An approach aimed to extend the applicability range of non-relativistic microscopic calculations of electronuclear response functions is reviewed. In the quasielastic peak region the calculations agree with experiment at momentum transfers up to abou
t 0.4 GeV/c while at higher momentum transfers, in the region about 0.4 - 1 GeV/c, a disagreement is seen. In view of this, to calculate the response functions a reference frame was introduced where dynamics relativistic corrections are small, and the results pertaining to it were transformed exactly to the laboratory reference frame. This proved to remove the major part of the disagreement with experiment. All leading order relativistic corrections to the transition charge operator and to the one--body part of the transition current operator were taken into account in the calculations. Furthermore, a particular model to determine the kinematics inputs of the non-relativistic calculations was suggested. This model provides the correct relativistic relationship between the reaction final-state energy and the momenta of the knocked-out nucleon and the residual system. The above mentioned choice of a reference frame in conjunction with this model has led to an even better agreement with experiment.
Techniques are proposed for solving integral equations of the first kind with an input known not precisely. The requirement that the solution sought for includes a given number of maxima and minima is imposed. It is shown that when the deviation of t
he approximate input from the true one is sufficiently small and some additional conditions are fulfilled the method leads to an approximate solution that is necessarily close to the true solution. No regularization is required in the present approach. Requirements on features of the solution at integration limits are also imposed. The problem is treated with the help of an ansatz proposed for the derivative of the solution. The ansatz is the most general one compatible with the above mentioned requirements. The techniques are tested with exactly solvable examples.
A procedure to solve few-body problems is developed which is based on an expansion over a small parameter. The parameter is the ratio of potential energy to kinetic energy for states having not small hyperspherical quantum numbers, K>K_0. Dynamic equ
ations are reduced perturbatively to equations in the finite-dimension subspace with Kle K_0. Contributions from states with K>K_0 are taken into account in a closed form, i.e. without an expansion over basis functions. Estimates on efficiency of the approach are presented.
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 histor
ical 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.
A procedure to solve few-body problems which is based on an expansion over a small parameter is developed. The parameter is the ratio of potential energy to kinetic energy in the subspace of states having not small hyperspherical quantum numbers, K>K
_0. Dynamic equations are reduced perturbatively to those in the finite subspace with K le K_0. The contribution from the subspace with K>K_0 is taken into account in a closed form, i.e. without an expansion over basis functions.
