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Modified J-matrix method for scattering.

Wim Vanroose¹, Jan Broeckhove, Frans Arickx

¹Departement Wiskunde-Informatica, Universiteit Antwerpen, Groenenborgerlaan 171, 2020 Antwerp, Belgium.

Physical Review Letters

|January 22, 2002

Summary

This study enhances the J-matrix technique for solving scattering problems with long-range interactions. The modified method significantly reduces computational effort by approximating scattering solutions effectively.

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Area of Science:

Quantum mechanics
Computational physics
Scattering theory

Background:

Solving scattering problems with long-range interactions is computationally intensive.
The J-matrix technique is a common method for scattering problems.
Approximations are often needed for complex potentials.

Purpose of the Study:

To modify the J-matrix technique for efficient handling of long-range interactions.
To reduce the numerical effort required for scattering calculations.
To provide accurate approximations for scattering solutions.

Main Methods:

Introducing additional terms into the asymptotic three-term recurrence relation.
Incorporating asymptotic effects of the potential into the recurrence relation.
Applying the modified technique to a Yukawa potential example.

Main Results:

The modified J-matrix technique effectively solves scattering problems with long-range interactions.
Solutions from the modified recurrence relation closely approximate exact scattering solutions.
A significant reduction in numerical effort is achieved.

Conclusions:

The enhanced J-matrix technique offers an efficient and accurate approach for scattering problems.
This method is particularly beneficial for potentials with long-range interactions.
The approach simplifies complex scattering calculations.

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