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Setting Limits on Supersymmetry Using Simplified Models

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Published on: November 15, 2013

Reconstructing the nucleon-nucleon potential by a new coupled-channel inversion method.

Andrey Pupasov¹, Boris F Samsonov, Jean-Marc Sparenberg

¹Physics Department, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russia.

Physical Review Letters

|May 17, 2011

Summary

This study introduces a novel supersymmetric transformation for the Schrödinger equation. This method precisely fits realistic mixing parameters, enabling the creation of exactly solvable potentials for neutron-proton interactions.

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Area of Science:

Quantum mechanics
Nuclear physics
Mathematical physics

Background:

Supersymmetric transformations offer powerful tools for solving quantum mechanical problems.
The two-channel Schrödinger equation with equal thresholds presents challenges in accurately modeling complex interactions.
Realistic potentials require precise fitting of scattering matrix and effective-range functions.

Purpose of the Study:

To present a second-order supersymmetric transformation for the two-channel Schrödinger equation.
To analytically modify the potential matrix while preserving eigenphase shifts.
To develop a method for precisely fitting realistic mixing parameters using Padé expansion.

Main Methods:

A second-order supersymmetric transformation is applied to the two-channel Schrödinger equation.
A Breit-Wigner term is added to the mixing parameter.
The potential matrix is modified analytically.
Padé expansion is used to fit the scattering matrix and effective-range function.

Main Results:

The transformation adds a Breit-Wigner term to the mixing parameter without altering eigenphase shifts.
The potential matrix is modified analytically.
The iterative application of transformations allows precise fitting of realistic mixing parameters.
An exactly solvable potential for the neutron-proton (3)S1-(3)D1 case is constructed.

Conclusions:

The presented supersymmetric transformation provides an effective method for analyzing two-channel Schrödinger equations.
This approach facilitates the accurate modeling of nuclear interactions, such as the neutron-proton (3)S1-(3)D1 case.
The method offers a pathway to constructing exactly solvable potentials for complex quantum systems.