Physical Sciences and Mathematics Commons^™

Semiclassically Modeling Hydrogen At Rydberg States Immersed In Electromagnetic Fields, Jaron Williams

Mathematics Senior Capstone Papers

Originally, closed-orbit theory was developed in order to analyze oscillations in the near ionization threshold (Rydberg) densities of states for atoms in strong external electric and magnetic fields. Oscillations in the density of states were ascribed to classical orbits that began and ended near the atom. In essence, observed outgoing waves following the classical path return and interfere with original outgoing waves, giving rise to oscillations. Elastic scattering from one closed orbit to another gives additional oscillations in the cross-section. This study examines how quantum theory can be properly used in combination with classical orbit theory in order to study …

Continuity Of Heavy Rydberg Behaviour In The Ungerade Ion-Pair States Of H2, Alexander M. Chartrand, Robert J. Donovan, Kenneth P. Lawley, Elizabeth Mccormack

Physics Faculty Research and Scholarship

Heavy Rydberg behaviour and absolute quantum defects are reported for resonances in the ungerade manifold of H₂ above the (1s, 3l) dissociation limit. The continuity of the vibrational progression of the B''B-bar state through the crossing with the 3p asymptote is demonstrated and a predominantly diabatic picture of the vibrational motion emerges, indicating that the ion-pair resonances possess little 6¹Σ_u⁺ state character.

Long-Range Interactions Of Hydrogen Atoms In Excited States. I. 2s-1s Interactions And Dirac-Δ Perturbations, Chandra Mani Adhikari, Vincent Debierre, Arthur N. Matveev, Nikolai N. Kolachevsky, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

The theory of the long-range interaction of metastable excited atomic states with ground-state atoms is analyzed. We show that the long-range interaction is essentially modified when quasidegenerate states are available for virtual transitions. A discrepancy in the literature regarding the van der Waals coefficient C₆ (2S ;1 S ) describing the interaction of metastable atomic hydrogen ( 2 S state) with a ground-state hydrogen atom is resolved. In the the van der Waals range a₀ ≪ R ≪ a₀ / α , where a₀ = ℏ / α m c is the Bohr radius and α …

Photon Beam Asymmetry Σ For Η And Η′ Photoproduction From The Proton, P. Collins, B. G. Ritchie, M. Dugger, A. V. Anisovich, M. Doring, E. Klempt, V. A. Nikonov, D. Rönchen, D. Sadasivan, A. Sarantsev, M. J. Amaryan, A. Klein

Physics Faculty Publications

Measurements of the linearly-polarized photon beam asymmetry Σ for photoproduction from the proton of η and η ′ mesons are reported. A linearly-polarized tagged photon beam produced by coherent bremsstrahlung was incident on a cryogenic hydrogen target within the CEBAF Large Acceptance Spectrometer. Results are presented for the γ p → η p reaction for incident photon energies from 1.070 to 1.876 GeV, and from 1.516 to 1.836 GeV for the γ p → η ′ p reaction. For γ p → η p , the data reported here considerably extend the range of measurements to higher energies, and are …

Observations Of The High Vibrational Levels Of The B′′B̄ 1Σu+ State Of H2, Alexander M. Chartrand, W. Duan, R. C. Ekey, Elizabeth Mccormack

Physics Faculty Research and Scholarship

Double-resonance laser spectroscopy via the E F ¹Σ_g⁺, v'=6, J'=0-2 state was used to probe the high vibrational levels of the B"B-bar ¹Σ_u⁺ state of molecular hydrogen. Resonantly-enhanced multiphoton ionization spectra were recorded by detecting ion production as a function of energy using a time of flight mass spectrometer. New measurements of energies for the v=51-66 levels for the B"B-bar state of H₂ are reported, which, taken with previous results, span the v=46-69 vibrational levels. Results for energy levels are compared to theoretical close-coupled calculations [L. Wolniewicz, T. …

Muonic Bound Systems, Virtual Particles, And Proton Radius, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

The proton radius puzzle questions the self-consistency of theory and experiment in light muonic and electronic bound systems. Here we summarize the current status of virtual particle models as well as Lorentz-violating models that have been proposed in order to explain the discrepancy. Highly charged one-electron ions and muonic bound systems have been used as probes of the strongest electromagnetic fields achievable in the laboratory. The average electric field seen by a muon orbiting a proton is comparable to hydrogenlike uranium and, notably, larger than the electric field in the most advanced strong-laser facilities. Effective interactions due to virtual annihilation …

Measurement Of The Formation Rate Of Muonic Hydrogen Molecules, V. A. Andreev, T. I. Banks, R. M. Carey, T. A. Case, S. M. Clayton, K. M. Crowe, J. Deutsch, J. Egger, S. J. Freedman, V. A. Ganzha, Tim Gorringe, F. E. Gray, D. W. Hertzog, M. Hildebrandt, P. Kammel, B. Kiburg, S. Knaack, P. A. Kravtsov, A. G. Krivshich, B. Lauss, K. R. Lynch, E. M. Maev, O. E. Maev, F. Mulhauser, C. Petitjean, G. E. Petrov, R. Prieels, G. N. Schapkin, G. G. Semenchuk, M. A. Soroka, Vladimir Tishchenko, A. A. Vasilyev, A. A. Vorobyov, M. E. Vznuzdaev, P. Winter

Physics and Astronomy Faculty Publications

Background: The rate λ_ppμ characterizes the formation of ppμ molecules in collisions of muonic pμ atoms with hydrogen. In measurements of the basic weak muon capture reaction on the proton to determine the pseudoscalar coupling g_P, capture occurs from both atomic and molecular states. Thus knowledge of λ_ppμ is required for a correct interpretation of these experiments.

Purpose: Recently the MuCap experiment has measured the capture rate Λ_S from the singlet pμ atom, employing a low-density active target to suppress ppμ formation [V. Andreev et al. (MuCap Collaboration), Phys. Rev. Lett. 110, 012504 (2013) …

Long-Range Atom-Wall Interactions And Mixing Terms: Metastable Hydrogen, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

We investigate the interaction of metastable 2S hydrogen atoms with a perfectly conducting wall, including parity-breaking S-P mixing terms (with full account of retardation). The neighboring 2P_1/2 and 2P_3/2 levels are found to have a profound effect on the transition from the short-range, nonrelativistic regime, to the retarded form of the Casimir-Polder interaction. The corresponding P state admixtures to the metastable 2S state are calculated. We find the long-range asymptotics of the retarded Casimir-Polder potentials and mixing amplitudes for general excited states, including a fully quantum electrodynamic treatment of the dipole-quadrupole mixing term. The decay width of the …

Data Analysis Techniques, Differential Cross Sections, And Spin Density Matrix Elements For The Reaction 𝛾p → Φp, K. P. Adhikari, D. Adikaram, M. J. Amaryan, C. E. Hyde, S. Koirala, S. E. Kuhn, M. Mayer, I. Niculescu, Et Al., The Clas Collaboration

Physics Faculty Publications

High-statistics measurements of differential cross sections and spin density matrix elements for the reaction γp→ϕp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s) from 1.97 to 2.84 GeV, with an extensive coverage in the ϕ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the ϕ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged- (ϕ→K⁺K⁻) and neutral- (ϕ→K⁰_SK⁰_L) K^{→ …}

Data Analysis Techniques, Differential Cross Sections, And Spin Density Matrix Elements For The Reaction ᵞp → Φp, K.P. Adhikari, D. Adikaram, M.J. Amaryan, A. Klein, S. Koirala, Clas Collaboration

Physics Faculty Publications

High-statistics measurements of differential cross sections and spin density matrix elements for the reaction ᵞp → ϕp have been made using the CLAS detector at Jefferson Lab. We cover center-of-mass energies (√s) from 1.97 to 2.84 GeV, with an extensive coverage in the ϕ production angle. The high statistics of the data sample made it necessary to carefully account for the interplay between the ϕ natural lineshape and effects of the detector resolution, that are found to be comparable in magnitude. We study both the charged-(ϕ → K⁺ K^-) and neutral( ϕ → (K^O_SK …

Low Energy (E, 2e) Study From The 1t₂ Orbital Of Ch₄, Shenyue Xu, Hari Chaluvadi, Xueguang Ren, Thomas Pfluger, Arne Senftleben, Chuangang Ning, Shuncheng Yan, Peng Zhang, Jie Yang, Xinwen Ma, Joachim Hermann Ullrich, Don H. Madison, Alexander Dorn

Physics Faculty Research & Creative Works

Single ionization of the methane (CH₄) 1t₂ orbital by 54 eV electron impact has been studied experimentally and theoretically. The measured triple differential cross sections cover nearly a 4π solid angle for the emission of low energy electrons and a range of projectile scattering angles. Experimental data are compared with theoretical calculations from the distorted wave Born approximation and the molecular three-body distorted wave models. It is found that theory can give a proper description of the main features of experimental cross section only at smaller scattering angles. For larger scattering angles, significant discrepancies between experiment and …

Relativistic Reduced-Mass And Recoil Corrections To Vacuum Polarization In Muonic Hydrogen, Muonic Deuterium, And Muonic Helium Ions, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order (Zα)⁴μ³/m²_N is evaluated for muonic hydrogen and deuterium and muonic helium ions (μ is the reduced mass and m_N is the nuclear mass). Relativistic corrections to vacuum polarization of order α(Zα)⁴μ are calculated, with a full account of the reduced-mass dependence. The results shift theoretical predictions. The radiative-recoil correction to vacuum polarization of order α(Zα)⁵-ln²(Zα) μ²/m_N is obtained in leading logarithmic approximation. …

Hydrogen-Deuterium Isotope Shift: From The 1s-2s-Transition Frequency To The Proton-Deuteron Charge-Radius Difference, Ulrich D. Jentschura, Arthur N. Matveev, Christian G. Parthey, Janis Alnis, Randolf Pohl, Th H. Udem, Nikolai N. Kolachevsky, Theodor Wolfgang Hansch

Physics Faculty Research & Creative Works

We analyze and review the theory of the hydrogen-deuterium isotope shift for the 1S-2S transition, which is one of the most accurately measured isotope shifts in any atomic system, in view of a recently improved experiment. A tabulation of all physical effects that contribute to the isotope shift is given. These include the Dirac binding energy, quantum electrodynamic effects, including recoil corrections, and the nuclear-size effect, including the pertaining relativistic and radiative corrections. From a comparison of the theoretical result Δf_th=670999566.90(66)(60)kHz (exclusive of the nonrelativistic nuclear-finite-size correction) and the experimental result Δf_expt=670994334605(15) Hz, we infer the …

Three-Body Dynamics In Single Ionization Of Atomic Hydrogen By 75 Kev Proton Impact, Ahmad Hasan, Michael Schulz, Aaron C. Laforge, Jason S. Alexander, M. F. Ciappina, M. A. Khakoo, Kisra Nayomal Egodapitiya

Physics Faculty Research & Creative Works

Doubly differential cross sections for single ionization of atomic hydrogen by 75 keV proton impact have been measured and calculated as a function of the projectile scattering angle and energy loss. This pure three-body collision system represents a fundamental test case for the study of the reaction dynamics in few-body systems. A comparison between theory and experiment reveals that three-body dynamics is important at all scattering angles and that an accurate description of the role of the projectile-target-nucleus interaction remains a major challenge to theory.

Reexamining Blackbody Shifts For Hydrogenlike Ions, Ulrich D. Jentschura, Martin K. Haas

Physics Faculty Research & Creative Works

We investigate blackbody-induced energy shifts for low-lying levels of atomic systems, with a special emphasis on transitions used in current and planned high-precision experiments on atomic hydrogen and ionized helium. Fine-structure- and Lamb-shift-induced blackbody shifts are found to increase with the square of the nuclear charge number, whereas blackbody shifts due to virtual transitions decrease with increasing nuclear charge as the fourth power of the nuclear charge. We also investigate the decay width acquired by the ground state of atomic hydrogen, due to interaction with blackbody photons. The corresponding width is due to an instability against excitation to higher excited …

Measurement Of Ep→Epπᵒ Beam Spin Asymmetries Above The Resonance Region, Clas Collaborative, M. J. Amaryan, H. Bagdasaryan, S. Bültmann, S. L. Careccia, K. V. Dharmawardane, G. E. Dodge, G. Gavalian, N. Guler, C. E. Hyde-Wright, N. Kalantarians, A. Klien, A. V. Klimenko, S. E. Kuhn, M. R. Niroula, S. Tkachenko, L. B. Weinstein, J. Zhang

Physics Faculty Publications

The beam spin asymmetry (BSA) in the exclusive reaction ^→ep→epπ0 was measured with the CEBAF 5.77 GeV polarized electron beam and Large Acceptance Spectrometer (CLAS). The x_B,Q²,t , and ϕ dependences of the π⁰ BSA are presented in the deep inelastic regime. The asymmetries are fitted with a sinϕ function and their amplitudes are extracted. Overall, they are of the order of 0.04–0.11 and roughly independent of t . This is the signature of a nonzero longitudinal-transverse interference. The implications concerning the applicability of a formalism based on generalized parton distributions, as well as …

Studies Of Breakdown In A Pressurized Rf Cavity, M. Bastaninejad, A. A. Elmustafa, C. M. Ankenbrandt, A. Moretti, M. Popovic, K. Yonehara, D. M. Kaplan, M. Alsharo'a, P. M. Hanlet, R. P. Johnson, M. Kuchnir, D. Newsham, D. V. Rose, C. Thoma, D. R. Welch

Mechanical & Aerospace Engineering Faculty Publications

Microscopic images of the surfaces of metallic electrodes used in high-pressure gas-filled 805 MHz RF cavity experiments [1] have been used to investigate the mechanism of RF breakdown [2]. The images show evidence for melting and boiling in small regions of ∼10 micron diameter on tungsten, molybdenum, and beryllium electrode surfaces. In these experiments, the dense hydrogen gas in the cavity prevents electrons or ions from being accelerated to high enough energy to participate in the breakdown process so that the only important variables are the fields and the metallic surfaces. The distributions of breakdown remnants on the electrode surfaces …

Two-Loop Bethe Logarithms For Non- S Levels, Ulrich D. Jentschura

Physics Faculty Research & Creative Works

Two-loop Bethe logarithms are calculated for excited P and D states in hydrogenlike systems, and estimates are presented for all states with higher angular momenta. These results complete our knowledge of the P and D energy levels in hydrogen at the order of α⁸ m_ec², where me is the electron mass and c is the speed of light, and scale as Z⁶, where Z is the nuclear charge number. Our analytic and numerical calculations are consistent with the complete absence of logarithmic terms of order (απ)² (Zα)⁶ ln [(Zα)^-2] …

Young-Type Interference In (E, 2e) Ionization Of H₂, D. S. Milne-Brownlie, Matthew S. Foster, Junfang Gao, B. Lohmann, Don H. Madison

Physics Faculty Research & Creative Works

We have investigated the electron impact single ionization of the hydrogen molecule, with fully determined kinematics. The experimental and theoretical results are compared with He ionization under the same conditions. The results indicate that the ejected electron angular distribution for H₂ is modified due to Young-type interference between ionization amplitudes for scattering from the two centers in the hydrogen molecule. The observable result is a suppression of the backward scattering (recoil) peak compared with the binary peak.

Quantum Electrodynamic Corrections To The Hyperfine Structure Of Excited S States, Ulrich D. Jentschura, Vladimir A. Yerokhin

Physics Faculty Research & Creative Works

State-dependent quantum electrodynamic corrections are evaluated for the hyperfine splitting of nS states for arbitrary principal quantum number n. The calculations comprise both the self-energy and the vacuum-polarization correction of order α(Zα) 2 EF and the recoil correction of order (Zα)² (m/M) E_F. Higher-order corrections are summarized and partly reevaluated as well. Accurate predictions for hydrogen hyperfine splitting intervals of nS states with n=2,...,8 are presented. The results obtained are important due to steady progress in hydrogen spectroscopy for transitions involving highly excited S states.

Theoretical Treatment Of Electron-Impact Ionization Of Molecules, Junfang Gao, Jerry Peacher, Don H. Madison

Physics Faculty Research & Creative Works

There is currently no reliable theory for calculating the fully differential cross section (FDCS) for low energy electron-impact ionization of molecules. All of the existing experimental FDCS data represent averages over all molecular orientations and this can be an important theoretical complication for calculations that are computer intensive. We have found that using an averaged molecular orbital is an accurate approximation for ionization of ground states. In this paper, we will describe the approximation, discuss its expected range of validity and show some FDCS results using the approximation for ionization of H2 and N2

Photoionization Broadening Of The 1s-2s Transition In A Beam Of Atomic Hydrogen, Nikolai N. Kolachevsky, Martin K. Haas, Ulrich D. Jentschura, Maximilian Herrmann, Peter Fendel, Marc P. Fischer, Ronald Holzwarth, Th H. Udem, Christoph H. Keitel, Theodor Wolfgang Hansch

Physics Faculty Research & Creative Works

We consider the excitation dynamics of the two-photon 1S - 2S transition in a beam of atomic hydrogen by 243 nm laser radiation. Specifically, we study the impact of ionization damping on the transition line shape, caused by the possibility of ionization of the 2S level by the same laser field. Using a Monte Carlo simulation, we calculate the line shape of the 1S - 2S transition for the experimental geometry used in the two latest absolute frequency measurements [M. Niering, Phys. Rev. Lett. 84, 5496 (2000) and M. Fischer, Phys. Rev. Lett. 92, 230802 (2004)]. The calculated line shift …

Differential Cross Sections For 𝛾 + P → K⁺ + Y For Λ And Σ⁰ Hyperons, H. Bagdasaryan, M. Bektasoglu, S. L. Careccia, S. Bültmann, G. E. Dodge, N. Guler, C. E. Hyde-Wright, H. G. Juengst, A. V. Klimenko, S. E. Kuhn, S. Tkachenko, L. B. Weinstein, J. Zhang, Et Al., Clas Collaboration

Physics Faculty Publications

High-statistics cross sections for the reactions 𝛾 + p → K⁺ + Λ and 𝛾 + p → K⁺ + Σ⁰ have been measured using CLAS at Jefferson Lab for center-of-mass energies W between 1.6 and 2.53 GeV, and for -0.85 < cos θ _K^c.m. < +0.95. In the K⁺ + Λ channel we confirm a resonance-like structure near W=1.9 GeV at backward kaon angles. The position and width of this structure change with angle, indicating that more than one resonance is likely playing a role. The K⁺ + Λ channel at forward angles and all energies is well described by a t-channel scaling characteristic of Regge exchange, whereas the same scaling applied to the K⁺ + Σ⁰ channel is less successful. Several existing theoretical models are compared to the data, but none provide a good representation of the results.

Precise Calculation Of Transition Frequencies Of Hydrogen And Deuterium Based On A Least-Squares Analysis, Ulrich D. Jentschura, Svetlana A. Kotochigova, Eric Olivier Le Bigot, Peter J. Mohr, Barry N. Taylor

Physics Faculty Research & Creative Works

We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g factor of the electron, which was previously the most accurate prediction of QED.

Complete Two-Loop Correction To The Bound-Electron Factor, Krzysztof Pachucki, Andrzej Czarnecki, Ulrich D. Jentschura, Vladimir A. Yerokhin

Physics Faculty Research & Creative Works

Within a systematic approach based on dimensionally regularized nonrelativistic quantum electrodynamics, we derive a complete result for the two-loop correction to order ( α/ π )² ( Zα )⁴ for the g factor of an electron bound in an nS state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from g-factor measurements. D

Calculation Of Hydrogenic Bethe Logarithms For Rydberg States, Ulrich D. Jentschura, Peter J. Mohr

Physics Faculty Research & Creative Works

We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schrdinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly …

Self-Energy Values For P States In Hydrogen And Low-Z Hydrogenlike Ions, Ulrich D. Jentschura, Peter J. Mohr

Physics Faculty Research & Creative Works

We describe a nonperturbative (in Z α ) numerical evaluation of the one-photon electron self-energy for 3P_1/2 , 3P_3/2 , 4P_1/2, and 4P_3/2 states in hydrogenlike atomic systems with charge numbers Z = 1 to 5. The numerical results are found to be in agreement with known terms in the expansion of the self-energy in powers of Z α and lead to improved theoretical predictions for the self-energy shift of these states.

Muon Transfer From Muonic Hydrogen To Atomic Oxygen And Nitrogen, Anh-Thu Le, C. D. Lin

Physics Faculty Research & Creative Works

The results of diabatic hyperspherical close-coupling calculations are presented for the charge exchange of a negative muon from muonic hydrogen to oxygen and nitrogen for collision energies from 10^-3 to 10³ eV. It is shown that converged results can be obtained using a much smaller number of channels than in the traditional adiabatic approach. For the energy range below 10 eV our results for nitrogen are in good agreements with the available experimental data and the recent calculations within hyperspherical elliptic coordinates. However, discrepancies were found in the case of oxygen, where a p -wave shape resonance is …

Tunable Conductivity And Conduction Mechanism In An Ultraviolet Light Activated Electronic Conductor, Mariana I. Bertoni, Thomas O. Mason, Julia E. Medvedeva, Arthur J. Freeman, Kenneth R. Poeppelmeier, B. Delley

Physics Faculty Research & Creative Works

A tunable conductivity has been achieved by controllable substitution of an ultraviolet light activated electronic conductor. The transparent conducting oxide system H-doped Ca12-xMgxAl14O33 (x=0,0.1,0.3,0.5,0.8,1.0) presents a conductivity that is strongly dependent on the substitution level and temperature. Four-point dc-conductivity decreases with x from 0.26 S/cm (x=0) to 0.106 S/cm (x=1) at room temperature. At each composition the conductivity increases (reversibly with temperature) until a decomposition temperature is reached; above this value, the conductivity drops dramatically due to hydrogen recombination and loss. The observed conductivity behavior is consistent with the predictions of our first principles density functional calculations for the Mg-substituted …

Breakup Of H₂ In Singly Ionizing Collisions With Fast Protons: Channel-Selective Low-Energy Electron Spectra, Christina Dimopoulou, Robert Moshammer, Daniel Fischer, C. Hohr, Alexander Dorn, Pablo Daniel Fainstein, Jose R. Crespo Lopez-Urrutia, Claus Dieter Schroter, Holger Kollmus, Rido Mann, Siegbert Hagmann, Joachim Hermann Ullrich

Physics Faculty Research & Creative Works

The dissociation of H₂ in singly ionizing collisions with fast protons was analyzed using channel-selective low-energy electron spectra. Dissociative and nondissociative single ionization of H₂ by 6MeV proton impact was described in a kinematically by determining momentum vectors of electron and H⁺ fragment of H₂⁺ target ion, respectively. The electron spectra exhibited role of autoionization of doubly and singly excited states of H₂. The doubly and singly excited states of H₂ involve coupling between electronic and nuclear motion of molecule.