Conjugate position- and momentum-space electronic density distributions, quantum information theoretic insights on the spherically compressed He atom

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Abstract Despite extensive studies on the position-space electronic distributions for the ground state of the He atom trapped in an impenetrable spherical cavity, the corresponding momentum-space analysis has received little attention. The present article tries to bridge this gap by adopting an even-powered expansion of correlated coordinates in a Hylleraas basis consistent with the Dirichlet boundary condition. The corresponding momentum-space wavefunction is determined by the 3D Fourier transform of the explicitly correlated position-space wavefunctions. The analytic expression of the momentum-space wavefunction, and thereby the electronic density, allows us to examine the asymptotic limits of the same. With increased compression, the two-particle density distribution changes, and in the high compression regime, a crystalline-like structure in the contour map starts to appear. The corresponding topological complexity varies w.r.t. the cavity radius by maintaining symmetry along the equal momenta line. As a consequence, the one-particle momentum-space density and the derived Compton profile show oscillatory structure in the high-momentum regime. The evaluation of Shannon entropy provides further insights into the problem from the quantum information theoretic point of view. The estimation of position and momentum entanglement entropy measures is carried out here for the first time to exhibit the complete picture of the momentum correlation. Our investigation yields that despite showing all the contrasting differences in various density distributions and statistical information measures of the conjugate position and momentum spaces, the quantum correlation measure in terms of entanglement entropy remains invariant. Additionally, the Compton profiles are theoretically evaluated and subsequently compared with available theoretical and experimental results, demonstrating overall good agreement and consistency.

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