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Self-Energy Correction to the Two-Photon Decay Width in Hydrogenlike
Atoms

Author:

U. D. JentschuraPublished: Oct 2004

We investigate the gauge invariance of the leading logarithmic radiativecorrection to the two-photon decay width in hydrogenlike atoms. It is shownthat an effective treatment of the correction using a Lamb-shift "potential"leads to equivalent results in both the length as well as the velocity gaugesprovided all relevant correction terms are taken into account. Specifically,the relevant radiative corrections are related to the energies that enter intothe propagator denominators, to the Hamiltonian, to the wave functions, and tothe energy conservation condition that holds between the two photons; the formof all of these effects is different in the two gauges, but the final result isshown to be gauge invariant, as it should be. Although the actual calculationonly involves integrations over nonrelativistic hydrogenic Green functions, thederivation of the leading logarithmic correction can be regarded as slightlymore complex than that of other typical logarithmic terms. The dominantradiative correction to the 2S two-photon decay width is found to be -2.020536(alpha/pi) (Zalpha)^2 ln[(Zalpha)^-2] in units of the leading nonrelativisticexpression. This result is in agreement with a length-gauge calculation [S. G.Karshenboim and V. G. Ivanov, e-print physics/9702027], where the coefficientwas given as -2.025(1).

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Pseudospectral Calculation of the Wavefunction of Helium and the
Negative Hydrogen Ion

Authors:

Paul E. Grabowski, David F. ChernoffPublished: Sep 2009

We study the numerical solution of the non-relativistic Schr\"{o}dingerequation for two-electron atoms in ground and excited S-states usingpseudospectral (PS) methods of calculation. The calculation achievesconvergence rates for the energy, Cauchy error in the wavefunction, andvariance in local energy that are exponentially fast for all practicalpurposes. The method requires three separate subdomains to handle thewavefunction's cusp-like behavior near the two-particle coalescences. The useof three subdomains is essential to maintaining exponential convergence. Acomparison of several different treatments of the cusps and the semi-infinitedomain suggest that the simplest prescription is sufficient. For many purposesit proves unnecessary to handle the logarithmic behavior near thethree-particle coalescence in a special way. The PS method has many virtues: noexplicit assumptions need be made about the asymptotic behavior of thewavefunction near cusps or at large distances, the local energy is exactlyequal to the calculated global energy at all collocation points, local errorsgo down everywhere with increasing resolution, the effective basis usingChebyshev polynomials is complete and simple, and the method is easilyextensible to other bound states. This study serves as a proof-of-principle ofthe method for more general two- and possibly three-electron applications.

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A self-calibrating SI-traceable broadband Rydberg atom-based
radio-frequency electric field probe and measurement instrument

Authors:

David Alexander Anderson, Rachel Elizabeth Sapiro, Georg RaithelPublished: Oct 2019

We present a self-calibrating, SI-traceable broadband Rydberg-atom-basedradio-frequency (RF) electric field probe (the Rydberg Field Probe or RFP) andmeasurement instrument (Rydberg Field Measurement System or RFMS). The RFMScomprises an atomic RF field probe (RFP), connected by a ruggedized fiber-opticpatch cord to a portable mainframe control unit with a software interface forRF measurement and analysis including real-time field readout and RF waveformvisualization. The instrument employs electromagnetically induced transparency(EIT) readout of spectral signatures from RF-sensitive Rydberg states of anatomic vapor for continuous, pulsed, and modulated RF field measurement. TheRFP exploits resonant and off-resonant Rydberg-field interactions to realizebroadband RF measurements at frequencies ranging from ~10 MHz to sub-THz over awide dynamic range. The RFMS incorporates an RF-field-free atomic reference anda laser-frequency tracker to ensure reliability and accuracy of the RFmeasurement. We characterize the RFP and measure polar field and polarizationpatterns of the RFP at 12.6 GHz RF in the far-field of a standard gain hornantenna. Measurements at 2.5 GHz are also performed. Measured patterns are ingood agreement with simulations. A detailed calibration procedure anduncertainty analysis are presented that account for deviations from anisotropic response over a $4\pi$ solid angle, arising from dielectricstructures external to the atomic measurement volume. Contributions to themeasurement uncertainty from the fundamental atomic measurement method andassociated analysis as well as material, geometry, and hardware design choicesare accounted for. A calibration (C) factor is used to establishabsolute-standard SI-traceable calibration of the RFP. Pulsed and modulated RFfield measurement, and time-domain RF-pulse waveform imaging are alsodemonstrated.

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Giant dipole oscillations and ionization of heavy atoms by intense
electromagnetic fields

Author:

M. ApostolPublished: Jun 2019

Binding energy of heavy atoms is estimated by means of the Thomas-Fermimodel, giant dipole oscillation are highlighted and ionization is discussed.

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Interference in Electron-Molecule Elastic Scattering: s-, p- and
d-spherical waves

Authors:

A. S. Baltenkov, S. T. Manson, A. Z. MsezanePublished: Sep 2018

General formulas describing the multiple scattering of electron by polyatomicmolecules have been derived within the framework of the model ofnon-overlapping atomic potentials. These formulas are applied to differentcarbon molecules, both for fixed-in-space and randomly oriented molecules.

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Resistive cooling of highly charged ions in a Penning trap to a
fluid-like state

Authors:

Ebrahimi, M. S., et alPublished: Sep 2018

We have performed a detailed experimental study of resistive cooling of largeensembles of highly charged ions such as Ar$^{13+}$ in a cryogenic Penningtrap. Different from the measurements reported in [M. Vogel et al., Phys. Rev.A, 043412 (2014)], we observe purely exponential cooling behavior whenconditions are chosen to allow collisional thermalization of the ions. Weprovide evidence that in this situation, resistive cooling time constants andfinal temperatures are independent of the initial ion energy, and that thecooling time constant of a thermalized ion ensemble is identical to thesingle-ion cooling time constant. For sufficiently high ion number densities,our measurements show discontinuities in the spectra of motional resonanceswhich indicate a transition of the ion ensemble to a fluid-like state whencooled to temperatures below approximately 14 K. With the final ion temperaturepresently being 7.5 K, ions of the highest charge states are expected to formion crystals by mere resistive cooling, in particular not requiring the use oflaser cooling.

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The Proton Radius Puzzle- Why We All Should Care

Author:

Gerald A. MillerPublished: Sep 2018

The status of the proton radius puzzle (as of the date of the Confer- ence)is reviewed. The most likely potential theoretical and experimentalexplanations are discussed. Either the electronic hydrogen experiments were notsufficiently accurate to measure the proton radius, the two- photon exchangeeffect was not properly accounted for, or there is some kind of new physics. Iexpect that upcoming experiments will resolve this issue within the next yearor so.Ta

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Scattering of cold $^4$He on $^4$He$-^{6,7}$Li and $^4$He$-^{23}$Na
molecules

Authors:

M. A. Shalchi, A. Delfino, T. Frederico, Lauro TomioPublished: Sep 2018

We predict $s-$wave elastic cross-sections $\sigma$ for low-energyatom-molecule collisions with kinetic energies up to 40 mK, for the $^4$Hecollision with weakly bound diatomic molecules formed by $^4$He with $^7$Li,$^6$Li and $^{23}$Na. Our scattering calculations are performed by usingdiatomic and triatomic molecular binding energies obtained from severalavailable realistic models as input in a renormalized zero-range model, as wellas a finite-range one-term separable potential in order to quantify therelevance of range corrections to our predictions. Of particular relevance forpossible experimental realization, we show the occurrence of a zero in $\sigma$for the collision of cold $^4$He on $^4$He$-^{23}$Na molecule below 20 mK. Alsoour results for the elastic collision $^4$He on $^4$He$-^{6,7}$Li moleculessuggest that $\sigma$ varies considerably for the realistic models studied. Asthe chosen molecules are weakly bound and the scattering energies are very low,our results are interpreted on the light of the Efimov physics, which explainsthe model independent and robustness of our predictions, despite somesensitivity on the potential range.

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The Static Dipole Polarizability of Palladium from Relativistic Coupled
Cluster Theory

Authors:

Paul Jerabek, Peter Schwerdtfeger, Jeffrey K. NaglePublished: Sep 2018

Nonrelativistic and relativistic coupled-cluster calculations extrapolated tothe complete basis set limit including excitations up to the quintuple level(CCSDTQP) were carried out to accurately determine the static electric dipolepolarizability of the closed-shell palladium atom. The resulting value of$\alpha$ = 26.14(10) a.u. implies that palladium has the smallest dipolepolarizability of all known elemental metal atoms due to its unique4d$^{10}$5s$^0$ configuration. Relativistic effects are found to be alreadysizeable ($\Delta_R\alpha$= +1.86~a.u.) compared to electron correlation($\Delta_C\alpha$= +5.06~a.u.), and need to be included for the accuratedetermination of the dipole polarizability. We also report a value of thesecond hyperpolarizability to be $\gamma\approx$ 40,000~a.u., but here thecoupled-cluster contributions are not yet converged out with respect to higherthan quintuple excitations.

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Near-K-edge single, double, and triple photoionization of C+ ions

Authors:

Müller, A., et alPublished: Sep 2018

Single, double, and triple ionization of the C+ ion by a single photon havebeen investigated in the energy range 286 to 326 eV around the K-shellsingle-ionization threshold at an unprecedented level of detail. At energyresolutions as low as 12 meV, corresponding to a resolving power of 24000,natural linewidths of the most prominent resonances could be determined. Fromthe measurement of absolute cross sections, oscillator strengths, Einsteincoefficients, multi-electron Auger decay rates and other transition parametersof the main K-shell excitation and decay processes are derived. The crosssections are compared to results of previous theoretical calculations. Mixedlevels of agreement are found despite the relatively simple atomic structure ofthe C+ ion with only 5 electrons. This paper is a follow-up of a previousLetter [M\"uller et al., Phys. Rev. Lett. 114, 013002 (2015)].

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