Ionization of ${\mathrm{H}}_{2}^{+}$ molecular ions by twisted Bessel light

Ionization of $H_{2}^{+}$ molecular ions by twisted Bessel light

A. A. Peshkov, S. Fritzsche, and A. Surzhykov

Phys. Rev. A 92, 043415 – Published 20 October 2015

Abstract

The photoionization of $H_{2}^{+}$ molecular ions is investigated for Bessel beams of twisted light. In particular, the angle-differential photoionization cross sections are evaluated for a macroscopic target of randomly distributed but initially aligned ions by using the nonrelativistic first-order perturbation theory. Detailed calculations of these cross sections and angular distributions are performed for different setups of the electron detectors and for selected opening angles of the Bessel beams and are compared with those for incident plane-wave radiation. It is shown that the modification in the angular distributions of the photoelectrons can be understood quite easily from the variations in the intensity pattern of the Bessel beams, relative to the size of the $H_{2}^{+}$ molecular ions.

Received 10 August 2015

DOI:https://doi.org/10.1103/PhysRevA.92.043415

Authors & Affiliations

A. A. Peshkov^1,*, S. Fritzsche^1,2, and A. Surzhykov¹

¹Helmholtz-Institut Jena, D-07743 Jena, Germany
²Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, D-07743 Jena, Germany

^*anton.peshkov@uni-jena.de

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Vol. 92, Iss. 4 — October 2015

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Figure 1
Coordinates that are used to describe the hydrogen molecular ion $H_{2}^{+}$ . If the origin is chosen at the midpoint of the internuclear axis, the position vector $r$ of the electron can easily be written also in terms of the positions of the two nuclei as $r \pm R / 2$ .
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Figure 2
Geometry for the ionization of $H_{2}^{+}$ molecules by twisted light. While the quantization axis ( $z$ axis) is taken along the propagation direction of the incident beam, the $H_{2}^{+}$ molecular ion is supposed to lie in the $x z$ plane. Moreover, the molecule is aligned with angle $γ$ with respect to the $z$ axis and its center (of mass), i.e., the origin of the intermolecular coordinates, is displaced by the impact parameter $b$ from the beam axis. Finally, the two angles $ϑ_{f}$ and $φ_{f}$ describe the detector for observing the emitted photoelectrons.
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Figure 3
Angle-differential photoionization cross sections as a function of the photon energy of the incident light. Results are presented for selected angles $(ϑ_{f}, φ_{f})$ of the emitted electrons as well as for different orientations of the molecules. Cross sections (12) for incident plane waves (black solid lines) are compared with those for Bessel beams (27) with opening angles $θ_{k} = 5^{\circ}$ (red dashed lines) and $θ_{k} = 30^{\circ}$ (blue dash-dotted lines), respectively.
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Figure 4
Transverse intensity profile of a Bessel beam with opening angle $θ_{k} = 30^{\circ}$ , projection of the TAM $m = 3$ , helicity $λ = 1$ , and for the two photon energies $ℏ ω = 5$ keV (left) and $ℏ ω = 10$ keV (right). For comparison, we also display the size of a $H_{2}^{+}$ molecular ion; see the text for further discussion.
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Figure 5
Angle-differential photoionization cross section as a function of the polar angle $ϑ_{f}$ (of the detector) for $H_{2}^{+}$ molecular ions, aligned under the angle $γ = 45^{\circ}$ , and if the photoelectrons are observed in the $x z$ plane $(φ_{f} = 0^{\circ})$ . Plane-wave results (black solid lines) are compared with the photoionization by means of a Bessel beam with opening angle $θ_{k} = 30^{\circ}$ (blue dash-dotted lines) and are shown for the photon energies $ℏ ω = 1$ keV (top) and $ℏ ω = 3$ keV (bottom).
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Figure 6
Comparison of the photoelectron angular distribution as a function of the angle $φ_{f}$ for incident plane waves (black solid lines) and Bessel beams with opening angle $θ_{k} = 30^{\circ}$ (blue dash-dotted lines). The $H_{2}^{+}$ molecular ions are assumed to be aligned again under the angle $γ = 45^{\circ}$ with regard to the $z$ axis. Results in arbitrary units are shown for four different photon energies: (a) $ℏ ω = 0.5$ keV, (b) $ℏ ω = 3$ keV, (c) $ℏ ω = 7$ keV, and (d) $ℏ ω = 10$ keV. The polar angle of emitted electrons $ϑ_{f} = 20^{\circ}$ is fixed.
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Physical Review A

covering atomic, molecular, and optical physics and quantum information

Ionization of $H_{2}^{+}$ molecular ions by twisted Bessel light

A. A. Peshkov, S. Fritzsche, and A. Surzhykov

Phys. Rev. A 92, 043415 – Published 20 October 2015

Abstract

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Physical Review A

covering atomic, molecular, and optical physics and quantum information

Ionization of H2+ molecular ions by twisted Bessel light

A. A. Peshkov, S. Fritzsche, and A. Surzhykov

Phys. Rev. A 92, 043415 – Published 20 October 2015

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Ionization of $H_{2}^{+}$ molecular ions by twisted Bessel light