The Stark effect on $ H_2^+ $-like molecules (original) (raw)

0 the Stark Effect on H+2-LIKE Molecules

2016

We consider the vibrational energy levels of the first two electronic states of the molecule ion H + 2. The Born-Oppenheimer method applied to the case of the Stark effect on a H + 2-like molecule gives existence of sharp resonances localized in the same interval of energy of the vibrational levels.

Stark effect in quasi-hydrogenic species

Le Journal de Physique Colloques

L'analyse des spectres de photoionisation d'atomes à un électron optique en présence d'un champ électrique peut être faite en partant du modèle hydrogénoïde. Le problème de l'effet Stark de l'hydrogène peut être résolu de façon exacte, l'hamiltonien correspondant étant séparable en coordonnées paraboliques. On définit des densités partielles d'états et on montre qu'au-dessus de la limite classique d'ionisation par champ le spectre de l'hydrogène comporte des états quasi-discrets superposés à des états continus, les différents états n'étant pas couplés. Deux expériences concernant les spectres de photoionisation Stark du rubidium montrent l'importance des perturbations liées à l'interaction spin-orbite, comme par exemple la stabilisation d'un état Stark par le champ électrique.

Different approach to the Stark effect: Application to the hydrogen ground state

Physical Review A, 1990

A method is proposed to evaluate the energy levels and wave functions of atomic hydrogen in a uniform electric field. A self-consistent criterion is used and the method proves to be sufficiently accurate and easy to implement even for high electric-field strengths. We present the results obtained for the ground-state level and compare them with those obtained by other authors. 'Perturbation theory (see Ref. 3). Reference 4. 'Reference S. Values for polynomials of degree 15.

On broad resonances in the hydrogenic stark effect

Physics Letters A, 1988

In the hydrogenic Stark problem, the comparison equation method is used to study poles of the S-matrix close to the positive real axis in the complex energy plane, simple WKB-type formulae which determine parameters of the resonances are derived.

Stark effect of hydrogenic ions

Physical Review A, 1982

Considering Stark-effect applications in atomic physics and especially in plasma spectroscopy, we established several formulas for spectral line intensity, energy level, and ionization rate. In particular, by means of the systematic numerical check on an intermediate formula [Eq. (36d) in the text], we show that the ionization rate may be expressed completely in terms of the energy level according to 1 BE(ni, n2, m, A,) I (ni, n2, m, k) = exp[ K(n~-, n2, m, k)],. 2' Bn2 where A, =(ni+n2+m+1) F/4Z, and 2n2+m +1 n2!(n2+ m)! K(n], n2, m, i,) =-+ln +3(n2n]) 6A, 2m ]3 BE(n],n2m, A, ') dA' n ' ' '-1+6(2n2+m +1)A, ' Bn2 A. '2 The two factors on the right-hand side of (i) are interpreted, respectively, as the atomicelectron-collision frequency and transmission coefficient through the potential barrier created by the electric field F. By using the ninth-order perturbation series for resonance energy E(ni, n2, m, A,) it is found that (i) is in fairly good agreement with the most recent numerical solutions of the Schrodinger equation. A discussion follows in connection with other analytical and empirical formulas.

Static properties and the Stark effect of the ground state of the HD molecular ion

Physical Review A, 2000

We have calculated static properties of the ground state of the HD ÷ ion and its lowest-lying P-state without making use of the Born-Oppenheimer approximation, as was done in the case of H2 ÷ and D2 ÷ [Phys. Rev. A 58, 2787 (1998)]. The ion is treated as a three-body system whose ground state is spherically symmetric. The wavefunction is of generalized Hylleraas type, but it is necessary to include high powers of the internuclear distance to localize the nuclear motion. We obtain good values of the energies of the ground S-state and lowest P-state and compare them with earlier calculations. Expectation values are obtained for various operators, the Fermi contact parameters, and the permanent quadrupole moment. The cusp conditions are also calculated.The polarizability was then calculated using second-order perturbation theory with intermediate P pseudostates. Since the nuclei in HD ÷ are not of equal mass there is dipole coupling between the lowest two rotational states, which are almost degenerate. This situation is carefully analyzed, and the Stark shift is calculated variationally as a function of the applied electric field.

Quantum and classical study of vibrational states of H+2 and H+3 molecules

International Journal of Quantum Chemistry, 2003

In this work, we present calculations of the vibrational energy levels of the H 2 ϩ and H 3 ϩ systems using the correlation function quantum Monte Carlo (CFQMC) and normal model analysis. The classical results are a qualitative first approximation of the normal modes. The results of the CFQMC calculations show the importance of the quantum effects as well as anharmonicity in these systems.

Stark Ionization of Atoms and Molecules within Density Functional Resonance Theory

The Journal of Physical Chemistry Letters, 2013

We show that the energetics and lifetimes of resonances of finite systems under an external electric field can be captured by Kohn-Sham density functional theory (DFT) within the formalism of uniform complex scaling. Properties of resonances are calculated self-consistently in terms of complex densities, potentials and wavefunctions using adapted versions of the known algorithms from DFT. We illustrate this new formalism by calculating ionization rates using the complex-scaled local density approximation and exact exchange. We consider a variety of atoms (H, He, Li and Be) as well as the H 2 molecule. Extensions are briefly discussed.