The Lorentz Integral Transform and its Inversion

Abstract

The Lorentz integral transform method is briefly reviewed. The issue of the inversion of the transform, and in particular its ill-posedness, is addressed. It is pointed out that the mathematical term ill-posed is misleading and merely due to a historical misconception. In this connection standard regularization procedures for the solution of the integral transform problem are presented. In particular a recent one is considered in detail and critical comments on it are provided. In addition a general remark concerning the concept of the Lorentz integral transform as a method with a controlled resolution is made.

10 pages, this version has been made more self-contained

References in corpus (10)

• The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions
• alpha-particle photoabsorption with a realistic nuclear force
• The ${}^4$He total photo-absorption cross section with two- plus three-nucleon interactions from chiral effective field theory
• Role of final state interaction and of three-body force on the longitudinal response function of 4He
• Low-Energy Inelastic Neutrino Reactions on 4He
• Photodisintegration of light nuclei for testing a correlated realistic interaction in the continuum
• Improved transverse (e,e') response function of 3He at intermediate momentum transfers
• The Transverse Electron Scattering Response Function of 3He
• Threshold 3He and 3H Transverse Electron Scattering Response Functions
• On the ill-posed character of the Lorentz integral transform

Cited by in corpus (13)

• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Modern Ab Initio Approaches and Applications in Few-Nucleon Physics with A \ge 4
• Bound state techniques to solve the multiparticle scattering problem
• Spectral density estimation with the Gaussian Integral Transform
• Artificial quantum thermal bath: Engineering temperature for a many-body quantum system
• Spectral density reconstruction with Chebyshev polynomials
• Relativistic effects in ab-initio electron-nucleus scattering
• Energy Resolution with the Lorentz integral transform
• Transverse electron scattering response function of ${}^3$He with $\Delta$-isobar degrees of freedom
• Faster spectral density calculation using energy moments
• Photon Scattering with the Lorentz Integral Transform Method
• On calculating response functions via their Lorentz integral transforms
• Calculation of the astrophysical S-factor S_12 with the Lorentz integral transform