Search

Transport codes used for space radiation protection require accurate nuclear fragmentation cross sections as input. The fragmentation process is modeled in two stages: a fast step, called abrasion or knockout, and a slower step, called evaporation or ablation. In this work, the ablation step is calculated via Monte Carlo (MC) methods using the recently modified legacy EVAporation (EVA) code. The code is based on the Weisskopf-Ewing particle emission formalism and has been extensively overhauled and modernized. Updates include a new nuclear mass table and modifications to the nuclear level density expression. The new formulation enables calculated results to exhibit the odd-even effect observed in experimental measurements. The revised ablation code, EVAporation-University of Tennessee, Knoxville (EVA-UTK), has been coupled with the quantum multiple scattering abrasion formalism incorporated in the nuclear fragmentation code, Optical PoTential FRAGmentation (OPTFRAG), and resulted in substantial improvements in agreement between fragmentation cross section estimates and experimental measurements.

A program of comparing American (NASA) and Russian (ROSCOSMOS) space radiation transport codes has recently begun, and the first paper directly comparing the NASA and ROSCOSMOS space radiation transport codes, HZETRN and SHIELD respectively has recently appeared. The present work represents the second time that NASA and ROSCOSMOS calculations have been directly compared, and the focus here is on models of pion production cross sections used in the two transport codes mentioned above. It was found that these models are in overall moderate agreement with each other and with experimental data. Disagreements that were found are discussed.

The space radiation environment comprises all of the nuclei in the periodic table with energies that extend from a fraction of an MeV/n to TeV/n. The vast range of projectile–target and energy combinations necessitates highly efficient and accurate cross section codes for use in radiation transport codes. As particles in the space radiation environment impinge on shielding materials, nuclear reactions, such as nuclear fragmentation, occur. One way of estimating nuclear fragmentation cross sections is to use an abrasion–ablation model, which describes how nucleons are dislodged from the nuclei as a result of nuclear collisions and the mechanism by which excited pre-fragments decay via particle emission to more stable states. The well-known partial wave solution method cannot be used directly for the computation of abrasion cross sections. Instead, abrasion cross sections may be computed by slightly altering the Eikonal solution method, which is a high energy (small scattering angle) approximation that depends on the nucleus–nucleus optical potential. The aim of the current work is to present two efficient methods for the computation of the Eikonal phase shift function. Analytic formulas of the optical potential are presented in the position-space representation for nuclei that are well-represented by harmonic-well nuclear matter densities (A < 20), which reduces the Eikonal phase factor to an integration over a single dimension. Next, the Eikonal phase function is presented in the momentum-space representation, which is particularly useful when the Fourier transform of the position-space optical potential is known. These new methods increase the computational efficiency by three orders of magnitude and allow for rapid prediction of elastic differential, total, elastic, and reaction cross sections in the Eikonal approximation.

Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world's best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic Three-Dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scattering Theory (MST) that uses 5 parameterizations---3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations---predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame ($T_{\rm Lab}$) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which $T_{\rm Lab}>$ 220 MeV/n.

in the second half of the 19 th century (1864, 1878, 1894, 1895, and 1896). The incident proton energy distributions for these solar particle events are assumed to be similar to that of the November 1960 event, one of the most energetic of the modern space era. The crewmembers are assumed to be located at the mean surface elevation on Mars, at the lowest elevation on Mars in the Hellas Impact Basin, and on the summit of Olympus Mons, the highest surface elevation on Mars. The crewmembers are assumed to be shielded by the overlying carbon dioxide atmosphere of Mars, and locally shielded by a space suit, a surface landing spacecraft, or a surface habitat. These estimates are compared with current NASA Permissible Exposure Limits.

Radiation exposure estimates for crew members on the surface of Mars may vary widely because of the large variations in terrain altitude. The maximum altitude difference between the highest (top of Olympus Mons) and the lowest (bottom of the Hellas impact basin) points on Mars is about 32 km. In this work estimates of radiation exposures as a function of altitude, from the Hellas impact basin to Olympus Mons, are made for a solar particle event proton radiation environment comparable to the Carrington event of 1859. We assume that the proton energy distribution for this Carrington-type event is similar to that of the Band Function fit of the February 1956 event. In this work we use the HZETRN 2010 radiation transport code, originally developed at NASA Langley Research Center, and the Computerized Anatomical Male and Female human geometry models to estimate exposures for aluminum shield areal densities similar to those provided by a spacesuit, surface lander, and permanent habitat as a function of altitude in the Mars atmosphere. Comparisons of the predicted organ exposures with current NASA Permissible Exposure Limits (PELs) are made.

It is well known that multiple scattering theories are very useful in the study of nucleon–nucleus and nucleus–nucleus scattering processes. The derivation of a nonrelativistic multiple scattering theory (NRMST) is well-established and clear. A key component to the formulation of an NRMST is the ability to separate the unperturbed Hamiltonian from the residual interaction. For the relativistic problem, it is not clear how to perform this separation starting from a field theoretical Lagrangian. Instead, one starts from an infinite set of Feynman diagrams, which play the role of the kernel in the Bethe–Salpeter equation for nucleus–nucleus scattering. Once the kernel is defined, it is straightforward to develop a relativistic multiple scattering theory (RMST). To be more complete than previous studies, delta degrees of freedom are included, which is a minimum requirement to explain pion production. It is demonstrated that an RMST can be formulated by expressing the kernel in a form that is similar to the re...

A numerical Gram–Schmidt orthonormalization procedure is presented for constructing an orthonormal basis function set from a non-orthonormal set, when the number of basis functions is large. This method will provide a pedagogical illustration of the Gram–Schmidt procedure and can be presented in classes on numerical methods or computational physics.

The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann–Schwinger equation with the first order optical potential that was employed in the calculation.