Anomaly-free singularities in the generalized Kohn variational method
Anomaly-free singularities in the generalized Kohn variational method
复制标题
广义 Kohn 变分法中的无异常奇点
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
M. Plummer
中科院分区：
文献类型：
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作者：
J. N. Cooper;E. Armour;M. Plummer
对低能(e+-H2)弹性散射的Kohn变分计算中的奇点进行了分析。如果使用足够精确的试探波函数，我们认为，我们对Kohn变分原理的实现必然会产生不虚假的奇点。为了避免散射相移计算中的反常行为，我们提出了两种优化试探波函数自由参数的方法，第一种方法是基于这种奇异性的存在。第二种方法是广义Kohn方法的一种更传统的优化方法。观察到两种优化方案的结果非常一致；此外，它们给出的结果被认为与复数Kohn方法得到的结果有效地等价。第一种优化方案的优点是它不需要Kohn方程的显式解。我们给出了使用任何一种优化方案都无法避免的异常的例子，但表明通过考虑试函数的非线性参数的变化来避免这些异常是可能的。
We have carried out an analysis of singularities in Kohn variational calculations for low-energy (e+–H2) elastic scattering. Provided that a sufficiently accurate trial wavefunction is used, we argue that our implementation of the Kohn variational principle necessarily gives rise to singularities which are not spurious. We propose two approaches for optimizing a free parameter of the trial wavefunction in order to avoid anomalous behavior in scattering phase shift calculations, the first of which is based on the existence of such singularities. The second approach is a more conventional optimization of the generalized Kohn method. Close agreement is observed between the results of the two optimization schemes; further, they give results which are seen to be effectively equivalent to those obtained with the complex Kohn method. The advantage of the first optimization scheme is that it does not require an explicit solution of the Kohn equations to be found. We give examples of anomalies which cannot be avoided using either optimization scheme but show that it is possible to avoid these anomalies by considering variations in the nonlinear parameters of the trial function.