271,215 research outputs found
Relativistic (Zα)2 Corrections and Leading Quantum Electrodynamic Corrections to the Two-Photon Decay Rate of Ionic States
We calculate the relativistic corrections of relative order (Zα) 2 to the two-photon decay rate of higher excited S and D states in ionic atomic systems, and we also evaluate the leading radiative corrections of relative order α (Zα) 2 ln [(Zα) -2]. We thus complete the theory of the two-photon decay rates up to relative order α3 ln (α). An approach inspired by nonrelativistic quantum electrodynamics is used. We find that the corrections of relative order (Zα) 2 to the two-photon decay are given by the Zitterbewegung, by the spin-orbit coupling and by relativistic corrections to the electron mass, and by quadrupole interactions. We show that all corrections are separately gauge invariant with respect to a hybrid transformation from velocity to length gauge, where the gauge transformation of the wave function is neglected. The corrections are evaluated for the two-photon decay from 2S, 3S, 3D, and 4S states in one-electron (hydrogenlike) systems, with 1S and 2S final states
Quantum Entanglement in -Spherium
There are very few systems of interacting particles (with continuous
variables) for which the entanglement of the concomitant eigenfunctions can be
computed in an exact, analytical way. Here we present analytical calculations
of the amount of entanglement exhibited by -states of \emph{spherium}. This
is a system of two particles (electrons) interacting via a Coulomb potential
and confined to a -sphere (that is, to the surface of a -dimensional
ball). We investigate the dependence of entanglement on the radius of the
system, on the spatial dimensionality , and on energy. We find that
entanglement increases monotonically with , decreases with , and also
tends to increase with the energy of the eigenstates. These trends are
discussed and compared with those observed in other two-electron atomic-like
models where entanglement has been investigated.Comment: 14 pages, 6 figures. J. Phys. A (2015). Accepte
The relationship between entanglement, energy and level degeneracy in two-electron systems
The entanglement properties of two-electron atomic systems have been the subject of considerable research activity in recent years. These studies are still somewhat fragmentary, focusing on numerical computations on particular states of systems such as helium, or on analytical studies of model systems such as the Moshinsky atom. Some general trends are beginning to emerge from these studies: the amount of entanglement tends to increase with energy and, in the case of excited states, entanglement does not necessarily tend to zero in the limit of vanishing interaction between the two constituting particles. A physical explanation of these properties, shared by the different two-electron models investigated so far, is still lacking. As a first step towards this goal, we perform here, via a perturbative approach, an analysis of entanglement in two-electron models that sheds new light on the physical origin of the aforementioned features and on their universal character.Fil: Majtey, Ana Paula. Universidad de Granada; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Plastino, Ángel Ricardo. Universidad de Granada; España. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dehesa, J. S.. Universidad de Granada; Españ
Analytical energy gradient in variational calculations of the two lowest 3P states of the carbon atom with explicitly correlated Gaussian basis functions
Variational calculations of ground and excited bound states on atomic and molecular systems
performed with basis functions that explicitly depend on the interparticle distances can generate
very accurate results provided that the basis function parameters are thoroughly optimized by the
minimization of the energy. In this work we have derived the algorithm for the gradient of the
energy determined with respect to the nonlinear exponential parameters of explicitly correlated
Gaussian functions used in calculating n-electron atomic systems with two p-electrons and n−2
s-electrons. The atomic Hamiltonian we used was obtained by rigorously separating out the kinetic
energy of the center of mass motion from the laboratory-frame Hamiltonian and explicitly depends
on the finite mass of the nucleus. The advantage of having the gradient available in the variational
minimization of the energy is demonstrated in the calculations of the ground and the first excited 3P
state of the carbon atom. For the former the lowest energy upper bound ever obtained is reporte
Quantum Electrodynamics of qubits
Systematic description of a spin one-half system endowed with magnetic moment
or any other two-level system (qubit) interacting with the quantized
electromagnetic field is developed. This description exploits a close analogy
between a two-level system and the Dirac electron that comes to light when the
two-level system is described within the formalism of second quantization in
terms of fermionic creation and annihilation operators. The analogy enables one
to introduce all the powerful tools of relativistic QED (albeit in a greatly
simplified form). The Feynman diagrams and the propagators turn out to be very
useful. In particular, the QED concept of the vacuum polarization finds its
close counterpart in the photon scattering off a two level-system leading via
the linear response theory to the general formulas for the atomic
polarizability and the dynamic single spin susceptibility. To illustrate the
usefulness of these methods, we calculate the polarizability and susceptibility
up to the fourth order of perturbation theory. These {\em ab initio}
calculations resolve some ambiguities concerning the sign prescription and the
optical damping that arise in the phenomenological treatment. We also show that
the methods used to study two-level systems (qubits) can be extended to
many-level systems (qudits). As an example, we describe the interaction with
the quantized electromagnetic field of an atom with four relevant states: one S
state and three degenerate P states.Comment: 23 pages, 6 figure
Quantum entanglement in exactly soluble atomic models: The Moshinsky model with three electrons, and with two electrons in a uniform magnetic field
We investigate the entanglement-related features of the eigenstates of two exactly soluble atomic models: a one-dimensional three-electron Moshinsky model, and a three-dimensional two-electron Moshinsky system in an external uniform magnetic field. We analytically compute the amount of entanglement exhibited by the wavefunctions corresponding to the ground, first and second excited states of the three-electron model. We found that the amount of entanglement of the system tends to increase with energy, and in the case of excited states we found a finite amount of entanglement in the limit of vanishing interaction. We also analyze the entanglement properties of the ground and first few excited states of the two-electron Moshinsky model in the presence of a magnetic field. The dependence of the eigenstates' entanglement on the energy, as well as its behaviour in the regime of vanishing interaction, are similar to those observed in the three-electron system. On the other hand, the entanglement exhibits a monotonically decreasing behavior with the strength of the external magnetic field. For strong magnetic fields the entanglement approaches a finite asymptotic value that depends on the interaction strength. For both systems studied here we consider a perturbative approach in order to shed some light on the entanglement's dependence on energy and also to clarify the finite entanglement exhibited by excited states in the limit of weak interactions. As far as we know, this is the first work that provides analytical and exact results for the entanglement properties of a three-electron model.Fil: Bouvrie, P. A.. Universidad de Granada; EspañaFil: Majtey, Ana Paula. Universidad de Granada; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Plastino, Ángel Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata; ArgentinaFil: Sánchez Moreno, P.. Universidad de Granada; EspañaFil: Dehesa, J. S.. Universidad de Granada; Españ
Fifth Force and Hyperfine Splitting in Bound Systems
Two recent experimental observations at the ATOMKI Institute of the Hungarian
Academy of Sciences (regarding the angular emission pattern of
electron-positron pairs from nuclear transitions from excited states in 8Be and
4He) indicate the possible existence of a particle of a rest mass energy of
roughly 17 MeV. The so-called X17 particle constitutes a virtual state in the
process, preceding the emission of the electron-positron pair. Based on the
symmetry of the nuclear transitions ( to and to ), the
X17 could either be a vector, or a pseudoscalar particle. Here, we calculate
the effective potentials generated by the X17, for hyperfine interactions in
simple atomic systems, for both the pseudoscalar as well as the vector X17
hypotheses. The effective Hamiltonians are obtained in a general form which is
applicable to both electronic as well as muonic bound systems. The effect of
virtual annihilation and its contribution to the hyperfine splitting also is
considered. Because of the short range of the X17-generated potentials, the
most promising pathway for the observation of the X17-mediated effects in bound
systems concerns hyperfine interactions, which, for states, are given by
modifications of short-range (Dirac-delta) potentials in coordinate space. For
the pseudoscalar hypothesis, the exchange of one virtual X17 quantum between
the bound lepton and the nucleus exclusively leads to hyperfine effects, but
does not affect the Lamb shift. Effects due to the X17 are shown to be
drastically enhanced for muonic bound systems. Prospects for the detection of
hyperfine effects mediated by X17 exchange are analyzed for muonic deuterium,
muonic hydrogen, muonium, true muonium ( bound system), and
positronium.Comment: 14 pages; RevTe
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