广义Kohn变分法中的无异常奇点
Anomaly-free singularities in the generalized Kohn variational method
摘要：
本文对低能e^{+}- H_{2}弹性散射的Kohn变分计算中的奇异性进行了分析。只要使用足够精确的试探波函数，我们认为，我们的科恩变分原理的实施必然会产生奇异性，这是不虚假的。我们提出了两种方法来优化审判波函数的自由参数，以避免在散射相移计算，其中第一个是基于这种奇异性的存在异常行为。第二种方法是广义Kohn方法的更常规的优化。两个优化方案的结果之间观察到密切的协议，进一步，他们给出的结果被认为是有效地等同于那些与复杂的Kohn方法。第一个优化方案的优点是，它不需要显式的解决方案的Kohn方程被发现。我们给出的异常，不能避免使用任何优化方案的例子，但表明，它是可能的，以避免这些异常，通过考虑非线性参数的变化的审判功能。
英文摘要：
We have carried out an analysis of singularities in Kohn variational calculations for low energy e^{+}-H_{2} 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 behaviour 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.
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