K. Dietrich

A more detailed calculation of particle evaporation and fission of compound nuclei

Abstract We consider particle evaporation and fission of an ensemble of hot, rotating compound nuclei as a stochastic process. We derive a set of coupled differential equations formed by a Fokker-Planck equation describing fission, and master equations for calculating particle evaporation. From these equations, we are able to determine multiplicities of prefission neutrons, protons and α-particles, their energy spectra and their angular momentum distributions. A comparison of our results with experimental data provides us with information regarding the reduced friction coefficient β, the fission barrier height and the level density parameter. For different iridium isotopes, ( 181,185,187 Ir), 185 Os and 158 Er, we obtain as an upper limit β ⩽8.0×10 21 s −1 .

Light-particle emission from the fissioning nuclei 126 Ba, 188 Pt and 266,272,278 110: Theoretical predictions and experimental results

Abstract We present a comparison of our model treating fission dynamics in conjunction with light-particle ( n,p,α ) evaporation with the available experimental data for the nuclei 126 Ba, 188 Pt and three isotopes of the element Z=110 . The dynamics of the symmetric fission process is described through the solution of a classical Langevin equation for a single collective variable characterizing the nuclear deformation along the fission path. A microscopic approach is used to evaluate the emission rates for prefission light particles. Entrance-channel effects are taken into account by generating an initial spin distribution of the compound nucleus formed by the fusion of two deformed nuclei with different relative orientations.

Evaporation of light particles from a hot, deformed and rotating nucleus☆

Abstract The dependence of the transimission coefficient on the deformation, the collective rotation and excitation energy of the compound nucleus emitting light particles is introduced in the framework of Weisskopfs evaporation theory. The competition between fission and particle evaporation is treated by a Langevin equation for the fission variable coupled to the emission process. Detailed calculations are presented on the decay of different Gd and Yb isotopes at an excitation energy of about 250 MeV. These calculations demonstrate the importance of the effects of nuclear deformation and of the initial spin distribution on the evaporation.

On the general form of the cross section of deep inelastic collisions

Abstract The general form of the energy-averaged “macroscopic” cross section for deep inelastic (DI) collisions is derived on the basis of semiclassical approximations. The amplitude for DI reactions is related to the incompletely relaxed part of the fluctuating S -matrix. The possibility of diffraction effects modifying the DI cross section is investigated. In the limit of a classical treatment of the external variables, the average DI cross section is shown to be uniquely determined by a classical distribution function.

Scaling properties in the hydrodynamical description of heavy-ion reactions

Abstract We discuss scaling properties of heavy-ion reactions which are consequences of a simple hydrodynamical model. In certain kinematic regions the experimentally observed inclusive cross sections satisfy this scaling and so do the cross sections numerically calculated using hydrodynamics. The simple thermal model obeys the same scaling laws, but leads to a differential cross section with a characteristically different shape at very high and very low energies of the outgoing nucleons. The specific experimental data analyzed do not show evidence for a hydrodynamical flow.

Stability of Bubble Nuclei through Shell Effects

We investigate the shell structure of bubble nuclei in simple phenomenological shell models and study their binding energy as a function of the radii and of the number of neutron and protons using Strutinskys method. Shell effects come about, on the one hand, by the high degeneracy of levels with large angular momentum and, on the other, by the big energy gaps between states with a different number of radial nodes. Shell energies down to -40 MeV are shown to occur for certain magic nuclei. Estimates demonstrate that the calculated shell effects for certain magic numbers of constituents are probably large enough to produce stability against fission, alpha-, and beta-decay. No bubble solutions are found for mass number A < 450.

On the shell structure of nuclear bubbles

Abstract We investigate the shell structure of spherical nuclear bubbles in simple phenomenological shell model potentials. The bunching is produced by the energy gaps between single-particle states with a different number of radial nodes. The shell correction energies for doubly magic bubbles may be as large as −40 MeV and probably imply a very long lifetime against spontaneous fission. β-stability occurs for ratios of the neutron number N to the proton number Z which differ markably from the β-stability valley of ordinary compact nuclei. The α-decay probability is shown to be very small for proton rich bubbles with a moderately large outer radius. Metastable islands of nuclear bubbles are shown to exist for nucleon numbers in the range A = 450–3000.

Kinetic energy and angular distributions of instantaneous fission fragments in a classical model

The process of instantaneous fission in deep inelastic collisions is investigated in a classical model. Kinetic energies and angular distributions of the fragments are calculated for the proposed reaction Pb+U atEcminc=750 MeV; an experimental setup for the separation of the fragments originating from instantaneous fission from the fragments of thermal fission is explained. We also discuss fusion following instantaneous fission as a mechanism for the production of superheavy elements and arrive at rather promising estimates.

Electromagnetic emission from damped vibrations of fission fragments

We calculate the electromagnetic radiation generated by the damped quadrupole surface vibrations of two fragments originating from the spontaneous fission of a heavy nucleus. We investigate the dependence of the spectral energy distribution of the radiation on the parameters of the model and on the initial conditions. The sensitivity of the results to the model parameters shows that theγ emission may be a good test of transport theories used in the description of this type of phenomena.

Effects of quantum diffraction in statistical theories of heavy ion reactions: (II). Applications

Abstract We use the general expressions of the coarse cell cross sections defined in part I of this paper to calculate the distributions in angle and energy of the final nuclides produced in deep inelastic collisions. The diffraction effects arising from absorption into fusion channels for small impact parameters are investigated for the systems 86 36 Kr on 120 50 Sn at E lab = 514 MeV, 132 54 Xe on 208 82 Pb at 1000 MeV and 136 54 Xe on 209 83 Bi at 1130 MeV. The energy spectra of the ions emitted in deep inelastic collisions of symmetric systems are analysed for the collision 40 20 Ca on 40 20 Ca at E lab = 284 and 400 MeV. Here the quantal effects resulting from the existence of an inner rainbow angle in the average deflection functions are of importance.