Triple photoionization of Lithium near threshold

Solving the full classical four-body Coulomb problem numerically using a Wigner initial distribution we formulate a classical-quantum hybrid approach to study triple ionization by single photon absorption from the Li ground state in the threshold region. We confirm the Wannier threshold law σ ∝ Eα and we show that the α determined in the interval between 2−5 eV deviates from the analytical threshold value of 2.16 which we find in the interval between 0.1 − 2 eV. PACS numbers: 3.65.Sq, 32.80.Fb, 34.80.Dp Triple photoionization of Lithium is the most fundamental atomic process involving three bound electrons. Only recently Wehlitz et al. succeeded in measuring the triple photoionization cross section down to 2 eV above threshold [1, 2]. Subsequent experiments have produced various double ionization cross sections, also very close to threshold. For Lithium [3] and most recently Beryllium [4], it was demonstrated convincingly that the double photoionization cross section has small oscillations superimposed on the rising smooth cross section. This has cast some doubt on the validity of Wannier’s (classically derived) threshold law [5,6] which predicts very close to threshold a power law behavior of the cross section, σ(Eω) ∝ (Eω/I − 1) α , (1) where Eω is the photon energy, I the respective threshold energy and α a characteristic exponent which is related to the stability of a classical fixed point of the N -electron dynamics [7]. For the present case of Lithium triple ionization (I = 7.478 a.u.) the experimental results reach only down to 2 eV above threshold [2]. The corresponding fit of the experimental data with Eq. (1) yields αexp = 2.05 close to the theoretical value of α = 2.16 derived by Klar and Schlecht [8]. It is known from the well studied twoelectron escape case [9] that a Wannier exponent fitted to a cross section over an energy interval which is close but a finite distance away from threshold yields always a smaller α than the analytically predicted one. Hence, the experimental value is consistent with Wannier’s prediction but not conclusive since one does not know what happens closer to threshold. The present classical study deals for the first time with the full four-body problem close to threshold and provides the triple photoionization (TPI) probability starting at E = 0.9 eV excess energy. We are able to confirm that, indeed, the Wannier threshold law with an exponent of α = 2.16 is reached, but only for energies E ≡ Eω − I < 2eV. Letter to the Editor 2 By successively fitting finite energy intervals above the threshold I to our result, we can confirm the experimental result for α. We formulate the TPI process from the Li ground state (1s2s) as a two step process [10,11]. First, one electron absorbs the photon (photo-electron). Then, due to the electronic correlations, redistribution of the energy takes place resulting in three electrons escaping to the continuum. We express the above two step process as