Study of Analytic Statistical Model for Decay of Light and Medium Mass Nuclei in Nuclear Fragmentation

The angular momentum independent statistical decay model is often applied using a Monte-Carlo simulation to describe the decay of prefragment nuclei in heavy ion reactions. This paper presents an analytical approach to the decay problem of nuclei with mass numbers less than 60, which is important for galactic cosmic ray (GCR) studies. This decay problem of nuclei with mass number less than 60 incorporates well-known levels of the lightest nuclei (A < 11) to improve convergence and accuracy. A sensitivity study of the model level density function is used to determine the impact on mass and charge distributions in nuclear fragmentation. This angular momentum independent statistical decay model also describes the momentum and energy distribution of emitted particles (n, p, d, t, h, and a) from a prefragment nucleus. Introduction The description of heavy ion fragmentation is important for assessing damage to human cells and microelectronic equipment during spaceflight and on high-altitude airplane flights. Currently, few measurements of fragmentation cross sections are available because many collision pairs of interest exist for assessing the full galactic cosmic ray (GCR) spectrum interacting with various materials of interest. Other reasons include the unavailability of heavy ion accelerators and the high cost of measurement programs. Physical models (ref. 1) of heavy ion reactions must instead be used to provide databases for radiation transport codes (ref. 2) from which damage assessment may be made. Heavy ion fragmentation is usually described as a two-step process of abrasion-ablation. Abrasion describes the geometric overlap of two nuclei and the accompanying loss of material (nucleons) in the overlap region, with the size of this region dependent on the impact parameter of the collision. The large piece of nuclear matter remaining after the abrasion step is called the prefragment nucleus. Ablation occurs when the prefragment nucleus is in a state of excitation and decays by particle emission to a stable configuration. The abrasion step is described by using geometric pictures (refs. 1 and 3) or optical models (refs. 4 and 5), and more recently with quantum models (refs. 6 and 7). The ablation step is described in the geometric picture (ref. 1) with the Rudstam charge distribution formulas and in the optical model approach with Monte-Carlo codes (refs. 8 and 9) for the statistical decay of an equilibrated system. Development of nuclear databases for GCR studies requires reaction models that are computationally efficient and accurate. References 6 and 10 detail efficient computational procedures for describing the abrasion step of the reaction. The present report describes the analytic solution to the statistical decay model (refs. 11–13) and a sensitivity study of available nuclear level density models. Statistical decay codes are often applied to a large number of nuclei, including ones with very large mass number A (A > 60), which are not of interest in GCR studies. This report focuses on a restricted range of nuclei typical of the prefragments formed during GCR fragmentation and uses analytic methods that are easily coupled to abrasion and excitation energy models. This approach incorporates the well-known levels of the lighter mass nuclei and applies the statistical decay model to heavier mass nuclei. The statistical approach examines the decay (or evaporation cascade) of heavier mass prefragments (A > 11), along with the decay at higher energies of some lighter mass nuclei where the decay properties are not well-known. The energy and momentum spectra of the emitted particles (n, p, d, t, h, and α) during decay are also represented consistently in the same statistical model. This report also describes the analytic solutions for fragment formation from an initial excited nucleus and the energy and momentum spectrum of the emitted or evaporated light ions. Physical inputs are then described, and numerical examples of the models are presented. A 12 ≤ ( )