Modification of Effective Range Theory in the Presence of a Long-Range (1/R4) Potential (Classic Reprint)

New insights into how long-range forces reshape scattering analysis .

This volume explains how a polarization-like 1/r potential changes the usual effective range theory and introduces a modified framework for low-energy scattering.

Two concise sections frame the problem: it shows why the standard power-series expansion breaks down for long-range potentials and then builds a revised approach that stays valid for these cases. Readers will see how the Schrödinger equation is solved when the potential falls off as a multiple of 1/r and how new quantities emerge to describe low-energy behavior.

• Learn why long-range interactions invalidate the classic k cot Ti(L) expansion and how to adapt the theory accordingly.
• See how mathematical solutions to the Schrödinger equation guide the modified effective range expansion.
• Understand expansions about zero energy and about the energy of a bound state in the presence of polarization potentials.
• Explore practical implications for modeling low-energy scattering in atomic and molecular contexts.

Ideal for readers of advanced physics, especially those studying scattering theory, quantum mechanics, and atomic or molecular interactions.