Trajectory calculations for particle-particle correlations: Probes of source lifetime, rotational motion, momentum conservation and particle-unstable fragments

Abstract In heavy-ion induced nuclear reactions one can produce transient systems with excitation energies up to 5 MeV per nucleon and spins up to ≈ 100 h , The equilibrium statistical model can predict the mean lifetime for particle emission from moderately hot nuclei provided they are completely thermalized. However, as the excitation energy is increased, one expects to reach a situation of incomplete equilibration and hence a breakdown of the simplest equilibrium model. Determinations of the lifetime for (or intervals between) particle or fragment emissions can be useful both for testing the equilibrium model at low temperatures as well as for characterizing pre-equilibrium emission from partially thermalized nuclei. Direct measurements of the time delays between ejectile pairs are not possible because the timescale of 10 −22 to 10 −20 s is much too short. However, for such short lifetimes the flight distance of the first particle (before birth of the second) is often less than ≈ 50 fm. Therefore, the long range Coulomb and possibly nuclear forces can give final state interactions that affect their final relative momentum; these perturbations can be observed in coincidence measurements. The net effect is best demonstrated by means of a correlation function, which can be interpreted by comparison to a reaction simulation. By such comparisons one can characterize the mean time intervals between emissions. The simulation programs MENEKA and COULGAN have been written for this purpose: they are Monte Carlo programs based on the following elements: a) Particles are emitted from the surface of an excited nucleus with a distribution of orbital angular momenta. b) Emission energies of the particles are chosen to reproduce experimental measurements or theoretical calculations. c) The distribution of time delays between particle emissions is given by exponential decay laws. d) A three-body trajectory is followed for the two particles and for the recoil nucleus. e) An event is accepted as a valid coincidence if the particle pair satisfies experimental requirements of detector thresholds and geometry. Particle trajectories are calculated numerically using time steps that are controlled by the requirement for energy conservation. An ancillary program SHOWTRAJ can be used to display and study trajectories event by event.