The information theory of the helium atom in screened Coulomb potentials

Martínez‐Flores, César

doi:10.1002/qua.26529

Cited by 16 publications

(7 citation statements)

References 59 publications

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“…However, due to unavailability of the reference value and to strengthen the importance of the present methodology, we have estimated the value of R α , T α , and E O α for some specific values of α considering the case of a He atom (Z = 2) and R = 100 a.u. We note that the present results are very consistent with the available literature values for free He atoms [24,134]. For instance, Martínez-Flores [134] reported the values of R 0.5 and R 2.0 for a free He atom (Z = 2) as 3.99 917 a.u.…”

Section: Quantum Information Measuressupporting

confidence: 92%

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Stability of a two-electron system under pressure confinement: structural and quantum information theoretical analysis

Mondal

Sadhukhan

Sen

et al. 2023

J. Phys. B: At. Mol. Opt. Phys.

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The stability of two-electron Zee system trapped inside an impenetrable spherical cavity are analyzed using explicitly correlated multi-exponent Hylleraas type basis set in the framework of Ritz variational method. The wavefunction is considered to be consistent with the Dirichlet's boundary condition. Four different Z\in [1,(Z_c)_b,0.25,0.0] values are considered, where (Z_c)_b denotes the critical nuclear charge beyond which the system is embedded in discrete positive energy continuum due to the impenetrable nature of the cavity. The energy contribution due to total correlation (in the presence of both radial and angular correlation) effect, the radial correlation limit and angular correlation limit are also studied in details. The thermodynamic pressure felt by the two-electron Zee system inside the cavity is estimated and a formula replicating the behaviour between the pressure and volume of the cavity is deduced by fitting procedure. Different geometrical properties e.g. radial moments [\langle r_1^p\rangle, \langle r_1r_2\rangle, \langle r_{12}^p\rangle, \langle r_< \rangle, \langle r_>\rangle, p = 1-3], angular moments [\langle\cos\theta_1\rangle, \langle\cos\theta_{12}\rangle] and related important physical quantities are determined. The variation of Kirkwood and Buckingham polarizabilities w.r.t. the pressure felt by the two-electron Zee system are analyzed. The one-electron radial density is estimated for each pair of (Z,R), which has been employed to generate the electrostatic potential as well as different information theoretical measures like Shannon entropy, Fisher entropy, R'{e}yni entropy, Tsalis entropy and Onicescu informational energy. The chosen set of information theoretical measures have been found to be the sensitive tools for describing the changes in the electronic structure due to the spatial confinement. An interesting interplay between the electronic and the nuclear contribution to the classical electrostatic potential is observed leading to the shift in the position of its characteristic minimum due to the compression. Wherever possible, a comparison is made in order to ascertain a high accuracy of our numerical results. The procedure of analytic evaluation of the integrals needed to estimate the atomic properties under consideration are discussed in details.

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Section: Quantum Information Measuressupporting

confidence: 92%

“…We note that the present results are very consistent with the available literature values for free He atoms [24,134]. For instance, Martínez-Flores [134] reported the values of R 0.5 and R 2.0 for a free He atom (Z = 2) as 3.99 917 a.u. and 1.65 756 a.u., respectively.…”

Section: Quantum Information Measuressupporting

confidence: 92%

Stability of a two-electron system under pressure confinement: structural and quantum information theoretical analysis

Mondal

Sadhukhan

Sen

et al. 2023

J. Phys. B: At. Mol. Opt. Phys.

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“…In our HF calculations, we identify this threshold at the critical screening values of λ c ∼ 0.424 and ∼ 0.741 a.u. for the DHS and ECSC, respectively, in agreement with other HF results [72].…”

Section: Ground State Propertiessupporting

confidence: 91%

Dipole and generalized oscillator strengths-dependent electronic properties of helium atoms immersed in a plasma

Martínez‐Flores

Cabrera‐Trujillo

2021

Eur. Phys. J. D

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Atoms subjected to extreme environmental conditions are of fundamental importance due to the modification of their electronic properties. In this work, we study the helium atom when immersed in a plasma environment. In order to describe the plasma medium, we use two models when solving the Schrödinger equation in a restricted Hartree-Fock approach: the Debye-Hückel screened (DHS) potential and a more general exponential-cosine screened Coulomb (ECSC) potential. The plasma length parameter, λ, in both model potentials characterizes the plasma screening effects which cause an increase or decrease in the electronic properties of the helium atom. We report results for the total electronic ground state energy, orbital energy, dipole oscillator strengths, generalized oscillator strengths (GOS), mean excitation energy, electrostatic dipole polarizability, and electronic stopping cross section. We find that the ECSC plasma model produces a less bound system than the DHS plasma model at the same value of the screening length, λ. However, the ECSC model potential has a stronger dipole transition from the 1s to the 2p and 3p states than the DHS model potential. Also, the ECSC potential predicts a higher static dipole polarizability than the DHS model potential, with a consequent lower mean excitation energy. We also find a larger GOS for the ECSC than for the DHS for the same momentum transfer at the same value of the screening length, λ. Consequently, the ECSC mode potential produces a larger electronic stopping cross section than the DHS for the same λ and projectile velocity. In the limit of λ → ∞, we have excellent agreement with the free helium properties. These quantitative values for the electronic properties would be useful for the investigations of the atomic structure and collisions of helium atoms immersed in plasmas.

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“…Many studies in chemistry related with non-additive entropies are available in the literature, for instance [56][57][58][59][60][61][62][63][64][65]. The q-generalization [66,67] of the ubiquitous Arrhenius Law deserves a special mention.…”

Section: (C) Chemistrymentioning

confidence: 99%

Non-additive entropies and statistical mechanics at the edge of chaos: a bridge between natural and social sciences

Tsallis

2023

Phil. Trans. R. Soc. A.

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The Boltzmann–Gibbs (BG) statistical mechanics constitutes one of the pillars of contemporary theoretical physics. It is constructed upon the other pillars—classical, quantum, relativistic mechanics and Maxwell equations for electromagnetism—and its foundations are grounded on the optimization of the BG (additive) entropic functional S BG = − k ∑ i p i ln ⁡ p i . Its use in the realm of classical mechanics is legitimate for vast classes of nonlinear dynamical systems under the assumption that the maximal Lyapunov exponent is positive (currently referred to as strong chaos ), and its validity has been experimentally verified in countless situations. It fails however when the maximal Lyapunov exponent vanishes (referred to as weak chaos ), which is virtually always the case with complex natural, artificial and social systems. To overcome this type of weakness of the BG theory, a generalization was proposed in 1988 grounded on the non-additive entropic functional S q = k ( ( 1 − ∑ i p i q ) / ( q − 1 ) ) ( q ∈ R ; S 1 = S BG ) . The index q and related ones are to be calculated, whenever mathematically tractable, from first principles and reflect the specific class of weak chaos. We review here the basics of this generalization and illustrate its validity with selected examples aiming to bridge natural and social sciences. This article is part of the theme issue ‘Thermodynamics 2.0: Bridging the natural and social sciences (Part 2)’.

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The information theory of the helium atom in screened Coulomb potentials

Cited by 16 publications

References 59 publications

Stability of a two-electron system under pressure confinement: structural and quantum information theoretical analysis

Stability of a two-electron system under pressure confinement: structural and quantum information theoretical analysis

Dipole and generalized oscillator strengths-dependent electronic properties of helium atoms immersed in a plasma

Non-additive entropies and statistical mechanics at the edge of chaos: a bridge between natural and social sciences

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