Related papers: Asymptotics of phase and wave functions
The asymptotic behavior of the molecular continuum wave function has been analyzed within a model of non-overlapping atomic potentials. It is been shown that the representation of the wave function far from a molecule as a plane wave and…
Asymptotic representations for large values of the hyperradius are constructed for the scattering wave function of a system of $ N $ particles considered as a generalized function of angular variable coordinates. The coefficients of the…
For calculation of the single-channel nucleon-nucleon scattering a phase-functions method has been proposed. Using a phase-functions method the following phase shifts of a np- scattering numerically for 1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-,…
The main features of obtaining the asymptotic behaviour of the electric structure function A(p) at large values of the transmitted momentum are analysed. The asymptotic behaviour of the structure function A(p) was determined to take into…
Asymptotic expressions for the radial and full wave functions of a three{body bound halo nuclear system with two charged particles in relative coordinates are obtained in explicit form, when the relative distance between two particles tends…
For calculation of the single-channel nucleon-nucleon scattering a phase-functions method has been considered. Using a phase-functions method the following phase shifts of a nucleon-nucleon scattering are calculated numerically: nn (1S0-,…
A known phase-functions method has been considered for calculation of a single-channel nucleon-nucleon scattering. The phase shifts of np- scattering turn out for modern realistic phenomenological nucleon-nucleon potentials Reid93 but…
The Levinson theorem for two-dimensional scattering is generalized for potentials with inverse square singularities. By this theorem, the number of bound states in a given m-th partial wave is related to the phase shift and the singularity…
We study certain resonance-counting functions for potential scattering on infinite cylinders or half-cylinders. Under certain conditions on the potential, we obtain asymptotics of the counting functions, with an explicit formula for the…
For a single-channel nucleon-nucleon scattering, a well-known and convenient variable phase approach is considered, which is widely used for practical problems of atomic and nuclear physics. Approximation of the $pp$- and $np$- scattering…
One to one correspondence between the decay law of the von Neumann-Wigner type potentials and the asymptotic behaviour of the wave functions representing bound states in the continuum is established.
We propose a simple, intuitive alternative method of deriving the rule for connecting asymptotic wave function amplitudes to scattering probabilities. This is illustrated using the standard example of a 1-D particle reflecting or…
Uniform asymptotic approximations are obtained for the prolate spheroidal wave functions, in the high-frequency case. The results are obtained by an application of certain existing asymptotic solutions of differential equations, and involve…
The asymptotic behavior at infinity of oscillatory integrals is in detail investigated by using the Newton polyhedra of the phase and the amplitude. We are especially interested in the case that the amplitude has a zero at a critical point…
Distance-dependent phase shifts, amplitude functions, and radial wave functions for neutron-alpha elastic scattering are studied using the Variable Phase Approach. The microscopic KKNN potential is employed to calculate scattering…
For calculation of the single-channel nucleon-nucleon scattering a phase-functions method has been proposed. Using a phase-functions method the following phase shifts of np- scattering numerically for 1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-,…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
We consider a three-dimensional Fourier integral in which the exponent in the exponential factor is the product of some phase function and a large parameter. The asymptotics of this integral is sought when the large parameter tends to…
We derive asymptotic behaviors of the Nambu-Bethe-Salpeter (NBS) wave function at large space separations for systems with more than 2 particles in quantum field theories. To deal with $n$-particles in the center of mass flame coherently,…
A general problem of $2\rightarrow N_f$ scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in $(3+1)$ D, vortex particles with orbital angular…