D. A. Savin

Extrapolation of scattering data to the negative-energy region

Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed into forms convenient for extrapolating to the negative-energy region and obtaining the information about bound-state properties. Alternative ways of extrapolation are discussed. Analytic properties of separate terms entering these expressions for the effective-range function and the partial-wave scattering amplitude are investigated.

Analytic continuation of scattering data to the region of negative energies for systems that have one and two bound states

An exactly solvable potential model is used to study the possibility of deducing information about the features of bound states for the system under consideration (binding energies and asymptotic normalization coefficients) on the basis of data on continuum states. The present analysis is based on an analytic approximation and on the subsequent continuation of a partial-wave scattering function from the region of positive energies to the region of negative energies. Cases where the system has one or two bound states are studied. The α+d and α+12C systems are taken as physical examples. In the case of one bound state, the scattering function is a smooth function of energy, and the procedure of its analytic continuation for different polynomial approximations leads to close results, which are nearly coincident with exact values. In the case of two bound states, the scattering function has two poles—one in the region of positive energies and the other in the region of negative energies between the energies corresponding to the two bound states in question. Padéapproximants are used to reproduce these poles. The inclusion of these poles proves to be necessary for correctly describing the properties of the bound states.

Studying the general properties of potentials by means of dimensionless scaling variables

The general properties of the three-parametric Woods-Saxon potential and the two-parametric Hulthen and square-well potentials are studied by converting them to dimensionless scaling variables. The relations between the parameters of the potentials and such characteristics of a system as binding energies and the asymptotic normalization coefficients of wave functions are investigated.

Analytic continuation of the effective-range expansion as a method for determining the features of bound states: Application to the 6Li nucleus

The scattering function (effective-range function) for the two-channel elastic scattering of charged particles is used to analyze dα scattering at low energies. In order to construct this function, use is made of various sets of phase shifts and mixing parameter, both those that were obtained by solving Faddeev equations in the three-body (n, p, α) model and those that were deduced from available phaseshift analyses. By means of an analytic continuation of the scattering function to the point of the pole corresponding to the bound state of the 6Li nucleus, the values of the vertex constants and asymptotic normalization coefficients are found for the process 6Li → α + d. Possible means for refining these results are discussed.

SS-HORSE method for studying resonances

A new method for analyzing resonance states based on the Harmonic-Oscillator Representation of Scattering Equations (HORSE) formalism and analytic properties of partial-wave scattering amplitudes is proposed. The method is tested by applying it to the model problem of neutral-particle scattering and can be used to study resonance states on the basis of microscopic calculations performed within various versions of the shell model.

Asymptotic Normalization Coefficients in a Potential Model Involving Forbidden States

It is shown that values obtained for asymptotic normalization coefficients by means of a potential fitted to experimental data on elastic scattering depend substantially on the presence and the number n of possible forbidden states in the fitted potential. The present analysis was performed within exactly solvable potential models for various nuclear systems and various potentials without and with allowance for Coulomb interaction. Various methods for changing the number n that are based on the use of various versions of the change in the parameters of the potential model were studied. A compact analytic expression for the asymptotic normalization coefficients was derived for the case of the Hulthén potential. Specifically, the d + α and α + 12C systems, which are of importance for astrophysics, were examined. It was concluded that an incorrect choice of n could lead to a substantial errors in determining the asymptotic normalization coefficients. From the results of our calculations, it also follows that, for systems with a low binding energy and, as a consequence, with a large value of the Coulomb parameter, the inclusion of the Coulomb interaction may radically change the asymptotic normalization coefficients, increasing them sharply.

SS-HORSE Method for Analysis of Resonances: Charged-Particle Scattering

The method for analyzing resonance states based on the harmoni©oscillator representation of scattering equations (HORSE) and on analytic properties of partial-wave scattering amplitudes which has been proposed earlier, is generalized to the case of charged-particle scattering. The method in question is tested by applying it to the model problem of pα scattering and can be used to study resonance states on the basis of microscopic calculations within various versions of the shell model.

New approach to folding with the Coulomb wave function

Due to the long-range character of the Coulomb interaction theoretical description of low-energy nuclear reactions with charged particles still remains a formidable task. One way of dealing with the problem in an integral-equation approach is to employ a screened Coulomb potential. A general approach without screening requires folding of kernels of the integral equations with the Coulomb wave. A new method of folding a function with the Coulomb partial waves is presented. The partial-wave Coulomb function both in the configuration and momentum representations is written in the form of separable series. Each term of the series is represented as a product of a factor depending only on the Coulomb parameter and a function depending on the spatial variable in the configuration space and the momentum variable if the momentum representation is used. Using a trial function, the method is demonstrated to be efficient and reliable.

The possibility of using screened coulomb potentials in calculating asymptotic normalization coefficients

The dependence of asymptotic normalization coefficients of nuclear wave functions on methods for taking Coulomb interaction into account is studied. Calculations are performed both with the total Coulomb potential and with the Coulomb potential truncated at large distances. Both sharp and smooth truncation is used.

Exchange mechanism of dα interaction and vertex constants of 6Li

In this work, we use a model for describing the dα interaction in a 6Li nucleus, in which the dα nuclear potential is written as the sum of the local folding potential and a nonlocal term originating from the deuteron exchange mechanism and corresponding to a three-deuteron component of the 6Li wave function. This model was used to calculate the nuclear vertex constants and the corresponding asymptotic normalization coefficients of 6Li in the dα channel. Both values L = 0 and L = 2 of relative dα orbital angular momentum L were considered. Calculations were performed with and without allowance for the Coulomb dα interaction.