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arXiv · 1711.01950

Highly excited bound-state resonances of short-range inverse power-law potentials

Shahar Hod
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Abstract

We study analytically the radial Schrödinger equation with long-range attractive potentials whose asymptotic behaviors are dominated by inverse power-law tails of the form $V(r)=-β_n r^{-n}$ with $n>2$. In particular, assuming that the effective radial potential is characterized by a short-range infinitely repulsive core of radius $R$, we derive a compact {\it analytical} formula for the threshold energy $E^{\text{max}}_l=E^{\text{max}}_l(n,β_n,R)$ which characterizes the most weakly bound-state resonance (the most excited energy level) of the quantum system.

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Shahar Hod. 2017-11-06. Highly excited bound-state resonances of short-range inverse power-law potentials. https://doi.org/10.1140/epjc%2Fs10052-017-5362-z

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