Coulomb Excitation of Multi-Phonon Levels of the Giant Dipole Resonance

A closed expression is obtained for the cross-section for Coulomb excitation of levels of the giant dipole resonance of given angular momentum and phonon number. Applications are made to the Goldhaber-Teller and Steinwedel-Jensen descriptions of the resonance, at non-relativistic and relativistic bombarding energies.Comment: 16 pages, 5 figure

Long-Time Behavior of Velocity Autocorrelation Function for Interacting Particles in a Two-Dimensional Disordered System

The long-time behavior of the velocity autocorrelation function (VACF) is investigated by the molecular dynamics simulation of a two-dimensional system which has both a many-body interaction and a random potential. With strengthening the random potential by increasing the density of impurities, a crossover behavior of the VACF is observed from a positive tail, which is proportional to t^{-1}, to a negative tail, proportional to -t^{-2}. The latter tail exists even when the density of particles is the same order as the density of impurities. The behavior of the VACF in a nonequilibrium steady state is also studied. In the linear response regime the behavior is similar to that in the equilibrium state, whereas it changes drastically in the nonlinear response regime.Comment: 12 pages, 5 figure

Theory of Second and Higher Order Stochastic Processes

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial example is $\ddot x = R(t)$, where $R(t)$ is not a Gaussian white noise). The stochastic process is discretized into $n$ time-steps, all possible realizations are summed up and the continuum limit is taken. This procedure often yields closed form formulas for the joint probability distributions. Completely worked out examples include all Gaussian random forces and a large class of Markovian (non-Gaussian) forces. This approach is also useful for deriving Fokker-Planck equations for the probability distribution functions. This is worked out for Gaussian noises and for the Markovian dichotomous noise.Comment: 35 pages, PlainTex, accepted for publication in Phys Rev. E

The Semiclassical Coulomb Interaction

The semiclassical Coulomb excitation interaction is at times expressed in the Lorentz gauge in terms of the electromagnetic fields and a contribution from the scalar electric potential. We point out that the potential term can make spurious contributions to excitation cross sections, especially when the the decay of excited states is taken into account. We show that, through an appropriate gauge transformation, the excitation interaction can be expressed in terms of the electromagnetic fields alone.Comment: 12 pages. Phys. Rev. C, Rapid Communication, in pres

Structure Effects on Coulomb Dissociation of 8^8B

Coulomb Dissociation provides an alternative method for determining the radiative capture cross sections at astrophysically relevant low relative energies. For the breakup of $^8$B on $^{58}$Ni, we calculate the total Coulomb Dissociation cross section and the angular distribution for E1, E2 and M1. Our calculations are performed first within the standard first order semiclassical theory of Coulomb Excitation, including the correct three body kinematics, and later including the projectile-target nuclear interactions.Comment: 6 pages, proceedings from International Workshop on RNB, Puri, India, January 1998 - to be published in J. Phys.

Effect of boundary conditions on diffusion in two-dimensional granular gases

We analyze the influence of boundary conditions on numerical simulations of the diffusive properties of a two dimensional granular gas. We show in particular that periodic boundary conditions introduce unphysical correlations in time which cause the coefficient of diffusion to be strongly dependent on the system size. On the other hand, in large enough systems with hard walls at the boundaries, diffusion is found to be independent of the system size. We compare the results obtained in this case with Langevin theory for an elastic gas. Good agreement is found. We then calculate the relaxation time and the influence of the mass for a particle of radius $R_s$ in a sea of particles of radius $R_b$. As granular gases are dissipative, we also study the influence of an external random force on the diffusion process in a forced dissipative system. In particular, we analyze differences in the mean square velocity and displacement between the elastic and inelastic cases.Comment: 15 figures eps figures, include

Liquid-Solid Phase Transition of the System with Two particles in a Rectangular Box

We study the statistical properties of two hard spheres in a two dimensional rectangular box. In this system, the relation like Van der Waals equation loop is obtained between the width of the box and the pressure working on side walls. The auto-correlation function of each particle's position is calculated numerically. By this calculation near the critical width, the time at which the correlation become zero gets longer according to the increase of the height of the box. Moreover, fast and slow relaxation processes like $\alpha$ and $\beta$ relaxations observed in supper cooled liquid are observed when the height of the box is sufficiently large. These relaxation processes are discussed with the probability distribution of relative position of two particles.Comment: 6 figure

Intermediate energy Coulomb excitation as a probe of nuclear structure at radioactive beam facilities

The effects of retardation in the Coulomb excitation of radioactive nuclei in intermediate energy collisions (Elab ~100 MeV/nucleon) are investigated. We show that the excitation cross sections of low-lying states in 11Be, {38,40,42}S and {44,46}Ar projectiles incident on gold and lead targets are modified by as much as 20% due to these effects. The angular distributions of decaying gamma-rays are also appreciably modified.Comment: 21 pages, 3 figures, Phys. Rev. C, in pres

Internal Anisotropy of Collision Cascades

We investigate the internal anisotropy of collision cascades arising from the branching structure. We show that the global fractal dimension cannot give an adequate description of the geometrical structure of cascades because it is insensitive to the internal anisotropy. In order to give a more elaborate description we introduce an angular correlation function, which takes into account the direction of the local growth of the branches of the cascades. It is demonstrated that the angular correlation function gives a quantitative description of the directionality and the interrelation of branches. The power law decay of the angular correlation is evidenced and characterized by an exponent and an angular correlation length different from the radius of gyration. It is demonstrated that the overlapping of subcascades has a strong effect on the angular correlation.Comment: RevteX, 8 pages, 6 .eps figures include

Velocity autocorrelation function of a Brownian particle

In this article, we present molecular dynamics study of the velocity autocorrelation function (VACF) of a Brownian particle. We compare the results of the simulation with the exact analytic predictions for a compressible fluid from [6] and an approximate result combining the predictions from hydrodynamics at short and long times. The physical quantities which determine the decay were determined from separate bulk simulations of the Lennard-Jones fluid at the same thermodynamic state point.We observe that the long-time regime of the VACF compares well the predictions from the macroscopic hydrodynamics, but the intermediate decay is sensitive to the viscoelastic nature of the solvent.Comment: 7 pages, 6 figure