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arXiv 1509.00510nucl-th
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低能统计复合核反应的Monte-Carlo随机矩阵方法

Random-matrix approach to the statistical compound nuclear reaction at low energies using the Monte-Carlo technique

T. Kawano, P. Talou, H. A. Weidenmüller

摘要:

利用随机矩阵方法和蒙特卡罗模拟,我们生成了化合物-核反应的散射矩阵和截面。在没有直接反应的情况下,我们将平均截面与高斯正交包络(GOE)三重积分给出的解析解进行比较,并与统计方法的预测进行比较,例如Moldauer、Hofmann、Richert、Tepel和Weidenmüller以及Kawai、Kerman和McVoy的预测。我们发现完美的协议与GOE三重积分,并显示后者的方法的有效性的限制。我们建立了一个标准的能量平均间隔的宽度,使整体平均和能量平均散射矩阵之间的相对差异低于一个给定的界限。直接反应模拟的能量无关的背景矩阵。在这种情况下,在整个蒙特卡罗模拟上平均的横截面与Engelbrecht-Weidenmüller变换结果完全一致。显示了其他近似方法的局限性。

英文摘要:

Using a random-matrix approach and Monte-Carlo simulations, we generate scattering matrices and cross sections for compound-nucleus reactions. In the absence of direct reactions we compare the average cross sections with the analytic solution given by the Gaussian Orthogonal Ensemble (GOE) triple integral, and with predictions of statistical approaches such as the ones due to Moldauer, to Hofmann, Richert, Tepel, and Weidenmüller, and to Kawai, Kerman, and McVoy. We find perfect agreement with the GOE triple integral and display the limits of validity of the latter approaches. We establish a criterion for the width of the energy-averaging interval such that the relative difference between the ensemble-averaged and the energy-averaged scattering matrices lies below a given bound. Direct reactions are simulated in terms of an energy-independent background matrix. In that case, cross sections averaged over the ensemble of Monte-Carlo simulations fully agree with results from the Engelbrecht-Weidenmüller transformation. The limits of other approximate approaches are displayed.

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