States Of Hydrogen-like Ions Research Articles

Rydberg states of hydrogenlike ions in a braneworld model

Precise measurements of optical transition frequencies between Rydberg states of hydrogen-like ions could be used to obtain an improved value of the Rydberg constant, by avoiding the uncertainties about the proton radius. Motivated by this perspective, we investigate the influence of the gravitational interaction on the energy levels of Hydrogen-like ions in Rydberg states in a braneworld model. As it is known, in this scenario, the gravitational interaction is amplified in short distances. We show that, for Rydberg states, the main contribution for the gravitational potential energy does not come from the rest energy concentrated on the nucleus but from the energy of the electromagnetic field created by its electric charge. The reason is connected to the fact that, when the ion is in a Rydberg state with high angular momentum, the gravitational potential is not computable in zero-width brane approximation due to the gravitational influence of the electrovacuum in which the lepton is moving. Considering a thick brane scenario, we calculate the gravitational potential energy associated to the nucleus charge in terms of the confinement parameter of the electric field in the brane. We show that the gravitational effects on the energy levels of a Rydberg state can be amplified by hidden dimensions even when the compactification scale is shorter than the Bohr radius.

Angular and polarization analysis for two-photon decay of2shyperfine states of hydrogenlike uranium

The amplitude of two-photon transitions between hyperfine states in hydrogenlike ions is derived based on relativistic Dirac equation and second order perturbation theory. We study angular and linear polarization properties of the photon pair emitted in the decay of $2s$ states, where spin-flip and non-spin-flip transitions are highlighted. We pay particular attention to hydrogenlike uranium, since it is an ideal candidate for investigating relativistic and high-multipole effects, such as spin-flip transitions. Two types of emission patterns are identified: i) non-spin-flip transitions are found to be characterized by an angular distribution of the type $W(\theta)\sim1+\cos^2\theta$ while the polarizations of the emitted photons are parallel; ii) spin-flip transitions have somewhat smaller decay rates and are found to be characterized by an angular distribution of the type $W(\theta)\sim1-1/3\cos^2\theta$ while the polarizations of the emitted photons are orthogonal, where $\theta$ is the angle between photons directions. Deviations due to non-dipole and relativistic contributions are evaluated for both types of transitions. This work is the first step toward exploring the effect of nucleus over the the angular and polarization properties of the photon pairs emitted by two-photon transitions.

Self-energy correction to the hyperfine splitting for excited states

The self-energy corrections to the hyperfine splitting is evaluated for higher excited states in hydrogenlike ions, using an expansion in the binding parameter Zalpha, where Z is the nuclear charge number, and alpha is the fine-structure constant. We present analytic results for D, F and G states, and for a number of highly excited Rydberg states with principal quantum numbers in the range 13 <= n <= 16, and orbital angular momenta l = n-2 and l = n-1. A closed-form, analytic expression is derived for the contribution of high-energy photons, valid for any state with l <= 2$ and arbitrary n, l and total angular momentum j. The low-energy contributions are written in the form of generalized Bethe logarithms and evaluated for selected states.

Nuclear-size correction to the Lamb shift of one-electron atoms

The nuclear-size effect on the one-loop self-energy and vacuum polarization is evaluated for the $1s$, $2s$, $3s$, $2{p}_{1/2}$, and $2{p}_{3/2}$ states of hydrogen-like ions. The calculation is performed to all orders in the nuclear binding strength parameter $Z\ensuremath{\alpha}$. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter $Z\ensuremath{\alpha}$. Extrapolation of the all-order numerical results obtained toward $Z=1$ provides results for the radiative nuclear-size effect on the hydrogen Lamb shift.

The influences of the finite nuclear size effects on the energy levels and wavefunctions of hydrogen-like ions

Based on the relativistic theory, the wavefunctions and low-lying levels of highly charged states of hydrogen-like ions for the shells n=1—3 were calculated using different nuclear models——point-like nuclear and Fermi nuclear models with two parameters, respectively. The influence of the finite nuclear size on wavefunctions and level energies were analysed. Furthermore, a fitting formula related to nuclear parameter a and c in Fermi nuclear model for finite nuclear effects on the atomic level energy is deduced. The mutual influence between the relativistic effect and the finite nuclear size effects were discussed. It is found that there is a strong coupling between relativistic effect and finite nuclear size effects for high-Z elements.

Creation of coherent superposition states in hydrogenlike ions via multiphoton resonant excitation

On the basis of the analytical solution of the Dirac equation the resonant multiphoton excitation of highly charged hydrogenlike ions in a strong high-frequency laser field is investigated. It is shown that the dynamics of the relativistic system is equivalent to two independent four-level systems (in the electrical-dipole approximation). The time evolution of the system is found using the nonperturbative resonant approach. We predict that due to multiphoton excitation by an appropriate laser pulse one can achieve various coherent superposition states in atomic or ionic systems with a high nuclear charge.

Self-energy correction to the hyperfine splitting of the 1 s and 2 s states in hydrogenlike ions

The one-loop self-energy correction to the hyperfine structure splitting of the 1s and 2s states of hydrogenlike ions is calculated both for the point and finite nucleus. The results of the calculation are combined with other corrections to find the ground state hyperfine splitting in lithiumlike ^{209}Bi^{80+} and ^{165}Ho^{64+}.

Laser induced recombination to excited states of hydrogen-like ions

We investigate the laser induced recombination of electrons to excited states of hydrogen-like ions. The time integration and averaging over incidente− energies are performed analytically for a model Hamiltonian, which takes into account the degeneracy of the states and possible resonant transitions to lower lying states. The range of validity of the model assumptions is determined by comparison with numerical calculations using the exact Hamiltonian. For an arrangement of merged laser, ion and electron beams we calculated the recombination yields as a function of the laser pulse energy to then=5 to 20 states of hydrogen like ions with nuclear charges fromZ=1 to 4.

Excitation of arbitrary states of hydrogen-like ions by the impact of a charged particle. II

A method for obtaining cross sections for 1s to ns and 1s to np excitations of hydrogen-like ions under the impact of a charged particle is developed within the framework of the Coulomb-modified Glauber approximation. The scattering amplitudes in the present case turn out to be simple one-dimensional integrals in real space that can be evaluated numerically with convenience for all n and for the asymptotic case n to infinity . The calculation of cross sections by means of the present method is straightforward and requires only nominal computer time.

Collrad: A code for calculating the quasi-steady state population densities of excited states of hydrogen-like ions

Collrad: A code for calculating the quasi-steady state population densities of excited states of hydrogen-like ions

Evaluation of the Coulomb-modified Glauber amplitudes for excitation of arbitrary states of hydrogenlike ions under the impact of a charged particle

The $1s\ensuremath{\rightarrow}\mathrm{ns}$ and $1s\ensuremath{\rightarrow}\mathrm{np}$ Coulomb-modified Glauber amplitudes for the excitation of hydrogenlike ions under the impact of a charged particle are reduced to simple one-dimensional integrals in real space that can be evaluated numerically with convenience irrespective of the magnitude of $n$.

Role of transitions with different changes of the electron orbital angular momentum projection in the proton ionisation of the 1s and 2s states of hydrogen-like ions

In the first Born approximation the ionisation probabilities of the ns states (n=1 and 2) of hydrogen-like ions by nuclei corresponding to the transitions with the different changes in the orbital angular momentum projection of the relative motion h(cross) mu have been calculated at a fixed impact parameter rho . It has been shown within the 5% accuracy that the total ionisation probability and cross section are determined by the transitions with mod mu mod <or=2 n.

Collrad: A code for calculating the quasi-steady state population densities of excited states of hydrogen-like ions

Collrad: A code for calculating the quasi-steady state population densities of excited states of hydrogen-like ions