Quantal-classical correspondence impulse theory

¹School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA.

|September 16, 2000

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This study introduces a new classical impulse cross section for atomic collisions, enabling precise calculations of nl-n(

Area of Science:

Background:

Classical mechanics often struggles to accurately describe atomic-scale interactions.
Previous models for collisional transitions lacked a direct classical correspondence.
Understanding collisional dynamics is crucial for various physical and chemical processes.

Purpose of the Study:

To derive a novel quantal impulse cross section suitable for classical interpretation.
To establish a general classical expression for nl-n(')l(') collisional transitions.
To unify different collision and recombination process calculations.

Main Methods:

Demonstration of compliance with the optical theorem and detailed balance.

Establishing a connection with the classical binary encounter approximation.

Main Results:

A novel form of the quantal impulse cross section is presented.
The first general classical expression for nl-n(')l(') collisional transitions is obtained.
The derived cross sections satisfy fundamental physical principles like the optical theorem and detailed balance.
A clear link to the classical binary encounter approximation is established.

Conclusions:

The developed method provides a unified approach to studying collision and recombination processes.
This work offers a direct classical pathway for understanding quantal impulse cross sections.
The findings open new avenues for research in atomic and molecular collisions.