Bound and resonance states near the critical charge region in two-electron atoms

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The critical screening parameters (λc) of one-electron systems in circular states under short-range screened Coulomb potentials are investigated using the generalized pseudospectral method. High-precision values of λc are obtained for bound states with the principal quantum number n up to a thousand. The polynomial ﬁttings based on the numerical values indicate that the high-Rydberg limits of the n^2-scaled critical screening parameters, i.e., n^2λc, are equal to 2/e, 1.295220475783830, and 0.543564037493402, respectively, for the Debye-Hückel, Hulthén, and exponential cosine screened Coulomb potentials. It is surprisingly found that these high-Rydberg limits can be well-reproduced from Bohr's correspondence principle together with the semi-classical model of the hydrogen atom. We further show that both the present numerical calculations and the semi-classical analysis can be extended to other short-range potentials such as the generalized exponential, Lennard-Jones, modiﬁed Pöschl‒Teller, shifted Morse, Woods-Saxon, and Manning‒Rosen potentials that attract wide interest in atomic, molecular, and nuclear physics.

Section: Manning-rosen Potential (Mrp)supporting

confidence: 56%

Section: Bohr's Correspondence Principle For the High-rydberg Limit O...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Critical screening parameters of one-electron systems with screened Coulomb potentials: circular Rydberg states

Jiao

Liu

et al. 2023

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“…That particular Z value is referred to as the critical nuclear charge of the system (Z c ). In this context, the study of the critical stability of two-electron systems has gained considerable interest [20,[63][64][65][66][67][68][69][70][71][72][73][74][75][76][77][78]. For a recent review on the bound state stability of H − ions in the Hartree-Fock theory in the unconfined state, refer to [79].…”

Section: Introductionmentioning

confidence: 99%

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

Mondal

Sadhukhan

Sen

et al. 2023

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.

“…The milestone for determining Z c for the ground state of twoelectron atoms was achieved by Estienne et al [17] employing a triplet-set Hylleraas basis and the value is precisely located at 0.911 028 224 077 255 73 (4). Karr [18] and our recent work [19] further extended the calculations into the resonance region and investigated the behavior of resonance state for the nuclear charge being much smaller than Z c .…”

Section: Introductionmentioning

confidence: 99%

Stability of the 2p2 3Pe state of two-electron atoms near to critical nuclear charge

Zheng

Jiao

Liu

et al. 2023

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Critical stability of the metastable bound 2p2 3Pe state of two-electron atoms near the critical nuclear charge Zc (smaller than which the bound state ceases to exist) is investigated by employing the explicitly correlated Hylleraas-conﬁguration interaction basis function. Our numerical calculation shows that, when the nuclear charge decreases to Zc, the ionization energy of the system approaches zero linearly and this behavior is fully consistent with the Hellmann-Feynman theorem. Radial and angular physical quantities as well as the inner and outer electron radial density distributions are calculated to reveal the classical geometric structure of the two-electron atom. The inner electron can be well modeled by a hydrogenic model in the 2p state and its density distribution does not change much as the nuclear charge is changed. The outer electron, which is still localized in a ﬁnite region near the nucleus before the system transforms into a well-deﬁned resonance, is shifted notably into a far-distance region. The critical stability of the system near the bound-continuum limit is therefore dominated by the outer electron.