arXiv subjects

Anjan Sadhukhan

Publications and source records attributed to Anjan Sadhukhan.

2 recordsLinked to original sources

arXiv2026

Elimination of angular dependency in the quantum three-body problem made easy

We present a systematic account of the separation of the angular degrees of freedom from the nonrelativistic Schrödinger equation for a three-body quantum system with arbitrary masses, charges, total angular momentum, and parity. The resulting reduced Schrödinger equation (RSE) for the partial-wave components, expressed as functions solely of the interparticle distances, is reported in a compact matrix operator form. The remnants of the angular dependence, essential for the hermiticity of the RSE and consequently the stability of variational computations, appear in the RSE formalism as additional angular factors, derived by expanding minimal bipolar harmonics into a basis of Wigner functions \texorpdfstring{$\mathcal{D}$}{D}. We validate the final form of the RSE by computing accurate energy levels for helium states using an explicitly correlated Hylleraas-type basis. This work serves as a self-contained reference for the RSE formulation, consolidating elements previously scattered throughout the literature, thereby offering a convenient foundation for further analytical and numerical studies of general three-body quantum systems.

physics.atom-ph↗

arXiv2025

An Algorithm for Automated Extraction of Resonance Parameters from the Stabilization Method

The application of the stabilization method [A.~U.\ Hazi and H.~S.\ Taylor, Phys.~Rev.~A {\bf 1}, 1109 (1970)]) to extract accurate energy and lifetimes of resonance states is challenging: The process requires labor-intensive numerical manipulation of a large number of eigenvalues of a parameter-dependent Hamiltonian matrix, followed by a fitting procedure. In this article, we present \dosmax, an efficient algorithm implemented as an open-access \texttt{Python} code, which offers full automation of the stabilization diagram analysis in a user-friendly environment while maintaining high numerical precision of the computed resonance characteristics. As a test case, we use \dosmax to analyze the natural parity doubly-excited resonance states (${}^{1}\textnormal{S}^{\textnormal{e}}$, ${}^{3}\textnormal{S}^{\textnormal{e}}$, ${}^{1}\textnormal{P}^{\textnormal{o}}$, and ${}^{3}\textnormal{P}^{\textnormal{o}}$) of helium, demonstrating the accuracy and efficiency of the developed methodology. The presented algorithm is applicable to a wide range of resonances in atomic, molecular, and nuclear systems.

physics.comp-ph↗