采用基组大小和坐标标度两个参数的共振态实稳化
Real stabilization of resonance states employing two parameters: basis set size and coordinate scaling
摘要：
用实基函数的变分展开方法研究了单粒子和双粒子哈密顿量的共振态。共振能量，$E_r$，和宽度，$Γ$，使用状态密度和${\mathcal L}^2$黄金法则式计算。我们提出了一个配方，充分选择一些变分问题的解决方案。得到的一组近似能量显示出一个非常有规律的行为与基础集的大小，$N$。事实上，这些特定的变分特征值显示出一个相当简单的缩放行为和收敛时，$N\rightarrow \infty$。按照同样的处方选择特定的解决方案的变分问题，我们得到一组近似宽度。使用表征近似能量的行为的标度函数作为指导，可以找到对谐振宽度的实际值的非常好的近似。
英文摘要：
The resonance states of one- and two-particle Hamiltonians are studied using variational expansions with real basis-set functions. The resonance energies, $E_r$, and widths, $Γ$, are calculated using the density of states and an ${\mathcal L}^2$ golden rule-like formula. We present a recipe to select adequately some solutions of the variational problem. The set of approximate energies obtained shows a very regular behaviour with the basis-set size, $N$. Indeed, these particular variational eigenvalues show a quite simple scaling behaviour and convergence when $N\rightarrow \infty$. Following the same prescription to choose particular solutions of the variational problem we obtain a set of approximate widths. Using the scaling function that characterizes the behaviour of the approximate energies as a guide, it is possible to find a very good approximation to the actual value of the resonance width.
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