Recoil corrections to muonic atom energy levels

The relativistic correction due to nuclear recoil is calculated for a distributed nuclear charge using the effective potential model of Grotch and Yennie. For the lowest states the results differ substantially from the well-known point nucleus values and disagree somewhat with the recent calculation of Fricke.     

Electron-electron correction to the chemical binding energy of hydrogen atoms in α-palladium hydrides

We show that the modification of the electron-electron term resulting from the binding of a pair of hydrogen impurities in α-palladium hydrides cancels the corresponding modification of the one-electron band energies.     

Shell correction to atomic energy

A method for calculating a shell correction to total atomic energy within the framework of statistical theory is proposed. It is shown that the shell correction which defines the energy component which oscillates with Z is of the relative order of magntiude Z^–1. The results obtained agree well with calculations by the Hartree-Fock method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 81–86, February, 1984.     

Recoil correction to the bound-electron g factor in H-like atoms to all orders in alphaZ

The nuclear-recoil correction to the bound-electron g factor in H-like atoms is calculated to first order in m/M and to all orders in alphaZ. The calculation is performed in the range Z = 1--100. A large contribution of terms of order (alphaZ)(5) and higher is found. Even for hydrogen, the higher-order correction exceeds the (alphaZ)(4) term, while for uranium it is above the leading (alphaZ)(2) correction. As a result, one of the main sources of the theoretical uncertainty for the bound-electron g factor is eliminated.     

Recoil proton distribution in high energy photoproduction processes

For high energy linearly polarized photon–proton scattering we have calculated the azimuthal and polar angle distributions on a recoil proton in the inclusive experimental setup. We have taken into account the production of lepton and pseudoscalar meson charged pairs in the point-like approximation. The typical values of the cross sections are of the order of hundreds of picobarn. The size of the polarization effects are of order of several percents. The results are generalized for the case of electroproduction processes on the proton at rest and for a high energy proton production process on a resting proton. PACS 25.20.Lj; 13.88.+e     

二维氢原子的相对论修正

求解了二维氢原子的狄拉克方程,得到了精确的相对论能级与波函数,并详细讨论了非相对论极限.     

The nuclear size correction to the energy levels of the light hydrogen-like and muonic atoms

A closed form expression for the nuclear size correction to the energy of the S states of the light hydrogen-like and muonic atoms is obtained in the second- and third-order perturbation theory.     

Thermodynamic functions of molecular hydrogen from ab initio energy levels

A tabulation is presented of the thermodynamic properties of molecular hydrogen (H₂, D₂ and HD), calculated using energy levels which had been obtained via a solution of the Schrödinger equation. The present results should be more accurate than prior computations based on spectroscopic extrapolation formulae. They provide the first example of an accurate determination of a bulk, macroscopic property directly from first principles (input: masses and Coulomb's law).

The results are tabulated for ortho, para, the equilibrium and the frozen (or ‘normal’) mixture (3 : 1 for H₂, 1 : 2 for D₂) over the temperature range 5–300 K and for the frozen mixture up to 6000 K.

The importance of anharmonicity and of quasi-bound levels at high temperatures is discussed.     

Relativistic corrections to the energy levels of hydrogen atoms in a strong magnetic field

Relativistic corrections to the binding energies of various states of the strongly magnetized hydrogen atom are estimated by a perturbation calculation.     

A simple theory of temperature-dependent energy levels: Application to He II

The statistical mechanics of interacting Bose quasi particles is considered for the case where energy levels are temperature-dependent and known from experiment. The results are applied to the thermodynamic properties of He II using neutron scattering data.     

Relativistic correction to the helium dimer interaction energy

The lowest-order relativistic correction to the helium-helium interaction energy has been calculated for the first time, using two independent methods based on expansions in explicitly correlated Gaussian functions. At the equilibrium interatomic distance of 5.6 bohr, this correction amounts to +15.4 +/- 0.6 mK. As a by-product, a new upper bound of -10.9985 K for the nonrelativistic Born-Oppenheimer interaction energy has been obtained.     

Stochastic geometry and perturbation of the energy levels of the hydrogen atom

The stochasticity of the metric of the microdomain gives rise to a perturbation of the energy levels of the hydrogen atom which is similar to the results obtained by Bethe.     

Radiative corrections to positronium energy levels

A systematic perturbation theory for the computation of positronium energy levels is presented. The proposed method is based on the Bethe-Salpeter equation and a zeroth-order kernel for which exact solutions are known explicitly. The cancellation of ultraviolet divergences arising in the perturbation series is discussed, and new contributions to the ground-state hyperfine splitting of positronium are evaluated up to order α⁶.     

用B样条函数计算氢分子离子的能级和波函数

采用B样条函数展开方法数值求解了氢分子离子的定态薛定谔方程,计算了不同核间距时氢分子离子的基态和第一激发态的能级,结果表明,将氢分子离子的核位置作为B样条函数的节点,即使对较大的核间距,基态和第一激发态的能级值仍可达到很高的精度,所得基态径向波函数与用GAUSSIAN化学软件计算的结果符合得很好.     

Quasipotential equation for hydrogen isotopes. Muonic atoms. Ground state energy levels

The quasipotential for the electromagnetic interaction of two particles of spin $\text{1}\text{2}$ or 1 with arbitrary electromagnetic interaction of two particles of spin $\text{1}\text{2}$ or 1 with arbitrary electromagnetic structure is constructed in the one-photon approximation. Todorov's quasipotential equation is applied to calculate the ground state energy levels of the muonic atoms pμ, dμ and tμ with accuracy 10^?3 eV.     

A quasi-analytical approach to study energy levels of atwo-electron quantum dot

Our approach is quasi-analytical. We consider the Hamiltonian of a two-electron quantum dot composed of quadratic plus Coulomb terms as well as a term related to the interaction with the external magnetic field. To avoid the complexity, the Taylor expansion of the effective potential is introduced into the problem and thereby a solution is found for the eigenvalues of the corresponding two-body Schrödinger equation in terms of the Wigner parameter. We have finally made a comparison with some other theoretical results.     

Ground-state energy of pionic hydrogen to one loop

We investigate the ground-state energy of the atom (pionic hydrogen) in the framework of QCD + QED. In particular, we evaluate the strong energy-level shift. We perform the calculation at next-to-leading order in the low-energy expansion in the framework of the relevant effective field theory. The result provides a relation between the strong energy shift and the pion-nucleon S-wave scattering lengths - evaluated in pure QCD - at next-to-leading order in isospin-breaking and in the low-energy expansion. We compare our result with available model calculations. Received: 11 June 2002 / Published online: 9 October 2002     

Second-order correction to the positronium ground-state energy in ionic crystals

Upper and lower bounds on the second-order correction to the positronium ground-state energy due to the influence of the crystalline field in an ionic crystal are obtained, and the corresponding formulas are derived. The approximation adopted in the numerical calculations is the model of a point-ion potential. It is shown that neglecting the contribution of states in the continuous energy spectrum of the electron—positron pair to the correction yields an unsatisfactory upper bound. V. I. Lenin Moscow State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 37–41, April, 1998.     

Summation of the perturbation theory high order contributions to the correlation correction for the energy levels of the caesium atom

Three dominating subsequences of diagrams are summarized: (1) screening of the residual Coulomb interaction; (2) particle-hole interaction in the polarization operator; (3) chaining of the self-energy correction. An accuracy of 0.1% is obtained for the caesium energy levels.