in deep inelastic heavy ion collisions.

The role of trajectory fluctuations on the first and second moments obtained in the mean trajectory approximation for the proton and neutron distributions of the projectile-like fragments produced in deep inelastic heavy ion collisions has been studied in the framework of stochastic transfer of single nucleons. At each instant of time the neutron and proton numbers of the colliding nuclei are considered to be given by dynamically evolving Gaussian distributions generating trajectory fluctuations. The first moments calculated in this method differ considerably from those obtained in the mean trajectory approximation for the systems with strong gradient in the driving force around the point of injection. The second moments, however, do not change appreciably for all the systems studied.

Semiclassical theory of direct and deep inelastic heavy ion collisions: V. I. Zagrebaev. Chuvash State University, Cheboksary 428000, USSR

Semiclassical theory of direct and deep inelastic heavy ion collisions: V. I. Zagrebaev. Chuvash State University, Cheboksary 428000, USSR

Semiclassical theory of direct and deep inelastic heavy ion collisions: V. I. Zagrebaev. Chuvash State University, Cheboksary 428000, USSR

Semiclassical theory of direct and deep inelastic heavy ion collisions: V. I. Zagrebaev. Chuvash State University, Cheboksary 428000, USSR

Open quantum system of two coupled harmonic oscillators for application in deep inelastic heavy ion collisions

On the basis of the theory of Lindblad (1976) for open quantum systems the author derives master equations for a system consisting of two harmonic oscillators. The time dependence of expectation values, Wigner function and Weyl operator are obtained and discussed. The chosen system can be applied for the description of the charge and mass asymmetry degrees of freedom in deep inelastic collisions in nuclear physics.