## Role of the Binding Energy on Nondipole Effects in Single-Photon Ionization

Almost 100 years ago, Sommerfeld and Schur predicted that the momentum distribution of ions and electrons in single-photon ionization depends not only on the photon momentum but also on the binding energy of the photoelectron (Ann. Phys. (N.Y.) **396**, 409 (1930)). The influence of the photon momentum was confirmed experimentally only recently by Grundmann et al. (Phys. Rev. Lett. **124**, 233201 (2020)) under conditions where the binding energy was negligible. In our recent work, we experimentally study the influence of the binding energy on nondipole effects in K-shell single-photon ionization of atoms (Ne(1s) I_{p} = 870 eV, Ar(1s) I_{p} = 3206 eV, Kr(1s) I_{p} = 14326 eV). We find that for each ionization event, as expected by momentum conservation, the photon momentum is transferred almost fully to the recoiling ion (see Fig. 1). The photon brings in additional orbital angular momentum so that the electron momentum distribution becomes asymmetrically deformed along the light propagation direction with a mean value of 8/(5c)(Eγ - I_{p}) (see Fig. 2). The competition between the forward-directed photon momentum and the backward-directed recoil imparted by the photoelectron leads to a mean ion momentum of 1/(5c)(-3E_{γ}+ 8I_{p}). Which of the two counteracting effects prevails depends on the binding energy of the emitted electron. We show that at 20 keV photon energy, Ne^{+} and Ar^{+} photoions are pushed backward towards the radiation source, while Kr^{+} photoions are emitted forward along the light propagation direction (see Fig. 3).

**FIG.1.** Momentum distribution of Kr^{2+} ions from ionization by linearly polarized photons with E_{γ} = 20 keV. Horizontal axis: momentum component parallel to light propagation direction. Vertical axis: momentum parallel to polarization axis. The data shown are restricted to |k_{i}^{z}| < 2.5 a.u. The green dashed circle with a radius corresponding to the photoelectron momentum k_{e} = √
2(E_{γ}-I_{p})
is forward shifted by the photon momentum k_{γ} = 5.36 a.u.

**FIG.2.** Distributions of the photoelectron momentum k_{e}^{x} along the light propagation direction for (a) Ne, (b) Ar, (c) Kr, and photoelectron angular distributions for (d) Ne, (e) Ar, (f) Kr at a photon energy of E_{γ} = 20 keV (k_{γ} = 5.36 a.u.). The data are normalized to the maximum. Dots: experimental data, the statistical uncertainties are smaller than the size of the data points. Red dotted (blue solid) lines: theoretical calculations taking into account the first two expansion terms of the plane wave (the full e^{ikγr}) of the vector potential of the electromagnetic field.

**FIG.3.** Mean value of the measured electron (blue circles) and ion (red circles) momenta as functions of the binding energy I_{p} recorded at a photon energy of E_{γ} = 20 keV (k_{γ} = 5.36 a.u.). The statistical uncertainties are smaller than the size of the data points. Lines: predictions from Eqs. (2) and (3) of (Phys. Rev. Lett. **132**, 233002 (2024)). Note that positive values of the mean momenta correspond to emission in the direction of the photon propagation.

**Publication:**

Role of the Binding Energy on Nondipole Effects in Single-Photon Ionization

M. Schmidt, N. Melzer, M. Kircher, G. Kastirke, A. Pier, L. Kaiser, P. Daum, D. Tsitsonis, M. Astaschov, J. Rist, N. Anders, P. Roth, K. Lin, J. Drnec, F. Trinter, M. S. Schöffler, L. Ph. H. Schmidt, N. M. Novikovskiy, Ph. V. Demekhin, T. Jahnke, and R. Dörner

Phys. Rev. Lett. **132**, 233002

DOI: 10.1103/PhysRevLett.132.233002

**See online:**

Find the publication in Physical Review Letters.