Theory Division

Theoretical Quantum Dynamics and Quantum Electrodynamics

Ionic Quantum Dynamics and High-Precision Theory


Zoltán Harman
Max Planck Institute for Nuclear Physics
Saupfercheckweg 1
D-69117 Heidelberg

E-mail: harman (at)

Phone: +49 6221 516170
Fax: +49 6221 516152

In atomic systems with high nuclear charges, inner-shell electrons experience extremely high nuclear binding fields. The dynamics of electrons becomes relativistic and also the electronic probability density has a considerate overlap with the nuclear matter. These properties render highly charged ions an ideal tool for basic research in relativistic atomic structure theory, quantum electrodynamics at extreme fields, and nuclear size contributions. Accurate knowledge of the properties of highly charged ions is also necessary for the diagnostics of hot fusion plasmas and astrophysical plasmas. In few-electron ions, relativistic and nuclear effects are intertwined with large electron correlation contributions. Because of this complex interplay, accurate theoretical calculations are necessary to explain the physical phenomena observed in increasingly accurate experimental spectra.

Besides investigations on transition energies and spectral properties, quantum electrodynamic and nuclear corrections to the bound electron g factor are calculated. We also study the interaction of intense lasers in the optical as well as the x-ray regime with highly charged ions, and, furthermore, energetic collision, ionization and recombination processes. In theoretical simulations we describe the dynamics of charged particles in strong laser fields and develop efficient laser accelation schemes.

Group members:

Recent projects:

g factor of highly charged ions

An external static magnetic field gives rise to the Zeeman splitting of atomic energy levels, with a strength characterized by the dimensionless g factor of the atomic state. In the last decades, experimental techniques, in particular, measurements with Penning traps has reached a remarkable precision (see e.g. Ref. [1] and references therein), allowing for novel studies of fundamental physics. These include the test of bound-state quantum electrodynamics (QED) at high orders [1], and the extraction of nuclear properties such as nuclear radii [1-3], deformation parameters describing the deviation of the nuclear surface from a perfect sphere [2], and nuclear magnetic moments [4]. Furthermore, physical constants such as the electron mass can be determined with high accuracy from a comparision of experimental data and theoretical results.

Figure 1

Figure 1: Nuclear deformation correction to the bound electron g factor of 1s states in hydrogenic ions (red dots) as a function of the nuclear charge Z. The values are compared to other contributing terms such as one- and two-loop corrections (1L, 2L, respectively) of different orders of the coupling strength (Zα), the nuclear field shift (FS) assuming a spherical nucleus, and the nuclear recoil (rec) correction.

[1] S. Sturm, A. Wagner, B. Schabinger, J. Zatorski, Z. Harman, et al., Phys. Rev. Lett. 107, 023002 (2011)
[2] J. Zatorski, N. Oreshkina, C. H. Keitel, Z. Harman, Phys. Rev. Lett. 108, 063005 (2012)
[3] V. A. Yerokhin, Z. Harman, Phys. Rev. A 88, 042502 (2013)
[4] V. A. Yerokhin, K. Pachucki, Z. Harman, C. H. Keitel, Phys. Rev. Lett. 107, 043004 (2011)

Highly charged ions in x-ray and optical laser fields

Due to the small spatial extent of the bound electron wave functions and their large overlap with the atomic nucleus, inner-shell transitions of highly charged ions (HCI) are most sensitive to QED and nuclear effects. The associated spectra are also of great relevance for astrophysical line diagnostics aiming at determining physical parameters such as element decomposition, density, and temperature of the emitter medium [1]. These transitions are in the x-ray range, therefore, their efficient radiative excitation has been rather challenging until the advent of x-ray free electron lasers providing high intensities in the appropriate photon energy range. Optical transitions in HCI have been recently investigated by laser spectroscopic methods [2]. We calculate ionic transition energies and transition probabilities which are scrutinized in electron beam ion trap (EBIT) experiments [1,2]. Furthermore, schemes have been developed for high-precision metrology of HCI by a combination of x-ray and optical laser fields [3], and for the investigation of coherent ionic population dynamics [4]. In recent studies, we devise a setup for the generation of high-precision frequency combs in the x-ray regime [4,5], also in collaboration with the INTERATTO experimental research group of the Institute.

Figure 2

Figure 2: Scheme for the generation of x-ray frequency combs. (a) An ensemble of ions is driven by x rays (kX, brown), an auxiliary optical laser field (kL, red), both linearly polarized along the z direction, and an optical frequency comb (kC, green), linearly polarized along the x direction. All fields propagate in the y direction. The resonance fluorescence spectrum (kF, blue) exhibits an induced x-ray frequency-comb structure. (b) Four-level scheme used to describe the coherent interaction between He-like ions and the driving fields.

[1] S. Bernitt, G. V. Brown, J. K. Rudolph, et al., Nature 492, 225 (2012)
[2] K. Schnorr, V. Mäckel, N. S. Oreshkina, et al., Astrophys. J. 776, 121 (2013)
[3] O. Postavaru, Z. Harman, and C. H. Keitel, Phys. Rev. Lett. 106, 033001 (2011)
[4] S. M. Cavaletto, C. Buth, Z. Harman, et al., Phys. Rev. A 86, 033402 (2012)
[5] S. M. Cavaletto, Z. Harman, C. Buth, C. H. Keitel, arxiv:1302.3141 (2013)
[6] Z. Liu, C. Ott, S. M. Cavaletto, et al., arxiv:1309.6335 (2013)

Laser acceleration of charged particles

We perform theoretical investigations concerning the strong-field dynamics of ions in order to develop optimal schemes for laser ion acceleration. Laser-accelerated beams may find applications in basic research, medicine, and industry. As an example, cancer hadron therapy requires accelerated ion beams of high energy sharpness and a narrow spatial profile in order to accurately irradiate the tumor while sparing damage from the surrounding healthy tissue. As we have shown in theoretical simulations [1,2], linearly and radially polarized, tightly focused and thus extremely strong laser beams should permit the direct acceleration of light atomic nuclei up to energies that may offer the potentiality for medical applications and may allow one to build more economic cancer treatment facilities. In a different setting employing two identical crossed laser beams [3], ions originating from a laser-plasma process can be post-accelerated to form a beam of high intensity, energy and quality. In recent studies, the acceleration of protons by a chirped laser pulse is simulated using the particle-in-cell method to take into account plasma effects and has been found to be even more efficient than the set-ups described above [4,5]. Finally, the autoresonance laser acceleration of electrons in strong axial magnetic fields is investigated. This scheme is anticipated to yield electron beams with energies up to the 10-GeV regime with an ultrahigh energy resolution when applying multi-petawatt laser pulses [6].

Figure 3

Figure 3 (left): Ion trajectories (blue) calculated by a simulation of the acceleration in the focus of a radially polarized laser beam. The red arrows illustrate the radial and longitudinal field vectors and the propagation direction of the beam. (right): Post-acceleration of an ion beam generated in a laser-plasma interaction process by two crossed lasers.

[1] Y. I. Salamin, Z. Harman, and C. H. Keitel, Phys. Rev. Lett. 100, 155004 (2008) (see also: Informationsdienst Wissenschaft Online;; Photonik)
[2] Z. Harman, Y. I. Salamin, B. J. Galow, C. H. Keitel, Phys. Rev. A 84, 053814 (2011)
[3] B. J. Galow, Z. Harman, and C. H. Keitel, Opt. Express, 18, 25950 (2010)
[4] B. J. Galow, Y. I. Salamin, T. V. Liseykina, Z. Harman, C. H. Keitel, Phys. Rev. Lett. 107, 185002 (2011)
[5] Y. I. Salamin, J.-X. Li, B. J. Galow, Z. Harman, C. H. Keitel, Phys. Rev. A 85, 063831 (2012)
[6] B. J. Galow, J.-X. Li, Y. I. Salamin, Z. Harman, C. H. Keitel, Phys. Rev. ST Accel. Beams 16, 081302 (2013)

Correlated relativistic quantum dynamics in resonant recombination processes

In the process of radiative recombination (RR), a photon is directly emitted by an electron, i.e. it is the time-reverse of the photoelectric effect. Alternatively, in a two-step process, the incoming electron resonantly excites a bound electron during recombination, leading to dielectronic recombination (DR, see Fig. 3). Furthermore, in some ionic species, the simultaneous excitation of two bound electron may occur. This higher-order process may be termed as trielectronic recombination (TR). These photorecombination processes involving HCI in collisions with energetic electrons are important for a number of applications. In particular, DR is known as a source of the severe energy losses from high temperature plasmas such as magnetically confined fusion plasmas or stellar plasmas, and, thus, precise quantitative understanding of such phenomena is indispensable. We calculate cross sections and accurate resonance peak positions. These calculations are tested by high-resolution EBIT (see [1-4]) and storage ring measurements [5].

Figure 4

Figure 4: Level schemes illustrating the resonant processes of di-, tri- and quadrelectronic recombination in an initially carbonlike (six-electron) ion.

In the presence of a neighboring atom, electron-ion recombination can proceed resonantly via excitation of an electron in the atom, with subsequent relaxation through radiative decay, as illustrated on Fig. 4. In joint collaboration with the groups of Carsten Müller and Alexander B. Voitkiv it has been shown that this two-center dielectronic recombination (2CDR) process can largely dominate over single-center radiative recombination at internuclear distances as large as several nanometers [5]. It may play a significant role in dense plasma and chemical environments where it can substantially affect the quantum dynamics and time evolution of the system.

Figure 5

Figure 5: Level scheme depicting the two-center dielectronic recombination process. The electron recombining radiationlessly with center A transfers its energy to resonantly excite center B. (Figure from Ref. [4], copyright of the American Physical Society.)

[1] Z. Harman, I. I. Tupitsyn, A. N. Artemyev, et al., Phys. Rev. A 73, 052711 (2006)
[2] A. J. González Martínez, J. R. Crespo López-Urrutia, J. Braun, et al., Phys. Rev. A 73, 052710 (2006)
[3] C. Beilmann, O. Postavaru, R. Ginzel, et al., Phys. Rev. A 80, 050702(R) (2009)
[4] C. Beilmann, P. H. Mokler, S. Bernitt, et al., Phys. Rev. Lett. 107, 143201 (2011)
[5] D. Bernhardt, C. Brandau, Z. Harman, et al., Phys. Rev. A. 83, 020701 (R) (2011)
[6] C. Müller, A. B. Voitkiv. J. R. Crespo López-Urrutia, and Z. Harman, Phys. Rev. Lett. 104, 233202 (2010)

Resonant photoionization and photoexcitation of highly charged ions by synchrotron x-rays

The photoionization (PI) of atomic systems may proceed via a resonant two-step mechanism: In the first step, a photon is absorbed by resonant excitation to an autoionizing intermediate state embedded into the electronic continuum (see Fig. 4.). In the second step, the so-formed state autoionizes. Alternatively, the excited state may decay by the spontaneous emission of a photon. In the case of HCI, the photon energies needed are in the x-ray (short-wavelength) domain. In astrophysics, PI of HCI has been recently observed in high-resolution x-ray spectra of quasars, which display absorption lines due to the presence of HCI in the line of sight. Such data have revealed the hitherto only presumed existence of a tenuous warm-hot intergalactic medium, the so-called WHIM, comprising a large fraction of baryonic matter. For the identification and analysis of absorption lines due to HCI in astrophysical spectra, a large amount of reliable theoretical or experimental PI data is needed. We perform fully relativistic distorted wave calculations of PI and photoexcitation cross sections, transition energies and linewidths, accompanying recent measurements employing electron beam ion traps (EBIT) and synchrotrons as a source of x-ray photons in the keV range [1-3].

Figure 6

Figure 6: Resonant photoionization illustrated for the case of a four-electron ion. The electronic shell is resonantly excited by the x-ray photon to an autoionizing intermediate state, which subsequently decays by a correlated Auger process.

[1] M. C. Simon, J. R. Crespo López-Urrutia, C. Beilmann, M. Schwarz, Z. Harman, et al., Phys. Rev. Lett. 105, 183001 (2010) (see also: "Der letzte Schrei aus dem Schwarzen Loch", Press information by the Max Planck Society (in German); "Physicists produce black hole plasma in the lab",
[2] M. C. Simon, M. Schwarz, S. W. Epp, C. Beilmann, B. L. Schmitt, et al., J. Phys. B: At. Mol. Opt. Phys. 43, 065003 (2010)
[3] J. K. Rudolph, S. Bernitt, S. W. Epp, R. Steinbrügge, C. Beilmann, et al., Phys. Rev. Lett. 111, 103002 (2013)

Nuclear effects in highly charged ions

Isotope shift measurements of dielectronic recombination cross sections performed in storage rings, combined with our atomic structure calculations, allow one to extract information on the nuclear charge distribution of the isotopes involved and thus about the interplay of forces that act between the nuclear constituents. In a theoretical study, we analyze the dependence of electron interaction and QED contributions of the bound-state electronic transition energy on the nuclear size in order to determine the change of nuclear radii corresponding to the isotope shift in three-electron neodymium. Experimental isotope shifts have been measured with the ESR storage ring of the GSI Darmstadt [1]. This approach, based on a close collaboration of theory [2] and experiment, constitutes a new technique to determine nuclear charge radii.

Figure 7

Figure 7: The change of nuclear size or mass causes an isotope shift of the observed spectrum

The high-precision theory of multiply charged ions has been investigated in EBIT group of our institute. Extensive theoretical studies of the ground-state forbidden magnetic dipole transition in boronlike (five-electron) argon ions have been performed. The mass isotope shift associated with this line have been determined with high accuracy using the EBIT. The wavelengths of the above transition were compared for the isotopes 36Ar and 40Ar. The observed isotope shift has confirmed the relativistic theory of nuclear motional effects in many-body systems [3,4]. Calculations based on the fully relativistic recoil operator are in excellent agreement with the measured results.

[1] C. Brandau, C. Kozhuharov, Z. Harman, et al., Phys. Rev. Lett. 100, 073201 (2008)
[2] R. Schiopu, Z. Harman, W. Scheid, N. Grün, Eur. Phys. J. D 31, 21 (2004)
[3] R. Soria Orts, Z. Harman, J. R. Crespo López-Urrutia, et al., Phys. Rev. Lett. 97, 103002 (2006)
[4] Z. Harman, U. D. Jentschura, C. H. Keitel, et al., J. Phys.: Conf. Ser. 58, 133 (2007)