Related papers: Analytical Expressions for a Hyperspherical Adiaba…
For a particular case of three-body scattering in two dimensions, and matching analytical expressions at a transition point, we obtain accurate solutions for the hyperspherical adiabatic basis and potential. We find analytical expressions…
General expressions for the breakup cross sections in the lab frame for $1+2$ reactions are given in terms of the hyperspherical adiabatic basis. The three-body wave function is expanded in this basis and the corresponding hyperradial…
We explore the three-body problem in two dimensions using the adiabatic hyperspherical representation. We develop the main equations in terms of democratic hyperangular coordinates and determine several symmetry properties and boundary…
Application of the Hyperspherical Adiabatic expansion to describe three-body scattering states suffers the problem of a very slow convergence. Contrary to what happens for bound states, a huge number of hyperradial equations has to be…
This paper investigates the possible use of the Hyperspherical Adiabatic basis in the description of scattering states of a three-body system. In particular, we analyze a 1+2 collision process below the three-body breakup. The convergence…
We consider the three-boson problem with $\delta$-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the…
We examine a system of three-bosons confined to two dimensions in the presence of a perpendicular magnetic field within the framework of the adiabatic hyperspherical method. For the case of zero-range, regularized pseudo-potential…
We have used the hyperspherical adiabatic representation to describe the system of three identical bosons in an spin stretched state interacting by an attractive 1/r potential. A proposal has been made how such a system might be realized…
The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the $S$-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(t). We show that the application of the adiabatic…
Using the hyperspherical adiabatic method with the realistic nuclear potentials Argonne V14, Argonne V18, and Argonne V18 with the Urbana IX three-body potential, we calculate the adiabatic potentials and the triton bound state energies. We…
The asymptotic behavior of the optical potential, describing elastic scattering of a charged particle $\alpha$ off a bound state of two charged, or one charged and one neutral, particles at small momentum transfer $\Delta_{\alpha}$ or…
The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time.…
First, we show that, if there are no bound states, we can express the q.m. third cluster - involving 3 and fewer particles in Statistical Mechanics - as a formula involving adiabatic eigenphase shifts. This is for Boltzmann statistics. From…
We consider the scattering of nonrelativistic particles in three dimensions by a contact potential $\Omega\hbar^2\delta(r)/ 2\mu r^\alpha$ which is defined as the $a\to 0$ limit of $\Omega\hbar^2\delta(r-a)/2\mu r^\alpha$. It is surprising…
We formulate a fully microscopic approach to large-scale nuclear dynamics using a hyperradius as a collective coordinate. An adiabatic potential is defined by taking account of all possible configurations at a fixed hyperradius, and its…
It is shown that the single-particle spin-orbit coupling terms, which---in the cold atom context---are associated with synthetic gauge fields, can significantly and non-trivially modify the phase accumulation at small interparticle…
Active Brownian particles display self-propelled movement, which can be modelled as arising from a one-body force. Although their interparticle interactions are purely repulsive, for strong self propulsion the swimmers phase separate into…
We study the three-body problem in one dimension for both zero and finite range interactions using the adiabatic hyperspherical approach. Particular emphasis is placed on the threshold laws for recombination, which are derived for all…
The comprehensive computer simulation study of the phase diagram of the repulsive step potential system in three dimensions is represented. We show that the system with a simple purely repulsive isotropic potential demonstrates a number of…
Three-body systems in two dimensions with zero-range interactions are considered for general masses and interaction strengths. The problem is formulated in momentum space and the numerical solution of the Schr\"odinger equation is used to…