The generalized dynamical equation and the vacuum polarization effect in hydrogenlike atoms

Based on the generalized dynamical equation, vacuum polarization effects are studied within the scope of the bound state theory in quantum electrodynamics. We find a vacuum-polarization correction to the Lamb shift for the 1S state of the hydrogen atom on the order of (α/π)²(Zα)⁴ that is not considered in the standard theory of bound states in quantum electrodynamics.     

Electromagnetic energies of nuclei and the nuclear compton amplitude

The electromagnetic energy of a nucleus is derived in perturbation theory, which relates this quantity to the amplitude for the forward scattering of virtual photons on a nucleus (nuclear Compton amplitude). Using the gauge invariance of this amplitude, the energy is separated into Coulomb and transverse components. Our formalism, although basically nonrelativistic, admits corrections of order ($\text{v}\text{c}$)² to the nuclear charge operator. The energy is further separated into one-body terms, related to the n-p mass difference, and two-body terms which lead to the Breit interaction and the nuclear Lamb shift. These results are then related to electron scattering sum rules in the manner of Cottingham. Mesonic contributions to the electromagnetic energy are also discussed.     

Fine-structure effects in relativistic calculations of the static polarizability of the helium atom

We use the relativistic configuration-interaction method and the model potential method to calculate the scalar and tensor components of the dipole polarizabilities for the excited states 1s3p ³ P ₀ and 1s3p ³ P ₂ of the helium atom. The calculations of the reduced matrix elements for the resonant terms in the spectral expansion of the polarizabilities are derived using two-electron basis functions of the relativistic Hamiltonian of the atom, a Hamiltonian that incorporates the Coulomb and Breit electron-electron interactions. We formulate a new approach to determining the parameters of the Fuss model potential. Finally, we show that the polarizability values are sensitive to the choice of the wave functions used in the calculations. Zh. éksp. Teor. Fiz. 115, 494–504 (February 1999)     

Classical effects from a factorized spinor representation of Maxwell's equations

It was demonstrated in earlier work that the vector representation of electromagnetic theory can be factorized into a pair of two-component spinor field equations (Sachs & Schwebel, 1962). The latter is a generalization of the usual formalism, in the sense that in addition to predicting all of the effects that are implied by the vector theory, it predicts additional observable effects that are out of the domain of prediction of the Maxwell formalism. The latter extra predictions were derived in previous publications (Sachs & Schwebel, 1961, 1963; Sachs, 1968a, b). In this paper, the spinor formalism is applied to effects that are expected to agree with the predictions of the standard formalism—the Coulomb force between point charges and the measured speed of a charged particle which moves in an electric potential. While there are no vector or tensor variables involved in this formalism, the results are found, as expected, to be in agreement with the conventional representation of electromagnetic theory. The analysis serves the role of demonstrating that in the appropriate limiting case, the factorized spinor formulation of electromagnetism does predict the explicit classical effects that are also predicted by Maxwell's field equations. The paper also presents a derivation of the general form of the solutions of the spinor field equations.     

Hydrogen atom spectrum and the lamb shift in noncommutative QED

We have calculated the energy levels of the hydrogen atom as well as the Lamb shift within the noncommutative quantum electrodynamics theory. The results show deviations from the usual QED both on the classical and the quantum levels. On both levels, the deviations depend on the parameter of space/space noncommutativity.     

Complete Lamb-shift calculation to order α5 by applying the methods of non-relativistic quantum electrodynamics

Summary It is shown, for the first time to our knowledge, that the Lamb shift for the states of hydrogenic atoms can be almost completely calculated by applying the methods of non-relativistic quantum electrodynamics and without using the Dirac equation and the second quantization for the electron. By taking into account the spin-orbit interaction, the complete Lamb shift to order α⁵ is calculated for different hydrogenic states. The author of this paper has agreed to not receive the proofs for correction.     

Two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms

The two-time Green's function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and wave functions of degenerate and quasi-degenerate states. It also allows one to derive formulas for the transition and scattering amplitudes. Application of the method to resonance scattering processes yields a systematic theory for the spectral line shape. The practical ability of the method is demonstrated by deriving formulas for the QED and interelectronic-interaction corrections to energy levels and transition and scattering amplitudes in one-, two-, and three-electron atoms. Numerical calculations of the Lamb shift, the hyperfine splitting, the bound-electron g factor, and the radiative recombination cross section in heavy ions are also reviewed.     

Development of the Sachs Theory of Electrodynamics

The most general form of electrodynamics has been derived by Sachs [1] from the irreducible representations of the Einstein group. In this paper the Sachs theory is developed as a gauge theory with a vacuum four-current i _j . The B Cyclic Theorem O(3) electrodynamics is derived from a consideration of four-vectors appearing in the Sachs theory, and electromagnetic helicity, expressed in terms of the B ⁽³⁾ field of O(3) electrodynamics, is derived from the more general Sachs theory.     

Twenty-parameter eigenfunctions and energy values of the 23 S States of He and He-like Ions

Twenty-parameter calculations of the energies and wave functions of the first excited states 2³ S of He, Li⁺, Be⁺⁺, B⁺⁺⁺, O⁶⁺, Ne⁸⁺, Mg¹⁰⁺, have been carried out using Hylleraas' method. The energy values have been corrected for mass polarization. The coefficients of the best wave functions are listed. Similar calculations for the 2³ S state of the H^? ion yield an energy value which cannot be distinguished from the energy of a free H atom. For He and Li⁺, in addition, forty-parameter calculations have been carried out. The results compare well with the recent calculations of Pekeris using a somewhat different method. Even after the inclusion of the relativistic correction, the theoretical energy values deviate slightly from the observed. The differences, ?0·10±0·05 cm^?1 for He and ?1·07±0·10 cm^?1 for Li⁺, represent observed values of the Lamb shifts in the 2³ S states. These values agree within their uncertainties with the values predicted from quantum electrodynamics.     

Coupling of one and two quasiparticles to a Bohr-Mottelson core in195,196,197,198Hg

A new model for coupling the motion of particles to that of a quadrupole collective core with rotations andβ andγ vibrations is proposed. The Hamiltonian describing the core is obtained by quantising the classical Hamiltonian associated with the quadrupole degrees of freedom. The inertial parameters and the deformation energy surface are determined microscopically. The spherical shell model particles interacting among themselves by pairing are coupled to the core by aλ ²-pole (λ=0, 2, 4) potential. The theory is applied to^195–198Hg. The predicted results agree very well the experimental data. A comparison of the present model to the other formalism is also given.     

Hamilton's principle,covariant Hamiltonian,and canonical formalism in four and five dimensions

A discussion of the 1950s and 1960s on the existence of an explicit covariant canonical formalism is renewed. A new point of view is introduced where Hamilton's principle, based on the existence of a Hamiltonian, is postulated independently from the Lagrange formalism. The Hamiltonian is determined by transformation properties and dimensional considerations. The variation of the action without constraints leads to an explicit covariant canonical formalism and correct equations of motion. The introduction of the charge as a fifth momentum gives rise to a reformulation of classical relativistic point mechanics as a five-dimensionalU(1) gauge theory with a theoretically invisible extra dimension. A generalization to other gauge groups is given. The inversion of the proper time is introduced as a new particle-antiparticle symmetry that allows one to show that in the five-dimensional classical theory all particles have positive energy.     

The Breit equation as a zeroth-order approximation for calculation of the bound-state energy

An equation whose kernel is determined by the one-photon exchange between interacting particles is analyzed in the framework of the Bethe-Salpeter formalism. This equation is considered as a zeroth-order approximation in the calculation of the corrections to the energy levels. This is the Breit equation that takes into account additional small terms (with respect to the parameter (Zα)²). A procedure that employs the Brillouin-Wigner perturbation theory and makes it possible to sequentially take into account the corrections to the energy levels is considered.     

Structure of the low-lying states of 47Ti

Deformed configuration-mixing calculations for the nucleus ⁴⁷Ti have been performed in the framework of the projected Hartree-Fock formalism. For each of the angular momentum states, the Hamiltonian has been diagonalized in the basis of about ten of the lowest orthogonalized projected states. The resulting spectrum is in good agreement with the observed spectrum of negative parity states. The eigenstates of the Hamiltonian have been analysed for the possible existence of the “band structure”. Besides the “ground state” $\text{K =}\text{5}\text{2}$ band of states with deformation δ ≈ 0.15, another well defined band of states belonging to the $\text{K =}\text{1}\text{2}$ neutron excited intrinsic state is likely to exist. The calculated and experimental binding energies are in good agreement. The results of the detailed calculation have been extrapolated to obtain an estimate of the level density for ⁴⁷Ti up to 6 MeV excitation energy.     

A comparison of self broadening and shift of helium,neon and argon emission lines

Self broadening (van der Waals and resonance) and shift of Ne emission lines and van der Waals broadening and shift of He emission lines have been measured using a high pressure (0.5–3.0 atom), low current discharge. These results are compared with previous measurements in Ar and He to obtain a complete comparison of self broadening and shift of He, Ne and Ar emission lines. Oscillator strengths for the resonance transitions are obtained from the resonance broadening coefficients. The trend of the van der Waals broadening coefficients for the three noble gases is correctly predicted by a theory due to HINDMARSHet al.⁽⁴⁾ in which a Lennard-Jones potential is used in the impact theory formalism. The measured line shifts cannot be accounted for by this theory and reflect the need for more accurate quantum mechanical calculations.     

Lamb shift in atoms interacting with a strong laser field

Radiative corrections to the energy levels of an atom interacting with a strong laser field have been investigated. A formula for the Lamb shift of the laser-dressed states is derived, which makes it possible to calculate this shift with an error up to α². Original Russian Text ? R.Kh. Gainutdinov, A.A. Mutygullina, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 292–293.     

Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems

Through the entanglement of a collection of K non-interacting replicas of a system of N interacting Fermions, and making use of the properties of reduced density matrices the variational principle and the theorems of Hohenberg and Kohn are generalized to excited states. The generalization of the variational principle makes use of the natural orbitals of an N-particle density matrix describing the state of lowest energy of the entangled state. The extension of the theorems of Hohenberg and Kohn is based on the ground-state formulation of density functional theory but with a new interpretation of the concept of a ground state: It is the state of lowest energy of a system of KN Fermions that is described in terms of the excited states of the N-particle interacting system. This straightforward implementation of the line of reasoning of ground-state density functional theory to a new domain leads to a unique and logically valid extension of the theory to excited states that allows the systematic treatment of all states in the spectrum of the Hamiltonian of an interacting system.     

Multicluster solutions to a multinucleon problem and clustering phenomena

Various concepts of clustering phenomena are discussed. Precise multicluster solutions constructed by the present authors for an A-nucleon problem whose dynamical properties are described by a generalized Elliott Hamiltonian are used as a mathematical formalism of the theory of clustering phenomena in nuclei. It is shown that qualitative features of various clustering phenomena, such as the very fact of the existence of cluster states, their classification, and selectivity of reactions that populate them, are explained within the concept being discussed. The 2α + bineutron three-cluster states of the ¹⁰Be nucleus are classified, and their spectrum is calculated. It is demonstrated that the results of these calculations are in good agreement with experimental data.     

Theory of the lamb shift in muonic deuterium

We present new calculation of the Lamb shift (2P _1/2 ? 2S _1/2), fine splitting of the 2P state and hyperfine splitting of the 2S state in muonic deuterium (µd) using the quasipotential method in quantum electrodynamics. The vacuum polarization, nuclear structure, and recoil effects are calculated with the account of contributions of orders α ³, α ⁴, α ⁵, and α ⁶. The obtained numerical value of the Lamb shift 202.4139 meV can be considered as a reliable estimate for the comparison with forthcoming experimental data.     

Quantum mechanics derived from stochastic electrodynamics

The connection between stochastic electrodynamics (SED) and the quantum theory of matter is further explored. The main result is that the Fokker-Planck-like equation of SED can be recast into the form of a Schrödinger equation with radiative corrections, when the system is close to a state of equilibrium. The phase-space distribution can be written as Wigner's pseudo-distribution plus corrections due to the nonlinearity of the external force and to radiative effects. The radiative corrections predicted by the theory, namely the Lamb shift and the decay of excited atomic states, coincide with those predicted by QED. Moreover, the theory offers a clear physical interpretation of these phenomena as due to the coupling of the electric dipole of the system with the zero-point radiation field and to radiation reaction, respectively.     

The collective Lamb shift in nuclear γ-ray superradiance

The electromagnetic transitions of M?ssbauer nuclei provide almost ideal two-level systems to transfer quantum optical concepts into the regime of hard x-rays. If many identical atoms collectively interact with a resonant radiation field, one observes (quantum) optical properties that are strongly different from those of a single atom. The most prominent effect is the broadening of the resonance line known as collective enhancement, resulting from multiple scattering of real photons within the atomic ensemble. On the other hand, the exchange of virtual photons within the ensemble leads to a tiny energy shift of the resonance line, the collective Lamb shift, that remained experimentally elusive for a long time after its prediction. Here we illustrate how highly brilliant synchrotron radiation allows one to prepare superradiant states of excited M?ssbauer nuclei, an important condition for observation of the collective Lamb shift.