New inversion methods for the Lorentz Integral Transform

Abstract

The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross sections without explicit knowledge of final state wave functions. The necessary inversion of the transform has to be treated with great care, since it constitutes a so-called ill-posed problem. In this work new inversion techniques for the Lorentz Integral Transform are introduced. It is shown that they all contain a regularization scheme, which is necessary to overcome the ill-posed problem. In addition it is illustrated that the new techniques have a much broader range of application than the present standard inversion method of the Lorentz Integral Transform.

12 pages. 12 figures, revtex4. submitted to Eur.Phys.J. A

References in corpus (10)

• Benchmark Test Calculation of a Four-Nucleon Bound State
• Response Functions from Integral Transforms with a Lorentz Kernel
• Total Photoabsorption Cross Sections of A=6 Nuclei with Complete Final State Interaction
• Two-body Photodisintegration of ${}^4$He with Full Final State Interaction
• Is there a Pronounced Giant Dipole Resonance in ^4He?
• Longitudinal response functions of 3H and 3He
• Accurate Four-Body Response Function with Full Final State Interaction: Application to Electron Scattering off 4He
• Neutrino neutral reaction on 4He, effects of final state interaction and realistic NN force
• Calculation of Exclusive Cross Sections with the Lorentz Integral Transform Method
• Application of the Lorentz-Transform Technique to Meson Photoproduction

Cited by in corpus (34)

• Recent developments in no-core shell-model calculations
• The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions
• First principles description of the giant dipole resonance in 16O
• Giant and pigmy dipole resonances in 4He, 16,22O, and 40Ca from chiral nucleon-nucleon interactions
• The ${}^4$He total photo-absorption cross section with two- plus three-nucleon interactions from chiral effective field theory
• Electric dipole polarizability from first principles calculations
• The isoscalar monopole resonance of the alpha particle: a prism to nuclear Hamiltonians
• Role of final state interaction and of three-body force on the longitudinal response function of 4He
• Spectral density estimation with the Gaussian Integral Transform
• Inclusive electron scattering off 4He
• Benchmark calculation of inclusive electromagnetic responses in the four-body nuclear system
• Photonuclear sum rules and the tetrahedral configuration of ${}^4$He
• Search for three-nucleon force effects on the longitudinal response function of 4He
• Test of J-matrix inverse scattering potentials on electromagnetic reactions of few-nucleon systems
• The Lorentz Integral Transform and its Inversion
• 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
• The nuclear electric polarizability of 6He
• Case study: calculation of a narrow resonance with the LIT method
• Energy Resolution with the Lorentz integral transform
• Ab initio calculation of the 4He(e,e'd)d reaction
• Coupling the Lorentz Integral Transform (LIT) and the Coupled Cluster (CC) Methods: A way towards continuum spectra of "not-so-few-body" systems
• Transverse electron scattering response function of ${}^3$He with $\Delta$-isobar degrees of freedom
• Threshold 3He and 3H Transverse Electron Scattering Response Functions
• On the ill-posed character of the Lorentz integral transform
• Photon Scattering with the Lorentz Integral Transform Method
• ${\pi }^0$-Photoproduction on the deuteron via $\Delta$-excitation using the Lorentz Integral Transform
• On the Accuracy of Hyperspherical Harmonics Approaches to Photonuclear Reactions
• Method to solve integral equations of the first kind with an approximate input
• On calculating response functions via their Lorentz integral transforms
• The Lorentz integral transform (LIT) method
• Calculation of the astrophysical S-factor S_12 with the Lorentz integral transform
• Electromagnetic Reactions and Few-Nucleon Dynamics