English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study analytically the radial Schr\"odinger equation with long-rangeattractive potentials whose asymptotic behaviors are dominated by inversepower-law tails of the form $V(r)=-\beta_n r^{-n}$ with $n>2$. In particular,assuming that the effective radial potential is characterized by a short-rangeinfinitely repulsive core of radius $R$, we derive a compact {\it analytical}formula for the threshold energy$E^{\text{max}}_l=E^{\text{max}}_l(n,\beta_n,R)$ which characterizes the mostweakly bound-state resonance (the most excited energy level) of the quantumsystem.

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