Vacuum Polarization Potential Research Articles

The coulomb glory effect in collisions of antiprotons with heavy ions

The Coulomb glory effect in the back scattering of antiprotons with energies of from 100 eV to 3 keV from a bare nucleus of uranium and from uranium ions with closed shells is considered in terms of nonrelativistic and relativistic quantum theory. The appearance of Coulomb glory in collisions with multiply charged ions is caused by nucleus charge screening by filled electron shells. In scattering from a bare nucleus, the effect appears because of the screening properties of the vacuum polarization potential.

Tests of fundamental theories with heavy ions at low-energy regime

The current status of theoretical investigations of spectroscopic properties and fundamental interactions in highly charged ions is reviewed. Laying special attention on tests of quantum electrodynamics at strong fields recent progress in calculations of energy levels, hyperfine splitting and g factor values is reported. The parity nonconservation effect on the laser-induced \(2^3S_1-2^1S_0\) transition in heavy He-like ions is studied, which could serve as test scenario for the Standard Model in low-energy atomic physics. The Coulomb glory effect in collisions of antiprotons with heavy ions is considered. It is emphasized that observation of this effect in collisions of antiprotons with bare nuclei would exhibit the screening properties of the vacuum polarization potential. A new approach to the description of dynamic atomic processes in low-energy heavy-ion collisions is presented. As a first application of this approach, the charge transfer probabilities for the U91 + (1s) – U92 + collision are evaluated.

Lamb shift in muonic hydrogen—I. Verification and update of theoretical predictions

In view of the recently observed discrepancy of theory and experiment for muonic hydrogen [R. Pohl et al., Nature 466 (2010) 213], we reexamine the theory on which the quantum electrodynamic (QED) predictions are based. In particular, we update the theory of the 2 P–2 S Lamb shift, by calculating the self-energy of the bound muon in the full Coulomb + vacuum polarization (Uehling) potential. We also investigate the relativistic two-body corrections to the vacuum polarization shift, and we analyze the influence of the shape of the nuclear charge distribution on the proton radius determination. The uncertainty associated with the third Zemach moment 〈 r 3〉 2 in the determination of the proton radius from the measurement is estimated. An updated theoretical prediction for the 2 S–2 P transition is given.

Lamb shift in muonic hydrogen—II. Analysis of the discrepancy of theory and experiment

Currently, both the g factor measurement of the muon as well as the Lamb shift 2 S–2 P measurement in muonic hydrogen are in disagreement with theory. Here, we investigate possible theoretical explanations, including proton structure effects and small modifications of the vacuum polarization potential. In particular, we investigate a conceivable small modification of the spectral function of vacuum polarization in between the electron and muon energy scales due to a virtual millicharged particle and due to an unstable vector boson originating from a hidden sector of an extended standard model. We find that a virtual millicharged particle which could explain the muonic Lamb shift discrepancy alters theoretical predictions for the muon anomalous magnetic moment by many standard deviations and therefore is in conflict with experiment. Also, we find no parameterizations of an unstable virtual vector boson which could simultaneously explain both “muonic” discrepancies without significantly altering theoretical predictions for electronic hydrogen, where theory and experiment currently are in excellent agreement. A process-dependent correction involving electron screening is evaluated to have the right sign and order-of-magnitude to explain the observed effect in muonic hydrogen. Additional experimental evidence from light muonic atoms and ions is needed in order to reach further clarification.

Electron-impact ionization of hydrogenlike ions in QED theory

Relativistic cross sections for electron-impact ionization including quantum electrodynamic effects are studied for hydrogenlike ions in the two-potential formalism. Results are compared with other theoretical calculations and experimental data. Effects of the transverse-photon interaction as well as vacuum polarization potential between charges are analyzed. Systematic behaviors along the H-isoelectronic sequence are summarized.

Coulomb glory in low-energy antiproton scattering by a heavy nucleus: screening effect of vacuum polarization

Backward scattering of antiprotons by bare uranium is studied theoretically for antiproton energies within the interval 100 eV–1 keV. An observable maximum of the differential cross section in the backward direction (Coulomb glory) at some energies of the incident particle is revealed. The effect is due to the screening properties of the vacuum polarization potential and can be regarded as a manifestation of the vacuum polarization in non-relativistic collisions of heavy particles. Experimental observation can become feasible with new facilities for antiproton and ion research at GSI.

Backward scattering of low-energy antiprotons by highly charged and neutral uranium: Coulomb glory

Collisions of antiprotons with He-, Ne-, Ni-like, bare, and neutral uranium are studied theoretically for scattering angles close to $180\ifmmode^\circ\else\textdegree\fi{}$ and antiproton energies in the interval from $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ to $10\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. We investigate the Coulomb glory effect which is caused by a screening of the Coulomb potential of the nucleus and results in a prominent maximum of the differential cross section in the backward direction at some energies of the incident particle. We found that for larger numbers of electrons in the ion the effect becomes more pronounced and shifts to higher energies of the antiproton. On the other hand, a maximum of the differential cross section in the backward direction can also be found in the scattering of antiprotons on a bare uranium nucleus. The latter case can be regarded as a manifestation of the screening property of the vacuum-polarization potential in nonrelativistic collisions of heavy particles.

Laser-dressed vacuum polarization in a Coulomb field

We investigate quantum electrodynamic effects under the influence of an external, time-dependent electromagnetic field, which mediates dynamic modifications of the radiative corrections. Specifically, we consider the quantum electrodynamic vacuum-polarization tensor under the influence of two external background fields: a strong laser field and a nuclear Coulomb field. We calculate the charge and current densities induced by a nuclear Coulomb field in the presence of a laser field. We find the corresponding induced scalar and vector potentials. The induced potential, in first-order perturbation theory, leads to a correction to atomic energy levels. The external laser field breaks the rotational symmetry of the system. Consequently, the induced charge density is not spherically symmetric, and the energy correction therefore leads to a ``polarized Lamb shift.'' In particular, the laser generates an additional potential with a quadrupole moment. The corresponding laser-dressed vacuum-polarization potential behaves like $1∕{r}^{3}$ at large distances, unlike the Uehling potential, which vanishes exponentially for large $r$. The energy corrections are of the same order of magnitude for hydrogenic levels, irrespective of the angular momentum quantum number. The induced current leads to a transition dipole moment which oscillates at the second harmonic of the laser frequency and is mediated by second-order harmonic generation in the vacuum-polarization loop. In the far field, at distances $r⪢1∕\ensuremath{\omega}$ from the nucleus ($\ensuremath{\omega}$ is the laser frequency), the laser induces mutually perpendicular electric and magnetic fields, which give rise to an energy flux that corresponds to photon fusion leading to the generation of real photons, again at the second harmonic of the laser. Our investigation might be useful for other situations where quantum field theoretic phenomena are subjected to external fields of a rather involved structure.

Binding energy of the positronium negative ion: relativistic and QED energy shifts

The leading relativistic and QED corrections to the ground-state energy of the three-body system e−e+e− are calculated numerically using a Hylleraas correlated basis set. The accuracy of the nonrelativistic variational ground state is discussed with respect to the convergence of the energy with increasing size of the basis set, and also with respect to the variance of the Hamiltonian. The corrections to this energy include the lowest order Breit interaction, the vacuum polarization potential, one and two photon exchange contributions, the annihilation interaction and spin–spin contact terms. The relativistic effects and the residual interactions considered here decrease the one-electron binding energy from the nonrelativistic value of 0.012 005 070 232 980 107 69(28) au to 0.011 981 051 246(2) au (78 831 530 ± 5 MHz).

Exact two-loop vacuum polarization correction to the Lamb shift in hydrogenlike ions

We present a calculation scheme for the two-loop vacuum polarization correction of order \(\) to the Lamb shift of hydrogenlike high-Z atoms. The interaction with the external Coulomb field is taken into account to all orders in \(\). By means of a modified potential approach the problem is reduced to the evaluation of effective one-loop vacuum polarization potentials. An expression for the energy shift is deduced within the framework of partial wave decomposition performing appropriate subtractions. Exact results for the two-loop vacuum polarization contribution to the Lamb shift of K- and L-shell electron states in hydrogenlike Lead and Uranium are presented.

Two-loop ladder diagram for the vacuum polarization contribution in hydrogen-like ions

We discuss a calculation scheme for the two-loop ladder graph vacuum polarization contribution to the Lamb shift in hydrogen-like heavy ions. It is obtained by including the vacuum polarization potential self-consistently into the Dirac equation. Numerical values are presented for all systems with nuclear charge numbers . Possible limitations of our method are mentioned. In addition, we also present numerical values for the Wichmann - Kroll contribution to the Lamb shift for all hydrogen-like systems utilizing an extended nuclear charge distribution in the Z-range 30 - 100.

Vacuum-polarization potentials of extended nuclear charges

FORTRAN program VACPOL is presented that calculates accurately and efficiently the first-order vacuum-polarization potential of two electric charges as a function of their separation. The charges can be extended, with distributions specified by density functions that are most often used to model the distribution of charge in atomic nuclei. The code employs analytical methods of calculation, utilizing a Fourier-Bessel expansion of the potential and an analytical evaluation of the finite-radius Fourier transform of the point-charge Uehling potential.

Analytical evaluation of the finite-radius Fourier transform of the Uehling potential

The finite-radius Fourier transform of the first-order vacuum-polarization correction to the Coulomb potential of a point charge, required for a Fourier-Bessel evaluation of vacuum-polarization potentials of extended charges, is calculated by an efficient analytical method.

The ω− exotic atom

The energy levels of the ω − exotic atom formed by the ω − hyperon and a heavy nucleus are computed with accuracy ( v/ c) 2 and with account taken of the Uehling vacuum polarization potential. The possibility of precise measurements of the mass, magnetic, and quadrupole moments of the ω − hyperon by observing the X-ray transitions of the ω − hyperon captured to the atomic orbits is discussed.

Vacuum polarization in sub-coulomb 12C-12C scattering (II)

In order to extract the effect of vacuum polarization from 12C-12C elastic scattering data, a detailed theoretical study of the low-energy Mott cross section is performed. It is shown that the contributions of nuclear interaction, Coulomb excitation, bremsstrahlung can be neglected, while radiative corrections and nuclear polarizability can be described by a small additional potential. Screening by atomic electrons is corrected by a screening function, which acts on all potentials. Relativistic effects are accounted for using the “Todorov equation”. In order to overcome numerical difficulties for very long range potentials a WKB approximation and a semiquantal approach are discussed and compared. The study shows that the first-order vacuum-polarization potential contributes most to the correction of the cross section. All other contributions are at least one order of magnitude smaller.

The effects of vacuum polarization on thermonuclear reaction rates

view Abstract Citations (8) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Effects of Vacuum Polarization on Thermonuclear Reaction Rates Gould, Robert J. Abstract Added to the pure Coulomb potential, the contribution from vacuum polarization increases the barrier, reducing the wave function (u) for reacting nuclei within the range of nuclear forces. The cross section and reaction rate are then reduced accordingly by a factor proportional to u squared. The effect is treated by evaluating the vacuum polarization potential as a small correction to the Coulomb term, then computing u in a WKB formulation. The calculation is done analytically employing the small r power-series expansion for the Uehling potential to express the final result in terms of convenient parameters. At a temperature of 1.4 x 10 to the 7th K the (negative) correction is 1.3 percent for the fundamental fusion process p + p yields d + e(+) + nu. Publication: The Astrophysical Journal Pub Date: November 1990 DOI: 10.1086/169366 Bibcode: 1990ApJ...363..574G Keywords: Nuclear Astrophysics; Polarization Characteristics; Stellar Physics; Thermonuclear Reactions; Computational Astrophysics; Coulomb Collisions; Wentzel-Kramer-Brillouin Method; Astrophysics; NUCLEAR REACTIONS; QUANTUM MECHANICS full text sources ADS |

Phase shift analysis of all proton-proton scattering data below Tlab=350 MeV.

As a continuation of our 0--30 MeV analysis we present a multienergy phase shift analysis of all {ital pp} scattering data below {ital T}{sub lab}=350 MeV. In the description of all partial waves we take exactly into account the long-range potential consisting of the improved Coulomb potential (including the magnetic moment interaction), the vacuum polarization potential, and the tail of the one-pion-exchange potential. To describe the short-range interaction in the lower partial waves we use a {ital P}-matrix parametrization. The intermediate partial waves are treated either by optimal mapping techniques or by using the Nijmegen soft-core potential. The latter gives a better description of the data. The final data set comprises 1626 scattering observables. The best fit to this final data set results in {chi}{sup 2}/{ital N}{sub df}=1.117, where {ital N}{sub df}=1576 is the number of degrees of freedom. The {ital pp}{pi}{sup 0} pseudovector coupling constant is determined to be {ital f}{sub 0}{sup 2}=(74.9{plus minus}0.7){times}10{sup {minus}3}. Single-energy phase shifts and errors are also given.

K�ll�n-Sabry contribution to the lamb-shift in hydrogen-like atoms

The vacuum polarization potential of order α2(Zα) is evaluated. We tabulate the contribution to the Lamb-shift of K- and L-shell electrons in hydrogen-like atoms with 1≤Z≤110.

On the connection between the vacuum polarization potential in muonic atoms andg-2 of the muon

A simple connection, between the vacuum polarization potential used in muonic atoms and the muon anomaly arising from the second-order vertex graph with electron vacuum polarization insertions, is established. In particular, the leading log-term and the orderme/mμ term are essentially the same in the two cases. We make use of this connection to determine the vacuum polarization potential in order α3(Zα).

Effect of vacuum polarization on the excitation of hydrogen atom by electron impact

The vacuum polarization potential is included in the interaction Hamiltonian for 1S − 2S excitation of the hydrogen atom by electron impact. The excitation amplitude calculated field theoretically is found to be lowered by urn:x-wiley:01611712:media:ijmm467403:ijmm467403-math-0001 where t2 = 4|P−Q|2, P and Q being the momenta of the incident and scattered electrons respectively.