The disassembly of nuclear matter

A statistical model is applied for multi-fragment final states in nuclear collisions with bombarding energies E/A ≈ 100 MeV. A portion of the intermediate system formed is assumed to decay according to the available classical non-relativistic phase space, calculated in a grand canonical ensemble. The model correlates and predicts many experimental observables in terms of three parameters: the available energy per nucleon, the isospin asymmetry, and the effective interaction volume.     

Time-dependent Hartree-Fock calculations for 16O + 16O reactions

Head-on collisions between ¹⁶O nuclei are treated in the Time-Dependent Hartree-Fock (TDHF) approximation. Reactions at center-of-mass bombarding energies of 2 and 8 MeV per nucleon result in fusion-fission processes with strong internal excitation of the fragments.     

Monte Carlo method for the many-body scattering problem

The non-relativistic many-body scattering problem is cast in a form suitable for treatment by Monte Carlo methods. The formulation is based on resonant standing waves of the compound system, similar to those used in the R-matrix theory of nuclear reactions. Integral expressions are derived from which the scattering matrix elements at low energies can be evaluated. The method is demonstrated by application to simple one- and two-channel one-dimensional scattering problems.     

The statistical theory of multi-step compound and direct reactions

The theory of nuclear reactions is extended so as to include a statistical treatment of multi-step processes. Two types are distinguished, the multi-step compound and the multi-step direct. The wave functions for the system are grouped according to their complexity. The multi-step direct process involves explicitly those states which are open, while the multi-step compound involves those which are bound. In addition to the random phase assumption which is applied differently to the multi-step direct and to the multi-step compound cross-sections, it is assumed that the residual interaction will have non-vanishing matrix elements between states whose complexities differ by at most one unit. This is referred to as the chaining hypothesis. Explicit expressions for the double differential cross-section giving the angular distribution and energy spectrum are obtained for both reaction types. The statistical multi-step compound cross-sections are symmetric about 90°. The classical statistical theory of nuclear reactions is a special limiting case. The cross-section for the statistical multi-step direct reaction consists of a set of convolutions of single-step direct cross-sections. For the many step case it is possible to derive a diffusion equation in momentum space. Application is made to the reaction ¹⁸¹Ta(p, n)¹⁸¹W using the statistical multi-step compound formalism.     

Particles + core reduction of time-dependent Hartree-Fock

The orbitals of the TDHF determinant are divided into two classes. Those of the “core” are described by only a few collective parameters. The remaining “particle” orbitals are treated explicitly. A set of equations is derived describing the coupled evolution of the core and particles. The physical content and computational advantages of the method are illustrated in a one-dimensional model.     

Time-dependent Hartree-Fock calculations for 14N + 12C reactions

We present Time-Dependent Hartree-Fock calculations for the massasymmetric system ¹⁴N + ¹²C in the range 20 ? E_cm ? 114. A simplified effective interaction of the Skyrme form has been used and the orbital angular motion of the ions has been treated in the rotating frame approximation. The overall magnitude of the calculated fusion cross-section is in agreement with experiment. The calculated differential cross section for direct inelastic reaction products is proportional to ${}^1\text{sin θ}$. This is in contrast to the exponential decrease observed experimentally.