Radiative corrections and parity nonconservation in heavy atoms

The self-energy and the vertex radiative corrections to the effect of parity nonconservation in heavy atoms are calculated analytically in orders Z alpha^2 and Z^2 alpha^3 ln(lambda_C/r_0), where lambda_C and r_0 being the Compton wavelength and the nuclear radius, respectively. The value of the radiative correction is -0.85% for Cs and -1.41% for Tl. Using these results we have performed analysis of the experimental data on atomic parity nonconservation. The obtained values of the nuclear weak charge, Q_W=-72.90(28)_{exp}(35)_{theor} for Cs, and Q_W=-116.7(1.2)_{exp}(3.4)_{theor} for Tl, agree with predictions of the standard model. As an application of our approach we have also calculated analytically dependence of the Lamb shift on the finite nuclear size.Comment: 4 pages, 4 figure

Nature of the Darwin term and (Zα)4m3/M2{(Z\alpha)^4 m^3/M^2} contribution to the Lamb shift for an arbitrary spin of the nucleus

The contact Darwin term is demonstrated to be of the same origin as the spin-orbit interaction. The $(Z\alpha)^4 m^3/M^2$ correction to the Lamb shift, generated by the Darwin term, is found for an arbitrary nonvanishing spin of the nucleus, both half-integer and integer. There is also a contribution of the same nature to the nuclear quadrupole moment.Comment: 9 pages, latex, no figure

Induced Current and Aharonov-Bohm Effect in Graphene

The effect of vacuum polarization in the field of an infinitesimally thin solenoid at distances much larger than the radius of solenoid is investigated. The induced charge density and induced current are calculated. Though the induced charge density turned out to be zero, the induced current is finite periodical function of the magnetic flux $\Phi$. The expression for this function is found exactly in a value of the flux. The induced current is equal to zero at the integer values of $\Phi/\Phi_0$ as well as at half-integer values of this ratio, where $\Phi_0=2\pi\hbar c/e$ is the elementary magnetic flux. The latter is a consequence of the Furry theorem and periodicity of the induced current with respect to magnetic flux. As an example we consider the graphene in the field of solenoid perpendicular to the plane of a sample.Comment: 3 pages, 1 figure, version accepted to Phys. Rev.

Bremsstrahlung in alpha-Decay Reexamined

A high-statistics measurement of bremsstrahlung emitted in the alpha decay of 210Po has been performed, which allows to follow the photon spectra up to energies of ~ 500 keV. The measured differential emission probability is in good agreement with our theoretical results obtained within the quasi classical approximation as well as with the exact quantum mechanical calculation. It is shown that due to the small effective electric dipole charge of the radiating system a significant interference between the electric dipole and quadrupole contributions occurs, which is altering substantially the angular correlation between the alpha particle and the emitted photon.Comment: 10 pages, 5 figures, v2: fix of small typo

Virtual light-by-light scattering and the g factor of a bound electron

The contribution of the light-by-light diagram to the g factor of electron and muon bound in Coulomb field is obtained. For electron in a ground state, our results are in good agreement with the results of other authors obtained numerically for large Z. For relatively small Z our results have essentially higher accuracy as compared to the previous ones. For muonic atoms, the contribution is obtained for the first time with the high accuracy in whole region of Z.Comment: 10 pages, 3 figures, RevTe

Corrections to deuterium hyperfine structure due to deuteron excitations

We consider the corrections to deuterium hyperfine structure originating from the two-photon exchange between electron and deuteron, with the deuteron excitations in the intermediate states. In particular, the motion of the two intermediate nucleons as a whole is taken into account. The problem is solved in the zero-range approximation. The result is in good agreement with the experimental value of the deuterium hyperfine splitting.Comment: 7 pages, LaTe

Charge asymmetry in the differential cross section of high-energy e+e- photoproduction in the field of a heavy atom

First quasiclassical correction to the differential cross section of high-energy electron-positron photoproduction in the electric field of a heavy atom is obtained with the exact account of the field. This correction is responsible for the charge asymmetry ${\cal A}$ in this process. When the transverse momentum of at least one of the produced particles is much larger than the electron mass $m$, the charge asymmetry can be as large as tens percent. We also estimate the contribution $\tilde{\cal A}$ to the charge asymmetry coming from the Compton-type diagram. For heavy nuclei, this contribution is negligible. For light nuclei, $\tilde{\cal A}$ is noticeable only when the angle between the momenta of electron and positron is of order of $m/\omega$ ($\omega$ is the photon energy) while the transverse momenta of both particles are much larger than $m$.Comment: 19 pages, 7 figure

An integral method for solving nonlinear eigenvalue problems

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least $k$ column vectors, where $k$ is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show that the original nonlinear eigenvalue problem reduces to a linear eigenvalue problem of dimension $k$. No initial approximations of eigenvalues and eigenvectors are needed. The method is particularly suitable for moderately large eigenvalue problems where $k$ is much smaller than the matrix dimension. We also give an extension of the method to the case where $k$ is larger than the matrix dimension. The quadrature errors caused by the trapezoid sum are discussed for the case of analytic closed contours. Using well known techniques it is shown that the error decays exponentially with an exponent given by the product of the number of quadrature points and the minimal distance of the eigenvalues to the contour

Spectroscopic Temperature Determination of Degenerate Fermi Gases

We suggest a simple method for measuring the temperature of ultra-cold gases made of fermions. We show that by using a two-photon Raman probe, it is possible to obtain lineshapes which reveal properties of the degenerate sample, notably its temperature $T$. The proposed method could be used with identical fermions in different hyperfine states interacting via s-wave scattering or identical fermions in the same hyperfine state via p-wave scattering. We illustrate the applicability of the method in realistic conditions for $^6$Li prepared in two different hyperfine states. We find that temperatures down to 0.05 $T_{F}$ can be determined by this {\it in-situ} method.Comment: 7 pages, 4 figures, Revtex