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V. D. Efros

Publications and source records attributed to V. D. Efros.

At least 19 recordsLinked to original sources
arXiv2026

On the representation-free formalism in quantum mechanics

The widespread bra-ket formalism offers valuable tools for conducting representation-free considerations in quantum theory. However, it is not without its drawbacks. In this work, we discuss these drawbacks in detail and subsequently construct a new representation-free scheme. Similar to the bra-ket formalism, the present scheme provides essential means to facilitate representation-free considerations. At the same time, it is entirely free from the drawbacks of the bra-ket formalism. Unlike the dual-space bra-ket formalism, the present scheme allows both one-space and dual-space interpretations, which is a beneficial feature. The constructed universal scheme is very well-suited for performing representation-free practical calculations.

quant-ph↗
arXiv2021

Computing the coefficients of transformations between oscillator states

A program is created to compute recursively the Moshinsky brackets. It is very fast and provides highly accurate results. In the case of the double-precision computations with a single-processor consumer notebook, the computing time per bracket at any not small oscillator excitations is on the scale of 10^{-8} s and the accuracy is very good for the total number of quanta up to 80. The program is easy to handle.

physics.comp-ph↗
arXiv2019

Calculating reactions with use of no-core shell-model states

A scheme to compute reactions is described that uses the Slater determinants constructed of oscillator orbitals. Simple linear equations are suggested for this purpose and shown to be efficient in model examples. A universal method to evaluate the required matrix elements is given.

nucl-th↗
arXiv2017

An Approach to the Computation of Few/Many-Body Multichannel Reactions

A method to calculate reactions in quantum mechanics is outlined. It is advantageous, in particular, in problems with many open channels of various nature i.e. when energy is not low. In the method there is no need to specify reaction channels in a dynamics calculation. These channels come into play at merely the kinematics level and only after a dynamics calculation is done. This calculation is of the bound--state type while continuum spectrum states never enter the game.

nucl-th↗
arXiv2016

Relation between (e,e') sum rules in 6,7Li and 4He nuclei.Experiment and cluster model

The sums over (e,e') spectra of 6Li and 7Li nuclei which correspond to the longitudinal sum rule are studied. It is suggested that due to the cluster structure of the lithium isotopes these sums may approximately be expressed in terms of such a sum pertaining to the alpha-particle. Calculation of these sums is performed in the framework of cluster models with antisymmetrization done with respect to all the nucleons. At momentum transfers higher than 0.8 fm^{-1} the relations expressing the A=6 or 7 sum in terms of the A=4 sum prove to be valid with rather high accuracy. In the region of momentum transfers around 1 fm^{-1} the longitudinal correlation functions of 6Li and 7Li nuclei are found to be close to that of the alpha-particle. The experimental longitudinal sums in the range between 0.450 and 1.625 fm^{-1} are employed to perform comparison with those calculated in the framework of cluster models. Out of the mentioned experimental sums, those in the range between 0.750 and 1.000 fm^{-1} in the 6Li case and between 0.750 and 1.125 fm^{-1} in the 7Li case are obtained in the present work. In the 6Li case a complete agreement is found while in the 7Li case an agreement only at a qualitative level is observed.

nucl-th↗
arXiv2014

Some relativistic aspects of nuclear dynamics at the electrodisintegration of nuclei

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 about 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.

nucl-th↗
arXiv2014

Properties of the first excited state of 9Be derived from (gamma,n) and (e,e') reactions

Properties of the first excited state of the nucleus 9Be are discussed based on recent (e,e') and (gamma,n) experiments. The parameters of an R-matrix analysis of different data sets are consistent with a resonance rather than a virtual state predicted by some model calculations. The energy and the width of the resonance are deduced. Their values are rather similar for all data sets, and the energy proves to be negative. It is argued that the disagreement between the extracted B(E1) values may stem from different ways of integration of the resonance. If corrected, fair agreement between the (e,e') and one of the (gamma,n) data sets is found. A recent (gamma,n) experiment at the HIgS facility exhibits larger cross sections close to the neutron threshold which remain to be explained.

nucl-ex↗
arXiv2012

Method to solve integral equations of the first kind with an approximate input

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 the 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. Inversions of the Lorentz, Stieltjes and Laplace integral transforms are performed, and very satisfactory results are obtained. The method is useful, in particular, for the calculation of quantum-mechanical reaction amplitudes and inclusive spectra of perturbation-induced reactions in the framework of the integral transform approach.

math-ph↗
arXiv2009

The Lorentz Integral Transform and its Inversion

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.

nucl-th↗
arXiv2009

A small parameter approach for few-body problems

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 equations are reduced perturbatively to equations in the finite-dimension subspace with K\le 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.

nucl-th↗
arXiv2008

The Lorentz Integral Transform (LIT) method and its applications to perturbation induced reactions

The LIT method has allowed ab initio calculations of electroweak cross sections in light nuclear systems. This review presents a description of the method from both a general and a more technical point of view, as well as a summary of the results obtained by its application. The remarkable features of the LIT approach, which make it particularly efficient in dealing with a general reaction involving continuum states, are underlined. Emphasis is given on the results obtained for electroweak cross sections of few--nucleon systems. Their implications for the present understanding of microscopic nuclear dynamics are discussed.

nucl-th↗
arXiv2008

A Small Parameter Method for Few-Body Problems

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.

nucl-th↗
arXiv2005

Ab initio calculation of the 4He(e,e'd)d reaction

The two-body knock-out reaction 4He(e,e'd)d is calculated at various momentum transfers. The full four-nucleon dynamics is taken into account microscopically both in the initial and the final states. As NN interaction the central MT-I/III potential is used. The calculation shows a strong reduction of the coincidence cross section due to the final state interaction. Nonetheless the theoretical results exhibit a considerable overestimation of the experimental cross section at lower momentum transfer. Comparisons with other, less complete, calculations suggest that consideration of a more realistic ground state might not be sufficient for a good agreement with experiment, rather a more realistic final state interaction could play an essential role.

nucl-th↗
arXiv2002

Elimination of Rotational Degrees of Freedom in Expansion Methods for Three Nucleons

Euler angles determining rotations of a system as a whole are conveniently separated in three-particle basis functions. Analytic integration of matrix elements over Euler angles is done in a general form. Results for the Euler angle integrated matrix elements of a realistic NN interaction are listed. The partial wave decomposition of correlated three-body states is considered.

nucl-th↗
arXiv2002

Benchmark Calculation of the Three-Nucleon Photodisintegration

A benchmark is set on the three-nucleon photodisintegration calculating the total cross section with modern realistic two- and three-nucleon forces (AV18, UrbIX) using both the Faddeev equations and the Lorentz Integral Transform method. This test shows that the precision of three-body calculations involving continuum states is considerably higher than experimental uncertainties. Effects due to retardations, higher multipoles, meson exchange currents and Coulomb force are studied.

nucl-th↗
arXiv2001

Analytical E1 strength functions of two-neutron halo nuclei: the 6-He example

An analytical model is developed to study the spectra of electromagnetic dissociation of two-neutron halo nuclei without precise knowledge about initial and final states. Phenomenological three-cluster bound state wave functions, reproducing the most relevant features of these nuclei, are used along with no interaction final states. The 6-He nucleus is considered as a test case, and a good agreement with experimental data concerning the shape of the spectrum and the magnitude of the strength function is found.

nucl-th↗
arXiv1999

Electromagnetic response functions of few-nucleon systems

Inclusive electromagnetic reactions in few-nucleon systems are studied basing on accurate three- and four-body calculations. The longitudinal 4He(e,e') response function obtained at q\le 600 MeV/c completely agrees with experiment. The exact 4He spectral function obtained in a semirealistic potential model is presented, and the accuracy of the quasielastic response calculated with its help is assessed, as well as the accuracy of some simpler approximations for the response. The photodisintegration cross section of 3He obtained with the realistic AV14 NN force plus UrbanaVIII NNN force agrees with experiment. It is shown that this cross section is very sensitive to underlying nuclear dynamics in the E_γ\simeq 70-100 MeV region. In particular, the NNN nuclear force clearly manifests itself in this region.

nucl-th↗