Double differential cross sections of light charged particle emission in neutron induced reactions on ^54,56,57,58Fe

Abstract

The energy spectra and double differential cross sections of the light composite particle (deuteron, triton, helium and alpha-particle) emissions for n + ^54,56,57,58Fe reaction are studied by integrating the optical model, the intra-nuclear cascade model, direct reaction theories, equilibrium reaction theory and the exciton model which included the improved Iwamoto–Harada model. Theoretical calculated results are compared with existing experimental data.

Introduction

New accelerator-driven technologies that utilize spallations, such as the production of tritium and the transmutation of radioactive waste, is a growing interest in such type of reactions especially due to the emerging new ideas concerning the hybrid systems (Bowman et al., 1992). Such systems are supposed to use intense high-energy proton beams (1 GeV or more), which induce spallation reactions on heavy targets. A large number of high-energy neutrons as well as light charged particles are produced. The Accelerator-Driven System (ADS) require nuclear reaction data of common cross sections and especially need the data of neutron and proton induced energy-angle correlated spectra of secondary light particles (neutron, proton, deuteron, triton, helium and alpha-particle) as well as double differential cross sections to model the performance of the target/blanket assembly and to predict neutron production, activation, heating, shielding requirements, and material damage. To meet these needs, better nuclear data libraries for neutron and proton induced reactions are required for transport calculations to guide engineering design over the incident neutron energies up to 200 MeV where many reaction mechanisms compete. The development of high-quality nuclear data for iron are particularly important due to their role as an important structural and target material in many Accelerator-Driven System designs.

The evaluated data (Chadwick et al., 1999) with GNASH code (Young et al., 1996) for n + ^54,56,57Fe reactions in ENDF/B-VII (Chadwick et al., 2006) provide a complete representation of the nuclear data needed for transport, damage, heating, radioactivity, and shielding applications over the incident neutron energy up to 150 MeV. Production cross sections and emission spectra are given for neutrons, protons, deuterons, tritons, alpha particles, γ-rays, and all residual nuclides produced (A > 5) in the reaction chains. The double differential cross sections for all outgoing particles are based on Kalbach systematics (Kalbach, 1977). The results are in agreement with the experimental spectra for neutron and proton emission, but the results are lower than those of the experimental spectra for deuteron, triton, helium and alpha-particle emission.

In the field of nucleon-induced reactions, few experimental results are available at incident energies above 20 MeV. Due to specific experimental difficulties, experimental results concerning light charged particle production in fast neutron induced reactions at the incident energies above 20 MeV are rather scarce. Since several years some groups were involved in such measurements of the interaction of fast neutrons with different target nuclei, and the angle-integrated spectra and double differential cross sections for emission protons, deuterons, tritons, heliums and alphas were given.

A consistent experimental data set for light charged particle emission induced by fast neutrons on natural iron, ⁵⁹Co, ²⁰⁹Bi, and uranium covering the incident neutron energy range 25–65 MeV were given for the first time (Kerveno et al., 2002, Raeymackers et al., 2004, Raeymackers et al., 2003). Experimental double differential cross sections and energy spectra are obtained for the four types of outgoing particles at several incident neutron energies.

A new set of experimental data concerning light charged particle production in 96 MeV neutron induced reactions on natural iron, lead, and uranium targets was reported (Blideanu et al., 2004). Double differential cross sections of charged particles have been measured over a wide angular ranges 20–160°.

The new experimental data provide complementary information on nucleon induced light charged particle emission and offer a larger base for testing the nuclear models.

The reproduction of light charged particles properties appears as one of the most challenging problems. Indeed, it has been shown (Blideanu et al., 2004) that different widely used models can describe the properties of emitted nucleons. However, they fail to properly account for the yield of light clusters. The exciton model of pre-equilibrium nuclear reaction theories and the quantum pre-equilibrium theories have been developed. The exciton model originated by Griffin (1966) has been used successfully to analyze the energy spectra. In this approach, the fast particle is emitted during the reequilibrium stage, which is characterized by a small exciton number. Although this model has been applied to many experimental data and has had much success, certain ambiguities still remain in the formulation of the composite particles emission. In the framework of the exciton model, the treatment of composite particles emissions is given originally by a simple arrangement factor (Cline, 1972), but the calculated spectra are much smaller than experimental data. In order to improve the results, several formulae have been proposed. Ribanský et al. (1973) proposed the intrinsic phase space factor and derived the cluster formation probability for each configuration. Although their results are quite good in fitting, the assumption of constant formation probability was done.

It is well-known that for nuclear reactions involving projectiles and ejectiles with different particle numbers, mechanisms like stripping, pick-up and knock-out play an important role and the exciton model does not cover these direct-like reactions. Therefore, Kalbach developed a phenomenological contribution for these mechanisms (Kalbach, 1986, Kalbach, 1988, Kalbach, 2000, Kalbach, 2005). It has recently been shown (Kalbach, 2000; Kerveno et al., 2002) that the new method gives a considerable improvement over the older methods, but it seemed to consistently underpredict neutron induced reaction cross sections.

The Kalbach systematics is based on the fact that direct reactions such as the nucleon pick-up process and the cluster knock-out process are not included in the exciton model. Therefore this approach calculates their associated contributions separately and adds them to the pre-equilibrium component calculated with the original exciton model. The double differential cross sections are obtained from the calculated energy spectra using the Kalbach systematics in the two nuclear reaction codes TALYS (Koning et al., 2004, Koning, 2005) and GNASH. The comparison of experimental data to the theoretical calculations done with TALYS code for n, p + ^54,56,57,58Fe reactions were given (Duijvestijn et al., 2006). The results reproduce better the order of magnitude and shape of the experimental spectra for neutron, proton and deuteron emission.

Iwamoto et al. (1982) developed a composite particle model based on the statistical phase space integration method. Their main physical idea is that some nucleons form the composite particles may come from the levels below the Fermi sea. The consideration is quite similar to pick-up process in direct reaction theory. The physical picture is more reasonable. But the calculated results indicated that this model overestimated the pre-formation probabilities of the composite particles. The study turns out that the integration over momentum space in the phase space integration has the superfluous part, which is the forbidden area restricted by excitation energy. Zhang et al., 1992, Zhang, 1994) improved Iwamoto et al. pick-up mechanism to reduce the pre-formation probabilities. According to the studies on pick-up mechanism, at low energies (E_n < 25 MeV), the dominant configuration is the nucleons pick-up below the Fermi surface. Shen (1994) gave the results of a composite particle projectile considering pickup-type reactions with one and two particles above the Fermi sea by energy-averaged and energy-angle correlated kernels, respectively.

The main objective of this work is to use the improved Iwamoto–Harada model to provide a comprehensive and improved description of the energy spectra and double differential cross sections of the light composite particle (d, t, ³He and α) emissions in the intermediate-energy range. The double differential cross sections and angle-integrated spectra for emission neutrons, protons, deuterons, tritons, heliums and alphas, and proton induced all cross sections of n + ^54,56,57,58Fe reactions are consistent calculated using nuclear theoretical models which integrate the optical model, the intra-nuclear cascade model, direct, pre-equilibrium and equilibrium reaction theories. The calculated results are compared with new experimental measured data.

Section 2 provides a description of the theoretical models used in this work. Section 3 gives analysis and comparisons of calculated results with experimental data. Section 4 gives simple conclusion.