Orbital Collapse in Exotic Atoms and Its Effect on Dynamics

TL;DR

This paper investigates the orbital collapse phenomenon in muonic atoms using DFT, TDSE, and CTMC methods, revealing an upper limit for muon-captured states and proposing a way to estimate this limit in exotic atoms.

Contribution

It introduces a novel analysis of orbital collapse in muonic atoms and proposes a simple method to estimate the critical angular momentum in exotic noble atoms.

Findings

Identification of a critical angular momentum $l_c$ where orbital collapse occurs.

Confirmation of an upper limit for muon-captured states in muon-Ar collisions.

Agreement between DFT, TDSE, and CTMC methods in estimating $l_c$.

Abstract

We study the energy structures of muonic Ar atoms and find the muon orbital collapses at a critical angular momentum $l_c$ using density-functional theory (DFT). The $l_c$ may provide an upper limit for the muon-captured states in muon-Ar collisions. We confirm the existence of this upper limit by calculating the state-specified capture probability using the time-dependent Schr\"odinger equation (TDSE) and a classical trajectory Monte Carlo (CTMC) methods with the single-active-particle approximation. Modifying the mapping between the classical binding energy and the principal quantum number led to a reasonable agreement in the state-specified muon capture probabilities obtained by the TDSE and CTMC methods. We also propose a simple method to estimate $l_c$ for exotic noble atoms from atomic model potentials. The estimated values agree with those calculated by DFT.