arXiv subjects

U. D. Jentschura

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

At least 19 recordsLinked to original sources

arXiv2026

Temperature-Dependent Dielectric Function of Calcium Fluoride

The optical properties of calcium fluoride (fluorspar, CaF2) are mainly determined by a strongly temperature-dependent giant infrared (IR) peak, and a series of nearly temperature-independent ultraviolet (UV) peaks. We find that the temperature dependence of the IR peak can be modeled, to good accuracy, by a radiation-reaction improved coupled-oscillator model (RRCO model), with temperature-dependent parameters. For the UV peaks, we find a convenient functional form which covers both the real as well as the imaginary parts of the dielectric function and provide a comparison to first-principles calculations based on time-dependent density-functional theory (TDDFT). The result is a compact functional form for the dielectric function of undoped CaF2 applicable to wide frequency and temperature ranges (0 < hbar omega < 60 eV, 22C < T < 500C). With the help of the temperature-dependent dielectric function, we obtain temperature-dependent values of the short-range and long-range asymptotics of atom-surface interactions with CaF2, for hydrogen, as well as ground-state and metastable helium. The giant IR absorption peak of CaF2 is shown to lead to a delayed onset of the fully retarded Casimir--Polder limit in the long-range interaction regime. We present arguments supporting a more general applicability of the RRCO model to materials of general interest.

cond-mat.mtrl-sci↗

arXiv2026

Precision Spectroscopy of 2S-nS Transitions in Atomic Hydrogen: A Determination of the Proton Charge Radius

We present absolute frequency measurements of 2S_{1/2}-nS_{1/2} two-photon transitions with n = 8, 9, and 10 in a cryogenic beam of atomic hydrogen. Each transition has been measured with a fractional uncertainty of approximately 2.6*10^(-12). Combining the results from this work and the 1S_{1/2}-2S_{1/2} transition frequency, we extract a root-mean-square proton radius of r_p = 0.8433(31) fm and a Rydberg frequency of cR_{\infty} = 3,289,841,960,252.9(9.7) kHz. These are in good agreement with the CODATA 2022 recommended values.

physics.atom-ph↗

arXiv2026

Tensor Polarizability of the Nucleus and Angular Mixing in Muonic Deuterium

We investigate the effects of the tensor polarizability of a nucleus on the bound-state energy levels, and obtain a general formula for the contribution of the tensor polarizability to the energy levels in two-body bound systems. In particular, it is demonstrated that the tensor polarizability leads to mixing between states with different orbital angular momenta. The effect of tensor polarizability is evaluated for the hyperfine-structure components of P states and for the mixing of S and D states in muonic deuterium.

physics.atom-ph↗

arXiv2026

Relativistic and Recoil Corrections to Light-Fermion Vacuum Polarization for Bound Systems of Spin-0, Spin-1/2, and Spin-1 Particles

In bound systems whose constituent particles are heavier than the electron, the dominant radiative correction to energy levels is given by light-fermion (electronic) vacuum polarization. In consequence, relativistic and recoil corrections to the one-loop vacuum-polarization correction are phenomenologically relevant. Here, we generalize the treatment, previously accomplished for systems with orbiting muons, to bound systems of constituents with more general spins: spin-0, spin-1/2, and spin-1. We discuss the application of our more general expressions to various systems of interest, including spinless systems (pionium), muonic hydrogen and deuterium, and devote special attention to the excited non-S states of deuteronium, the bound system of a deuteron and its antiparticle. The obtained energy corrections are of order alpha^5*m_r, where alpha is the fine-structure constant and m_r is the reduced mass.

hep-ph↗

arXiv2025

Short-Range Hard-Sphere Potential and Coulomb Interaction: Deser-Trueman Formula for Rydberg States of Exotic Atomic Systems

In exotic atomic systems with hadronic constituent particles, it is notoriously difficult to estimate the strong-interaction correction to energy levels. It is well known that, due to the strength of the nuclear interaction, the problem cannot be treated on the basis of Wigner-Brioullin perturbation theory. Recently, high-angular-momentum Rydberg states of exotic atomic systems with hadronic constituents have been identified as promising candidates for the search of New Physics in the low-energy sector of the Standard Model. In order to render this endeavor feasible, it is necessary to estimate the strong-interaction correction to the atomic energy levels. We thus derive a generalized Deser-Trueman formula for the induced energy shift for a general hydrogenic bound state with principal quantum number $n$ and orbital angular momentum quantum number~$\ell$, and find that the energy shift is given by the formula delta E = 2 alpha_{n, L} beta_L (a_h/a_0)^(2 L + 1) E_h/n^3, where alpha_{n,0} = 1, alpha_{n,L} is the product from s=1 to s=L of the expression (s^(-2) - n^(-2)), beta_L = (2 L + 1)/[(2 L + 1)!!]^2, where E_h is the Hartree energy, a_h is the hadronic radius and a_0 is the generalized Bohr radius. The square of the double factorial, [(2\ell + 1)!!]^2, in the denominator implies a drastic suppression of the effect for higher angular momenta.

physics.atom-ph↗

arXiv2025

Bound Deuteron-Antideuteron System (Deuteronium): Leading Radiative and Internal-Structure Corrections to Bound-State Energies

We evaluate the energy levels of the deuteronium bound system, which consists of a deuteron and an antideuteron, with a special emphasis on states with nonvanishing orbital angular momenta. The excited atomic bound states of deuteronium constitute probes for the understanding of higher-order quantum electrodynamic corrections for spin-1 particles in a bound system where the typical field strength of the binding Coulomb field (at a distance of the generalized Bohr radius) exceeds Schwinger's critical field strength. For states with nonvanishing angular momenta, effects due to the internal structure of the deuteron and virtual annihilation contributions are highly suppressed. Relevant transitions are found to be in a frequency range accessible by standard laser spectroscopic techniques. We evaluate the leading and next-to-leading energy corrections of orders alpha^3 m_d and alpha^4 m_d , where alpha is the fine-structure constant and m_d is the deuteron mass, and also investigate internal-structure corrections: hadronic vacuum polarization, finite-size effects, and strong-interaction corrections.

hep-ph↗

arXiv2025

Interferometric Differential High-Frequency Lock-In Probe for Laser-Induced Vacuum Birefringence

We propose a measurement of laser-induced vacuum birefringence through the use of pulsed lasers coupled to femtosecond optical enhancement cavities. This measurement technique features cavity-enhanced pump and probe pulses, as well as an independent control pulse. The control pulse allows for a differential measurement where the final signal is obtained using high-frequency lock-in detection, greatly mitigating time-dependent cavity birefringence as an important and possibly prohibitive systematic effect. In addition, the method features the economical use of laser power, and results in a relatively simple experimental setup.

physics.optics↗

arXiv2025

Coupled Oscillators and Dielectric Function

A generalized Sellmeier model, also referred to as the Lorentz-Dirac model, has been used for the description of the dielectric function of a number of technologically important materials in the literature. This model represents the frequency-dependent dielectric function as a sum over Green functions of classical damped harmonic oscillators, much in analogy with the functional form used for the dynamic polarizability of an atom, but with one important addition, namely, a complex-valued oscillator strength in the numerator. Here, we show that this generalized functional form can be justified based on the response function of coupled damped oscillators. The encountered analogies suggest an explanation for the generally observed success of the Lorentz--Dirac model in describing the dielectric function of crystals of consummate technological significance.

cond-mat.mtrl-sci↗

arXiv2024

Irreducible Three-Loop Vacuum-Polarization Correction in Muonic Bound Systems

Three-loop electronic vacuum-polarization corrections due to irreducible diagrams are evaluated for two-body muonic ions with nuclear charge numbers 1 <= Z <= 6. The corrections are of order alpha^3 (Zalpha)^2 m_r, where alpha is the fine-structure constant and m_r is the reduced mass. Numerically, the energy corrections are found to be of the same order-of-magnitude as the largest of the order alpha^2 (Zalpha)^6 m_r corrections, and are thus phenomenologically interesting. Our method of calculation eliminates numerical uncertainty encountered in other approaches.

hep-ph↗

arXiv2024

Reexamination of vacuum-polarization corrections to the self-energy in muonic bound systems

In muonic bound systems, the dominant radiative correction is due to vacuum polarization. Yet, for the interpretation of precision experiments, self-energy effects are also important. In turn, additional vacuum-polarization loops perturb the self-energy. Here, we show that combined self-energy vacuum-polarization effects can perturb the bound-state self-energy at the percent level in one-muon bound systems with nuclear charges Z = 1-6. We also update previous treatments of the corrections for muonic hydrogen, muonic deuterium, and muonic helium bound systems.

hep-ph↗

arXiv2024

Enhanced and Generalized One-Step Neville Algorithm: Fractional Powers and Access to the Convergence Rate

The recursive Neville algorithm allows one to calculate interpolating functions recursively. Upon a judicious choice of the abscissas used for the interpolation (and extrapolation), this algorithm leads to a method for convergence acceleration. For example, one can use the Neville algorithm in order to successively eliminate inverse powers of the upper limit of the summation from the partial sums of a given, slowly convergent input series. Here, we show that, for a particular choice of the abscissas used for the extrapolation, one can replace the recursive Neville scheme by a simple one-step transformation, while also obtaining access to subleading terms for the transformed series after convergence acceleration. The matrix-based, unified formulas allow one to estimate the rate of convergence of the partial sums of the input series to their limit. In particular, Bethe logarithms for hydrogen are calculated to 100 decimal digits. Generalizations of the method to series whose remainder terms can be expanded in terms of inverse factorial series, or series with half-integer powers, are also discussed.

math.NA↗

arXiv2024

Dimensional Regularization and Two-Loop Vacuum Polarization Operator: Master Integrals, Analytic Results and Energy Shifts

We present a complete reevaluation of the irreducible two-loop vacuum-polarization correction to the photon propagator in quantum electrodynamics, i.e. with an electron-positron pair in the fermion propagators. The integration is carried out by reducing the integrations to a limited set of master integrals, which are calculated using integration-by-parts identities. Dimensional regularization is used in D = 4-2*epsilon dimensions, and on-mass shell renormalization is employed. The one-loop effect is given to order epsilon, to be combined with the 1/epsilon divergence of the two-loop amplitude. Master integrals are given. Final evaluations of two-loop energy shifts for 1S, 2S, and 2P states are done analytically, and results are presented, with an emphasis on muonic hydrogen. For relativistic Dirac-Coulomb reference states, higher-order coefficients are obtained for the Zalpha-expansion. We compare the results obtained to the existing literature.

hep-ph↗

arXiv2024

Perturbative versus Non-Perturbative Renormalization

Approximated functional renormalization group (FRG) equations lead to regulator-dependent $β$-functions, in analogy to the scheme-dependence of the perturbative renormalization group (pRG) approach. A scheme transformation redefines the couplings to relate the $β$-functions of the FRG method with an arbitrary regulator function to the pRG ones obtained in a given scheme. Here, we consider a periodic sine-Gordon scalar field theory in $d=2$ dimensions and show that the relation of the FRG and pRG approaches is intricate. Although, both the FRG and the pRG methods are known to be sufficient to obtain the critical frequency $β_c^2 =8π$ of the model independently of the choice of the regulator and the renormalization scheme, we show that one has to go beyond the standard pRG method (e.g., using an auxiliary mass term) or the Coulomb-gas representation in order to obtain the $β$-function of the wave function renormalization. This aspect makes the scheme transformation non-trivial. Comparing flow equations of the two-dimensional sine-Gordon theory without any scheme-transformation, i.e., redefinition of couplings, we find that the auxiliary mass pRG $β$-functions of the minimal subtraction scheme can be recovered within the FRG approach with the choice of the power-law regulator with $b=2$, therefore constitutes a preferred choice for the comparison of FRG and pRG flows.

hep-th↗

arXiv2024

Retardation Effects in Atom-Wall Interactions

The onset of retardation effects in atom-wall interactions is studied. It is shown that the transition range from the 1/z^3 short-range (van der Waals) interaction to the 1/z^4 long-range (Casimir) retarded interaction critically depends on the atomic properties and on the dielectric function of the material. For simple non-alkali atoms (e.g., ground-state hydrogen and ground-state helium) interacting with typical dielectric materials such as intrinsic silicon, the transition to the retarded regime is shown to proceed at a distance of about 10 nm (200 Bohr radii). This is much shorter than typical characteristic absorption wavelengths of solids. Larger transition regimes are obtained for atoms with a large static polarizability such as metastable helium. We present a simple estimate for the critical distance, z_cr=137*(α(0)/Z)^(1/2) atomic units, where alpha(0) is the static polarizability (expressed in atomic units) and Z is the number of electrons of the atom.

cond-mat.other↗

arXiv2022

Foldy-Wouthuysen Transformation in Strong Magnetic Fields and Relativistic Corrections for Quantum Cyclotron Energy Levels

We carry out a direct, iterative Foldy--Wouthuysen transformation of a general Dirac Hamiltonian coupled to an electromagnetic field, including the anomalous magnetic moment. The transformation is carried out through an iterative disentangling of the particle and antiparticle Hamiltonians, in the expansion for higher orders of the momenta. The time-derivative term from the unitary transformation is found to be crucial in supplementing the transverse component of the electric field in higher orders. Final expressions are obtained for general combined electric and magnetic fields, including strong magnetic fields. The time-derivative of the electric field is shown to enter only in the seventh order of the fine-structure constant if the transformation is carried out in the standard fashion. We put special emphasis on the case of strong fields, which are important for a number of applications, such as electrons bound in Penning traps.

physics.atom-ph↗

arXiv2022

Quantum Electrodynamics of Dicke States: Resonant One-Photon Exchange and Entangled Decay Rate

We calculate the one-photon exchange contribution to the interatomic interaction potential between electrically neutral, identical atoms, one of which is assumed to be in an excited state, by matching the scattering matrix (S matrix) element with the effective Hamiltonian. This approach allows us to use covariant perturbation theory, where the two possible time orderings of emission and absorption are summarized in a single Feynman amplitude. Our results encompass the full retardation correction to the one-photon exchange van-der-Waals potential. We employ the temporal gauge for the virtual photon propagator. Based on the Feynman prescription, we obtain the imaginary part of the interaction energy, which leads to an interaction-induced correction to the decay rate. Our results lead to precise formulas for the distance-dependent enhancement and suppression of the decay rates of entangled superradiant and subradiant Dicke state, as a function of the interatomic distance. We apply the result to an example calculation involving two hydrogen atoms, one of which is in the ground state, the other in an excited P state.

physics.atom-ph↗

arXiv2022

Antimatter Free-Fall Experiments and Charge Asymmetry

We propose a method by which one could use modified antimatter gravity experiments in order to perform a high-precision test of antimatter charge neutrality. The proposal is based on the application of a strong, external, vertically oriented electric field during an antimatter free-fall gravity experiment in the gravitational field of the Earth. The proposed experimental setup has the potential to drastically improve the limits on the charge-asymmetry parameter ${\overline ε}_q$ of antimatter. On the theoretical side, we analyze possibilities to describe a putative charge-asymmetry of matter and antimatter, proportional to the parameters $ε_q$ and ${\overline ε}_q$, by Lagrangian methods. We found that such an asymmetry could be described by four-dimensional Lorentz-invariant operators that break CPT without destroying the locality of the field theory. The mechanism involves an interaction Lagrangian with field operators decomposed into particle or antiparticle field contributions. Our Lagrangian is otherwise Lorentz, as well as PT invariant. Constraints to be derived on the parameter ${\overline ε}_q$ do not depend on the assumed theoretical model.

hep-ph↗

arXiv2022

Temperature-dependent dielectric function of intrinsic silicon: Analytic models and atom-surface potentials

The optical properties of monocrystalline, intrinsic silicon are of interest for technological applications as well as fundamental studies of atom-surface interactions. For an enhanced understanding, it is of great interest to explore analytic models which are able to fit the experimentally determined dielectric function $ε(T_Δ, ω)$, over a wide range of frequencies and a wide range of the temperature parameter $T_Δ= (T-T_0)/T_0$, where $T_0 = 293\,{\rm K}$ represents room temperature. Here, we find that a convenient functional form for the fitting of the dielectric function of silicon involves a Lorentz-Dirac curve with a complex, frequency-dependent amplitude parameter, which describes radiation reaction. We apply this functional form to the expression $[ε(T_Δ, ω) -1]/[ ε(T_Δ, ω)+2]$, inspired by the Clausius-Mossotti relation. With a very limited set of fitting parameters, we are able to represent, to excellent accuracy, experimental data in the (angular) frequency range $0 < ω< 0.16 \, {\rm a.u.}$ and $0< T_Δ< 2.83$, corresponding to the temperature range $ 293\,{\rm K} < T < 1123\, {\rm K}$. Using our approach, we evaluate the short-range $C_3$ and the long-range $C_4$ coefficients for the interaction of helium atoms with the silicon surface. In order to validate our results, we compare to a separate temperature-dependent direct fit of $ε(T_Δ, ω)$ to the Lorentz-Dirac model.

cond-mat.mtrl-sci↗