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arXiv · 2504.03112

Numerical Assessment of Convergence in the Post Form Ichimura-Austern-Vincent model

Jin Lei
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Abstract

The Ichimura-Austern-Vincent (IAV) model provides a powerful theoretical framework for describing inclusive breakup reactions. However, its post-form representation presents significant numerical challenges due to the absence of a natural cutoff in the transition matrix integration. This work presents a systematic assessment of convergence methods for post-form IAV calculations, comparing the bin method and the Vincent-Fortune approach. We demonstrate that while the bin method offers implementation simplicity, it exhibits strong parameter dependence that compromises numerical stability. In contrast, the Vincent-Fortune method, which employs complex contour integration, achieves reliable convergence without arbitrary parameters. We further introduce a novel hybrid approach that integrates finite-range distorted wave Born approximation (DWBA) with the Vincent-Fortune technique, combining the accuracy of finite-range treatment at short distances with the numerical stability of zero-range approximations in the asymptotic region. Numerical results for deuteron and $^6$Li-induced reactions confirm the efficacy of this hybrid method, showing consistent agreement with experimental data while eliminating the convergence issues that plague traditional approaches. This advancement enables more reliable calculations of nonelastic breakup cross sections and facilitates the extension of the IAV formalism beyond DWBA to incorporate continuum-discretized coupled-channels (CDCC) wave functions for a more comprehensive treatment of breakup processes.

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Jin Lei. 2025-04-04. Numerical Assessment of Convergence in the Post Form Ichimura-Austern-Vincent model. https://arxiv.org/abs/2504.03112

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