arXiv subjects

L. U. Ancarani

Publications and source records attributed to L. U. Ancarani.

3 recordsLinked to original sources

arXiv2021

The momentum distribution of two bosons in one dimension with infinite contact repulsion in harmonic trap gets analytical

For a harmonically trapped system consisting of two bosons in one spatial dimension with infinite contact repulsion (hard core bosons), we derive an expression for the one-body density matrix $ρ_B$ in terms of centre of mass and relative coordinates of the particles. The deviation from $ρ_F$, the density matrix for the two fermions case, can be clearly identified. Moreover, the obtained $ρ_B$ allows us to derive a closed form expression of the corresponding momentum distribution $n_{B}(p)$. We show how the result deviates from the noninteracting fermionic case, the deviation being associated to the short range character of the interaction. Mathematically, our analytical momentum distribution is expressed in terms of one and two variables confluent hypergeometric functions. Our formula satisfies the correct normalization and possesses the expected behavior at zero momentum. It also exhibits the high momentum $1/p^4 $ tail with the appropriate Tan's coefficient. Numerical results support our findings.

physics.atom-ph↗

arXiv2020

Generalized Sturmian Functions in prolate spheroidal coordinates

With the aim of describing bound and continuum states for diatomic molecules, we develop and implement a spectral method that makes use of Generalized Sturmian Functions (GSF) in prolate spheroidal coordinates. In order to master all computational issues, we apply here the method to one--electron molecular ions and compare it with benchmark data for both ground and excited states. We actually propose two different computational schemes to solve the two coupled differential equations. The first one is an iterative 1d procedure in which one solves alternately the angular and the radial equations, the latter yielding the state energy. The second, named direct $2d$ method, consists in representing the Hamiltonian matrix in a two--dimensional GSF basis set, and its further diagonalization. Both spectral schemes are timewise computationally efficient since the basis elements are such that no derivatives have to be calculated numerically. Moreover, very accurate results are obtained with minimal basis sets. This is related on one side to the use of the natural coordinate system and, on the other, to the intrinsic good property of all GSF basis elements that are constructed as to obey appropriate physical boundary conditions. The present implementation for bound states paves the way for the study of continuum states involved in ionization of one or two--electron diatomic targets.

physics.atm-clus↗

arXiv2015

Quasi Sturmian Basis in Two-Electron Continuum Problems

A new type of basis functions is proposed to describe a two-electron continuum which arises as a final state in electron-impact ionization and double photoionization of atomic systems. We name these functions, which are calculated in terms of the recently introduced Quasi Sturmian functions, Convoluted Quasi Sturmian functions (CQS). By construction, the CQS functions look asymptotically like a six-dimensional spherical wave. The driven equation describing an $(e, 3e)$ process on helium in the framework of the Temkin-Poet model has been solved numerically using expansions on the basis CQS functions. The convergence behavior of the solution has been examined as the size of the basis has been increased. The calculations show that the convergence rate is significantly improved by introducing a phase factor corresponding the electron-electron interaction into the basis functions. Such a modification of the boundary conditions leads to appreciable change in the magnitude of the solution.

quant-ph↗