强耦合极限下配对问题的标度性质
Scaling properties of the pairing problem in the strong coupling limit
摘要：
我们研究了配对哈密顿量的激发态，在强耦合极限下给出了它们的能量展开式。为了评估配对相互作用的作用，我们应用形式主义的情况下，一个重原子核。我们表明，只有少数统计时刻的水平分布是足够的，以产生一个准确的估计的能量耦合$G$的值不太小，我们给出了一系列的前四项的解析表达式。此外，我们讨论的收敛半径$G_{\rm sing}$的扩展表明，它强烈依赖于的水平分布的细节。此外，$G_{\rm sing}$与耦合$G_{\rm crit}$的临界值无关，该临界值表征了配对哈密顿量的物理特性，因为它甚至可以在没有这些临界点的情况下存在。
英文摘要：
We study the excited states of the pairing Hamiltonian providing an expansion for their energy in the strong coupling limit. To assess the role of the pairing interaction we apply the formalism to the case of a heavy atomic nucleus. We show that only a few statistical moments of the level distribution are sufficient to yield an accurate estimate of the energy for not too small values of the coupling $G$ and we give the analytic expressions of the first four terms of the series. Further, we discuss the convergence radius $G_{\rm sing}$ of the expansion showing that it strongly depends upon the details of the level distribution. Furthermore $G_{\rm sing}$ is not related to the critical values of the coupling $G_{\rm crit}$, which characterize the physics of the pairing Hamiltonian, since it can exist even in the absence of these critical points.
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