Radiative double electron capture by bare nucleus with emission of one photon

Calculation of the cross-section for the process of double electron capture by bare nucleus with emission of a single photon is presented. The double electron capture is evaluated within the framework of Quantum Electrodynamics (QED). Line-Profile Approach (LPA) is employed. Since the radiative double electron capture is governed by the electron correlation, corrections to the interelectron interaction were calculated with high accuracy, partly to all orders of the perturbation theory

Automatic Generation of Matrix Element Derivatives for Tight Binding Models

Tight binding (TB) models are one approach to the quantum mechanical many particle problem. An important role in TB models is played by hopping and overlap matrix elements between the orbitals on two atoms, which of course depend on the relative positions of the atoms involved. This dependence can be expressed with the help of Slater-Koster parameters, which are usually taken from tables. Recently, a way to generate these tables automatically was published. If TB approaches are applied to simulations of the dynamics of a system, also derivatives of matrix elements can appear. In this work we give general expressions for first and second derivatives of such matrix elements. Implemented in a computer program they obviate the need to type all the required derivatives of all occuring matrix elements by hand.Comment: 11 pages, 2 figure

Virtual Resonant States in Two-Photon Decay Processes: Lower-Order Terms, Subtractions, and Physical Interpretations

We investigate the two-photon decay rate of a highly excited atomic state which can decay to bound states of lower energy via cascade processes. We show that a naive treatment of the process, based on the introduction of phenomenological decay rates for the intermediate, resonant states, leads to lower-order terms which need to be subtracted in order to obtain the coherent two-photon correction to the decay rate. The sum of the lower-order terms is exactly equal to the one-photon decay rate of the initial state, provided the naive two-photon decay rates are summed over all available two-photon channels. A quantum electrodynamics (QED) treatment of the problem leads to an "automatic" subtraction of the lower-order terms.Comment: 8 pages, RevTe

Multipole expansions in four-dimensional hyperspherical harmonics

The technique of vector differentiation is applied to the problem of the derivation of multipole expansions in four-dimensional space. Explicit expressions for the multipole expansion of the function r^n C_j (\hr) with \vvr=\vvr_1+\vvr_2 are given in terms of tensor products of two hyperspherical harmonics depending on the unit vectors \hr_1 and \hr_2. The multipole decomposition of the function (\vvr_1 \cdot \vvr_2)^n is also derived. The proposed method can be easily generalised to the case of the space with dimensionality larger than four. Several explicit expressions for the four-dimensional Clebsch-Gordan coefficients with particular values of parameters are presented in the closed form.Comment: 19 pages, no figure

Classification of finite dimensional uniserial representations of conformal Galilei algebras

With the aid of the $6j$-symbol, we classify all uniserial modules of $\mathfrak{sl}(2)\ltimes \mathfrak{h}_{n}$, where $\mathfrak{h}_{n}$ is the Heisenberg Lie algebra of dimension $2n+1$.Comment: Some references added, introduction expanded, title change

JJ-pairing interaction, number of states, and nine-jj sum rules of four identical particles

In this paper we study $J$-pairing Hamiltonian and find that the sum of eigenvalues of spin $I$ states equals sum of norm matrix elements within the pair basis for four identical particles such as four fermions in a single-$j$ shell or four bosons with spin $l$. We relate number of states to sum rules of nine-$j$ coefficients. We obtained sum rules for nine-$j$ coefficients $$and$$ summing over (1) even $J$ and $K$, (2) even $J$ and odd $K$, (3) odd $J$ and odd $K$, and (4) both even and odd $J,K$, where $j$ is a half integer and $l$ is an integer.Comment: 6 pages, no figure, updated version, to be published. Physical Review C, in pres

Shape coexistence in Lead isotopes in the interacting boson model with Gogny energy density functional

We investigate the emergence and evolution of shape coexistence in the neutron-deficient Lead isotopes within the interacting boson model (IBM) plus configuration mixing with microscopic input based on the Gogny energy density functional (EDF). The microscopic potential energy surface obtained from the constrained self-consistent Hartree-Fock-Bogoliubov method employing the Gogny-D1M EDF is mapped onto the coherent-state expectation value of the configuration-mixing IBM Hamiltonian. In this way, the parameters of the IBM Hamiltonian are fixed for each of the three relevant configurations (spherical, prolate and oblate) associated to the mean field minima. Subsequent diagonalization of the Hamiltonian provides the excitation energy of the low-lying states and transition strengths among them. The model predictions for the $0^{+}$ level energies and evolving shape coexistence in the considered Lead chain are consistent both with experiment and with the indications of the Gogny-EDF energy surfaces.Comment: 12 pages, 6 figures, 1 tabl

AC Stark shift of the Cs microwave atomic clock transitions

We analyze the AC Stark shift of the Cs microwave atomic clock transition theoretically and experimentally. Theoretical and experimental data are in a good agreement with each other. Results indicate the absence of a magic wavelength at which there would be no differential shift of the clock states having zero projections of the total angular momentum

Interplay of p-d and d-d charge transfer transitions in rare-earth perovskite manganites

We have performed both theoretical and experimental study of optical response of parent perovskite manganites RMnO_3 with a main goal to elucidate nature of clearly visible optical features. Starting with a simple cluster model approach we addressed the both one-center (p-d) and two-center (d-d) charge transfer (CT) transitions, their polarization properties, the role played by structural parameters, orbital mixing, and spin degree of freedom. Optical complex dielectric function of single crystalline samples of RMnO_3 (R=La, Pr, Nd, Sm, Eu) was measured by ellipsometric technique at room temperature in the spectral range from 1.0 to 5.0 eV for two light polarizations: E \parallel c and E \perp c. The comparative analysis of the spectral behavior of \varepsilon _1 and \varepsilon _2 is believed to provide a more reliable assignment of spectral features. We have found an overall agreement between experimental spectra and theoretical predictions based on the theory of one-center p-d CT transitions and inter-site d-d CT transitions. Our experimental data and theoretical analysis evidence a dual nature of the dielectric gap in nominally stoichiometric matrix of perovskite manganites RMnO_3, it is formed by a superposition of forbidden or weak dipole allowed p-d CT transitions and inter-site d-d CT transitions. In fact, the parent perovskite manganites RMnO_3 should rather be sorted neither into the CT insulator nor the Mott-Hubbard insulator in the Zaanen, Sawatzky, Allen scheme.Comment: 20 pages, 6 figure