O. A. Rubtsova

Solving three-body scattering problems in the momentum lattice representation

A brief description of the novel approach toward solving few-body scattering problems in a finite-dimensional functional space of the L{sub 2} type is presented. The method is based on the complete few-body continuum discretization in the basis of stationary wave packets. This basis, being transformed to the momentum representation, leads to the cell-lattice-like discretization of the momentum space. So the initial scattering problem can be formulated on the multidimensional momentum lattice, which makes it possible to reduce the solution of any scattering problem above the breakup threshold (where the integral kernels include, in general, some complicated moving singularities) to convenient simple matrix equations that can be solved on the real energy axis. The phase shifts and inelasticity parameters for the three-body nd elastic scattering with MT I-III NN potential both below and above the three-body breakup threshold calculated with the proposed wave-packet technique are in a very good agreement with the previous accurate benchmark calculation results.

DISCRETE QUANTUM SCATTERING THEORY

We formulate quantum scattering theory in terms of a discrete L2-basis of eigen differentials. Using projection operators in the Hilbert space, we develop a universal method for constructing finite-dimensional analogues of the basic operators of the scattering theory: S- and T-matrices, resolvent operators, and Möller wave operators as well as the analogues of resolvent identities and the Lippmann–Schwinger equations for the T-matrix. The developed general formalism of the discrete scattering theory results in a very simple calculation scheme for a broad class of interaction operators.

Three-body breakup within the fully discretized Faddeev equations

A novel approach is developed to find the three-body breakup amplitudes and cross sections within the modified Faddeev equation framework. The method is based on the lattice-like discretization of the three-body continuum with a three-body stationary wave-packet basis in momentum space. The approach makes it possible to simplify drastically all the three- and few-body breakup calculations due to discrete wave-packet representations for the few-body continuum and simultaneous lattice representation for all the scattering operators entering the integral equation kernels. As a result, the few-body breakup can be treated as a particular case of multi-channel scattering in which part of the channels represents the true few-body continuum states. As an illustration for the novel approach, an accurate calculations for the three-body breakup process

Wave-packet discretization of a continuum: Path toward practically solving few-body scattering problems

n+d\to n+n+p

Discrete representation of the spectral shift function and the multichannel S-matrix

with non-local and local

New general approach in few-body scattering calculations: Solving discretized Faddeev equations on a graphics processing unit

NN

Formulation of Quantum Scattering Theory in Terms of Proper Differentials (Stationary Wave Packets)

interactions are calculated. The results obtained reproduce nicely the benchmark calculation results using the traditional Faddeev scheme which requires much more tedious and time-consuming calculations.

Modern approaches for the theoretical description of multiparticle scattering and nuclear reactions

A new method for discretizing a three-body continuum with the aid of the L2 basis of stationary wave packets is considered within the problem of three-body scattering. Substantial advantages of employing this basis in solving problems of few-body scattering are demonstrated. Specific applications of this approach are exemplified by exploring the problem of scattering of a composite particle on a heavy nucleus with allowance for the excitation of this particle to continuum states. This is done within two alternative approaches: a direct wave-packet discretization of a three-body continuum and a method that is based on the Feshbach projection formalism. It is shown explicitly that the resulting scattering amplitudes are convergent as the number of wave-packet states that are taken into account is increased. The results obtained here are compared with the results of other authors whose treatment was based on alternative methods for discretizing a continuum.

Fast GPU-based calculations in few-body quantum scattering

A new method for solving the multichannel quantum scattering problem in a wide energy range based on the single diagonalization of the Hamiltonian matrix of the system in a finite-dimensional basis is briefly described. It has been shown that the interaction-matrix-induced shifts of the eigenvalues of the free Hamiltonian matrix in the continuous spectrum are directly related to the partial phase shifts. The two-channel scattering problem with shifted channel thresholds is considered for illustration.

Determination of neutron-neutron scattering length from the nd-breakup reaction: Experimental and theoretical aspects

Background: The numerical solution of few-body scattering problems with realistic interactions is a difficult problem that normally must be solved on powerful supercomputers, taking a lot of computer time. This strongly limits the possibility of accurate treatments for many important few-particle problems in different branches of quantum physics. Purpose: To develop a new general highly effective approach for the practical solution of few-body scattering equations that can be implemented on a graphics processing unit. Methods: The general approach is realized in three steps: (i) the reformulation of the scattering equations using a convenient analytical form for the channel resolvent operator; (ii) a complete few-body continuum discretization and projection of all operators and wave functions onto a