Referierte Publikationen


M. Vogel, G. Birkl, M. Ebrahimi, D. von Lindenfels, A. Martin, G. Paulus, W. Quint, S. Ringleb, T. Stöhlker, and M. Wiesel
Extreme-field physics in Penning traps
Hyperfine Interact., 236 :65 (April 2015)
We present two Penning trap experiments concerned with different aspects of the physics of extreme electromagnetic fields, the ARTEMIS experiment designed for bound-electron magnetic moment measurements in the presence of the extremely strong fields close to the nucleus of highly charged ions, and the HILITE experiment, in which well-defined ion targets are to be subjected to high-intensity laser fields.
H. Jörg, Z. Hu, H. Bekker, M. Blessenohl, D. Hollain, S. Fritzsche, A. Surzhykov, J. Crespo López-Urrutia, and S. Tashenov
Linear polarization of x-ray transitions due to dielectronic recombination in highly charged ions
Phys. Rev. A, 91 :042705 (April 2015)
The linear polarization of x rays produced by dielectronic recombination into highly charged xenon ions was measured at an electron beam ion trap using the Compton polarimetry technique. This opens numerous possibilities for diagnostics of anisotropies of hot plasmas. Moreover, it was observed that the polarization of x rays, following the dielectronic capture populating the [1s 2s2 2p1/2]_1 state, is highly sensitive to the Breit interaction. The experimental results for this transition rule out by 5σ calculations not taking the Breit interaction into account.
F. Karbstein, and R. Shaisultanov
Photon propagation in slowly varying inhomogeneous electromagnetic fields
Phys. Rev. D, 91 :085027 (April 2015)
Starting from the Heisenberg-Euler effective Lagrangian, we determine the photon current and photon polarization tensor in inhomogeneous, slowly varying electromagnetic fields. To this end, we consider background field configurations varying in both space and time, paying special attention to the tensor structure. As a main result, we obtain compact analytical expressions for the photon polarization tensor in realistic Gaussian laser pulses, as generated in the focal spots of high-intensity lasers. These expressions are of utmost importance for the investigation of quantum vacuum nonlinearities in realistic high-intensity laser experiments.
S. Rykovanov, C. Schroeder, E. Esarey, C. Geddes, and W. Leemans
Plasma Undulator Based on Laser Excitation of Wakefields in a Plasma Channel
Phys. Rev. Lett., 114 :145003 (April 2015)
An undulator is proposed based on the plasma wakefields excited by a laser pulse in a plasma channel. Generation of the undulator fields is achieved by inducing centroid oscillations of the laser pulse in the channel. The period of such an undulator is proportional to the Rayleigh length of the laser pulse and can be submillimeter, while preserving high undulator strength. The electron trajectories in the undulator are examined, expressions for the undulator strength are presented, and the spontaneous radiation is calculated. Multimode and multicolor laser pulses are considered for greater tunability of the undulator period and strength.
H. Gies, F. Karbstein, and N. Seegert
Quantum reflection of photons off spatio-temporal electromagnetic field inhomogeneities
New J. Phys., 17 :043060 (April 2015)
We reconsider the recently proposed nonlinear quantum electrodynamics effect of quantum reflection of photons off an inhomogeneous strong-field region. We present new results for strong fields varying both in space and time. While such configurations can give rise to new effects such as frequency mixing, estimated reflection rates based on previous one-dimensional studies are corroborated. On a conceptual level, we critically re-examine the validity regime of the conventional locally-constant-field approximation and identify kinematic configurations which can be treated reliably. Our results further underline the discovery potential of quantum reflection as a new signature of the nonlinearity of the quantum vacuum.
V. A. Yerokhin, A. Surzhykov, and S. Fritzsche
Relativistic configuration-interaction calculation of Kα transition energies in beryllium-like argon
Phys. Scripta, 90 :054003 (April 2015)
Relativistic configuration-interaction calculations have been performed for energy levels of the low-lying and core-excited states of beryllium-like argon, Ar14+. These calculations include the one-loop quantum electrodynamics (QED) effects as obtained by two different methods: the screening-potential approach and the model QED operator approach. The calculations are supplemented by a systematic estimation of the uncertainties of the theoretical predictions.
G. Weber, H. Ding, M. O. Herdrich, and A. Surzhykov
Towards a fast calculator for the radiation characteristics of radiative recombination and radiative electron capture
J. Phys.: Conf. Ser., 599 :012040 (April 2015)
The radiative capture of free electrons (radiative recombination) and bound electrons (radiative electron capture) are among the most important charge changing processes for fast, highly-charged ions. While total cross sections can be obtained by an approximate formula with reasonable accuracy, the estimation of angular distributions and polarization properties of the emitted radiation requires a fully relativistic treatment that is numerical expensive. Therefore we recently started the development of a fast calculator for these radiation characteristics. The program is based on a grid of rigorously calculated data points for free- electron capture into bare ions, between which interpolation is performed to obtain radiation characteristics for specific collision systems. Also capture into few-electron systems is taken into account in an approximate way. We present first results from this development.
D. Pincini, C. Mazzoli, H. Bernhardt, C. Katzer, F. Schmidl, I. Uschmann, and C. Detlefs
Crystallographic investigation of Au nanoparticles embedded in a SrTiO3 thin film for plasmonics applications by means of synchrotron radiation
J. Appl. Phys., 117 :105305 (March 2015)
Self-organized monocrystalline Au nanoparticles with potential applications in plasmonics are grown in a SrTiO3 matrix by a novel two-step deposition process. The crystalline preferred orientation of these Au nanoparticles is investigated by synchrotron hard x-ray diffraction. Nanoparticles preferentially align with the (111) direction along the substrate normal (001), whereas two in-plane orientations are found with [110]SrTiO3∥[110]Au and [100]SrTiO3∥[110]Au. Additionally, a smaller diffraction signal from nanoparticles with the (001) direction parallel to the substrate normal (001) is observed; once again, two in-plane orientations are found, with [100]SrTiO3∥[100]Au and [100]SrTiO3∥[110]Au. The populations of the two in-plane orientations are found to depend on the thickness of the gold film deposited in the first step of the growth.
I. A. Maltsev, V. M. Shabaev, I. I. Tupitsyn, A. I. Bondarev, Y. S. Kozhedub, G. Plunien, and T. Stöhlker
Electron-positron pair creation in low-energy collisions of heavy bare nuclei
Phys. Rev. A, 91 :032708 (March 2015)
A method for calculations of electron-positron pair-creation probabilities in low-energy heavy-ion collisions is developed. The approach is based on the propagation of all one-electron states via the numerical solving of the time-dependent Dirac equation in the monopole approximation. The electron wave functions are represented as finite sums of basis functions constructed from B-splines using the dual-kinetic-balance technique. The calculations of the created particle numbers and the positron energy spectra are performed for the collisions of bare nuclei at the energies near the Coulomb barrier with the Rutherford trajectory and for different values of the nuclear charge and the impact parameter. To examine the role of the spontaneous pair creation, the collisions with a modified velocity and with a time delay are also considered. The obtained results are compared with the previous calculations and the possibility of observation of the spontaneous pair creation is discussed.
H. Y. Wang, B. Liu, X. Q. Yan, and M. Zepf
Gamma-ray emission in near critical density plasmas at laser intensities of 10^21 W/cm2
Phys. Plasmas, 22 :033102 (March 2015)
We study synchrotron radiation emission from laser interaction with near critical density (NCD) plasmas at intensities of 10²¹ W/cm² using three-dimensional particle-in-cell simulations. It is found that the electron dynamics depend on the laser shaping process in NCD plasmas, and thus the angular distribution of the emitted photons changes as the laser pulse evolves in space and time. The final properties of the resulting synchrotron radiation, such as its overall energy, the critical photon energy, and the radiation angular distribution, are strongly affected by the laser polarization and plasma density. By using a 420 TW/50 fs laser pulse at the optimal plasma density (~1 nc), about 10⁸ photons/0.1% bandwidth are produced at multi-MeV photon energies, providing a route to ultraintense, femtosecond gamma ray pulses.
A. Akber, M. W. Reed, P. M. Walker, Yu. A. Litvinov, G. J. Lane, T. Kibédi, K. Blaum, F. Bosch, C. Brandau, J. J. Carroll, D. M. Cullen, I. J. Cullen, A. Y. Deo, B. Detwiler, C. Dimopoulou, G. D. Dracoulis, F. Farinon, H. Geissel, E. Haettner, M. Heil, R. S. Kempley, R. Knöbel, C. Kozhuharov, J. Kurcewicz, N. Kuzminchuk, S. Litvinov, Z. Liu, R. Mao, C. Nociforo, F. Nolden, W. R. Plass, Zs. Podolyak, A. Prochazka, C. Scheidenberger, D. Shubina, M. Steck, T. Stöhlker, B. Sun, T. P. D. Swan, G. Trees, H. Weick, N. Winckler, M. Winkler, P. J. Woods, and T. Yamaguchi
Increased isomeric lifetime of hydrogen-like ¹⁹²mOs
Phys. Rev. C, 91 :031301 (March 2015)
An excited metastable nuclear state of Os192 in a hydrogen-like charge state has been studied for the first time. It was populated in projectile fragmentation of a Au197 beam on a Be9 target with the UNILAC-SIS accelerators at GSI. Fragmentation products in the region of interest were passed through the fragment separator and injected into the experimental storage ring (ESR). Cooling of the injected beam particles enabled Schottky mass spectrometry to be performed. Analysis shows the lifetime of the state to be considerably longer than that of the neutral ion [t_neut=8.5(14)s]; this change is attributed to hindrance of internal conversion in hydrogen-like Os192. Calculations have been performed to estimate the lifetime, and the result has been compared with that measured experimentally. There is good agreement between the expected [t_H-like=13.0(24)s] and measured lifetimes (t_rest=15.1+1.5-1.3 s) from the internal decay of Os192m. This provides a test for the reliability of the values obtained from internal conversion coefficient calculations in highly ionized systems and is the first measurement of its kind to be performed using the ESR setup.
P. Wustelt, M. Möller, T. Rathje, A. M. Sayler, T. Stöhlker, and G.G. Paulus
Momentum-resolved study of the saturation intensity in multiple ionization
Phys. Rev. A, 91 :031401 (March 2015)
We present a momentum-resolved study of strong field multiple ionization of ionic targets. Using a deconvolution method we are able to reconstruct the electron momenta from the ion momentum distributions after multiple ionization up to four sequential ionization steps. This technique allows an accurate determination of the saturation intensity as well as of the electron release times during the laser pulse. The measured results are discussed in comparison to typically used models of over-the-barrier ionization and tunnel ionization.
D. Seipt, S. G. Rykovanov, A. Surzhykov, and S. Fritzsche
Narrowband inverse Compton scattering x-ray sources at high laser intensities
Phys. Rev. A, 91 :033402 (March 2015)
Narrowband x- and γ-ray sources based on the inverse Compton scattering of laser pulses suffer from a limitation of the allowed laser intensity due to the onset of nonlinear effects that increase their bandwidth. It has been suggested that laser pulses with a suitable frequency modulation could compensate this ponderomotive broadening and reduce the bandwidth of the spectral lines, which would allow one to operate narrowband Compton sources in the high-intensity regime. In this paper we therefore present the theory of nonlinear Compton scattering in a frequency-modulated intense laser pulse. We systematically derive the optimal frequency modulation of the laser pulse from the scattering matrix element of nonlinear Compton scattering, taking into account the electron spin and recoil. We show that, for some particular scattering angle, an optimized frequency modulation completely cancels the ponderomotive broadening for all harmonics of the backscattered light. We also explore how sensitively this compensation depends on the electron-beam energy spread and emittance, as well as the laser focusing.
P. Crump, C. Frevert, F. Bugge, S. Knigge, G. Erbert, G. Trankle, A. Pietrzak, R. Hüslewede, M. Zorn, J. Sebastian, J. Lotz, W. Fassbender, J. Neukum, J. Körner, J. Hein, and T. Topfer
Progress in high-energy-class diode laser pump sources
Proc. SPIE, 9348 :93480U (March 2015)
A new generation of diode-pumped high-energy-class solid-state laser facilities is in development that generate multijoule pulse energies at around 10 Hz. Currently deployed quasi-continuous-wave (QCW) diode lasers deliver average inpulse pump powers of around 300 W per bar. Increased power-per-bar helps to reduce the system size, complexity and cost per Joule and the increased pump brilliance also enables more efficient operation of the solid state laser itself. It has been shown in recent studies, that optimized QCW diode laser bars centered at 940…980 nm can operate with an average in-pulse power of >1000 W per bar, triple that of commercial sources. When operated at pulsed condition of 1 ms, 10 Hz, this corresponds to >1 J/bar. We review here the status of these high-energy-class pump sources, showing how the highest powers are enabled by using long resonators (4…6 mm) for improved cooling and robustly passivated output facets for high reliability. Results are presented for prototype passively-cooled single bar assemblies and monolithic stacked QCW arrays. We confirm that 1 J/bar is sustained for fast-axis collimated stacks with a bar pitch of 1.7 mm, with narrow lateral far field angle (<12° with 95% power) and spectral width (<12 nm with 95% power). Such stacks are anticipated to enable Joule/bar pump densities to be used near-term in commercial high power diode laser systems. Finally, we briefly summarize the latest status of research into bars with higher efficiencies, including studies into operation at sub-zero temperatures (-70°C), which also enables higher powers and narrower far field and spectra.
C. Jauregui, H.-J. Otto, N. Modsching, J. Limpert, and A. Tünnermann
Recent progress in the understanding of mode instabilities
Proc. SPIE, 9344 :93440J (March 2015)
In this work the latest progress in the understanding of mode instabilities is reviewed. Particular emphasis is put on the recently established influence of photodarkening on the mode instability threshold and its behavior. It is shown, for example, that even degradations of the output power in the order of a few percent can lead to very significant reductions of the mode instability threshold. Moreover, our analysis shows that photodarkening also alters the expected behavior of the mode instability threshold with respect to the signal wavelength and the seed power. Thus photodarkening is revealed as one of the main effects shaping the behavior of the mode instability threshold observed in experiments.
C. Jauregui, F. Stutzki, J. Limpert, and A. Tünnermann
Self-efficiency improvement and cooling in thulium-doped fibers
Proc. SPIE, 9344 :93441Q (March 2015)
A way to increase the efficiency of Thulium-doped fiber systems and simultaneously prevent the generation of heat by pumping the excited state around 1460 nm has been recently proposed by the authors. In this contribution we show that a Thulium-doped fiber amplifier can lase around 1460nm while simultaneously amplifying signals around 2 μm. Such an operation results in considerably higher amplification efficiencies and in lower operating temperatures without the need for an external pump around 1460 nm.
B. Manschwetus, N. Lin, J. Rothhardt, R. Guichard, T. Auguste, A. Camper, P. Breger, J. Caillat, M. Géléoc, T. Ruchon, R. Taïeb, B. Carré, and P. Salières
Self-Probing Spectroscopy of the SF 6 Molecule: A Study of the Spectral Amplitude and Phase of the High Harmonic Emission
J. Phys. Chem. A, 119 :6111 (March 2015)
We present characterizations of the attosecond pulse train produced in the high harmonic generation (HHG) from SF6 molecules irradiated by a strong pulsed laser field at 800 nm. At harmonic order 17, we observe a minimum in the amplitude of the emitted spectrum and a corresponding distortion in the phase. Our experimental results are compared to two models: a multicenter interference model focused on the effect of the structure of the SF6 molecule in HHG and a model focused on the interferences between multiple ionization channels in HHG. We find that the experimental results agree very well with the multiple ionization channels model, illustrating that HHG in molecules can be very complex and that it provides insights of the intramolecular electron dynamics during the interaction process.
C. Gaida, F. Stutzki, M. Gebhardt, F. Jansen, A. Wienke, U. D. Zeitner, F. Fuchs, C. Jauregui, D. Wandt, D. Kracht, J. Limpert, and A. Tünnermann
Sub-700 fs pulses at 152 W average power from a Tm-doped fiber CPA system
Proc. SPIE, 9344 :93441K (March 2015)
Thulium-based fiber lasers potentially provide for the demand of high average-power ultrafast laser systems operating at an emission wavelength around 2 μm. In this work we use a Tm-doped photonic-crystal fiber (PCF) with a mode field diameter of 36 μm enabling high peak powers without the onset of detrimental nonlinear effects. For the first time a Tm-doped PCF amplifier allows for a pump-power limited average output power of 241 W with a slope efficiency above 50%, good beam quality and linear polarization. A record compressed average power of 152 W and a pulse peak power of more than 4 MW at sub-700 fs pulse duration are enabled by dielectric gratings with diffraction efficiencies higher than 98% leading to a total compression efficiency of more than 70%. A further increase of pulse peak power towards the GW-level is planned by employing Tm-doped large-pitch fibers with mode field diameters well above 50 μm. The coherent combination of ultrafast pulses might eventually lead to kW-level average power and multi-GW peak power.
G. Weber, M. Herdrich, R. DuBois, P.-M. Hillenbrand, H. Beyer, L. Bozyk, T. Gassner, R. Grisenti, S. Hagmann, Y. Litvinov, F. Nolden, N. Petridis, M. Sanjari, D. Winters, and T. Stöhlker
Total projectile electron loss cross sections of U²⁸⁺ ions in collisions with gaseous targets ranging from hydrogen to krypton
Phys. Rev. ST Accel. Beams, 18 :034403 (March 2015)
Beam lifetimes of stored U^(28+) ions with kinetic energies of 30 and 50  MeV/u, respectively, were measured in the experimental storage ring of the GSI accelerator facility. By using the internal gas target station of the experimental storage ring, it was possible to obtain total projectile electron loss cross sections for collisions with several gaseous targets ranging from hydrogen to krypton from the beam lifetime data. The resulting experimental cross sections are compared to predictions by two theoretical approaches, namely the CTMC method and a combination of the DEPOSIT code and the RICODE program.
H.-J. Otto, N. Modsching, C. Jauregui, J. Limpert, and A. Tünnermann
Wavelength dependence of maximal diffraction-limited output power of fiber lasers
Proc. SPIE, 9344 :93441Y (March 2015)
The threshold-like onset of mode instabilities is currently the main limitation for the scaling of the average output power of fiber-laser systems with diffraction limited beam quality. In this contribution wavelength shifting of the seed signal has been experimentally investigated in order to mitigate mode instabilities. Against the expectations, it is experimentally shown that the highest mode instabilities threshold is reached around 1030 nm and not for the smallest wavelength separation between pump and signal wavelength. This finding implies that the quantum defect is not the sole significant source for thermal heating in the fiber.
T. Hahn, J. Bierbach, C. Rödel, D. Hemmers, M. Yeung, B. Dromey, S. Fuchs, A. Galestian, S. Kuschel, M. Zepf, G. Paulus, and G. Pretzler
Broadband XUV polarimetry of high harmonics from plasma surfaces using multiple Fresnel reflections
Appl. Phys. B, 118 :241 (February 2015)
High-harmonic generation (HHG) by nonlinear interaction of intense laser pulses with gases or plasma surfaces is the most prominent way of creating highly coherent extreme ultraviolet (EUV/XUV) pulses. In the last years, several scientific applications have been found which require the measurement of the polarization of the harmonic radiation. We present a broadband XUV polarimeter based on multiple Fresnel reflections providing an extinction rate of 5–25 for 17–45 nm which is particularly suited for surface harmonics. The device has first been tested at a gas harmonic source providing linearly polarized XUV radiation. In a further experiment using HHG from plasma surfaces, the XUV polarimeter allowed a polarization measurement of high harmonic radiation from plasma surfaces for the first time which reveals a linear polarization state as predicted for our generation parameters. The generation and control of intense polarized XUV pulses - together with the availability of broadband polarizers in the XUV - open the way for a series of new experiments. For instance, dichroism in the XUV, elliptically polarized harmonics from aligned molecules, or the selection rules of relativistic surface harmonics can be studied with the broadband XUV polarimeter.
K.-H. Blumenhagen, A. Gumberidze, R. Märtin, N. Schell, U. Spillmann, G. Weber, and T. Stöhlker
Characterization of a double-sided Si(Li) strip Compton polarimeter
J. Phys.: Conf. Ser., 583 :012043 (February 2015)
The response of a double-sided segmented Si(Li) detector system has been investigated. The detector has been irradiated with a collimated, highly linearly polarized beam of 53.2 keV photons from the synchrotron radiation source PETRA III at DESY. The detector was mounted on a platform that could be moved with μm precision thus allowing for a defined beam position on the detector surface. In this paper, the effects of the isolation gaps (gap width = 50 μm) between adjacent segments (strips) were studied, in particular with respect to the effect of charge sharing. The fraction of such charge sharing events increases from about 5% (beam hits center of a strip) to over 50% when the beam is focused just on a gap. The fraction of reconstructed Compton scattering events, which is interesting for Compton polarimetry, amounts to about 3% with the beam impinging at a strip center and 2.8% on average. It can therefore be concluded that events related to charge sharing do not critically degrade the performance of the detector as a Compton polarimter.
G. Weber, K.-H. Blumenhagen, H. Bräuning, H. Ding, S. Fritzsche, S. Hess, R. Märtin, U. Spillmann, A. Surzhykov, S. Trotsenko, D. F. A. Winters, V. A. Yerokhin, and T. Stöhlker
Compton polarimetry using double-sided segmented x-ray detectors
J. Phys.: Conf. Ser., 583 :012041 (February 2015)
Hard x-ray polarimetry of radiation emitted in collisions of heavy ions, electrons or photons with matter provides detailed information on the collision dynamics as well as of the atomic structure in the presence of extreme field strengths. Moreover, it also opens a route for polarization diagnosis of spin-polarized ion and electron beams which, for example, might be useful in future parity non-conservation studies. Owing to recent progress in the development of highly segmented solid-state detectors, a novel type of polarimeter for the hard x-ray regime has become available. Applied as Compton polarimeters, two-dimensional position-sensitive x-ray detectors now allow for precise and efficient measurements of x-ray linear polarization properties. In this report recent polarimetry studies using such detector systems are reviewed.
S. Kuhn, M. Tiegel, A. Herrmann, J. Körner, R. Seifert, F. Yue, D. Klöpfel, J. Hein, M.C. Kaluza, and C. Russel
Effect of hydroxyl concentration on Yb3+ luminescence properties in a peraluminous lithium-alumino-silicate glass
Opt. Mater. Express, 5 :430 (February 2015)
Ytterbium doped lithium-alumino-silicate glasses suitable for diode-pumped laser applications were investigated concerning the hydroxyl quenching of the Yb^(3+) fluorescence. Glasses of the nominal composition 18 mol% Li2O, 22 mol% Al2O3 and 60 mol% SiO2 with variable OH concentrations NOH (between 0.04 and 6.01 ∙ 1019 cm−3) and Yb3+ concentrations NYb (between 0.1 and 9 ∙ 1020 cm−3) were produced and a direct correlation between spontaneous emission decay rate and the product NYb ∙ NOH was observed. The radiative spontaneous emission rate in the glass host is around 1,000 s−1 (radiative lifetime 1.0 ms) and the microparameter for Yb-Yb energy migration, CYb-Yb, was found to be 1.358∙10^−38 cm^6 s−1. It was calculated that on average 17% of the OH groups in the glass contribute to the quenching of the Yb3+ fluorescence. By analysis of the UV edge of the glass it was concluded that melting under inert conditions leads to reduction of iron impurities to Fe2+, which can act as quenching sites for the Yb3+ ions and therefore may additionally reduce the energy storage capability of the laser material.
P.-M. Hillenbrand, S. Hagmann, D. H. Jakubassa-Amundsen, J. M. Monti, D. Banaś, K.-H. Blumenhagen, C. Brandau, W. Chen, P. D. Fainstein, E. De Filippo, A. Gumberidze, D. L. Guo, M. Lestinsky, Yu. A. Litvinov, A. Müller, R. D. Rivarola, H. Rothard, S. Schippers, M. S. Schöffler, U. Spillmann, S. Trotsenko, X. L. Zhu, and T. Stöhlker
Electron-capture-to-continuum cusp in U⁸⁸⁺+N₂ collisions
Phys. Rev. A, 91 :022705 (February 2015)
For the collision system U88+ -> N2 at a collision energy of 90 MeV/u, the energy distribution of electrons being nonradiatively captured from the target into the projectile continuum has been measured under an angle of 0∘ with respect to the projectile beam axis. This measurement of the electron-capture-to-continuum cusp with the highest effective projectile charge Z_eff,p=88 at a near-relativistic collision velocity of β≈0.41 is shown to be characterized by a strong asymmetry in the cusp shape. By comparing the data to measurements of the radiative-electron-capture-to-continuum cusp for the same collision system, the opposite asymmetry of the cusp is traced back to the varying underlying mechanisms. The experimental results are compared with the two theoretical calculations available for this process, one of them in the semirelativistic impulse approximation and the other in the nonrelativistic continuum-distorted-wave approach. A corresponding fully relativistic treatment may be motivated by the presented experimental data.