arXiv subjects

Robert A. Müller

Publications and source records attributed to Robert A. Müller.

8 recordsLinked to original sources

arXiv2021

Nonlinearities of King's plot and their dependence on nuclear radii

Investigations of isotope shifts of atomic spectral lines provide insights into nuclear properties. Deviations from the linear dependence of the isotope shifts of two atomic transitions on nuclear parameters, leading to a nonlinearity of the so-called King plot, are actively studied as a possible way of searching for the new physics. In the present work we calculate the King-plot nonlinearities originating from the Standard-Model atomic theory. The calculation is performed both analytically, for a model example applicable for an arbitrary atom, and numerically, for one-electron ions. It is demonstrated that the Standard-Model predictions of the King-plot nonlinearities are hypersensitive to experimental errors of nuclear charge radii. This effect significantly complicates identifications of possible King-plot nonlinearities originating from the new physics.

physics.atom-ph↗

arXiv2021

Impact of Earth's gravity on Gaussian beam propagation in hemispherical cavities

We theoretically investigate the influence of gravity on laser light in a hemispherical optical cavity, operating on Earth. The propagation of light in such a cavity is modeled by a Gaussian beam, affected by the Earth's gravitational field. On laboratory scale, this field is described by the spacetime of homogeneous gravity, known as Rindler spacetime. In that spacetime, the beam is bent downwards and acquires a height dependent phase shift. As a consequence the phase fronts of the laser light differ from those of a usual Gaussian beam. Assuming that the initial beam enters the cavity along its symmetry axis, these gravitational effects cause variations of the beam phase with every cavity round trip. Detailed calculations are performed to investigate how these phase variations depend on the beam parameters and the cavity setup. Moreover, we discuss the implications of our findings for cavity calibration techniques and cavity-based laser stabilization procedures.

gr-qc↗

arXiv2020

Gravitational light deflection in Earth-based laser cavity experiments

As known from Einstein's theory of general relativity, the propagation of light in the presence of a massive object is affected by gravity. In this work, we discuss whether the effect of gravitational light bending can be observed in Earth-based experiments, using high-finesse optical cavities. In order to do this, we theoretically investigate the dynamics of electromagnetic waves in the spacetime of a homogeneous gravitational field and give an analytical expression for the resulting modifications to Gaussian beam propagation. This theoretical framework is used to calculate the intensity profile at the output of a Fabry-Pérot cavity and to estimate the imprints of Earth's gravity on the cavity output signal. In particular, we found that gravity causes an asymmetry of the output intensity profile. Based on that, we discuss a measurement scheme, that could be realized in facilities like the GEO600 gravitational wave detector and the AEI 10 m detector prototype.

gr-qc↗

arXiv2019

Modification of multipole transitions by twisted light

A theoretical analysis is presented for the excitation of single many-electron atoms and ions by twisted (or vortex) light. Special emphasis is put on excitations that can proceed via several electric and magnetic multipole channels. We argue that the relative strength of these multipoles is very sensitive to the topological charge and kinematic parameters of the incident light and can be strongly modified with respect to the plane-wave case. Most remarkably, the modification of multipole transitions by twisted radiation can be described by means of a geometrical factor. This factor is independent of the shell structure of a particular target atom and just reflects the properties of the light beam as well as the position of an atom with respect to the vortex axis. An analytical expression for the geometrical factor is derived for Bessel photons and for a realistic experimental situation in which the position of an atom is not well determined. To illustrate the use of the geometrical factor for the analysis of (future) measurements, detailed calculations are presented for the $3s3p \, ^3P_1 \to 3s 3p \, ^1P_1$ excitation in neutral Mg.

physics.atom-ph↗

arXiv2019

Excitation of the $^{229}$Th nucleus via a two-photon electronic transition

We investigate the process of nuclear excitation via a two-photon electron transition (NETP) for the case of the doubly charged thorium. The theory of the NETP process has been devised originally for heavy helium-like ions. In this work, we study this process in the nuclear clock isotope $^{229}$Th in the $2+$ charge state. For this purpose, we employ a combination of configuration interaction and many-body perturbation theory to calculate the probability of NETP in resonance approximation. The experimental scenario we propose for the excitation of the low lying isomeric state in $^{229}$Th is a circular process starting with a two-step pumping stage followed by NETP. The ideal intermediate steps in this process depend on the supposed energy $\hbarω_N$ of the nuclear isomeric state. For each of these energies, the best initial state for NETP is calculated. Special focus is put on the most recent experimental results for $\hbarω_N$.

physics.atom-ph↗

arXiv2019

Electronic level structure of $\mathrm{Th}^+$ in the range of the $^{229m}\mathrm{Th}$ isomer energy

Using resonant two-step laser excitation of trapped $^{232}\mathrm{Th}^+$ ions, we observe 166 previously unknown energy levels of even parity within the energy range from 7.8 to 9.8 eV and angular momenta from $J=1/2$ to $7/2$. We also classify the high-lying levels observed in our earlier experiments by the total angular momentum and perform ab-initio calculations to compare their results with the observed level density. The observed levels can be relevant for the excitation or decay of the $^{229m}\mathrm{Th}$ isomeric nuclear state which lies in this energy range. The high density of electronic levels promises a strongly enhanced electronic bridge excitation of the isomer in $^{229}\mathrm{Th}^+$.

physics.atom-ph↗

arXiv2018

Hyperfine interaction with the $^{229}$Th nucleus and its low lying isomeric state

The thorium nucleus with mass number $A=229$ has attracted much interest because its extremely low lying first excited isomeric state at about $8$eV opens the possibility for the development of a nuclear clock. However, neither the exact energy of this nuclear isomer nor properties, such as nuclear magnetic dipole and electric quadrupole moment are known to a high precision so far. The latter can be determined by investigating the hyperfine structure of thorium atoms or ions. Due to its electronic structure and the long lifetime of the nuclear isomeric state, Th$^{2+}$ is especially suitable for such kind of studies. In this letter we present a combined experimental and theoretical investigation of the hyperfine structure of the $^{229}$Th$^{2+}$ ion in the nuclear ground and isomeric state. A very good agreement between theory and experiment is found for the nuclear ground state. Moreover, we use our calculations to confirm the recently presented experimental value for the nuclear magnetic dipole moment of the thorium nuclear isomer, which was in contradiction to previous theoretical studies.

physics.atom-ph↗

arXiv2017

Theoretical analysis of the electron bridge process in $^{229}$Th$^{3+}$

We investigate the deexcitation of the $^{229}$Th nucleus via the excitation of an electron. Detailed calculations are performed for the enhancement of the nuclear decay width due to this so called electron bridge (EB) compared to the direct photoemission from the nucleus. The results are obtianed for triply ionized thorium by using a B-spline pseudo basis approach to solve the Dirac equation for a local $x_α$ potential. This approach allows for an approximation of the full electron propagator including the positive and negative continuum. We show that the contribution of continua slightly increases the enhancement compared to a propagator calculated by a direct summation over bound states. Moreover we put special emphasis on the interference between the direct and exchange Feynman diagrams that can have a strong influence on the enhancement.

physics.atom-ph↗