Nonrelativistic structure calculations of two-electron ions in a strongly coupled plasma environment

Int J of Quantum Chemistry

et al. 2018

Comprehensive investigations on the structural modifications of negative hydrogen ion within an impenetrable spherical domain has been performed in the framework of Ritz variational method. Electron correlation plays a major role in the formation of H– ion. The Hylleraas‐type basis set expansion of wave function considered here incorporates the effect of electron correlation in an explicit manner. Energy values of 1s2 (1normalSnormale), 2p2 (3normalPnormale) and 1sn p (1,3normalPnormalo) states (n=2−5) of H– ion within confined domain have been calculated. Although the singly excited states do not exist for a “free” H– ion, well converged energy values of such states have been found within a wide range of confinement radius. The thermodynamic pressure felt by the ion inside the sphere is also estimated. The general trend shows successive destabilization of the excited energy levels with increase of pressure. The contribution of angular correlation in the energy values have been estimated. Evolution of 1s2 (1normalSnormale) and 2p2 (3normalPnormale) energy levels of H– ion as quasi‐bound states are being reported.

“…It means at a pressure of

0.4259 \times 10^{10}

0.3588 \times 10^{4}

Pa, the energy value of

{2 p}^{2} (^{3} {normalP}^{normale})

state lies above both 2s and 2p levels of hydrogen.…”

Section: Resultsmentioning

confidence: 99%

Explicitly correlated variational estimates of the energy levels of negative hydrogen ion under spatial confinement

Chandra¹,

Dutta²,

Int J of Quantum Chemistry

et al. 2018

“…Comprehensive reviews are now available on this topic. Theoretically, different types of confinement models can be realized for different physical situations, for example, atoms under plasma environment, endohedrally confined atoms and molecules in fullerene cages, impurities in quantum dots or nano crystals, matter under extreme pressure in zeolite sieves, or in the walls of nuclear reactors, and so forth. Moreover, the confined atom models assume contemporary significance in understanding the cores of Jovian planets such as Jupiter and Saturn .…”

Section: Introductionmentioning

confidence: 99%

“…To achieve high numerical accuracy in structure calculations of helium‐like systems in nonrelativistic regime, it is well known that the trial wave function should be expanded in Hylleraas‐type basis set (an explicit function of interelectronic distance r 12 ) consistent with the Dirichlet's boundary condition and the basis integrals are to be evaluated within a finite domain to incorporate the effect of impenetrable confinement. Recently Bhattacharyya et al solve the integral analytically in such a way that the problem of linear dependency for larger dimension is clearly avoided even for very strong confinement regime. As a result, the correlated Hylleraas basis set becomes flexible for a complete range of confining parameters and produces accurate energy levels for helium‐like ions.…”

Section: Introductionmentioning

confidence: 99%

Ritz variational calculation for the singly excited states of compressed two‐electron atoms

Int J of Quantum Chemistry

Bhattacharyya²,

Mukherjee³

2016

A detailed analysis on the effect of spherical impenetrable confinement on the structural properties of two-electron ions in S2 states has been performed. The energy values of 1sns [n5224] ( 3 S e ) states of helium-like ions (Z5125) are estimated within the framework of Ritz variational method using explicitly correlated Hylleraas-type basis sets. The correlated wave functions used here are consistent with the finite boundary conditions due to spherical confinement. A comparative study between the singlet and triplet states originating from a particular electronic configuration shows incidental degeneracy and the subsequent level-crossing phenomena. The thermodynamic pressure felt by the ion inside the sphere pushes the energy levels toward continuum. Critical pressures for the transition to strong confinement regime (where the singly excited two-electron energy levels cross the corresponding one-electron threshold) as well as for the complete destabilization are also estimated.correlation, pressure confinement, two-electron atom, variational method | I N T R O D U C T I O NStudies on the subject of confined atomic systems have started soon after the advent of quantum mechanics. In recent years, a paradigm shift in the facility for doing controlled experiment on confined atom and modern high-speed computational resources open up a new horizon for this subject. The modifications of the structural and spectral properties of the atom or the molecule depending on the number and degree of confining parameters is the interesting aspect of the problem. Comprehensive reviews [1][2][3] are now available on this topic. Theoretically, different types of confinement models can be realized for different physical situations, for example, atoms under plasma environment, [4,5] endohedrally confined atoms and molecules in fullerene cages, [6] impurities in quantum dots or nano crystals, [7,8] matter under extreme pressure in zeolite sieves, [9] or in the walls of nuclear reactors, [10] and so forth. Moreover, the confined atom models assume contemporary significance in understanding the cores of Jovian planets such as Jupiter and Saturn. [11] Nonspherical confinement models [12][13][14][15] are also assumed to deal with important quantum mechanical problems. Vast applicability of the outcomes from such studies in different branches of science and technology makes the subject a topic of immense interest in the recent times. [16][17][18] Hydrogen atom confined in impenetrable spherical cavity was first studied by Michels et al. [19] to model the effects of pressure on its energy and polarizability. Subsequently, many workers [20][21][22][23][24][25][26] have addressed this problem from different angles to develop a comprehensive understanding about such confined systems. Helium atom confined by such spherical cavity is a much complicated numerical problem as compared to the hydrogen-like ions for obvious reasons. For ions having two or more electrons, the effect of electron correlation plays an important role in the str...

“…Different properties of matter under high pressure in Zovian planets [30] or in case of geological sieves [31] can be explained by using such concepts of impenetrable confinement. Further modification of the inter-particle interaction in this model can successfully be used for atoms under dense plasma [32], endohedral atoms [24] etc.…”

Section: Introductionmentioning

confidence: 99%

Entanglement in helium atom confined in an impenetrable cavity

Kościk

2015

Eur. Phys. J. D

We explore ground-state entanglement properties of helium atom confined at the center of an impenetrable spherical cavity of varying radius by using explicitly correlated Hylleraas-type basis set. Results for the dependencies of the von Neumann and linear entanglement entropic measures on the cavity radius are discussed in details. Some highly accurate numerical results for the von Neumann and linear entropy are reported for the first time. It is found that the transition to the strong confinement regime is manifested by the entropies as an appearance of the inflection points on their variations.