Small recoil momenta double ionization of He and two-electron ions by high energy photons
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Small recoil momenta double ionization of He and two-electron ions by high energy photons Miron Ya. Amusia1,2 , Evgenii G. Drukarev3 , and Evgeny Z. Liverts1,a 1 2 3
Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel A. F. Ioffe Physical-Technical Institute, St. Petersburg 194021, Russia National Research Center “Kurchatov Institute” B. P. Konstantinov Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300, Russia Received 18 April 2020 / Received in final form 13 June 2020 Published online 25 August 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We calculate various differential and double differential characteristics of ionization by a single photon for H− , He and for the two-electron ions with Z = 3, 4, 5 in the region of the so-called quasi-free mechanism (QFM) domination. We employ highly accurate wave functions at the electron-electron coalescence line where coordinates of both ionized electrons coincide. We trace the Z dependence of the double differential distributions. For all considered targets we discuss the dependence of the photoelectron energy distribution on the photon energy. Our calculation demonstrated the rapid decrease of QFM contribution with increase of the difference in energy of two outgoing electrons, and with decrease of the angle between two outgoing momenta. As a general feature, we observe the decrease of QFM contribution with nuclear charge growth.
1 Introduction
becomes as small as the binding momentum µ, i.e.
By “high energy photoionization” we mean absorption of photons with energies ω much exceeding the single electron binding energies I, i.e. ω I. If only one photoelectron is emitted, the momentum transferred to the nucleus that is called the recoil momentum q, is estimated as q ≈ p with p being the momentum in high energy photoionization of photoelectrons. Thus, the recoil momentum strongly exceeds the characteristic binding momentum of the ionized object µ = (2mI)1/2 with m being the electron mass (we employ the relativistic system of units with ~ = c = 1), i.e. q µ. This is because photoionization with only one electron knocked out cannot take place on a free electron. Similar situation takes place for the double photoionization, in emission of two electrons by a single photon, if the photon energy ω is not too large. The sharing of energy is strongly unequal and q ≈ p1 ≈ (2mω)1/2 with p1 standing for momentum of the faster photoelectron, while the second electron is emitted with momentum p2 ∼ µ. However, with the increase of ω the role of so-called quasifree mechanism (QFM) suggested in [1] becomes more and more important. In the frame of QFM momenta of photoelectrons p1,2 and that of the photon k compose such configuration that the recoil momentum q = k − p1 − p2 , a
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(1)
q ∼ µ.
(2)
Since each act of transfer of large momentum q µ to the nucleus leads to the small fa
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