Related papers: Response Functions from Integral Transforms with a…
The accuracy of reconstruction of a response function from its Lorentz integral transform is studied in an exactly solvable model. An inversion procedure is elaborated in detail and features of the procedure are studied. Unlike results in…
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…
Integral transform approaches are numerous in many fields of physics, but in most cases limited to the use of the Laplace kernel. However, it is well known that the inversion of the Laplace transform is very problematic, so that the…
Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow…
The LIT approach is reviewed both for inclusive and exclusive reactions. It is shown that the method reduces a continuum state problem to a bound-state-like problem, which then can be solved with typical bound-state techniques. The LIT…
We calculate the unpolarised deep inelastic structure function of a relativistic deuteron within a covariant framework. An exact treatment of nucleon off-shell effects is shown to give corrections to the widely-used convolution model, even…
The longitudinal structure function of the d(e,e'p) exclusive cross section is calculated with the Lorentz integral transform method. In this approach final state interaction is fully taken into account, but without using a final state wave…
We present a consistent \emph{ab initio} computation of the longitudinal response function $R_L$ in $^{40}$Ca using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon…
Both the no-core shell model and the effective interaction hyperspherical harmonic approaches are applied to the calculation of different response functions to external electromagnetic probes, using the Lorentz integral transform method.…
Nuclear quantum many-body methods rely on integral transform techniques to infer properties of electroweak response functions from ground-state expectation values. Retrieving the energy dependence of these responses is highly non-trivial,…
Response functions are key observables for probing the structure and dynamics of many-body systems. We introduce and demonstrate a quantum-classical framework for computing response functions of general many-fermion systems that also…
Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the…
A non-conventional approach to calculating reactions in quantum mechanics is presented. Reaction observables are obtained with bound state calculation techniques. The accuracy of the method to calculate few-nucleon response functions is…
The method of integral transforms is first applied for studying the $^3$He longitudinal response functions. The transforms are calculated from localized bound-state-type solutions to an inhomogenous Schr\"odinger-type three-body equation.…
An exact inversion formula for the Lorentz integral transform (LIT) is provided together with the spectrum of the LIT kernel. The exponential increase of the inverse Fourier transform of the LIT kernel entering the inversion formula…
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{L}^1$--Godement theorem, which states that any invariant…
A new method for studying the many-body response functions is elaborated and first applied to the $^3$He longitudinal response. An integral transform of the response function is calculated from the bound-state-type equations for several…
Relativistic beams of heavy ions interacting with various nuclear targets allow to study a broad range of problems starting from nuclear equation of state to the traditional nuclear structure. Some questions which were impossible to answer…
High-resolution numerical simulations are utilized to examine isotropic turbulence in a compressible fluid when long wavelength velocity fluctuations approach light speed. Spectral analysis reveals an inertial sub-range of relativistic…
Integral transformations are useful mathematical tool to work out signals and wave-packets in electronic devices. They may be used in software protocols. Necessary knowledge may come from quantum field theory, in particular from quantum…