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The inversion of the Lorentz integral transform with controlled resolution

by Winfried Leidemann, Victor D. Efros, Veronica Yu. Shalamova

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Submission summary

As Contributors: Winfried Leidemann
Preprint link: scipost_201910_00028v1
Date accepted: 2019-11-07
Date submitted: 2019-10-15 02:00
Submitted by: Leidemann, Winfried
Submitted to: SciPost Physics Proceedings
Proceedings issue: 24th European Few Body Conference (University of Surrey, U.K.)
Academic field: Physics
Specialties:
  • Quantum Physics
Approach: Theoretical

Abstract

The Lorentz integral transform (LIT) method is briefly presented. The ill-posedness of the inversion is discussed and it is pointed out that the LIT is an integral transform with a controlled resolution. As application the dipole response of a three-particle system bound in a hypercentral potential is considered. The inversion is performed in two ways, both employ expansions of the response function and of the LIT on a basis set and a transformed basis set, respectively. A previous study of the process under consideration seemed to point to serious problems in the inversion process. In the present work, however, it is shown that the LIT approach can be carried out in a reliable way.

Published as SciPost Phys. Proc. 3, 037 (2020)



Submission & Refereeing History

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Submission scipost_201910_00028v1 on 15 October 2019

Reports on this Submission

Anonymous Report 1 on 2019-10-30 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_201910_00028v1, delivered 2019-10-30, doi: 10.21468/SciPost.Report.1274

Report

In this manuscript the authors present the Lorentz integral transform and its inversion, showing that this is a method with a controlled resolution.
They then discuss the case of the dipole response function of three nucleons in a hyper-central potential, for which Ref.[3] reported to have observed difficulties in the inversion of the Lorenz integral transform. The authors show instead that a reliable inversion can be found with a proper inversion method where the number of basis function as well as the choice of the basis function is varied.

The paper is well written and the results are sound. The discussion helps clarifying previous statements found in the literature, thus I recommend publication.

  • validity: high
  • significance: good
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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