arXiv subjects

U. D. Jentschura

Publications and source records attributed to U. D. Jentschura.

At least 91 records · Page 5Linked to original sources

arXiv2012

Pseudo-Hermitian Quantum Dynamics of Tachyonic Spin-1/2 Particles

We investigate the spinor solutions, the spectrum and the symmetry properties of a matrix-valued wave equation whose plane-wave solutions satisfy the superluminal (tachyonic) dispersion relation E^2 = p^2 - m^2, where E is the energy, p is the spatial momentum, and m is the mass of the particle. The equation reads (i gamma^mu partial_mu - gamma^5 m) psi = 0, where gamma^5 is the fifth current. The tachyonic equation is shown to be CP invariant, and T invariant. The tachyonic Hamiltonian H_5 = alpha.p + beta gamma^5 m breaks parity and is non-Hermitian but fulfills the pseudo-Hermitian property H_5(r) = P H^+_5(-r) P^{-1} = PP H^+_5(-r) PP^{-1} where P is the parity matrix and PP is the full parity transformation. The energy eigenvalues and eigenvectors describe a continuous spectrum of plane-wave solutions (which correspond to real eigenvalues for |p|>=m and evanescent waves, which constitute resonances and antiresonances with complex-conjugate pairs of resonance eigenvalues (for |p|<=m) . In view of additional algebraic properties of the Hamiltonian which supplement the pseudo-Hermiticity, the existence of a resonance energy eigenvalues E implies that E^*, -E, and -E^* also constitute resonance energies of H_5.

hep-ph↗

arXiv2012

Bound-free pair production in ultra-relativistic ion collisions at the LHC collider: Analytic approach to the total and differential cross sections

A theoretical investigation of the bound-free electron-positron pair production in relativistic heavy ion collisions is presented. Special attention is paid to the positrons emitted under large angles with respect to the beam direction. The measurement of these positrons in coincidence with the down--charged ions is in principle feasible by LHC experiments. In order to provide reliable estimates for such measurements, we employ the equivalent photon approximation together with the Sauter approach and derive simple analytic expressions for the differential pair--production cross section, which compare favorably to the results of available numerical calculations. Based on the analytic expressions, detailed calculations are performed for collisions of bare Pb$^{82+}$ ions, taking typical experimental conditions of the LHC experiments into account. We find that the expected count rate strongly depends on the experimental parameters and may be significantly enhanced by increasing the positron-detector acceptance cone.

hep-ph↗

arXiv2012

Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay

The quantum field theory of superluminal (tachyonic) particles is plagued with a number of problems, which include the Lorentz non-invariance of the vacuum state, the ambiguous separation of the field operator into creation and annihilation operators under Lorentz transformations, and the necessity of a complex reinterpretation principle for quantum processes. Another unsolved question concerns the treatment of subluminal components of a tachyonic wave packets in the field-theoretical formalism, and the calculation of the time-ordered propagator. After a brief discussion on related problems, we conclude that rather painful choices have to be made in order to incorporate tachyonic spin-1/2 particles into field theory. We argue that the field theory needs to be formulated such as to allow for localizable tachyonic particles, even if that means that a slight unitarity violation is introduced into the S matrix, and we write down field operators with unrestricted momenta. We find that once these choices have been made, the propagator for the neutrino field can be given in a compact form, and the left-handedness of the neutrino as well as the right-handedness of the antineutrino follow naturally. Consequences for neutrinoless double beta decay and superluminal propagation of neutrinos are briefly discussed.

hep-ph↗

arXiv2011

Einstein-Hopf drag, Doppler shift of thermal radiation and blackbody friction: A unifying perspective on an intriguing physical effect

The thermal friction force acting on an atom moving relative to a thermal photon bath has recently been calculated on the basis of the fluctuation-dissipation theorem. The thermal fluctuations of the electromagnetic field give rise to a drag force on an atom provided one allows for dissipation of the field energy via spontaneous emission. The drag force exists if the atomic polarizability has a nonvanishing imaginary part. Here, we explore alternative derivations. The damping of the motion of a simple harmonic oscillator is described by radiative reaction theory (result of Einstein and Hopf), taking into account the known stochastic fluctuations of the electromagnetic field. Describing the excitations of the atom as an ensemble of damped harmonic oscillators, we identify the previously found expressions as generalizations of the Einstein-Hopf result. In addition, we present a simple explanation for blackbody friction in terms of a Doppler shift of the thermal radiation in the inertial frame of the moving atom: The atom absorbs blue-shifted photons from the front and radiates off energy in all directions, thereby losing energy. The original plus the two alternative derivations provide for additional confirmation of an intriguing physical effect, and leave no doubt regarding its existence.

physics.atom-ph↗

arXiv2011

Semi-Analytic Approach to Higher-Order Corrections in Simple Muonic Bound Systems: Vacuum Polarization, Self-Energy and Radiative-Recoil

The current discrepancy of theory and experiment observed recently in muonic hydrogen necessitates a reinvestigation of all corrections to contribute to the Lamb shift in muonic hydrogen muH, muonic deuterium muD, the muonic 3He ion, as well as in the muonic 4He ion. Here, we choose a semi-analytic approach and evaluate a number of higher-order corrections to vacuum polarization (VP) semi-analytically, while remaining integrals over the spectral density of VP are performed numerically. We obtain semi-analytic results for the second-order correction, and for the relativistic correction to VP. The self-energy correction to VP is calculated, including the perturbations of the Bethe logarithms by vacuum polarization. Subleading logarithmic terms in the radiative-recoil correction to the 2S-2P Lamb shift of order alpha (Zalpha)^5 mu^3 ln(Zalpha)/(m_mu m_N) are also obtained. All calculations are nonperturbative in the mass ratio of orbiting particle and nucleus.

physics.atom-ph↗

arXiv2011

Numerical calculation of Bessel, Hankel and Airy functions

The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument is to be evaluated. The coefficients in the well-known uniform asymptotic expansions have a complex mathematical structure which involves Airy functions. For Bessel and Hankel functions, we present an adapted algorithm which relies on a combination of three methods: (i) numerical evaluation of Debye polynomials, (ii) calculation of Airy functions with special emphasis on their Stokes lines, and (iii) resummation of the entire uniform asymptotic expansion of the Bessel and Hankel functions by nonlinear sequence transformations. In general, for an evaluation of a special function, we advocate the use of nonlinear sequence transformations in order to bridge the gap between the asymptotic expansion for large argument and the Taylor expansion for small argument ("principle of asymptotic overlap"). This general principle needs to be strongly adapted to the current case, taking into account the complex phase of the argument. Combining the indicated techniques, we observe that it possible to extend the range of applicability of existing algorithms. Numerical examples and reference values are given.

math.NA↗

arXiv2011

Relativistic Reduced-Mass and Recoil Corrections to Vacuum Polarization in Muonic Hydrogen, Muonic Deuterium and Muonic Helium Ions

The reduced-mass dependence of relativistic and radiative effects in simple muonic bound systems is investigated. The spin-dependent nuclear recoil correction of order (Zalpha)^4 mu^3/m_N^2 is evaluated for muonic hydrogen and deuterium, and muonic helium ions (mu is the reduced mass and m_N is the nuclear mass). Relativistic corrections to vacuum polarization of order alpha (Zalpha)^4 mu 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 alpha (Zα)^5 ln^2(Zalpha) mu^2/m_N is obtained in leading logarithmic approximation. The results emphasize the need for a unified treatment of relativistic corrections to vacuum polarization in muonic hydrogen, muonic deuterium and muonic helium ions, where the mass ratio of the orbiting particle to the nuclear mass is larger than the fine-structure constant.

physics.atom-ph↗

arXiv2011

Black-Body Radiation Correction to the Polarizability of Helium

The correction to the polarizability of helium due to black-body radiation is calculated near room temperature. A precise theoretical determination of the black-body radiation correction to the polarizability of helium is essential for dielectric gas thermometry and for the determination of the Boltzmann constant. We find that the correction, for not too high temperature, is roughly proportional to a modified hyperpolarizability (two-color hyperpolarizability), which is different from the ordinary hyperpolarizability of helium. Our explicit calculations provide a definite numerical result for the effect and indicate that the effect of black-body radiation can be excluded as a limiting factor for dielectric gas thermometry using helium or argon.

physics.atom-ph↗

arXiv2011

Self-Energy Correction to the Hyperfine Splitting for Excited States

The self-energy corrections to the hyperfine splitting is evaluated for higher excited states in hydrogenlike ions, using an expansion in the binding parameter Zalpha, where Z is the nuclear charge number, and alpha is the fine-structure constant. We present analytic results for D, F and G states, and for a number of highly excited Rydberg states with principal quantum numbers in the range 13 <= n <= 16, and orbital angular momenta l = n-2 and l = n-1. A closed-form, analytic expression is derived for the contribution of high-energy photons, valid for any state with l <= 2$ and arbitrary n, l and total angular momentum j. The low-energy contributions are written in the form of generalized Bethe logarithms and evaluated for selected states.

physics.atom-ph↗

arXiv2011

Compton Upconversion of Twisted Photons: Backscattering of Particles with Non-Planar Wave Functions

Twisted photons are not plane waves, but superpositions of plane waves with a defined projection hbar m of the orbital angular momentum onto the propagation axis (m is integer and may attain values m >> 1). Here, we describe in detail the possibility to produce high-energy twisted photons by backward Compton scattering of twisted laser photons on ultra-relativistic electrons with a Lorentz-factor gamma=E/(m_e c^2) >> 1. When a twisted laser photon with the energy hbar omega ~ 1 eV performs a collision with an electron and scatters backward, the final twisted photon conserves the angular momentum m, but its energy hbar omega' is increased considerably: omega'/omega=4 gamma^2/(1+x), where x=4E hbar omega/(m_e c^2)^2. The S matrix formalism for the description of scattering processes is particularly simple for plane waves with definite 4-momenta. However, in the considered case, this formalism must be enhanced because the quantum state of twisted particles cannot be reduced to plane waves. This implies that the usual notion of a cross section is inapplicable, and we introduce and calculate an averaged cross section for a quantitative description of the process. The energetic upconversion of twisted photons may be of interest for experiments with the excitation and disintegration of atoms and nuclei, and for studying the photo-effect and pair production off nuclei in previously unexplored regimes.

physics.acc-ph↗

arXiv2011

Generation of High-Energy Photons with Large Orbital Angular Momentum by Compton Backscattering

Usually, photons are described by plane waves with a definite 4-momentum. In addition to plane-wave photons, "twisted photons" have recently entered the field of modern laser optics; these are coherent superpositions of plane waves with a defined projection hbar*m of the orbital angular momentum onto the propagation axis, where m is integer. In this paper, we show that it is possible to produce high-energy twisted photons by Compton backscattering of twisted laser photons off ultra-relativistic electrons. Such photons may be of interest for experiments related to the excitation and disintegration of atoms and nuclei, and for studying the photo-effect and pair production off nuclei in previously unexplored experimental regimes.

physics.acc-ph↗

arXiv2010

Proton Radius, Darwin-Foldy Term and Radiative Corrections

We discuss the role of the so-called Darwin-Foldy term in the evaluation of the proton and deuteron charge radii from atomic hydrogen spectroscopy and nuclear scattering data. The question of whether this term should be included or excluded from the nuclear radius has been controversially discussed in the literature. We attempt to clarify which literature values correspond to which conventions. A detailed discussion of the conventions appears useful because a recent experiment [R. Pohl et al., Nature vol. 466, p. 213 (2010)] has indicated that there is a discrepancy between the proton charge radii inferred from ordinary ("electronic") atomic hydrogen and muonic hydrogen. We also investigate the role of quantum electrodynamic radiative corrections in the determination of nuclear radii from scattering data, and propose a definition of the nuclear self energy which is compatible with the subtraction of the radiative corrections in scattering experiments.

physics.atom-ph↗

arXiv2010

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 2S-2P 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.

hep-ph↗

arXiv2010

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 vol. 466, p. 213 (2010)], we reexamine the theory on which the quantum electrodynamic (QED) predictions are based. In particular, we update the theory of the 2P-2S 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 2S-2P transition is given.

hep-ph↗

arXiv2010

Imaginary Cubic Perturbation: Numerical and Analytic Study

The analytic properties of the ground state resonance energy E(g) of the cubic potential are investigated as a function of the complex coupling parameter g. We explicitly show that it is possible to analytically continue E(g) by means of a resummed strong coupling expansion, to the second sheet of the Riemann surface, and we observe a merging of resonance and antiresonance eigenvalues at a critical point along the line arg(g) = 5 pi/4. In addition, we investigate the convergence of the resummed weak-coupling expansion in the strong coupling regime, by means of various modifications of order-dependent mappings (ODM), that take special properties of the cubic potential into account. The various ODM are adapted to different regimes of the coupling constant. We also determine a large number of terms of the strong coupling expansion by resumming the weak-coupling expansion using the ODM, demonstrating the interpolation between the two regimes made possible by this summation method.

math-ph↗

arXiv2010

Order-dependent mappings: strong coupling behaviour from weak coupling expansions in non-Hermitian theories

A long time ago, it has been conjectured that a Hamiltonian with a potential of the form x^2+i v x^3, v real, has a real spectrum. This conjecture has been generalized to a class of so-called PT symmetric Hamiltonians and some proofs have been given. Here, we show by numerical investigation that the divergent perturbation series can be summed efficiently by an order-dependent mapping (ODM) in the whole complex plane of the coupling parameter v^2, and that some information about the location of level crossing singularities can be obtained in this way. Furthermore, we discuss to which accuracy the strong-coupling limit can be obtained from the initially weak-coupling perturbative expansion, by the ODM summation method. The basic idea of the ODM summation method is the notion of order-dependent "local" disk of convergence and analytic continuation by an order-dependent mapping of the domain of analyticity augmented by the local disk of convergence onto a circle. In the limit of vanishing local radius of convergence, which is the limit of high transformation order, convergence is demonstrated both by numerical evidence as well as by analytic estimates.

math-ph↗

arXiv2010

Proposal for the determination of nuclear masses by high-precision spectroscopy of Rydberg states

The theoretical treatment of Rydberg states in one-electron ions is facilitated by the virtual absence of the nuclear-size correction, and fundamental constants like the Rydberg constant may be in the reach of planned high-precision spectroscopic experiments. The dominant nuclear effect that shifts transition energies among Rydberg states therefore is due to the nuclear mass. As a consequence, spectroscopic measurements of Rydberg transitions can be used in order to precisely deduce nuclear masses. A possible application of this approach to the hydrogen and deuterium, and hydrogen-like lithium and carbon is explored in detail. In order to complete the analysis, numerical and analytic calculations of the quantum electrodynamic (QED) self-energy remainder function for states with principal quantum number n=5,...,8 and with angular momentum L=n-1 and L=n-2 are described (j = L +/- 1/2).

physics.atom-ph↗

arXiv2010

Fundamental constants and tests of theory in Rydberg states of one-electron ions

The nature of the theory of circular Rydberg states of hydrogenlike ions allows highly-accurate predictions to be made for energy levels. In particular, uncertainties arising from the problematic nuclear size correction which beset low angular-momentum states are negligibly small for the high angular-momentum states. The largest remaining source of uncertainty can be addressed with the help of quantum electrodynamics (QED) calculations, including a new nonperturbative result reported here. More stringent tests of theory and an improved determination of the Rydberg constant may be possible if predictions can be compared with precision frequency measurements in this regime. The diversity of information can be increased by utilizing a variety of combinations of ions and Ryberg states to determine fundamental constants and test theory.

physics.atom-ph↗