A comparison of the multigroup and collocation methods for solving the low-energy neutron Boltzmann equation
A low-energy neutron transport algorithm for use in space-radiation protection is developed. The algorithm is based upon a multiple energy group analysis of the straight ahead Boltzmann equation utilizing a mean value theorem for integrals. The algorithm developed is then verified by using a collocation method solution on the same straight ahead Boltzmann equation. This algorithm was then coupled to the existing NASA Langley HZETRN (high charge and energy transport) code through the evaporation source term. Evaluation of the neutron fluence generated by the February 23, 1956 solar particle event for an aluminum-water shield-target configuration is then compared with the LAHET Monte Carlo calculation for the same shield-target configuration. The algorithm developed showed a great improvement in results over the unmodified HZETRN solution. A bidirectional modification of the evaporation source produced further improvement of the fluence.
Mean excitation energies for stopping powers in various materials composed of elements hydrogen through argon
The basic model of Lindhard and Scharff, known as the local plasma model, is utilized to study the effects of the chemical and physical state of the medium on its stopping power. Unlike previous work with the local plasma model, in which individual electron shifts in the plasma frequency were estimated empirically, the Pines correction derived for a degenerate Fermi gas is shown herein to provide a reasonable estimate even on the atomic scale. Thus, the model is moved to a completely theoretical base requiring no empirical adjustments, adjustments characteristics of past applications. The principal remaining error is in the overestimation of the low-energy absorption properties characteristic of the plasma model in the region of the atomic discrete spectrum, although higher energy phenomena are accurately represented and even excitation-to-ionization ratios are given with fair accuracy. Mean excitation energies for covalently bonded gases and solids, ionic gases and crystals, and metals are calculated using first-order models of the bonded states for which reasonable agreement with the recently evaluated data of Seltzer and Berger is obtained. Hence the methods described herein allow reasonable estimates of mean excitation energy for any physical-chemical combination of material media for stopping power applications.
Total and differential cross sections for pion production via coherent isobar and giant resonance formation in heavy-ion collisions
A quantal many-body formalism is presented that investigates pion production through the coherent formation of a nucleonic isobar in the projectile and its subsequent decay to various pion charge states along with concomitant excitation of the target to a coherent spin-isospin giant resonance via a peripheral collision of relativistic heavy ions. Total cross sections as a function of the incident energy per nucleon and Lorentz-invariant differential cross sections as a function of pion energy and angle are calculated. It is shown that the pion angular distributions, in coincidence with the target giant resonance excitations, might provide a well-defined signature for these coherent processes.
A simplified optical model description of heavy ion fragmentation
The fragmentation of 213 MeV/nucleon 40Ar ions by 12C targets is described within the context of a simple abrasion-ablation fragmentation model. The abrasion part of the theory utilizes a quantum-mechanical formalism based upon an optical model potential approximation to the exact nucleus-nucleus multiple-scattering series. The ablation stage of the fragmentation is treated as a compound nucleus evaporation. The decay probabilities for the various particle emission channels are computed using the EVAP-4 Monte Carlo computer program. Predictions for production cross sections for isotopes of sulfur, phosphorus, silicon, and aluminum are made and compared with experimental data. The model is also used to compare predicted and experimental element production cross sections for 1.88 GeV/nucleon 56Fe colliding with 12C and 208Pb targets.