Related papers: On recent calculations of resonances for the Stark…
We obtained accurate resonances for the Stark effect in hydrogen by means of three independent methods. Two of them are based on complex rotation of the coordinates and diagonalization of the Hamiltonian matrix (CRLM and CRCH). The other…
We discuss the resonances of Hamiltonians with constant electric field in one dimension in the limit of small field. These resonances occur near the real axis, near zeros of the analytic continuation of a reflection coefficient for…
The order dependent mapping method, its convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for Stark effect of the hydrogen atom. We perform a…
We calculate quantum mechanically exact wave functions of resonances in spectra of the hydrogen atom in crossed external fields and prove the existence of long-lived decaying quantum states localized at the Stark saddle point. A spectrum of…
Studies of atomic systems in electric fields are challenging because of the diverging perturbation series. However, physically meaningful Stark shifts and ionization rates can be found by analytical continuation of the series using…
We will study the splitting in the energy spectrum of the hydrogen atom subjected to a uniform electric field (Stark effect) with the Heisenberg algebra deformed leading to the minimum length. We will use the perturbation theory for cases…
This paper examines the Stark effect, as a first order perturbation of manifestly covariant hydrogen-like bound states. These bound states are solutions to a relativistic Schr\"odinger equation with invariant evolution parameter, and…
The Stark resonance parameters for the $3a_{1}$ molecular orbital of H$_{2}$O are computed by solving a system of partial differential equations in spherical polar coordinates. The starting point of the calculation is the quantum potential…
A classical model of the hydrogen atom in a static electric field is studied, basing upon the work [ Hooker A. et al, {\it Phys. Rev. A}, 55 (1997) 4609 ]. In that work the electrons are supposed to move along Kepler orbits around the…
The scattering theory of Lax and Phillips, originally developed to describe resonances associated with classical wave equations, has been recently extended to apply as well to the case of the Schroedinger equation in the case that the wave…
The largest uncertainty in calculations of hydrogen ground-state hyperfine splitting comes from corrections due to proton stucture. We review these corrections, with special mention of the inelastic, or polarizability, corrections which…
We calculate the DC Stark effect for three molecular hydrogen ions in the non-relativistic approximation. The effect is calculated both in dependence on the rovibrational state and in dependence on the hyperfine state. We discuss special…
An exterior complex scaling technique is applied to compute Stark resonance parameters for two molecular orbitals ($1b_{1}$ and $1b_{2}$) represented in the field-free limit in a single-center expansion. For electric DC field configurations…
For atoms described by a 1-dimensional Friedrichs model we present the following result: pre-existing resonances, when subjected to a small constant electric field (DC Stark effect), are unstable in the weak field limit. In contrast,…
We extend a previously developed model for the Stark resonances of the water molecule. The method employs a partial-wave expansion of the single-particle orbitals using spherical harmonics. To find the resonance positions and decay rates,…
We study the weighted averages of resonance clusters for the hydrogen atom with a Stark electric field in the weak field limit. We prove a semiclassical Szego-type theorem for resonance clusters showing that the limiting distribution of the…
The relativistic energies and widths of hydrogen-like ions exposed to the uniform electric field are calculated. The calculations are performed for the ground and lowest excited states using the complex scaling technique in combination with…
Recent results on muonic hydrogen [1] and the ones compiled by CODATA on ordinary hydrogen and $ep$-scattering [2] are $5\sigma$ away from each other. Two reasons justify a further look at this subject: 1) One of the approximations used in…
Let $H^{\varepsilon}=-\frac{d^2}{dx^2}+\varepsilon x +V$, $\varepsilon\geq0$, on $L^2(\mathbf{R})$. Let $V=\sum_{k=1}^Nc_k|\psi_k\rangle\langle\psi_k|$ be a rank $N$ operator, where the $\psi_k\in L^2(\mathbf{R})$ are real, compactly…
Motivated by recent experiments we analyse the classical dynamics of a hydrogen atom in parallel static and microwave electric fields. Using an appropriate representation and averaging approximations we show that resonant ionisation is…