Abrasion-Ablation Model for Neutron Production in Heavy Ion Reactions

In heavy ion reactions, neutron production at forward angles is observed to occur with a Gaussian shape that is centered near the beam energy and extends to energies well above that of the beam. This paper presents an abrasion-ablation model for making quantitative predictions of the neutron spectrum. To describe neutrons produced from the abrasion step of the reaction where the projectile and target overlap, we use the Glauber model and include effects of final-state interactions. We then use the prefragment mass distribution from abrasion with a statistical evaporation model to estimate the neutron spectrum resulting from ablation. Measurements of neutron production from Ne and Nb beams are compared with calculations, and good agreement is found. Introduction Neutrons produced from the nuclear interactions of cosmic rays with the Earth's atmosphere, aircraft or spacecraft structural shielding, or the self-shielding of the human body are responsible for a large fraction of the energy deposition to passengers on high-altitude aircraft (ref. 1) and to astronauts in low Earth orbit. The nuclear reactions leading to the production of secondary neutrons from cosmic rays are dominated by the nucleon component; however, a significant fraction of neutrons are also produced in the interactions of the primary helium and heavy ion components of the cosmic rays with shielding. (See ref. 2.) Models of neutron production in heavy ion reactions are thus important inputs for the assessment of radiation damage from cosmic rays. The study of neutron production from reactions induced by heavy ions may also present important insights into the theoretical modeling of the production of heavy fragments in these reactions. The abrasionablation model has been used for many years to describe mass yields in heavy ion collisions. (See refs. 3 to 6.) However, few attempts have been made to calculate nucleon production, including momentum distributions, in the abrasion-ablation model (ref. 7). Heavy ion fragment mass yields and nucleon production are ultimately related in these reactions, theoretically through the equations of motion or scattering amplitude. In references 8 and 9, measurements of inclusive neutron production in heavy ion collisions at 390A MeV and 800A MeV suggest that neutrons from the knockout stage of abrasion and the evaporation stage of ablation can be separated from the data. Madey and coworkers (refs. 8 and 9) have decomposed the neutron production data at forward angles into three Gaussian components of increasing widths. The narrowest component was attributed to evaporation neutrons, for which they found an effective temperature of around 2.7 MeV at 390A MeV and 3.3 MeV at 800A MeV. The second component of intermediate width was attributed to direct knockouts of neutrons. For this component, the width of the distribution was related to the internal momentum distribution of nucleons with Fermi momentum of about 250 MeV/c. The third and widest component was attributed to a high-momentum tail in the internal momentum distribution or to collective excitation effects. These results are useful because they suggest that some details of the different stages of the abrasion-ablation description can be uncovered from inclusive data where only the total distribution of neutrons is measured. In this paper, we extend the abrasion-ablation model as formulated by Hiifner, Sch_ffer, and Schtirmann to the evaluation of momentum distributions for nucleon production in heavy ion collisions (ref. 4). Using the Glauber model (ref. 10), we consider the spectrum of the knockouts in the overlap region of the collision. We also estimate the contribution of the final-state interactions of the knockouts for the projectile interacting with the prefragments. As in reference 4, the main approximations, other than the Glauber approximation, are derived from the treatment of the nuclear wave function, for which single-particle wave functions are used at all stages. In references 11 and 12, this formulation has been used to calculate proton production from 12C and 40Ar projectiles. Excitation energies from the abrasion stage are calculated in the geometric abrasion-ablation model (refs. 3 and 6) and used in the classical evaporation model (refs. 13 and 14) to estimate the neutron spectrum that originates in ablation. We then have a quantitative approach for considering the several mechanisms described in references 8 and 9 and can make comparisons that are consistent with the models describing heavy fragment yields. The neutrons produced in the abrasion stage have momentum distributions largely determined by the ground-state, one-body density matrix of the projectile. To explain the high-momentum component of the neutron spectrum, we consider recent models that account for correlation effects based on calculations of the momentum distributions n(p). (See refs. 15 and 16.) In many aspects, the physics of the calculations presented herearesimilarto thosecontainedin intranuclear cascadecodesthat use the Monte-Carlomethod. (See refs.17and18.)Theformalismwepresent isuseful first because of its simplicitybecause it involvesonlyafew numerical integrations andsecond because of its ability to testnuclearstructureinputs,suchastheone-body densitymatrix.In theremainder of thispaper, wefirst introducetheGlauber amplitudeandrecast theabrasion modelin termsof themomentumdistributions of the knockouts. Thefinal-stateinteractions arethenstudied bycorrecting transition densities forrescattering effects. Theenergyspectrumof neutronsdecayingfromprefragmentsare thenconsidered by usingtheclassical evaporationmodel.Finally, we makecomparisons with experiments and discussthe resultsof model calculations.