Clustering Pre-equilibrium Model Analysis for Nucleon-induced Alpha-particle Spectra up to 200 MeV

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The clustering exciton model of Iwamoto and Harada is applied to the analy- sis of pre-equilibrium (N; x ) energy spectra for medium-to-heavy nuclei up to 200 MeV. In this work, we calculate alpha-particle formation factors without any approximations that appear in the original model. The clustering process is also considered in both the primary and second pre-equilibrium emissions. We optimize the exciton and the cluster- ing model parameters simultaneously by looking at the experimental (N; xN) and (N; x ) energy spectra. The experimental alpha-particle spectra are well reproduced with a unique set of clustering model parameters, which is independent of incident neutrons/protons. The present analysis also implies that the clustering model parameter is not so di erent between the medium and heavy nuclei. Our calculations reproduce experimental data gen- erally well up to the incident energy of 150 MeV, but underestimations are seen above this energy. The exciton model, as it is frequently used in the nuclear data evaluation (1), predicts pre-equilibrium (N; xN) spectra generally well. However, a long-standing problem exists in the model calculation of the pre-equilibrium composite-particle spectra due to rather complicated reaction mechanism. The phenomenological models proposed by Kalbach (2,3) describe nucleon-transfer reaction process in the phase-space, in which many adjustable parameters are involved to fit experimental particle energy- spectra. Although a useful global parameterization is reported (2,3), extrapolation of the global pa- rameters beyond the experimental range needs much attention. We apply the clustering exciton model of Iwamoto and Harada (4) to calculate nucleon-induced pre-equilibrium alpha-particle spectra from medium-to-heavy nuclei. The model describes the pickup process within the exciton model framework, where the alpha-particle formation factor is calculated by the overlap integral of wave functions between the alpha-particle and four nucleons (include the nu- cleons below Fermi level). In this work, the formation factors are calculated by numerical integrations, while the original Iwamoto-Harada model employed the root-mean-square approximation (4) where no correlation exists between the coordinates in the phase-space. The clustering process is also con- sidered in both the primary and second pre-equilibrium emissions. We optimize the pre-equilibrium and the clustering model parameters simultaneously by looking at the experimental nucleon and alpha- particle energy spectra. In this paper, di erences between the exact calculation and the approximation are exhibited for the alpha-particle formation factor. Through the comparisons with experimental spectra at incident energies up to 200 MeV, we show the behavior of the clustering model parameter, the applicability and limitation of the model.