Ionisation near threshold

A kinematic region that is extremely difficult for quantum calculations is just above the ionisation threshold. Near threshold the two slow continuum electrons moving in the field of a positive ion are strongly correlated and suitable approximations are difficult to evaluate. The main features in the asymptotic region were first established theoretically by 

Wannier (1953) who treated the problem classically. The Wannier theory was confirmed by Peterkop (1971) and Ran (1971) using semiclassical methods. This earlier work, as well as more recent work on near-threshold ionisation, have all emphasised the role of radial and angular correlations in the final two-electron state. In the Wannier theory, and its semiclassical extensions, the details of the collision process and the structure of the target play no role, since only the asymptotic region is considered. 

Close to threshold the system must be viewed as consisting of a correlated pair of electrons attached to the ion. It is convenient to introduce the hyperspherical coordinates 

The Hamiltonian has radial (Kr) and angular Ka,Ke) kinetic energy operators in addition to the potential V (10.44). By treating these on par with V R,6fs,ot) and by assuming an initial quasi-ergodic distribution in phase space of the escape trajectories as they enter the Coulomb zone, Wannier was able to show that at threshold (small E) the total ionisation cross section was dominated by the instability in the escape trajectories and was given by 

This is known as the Wannier threshold law and for Z = 1, 2, 3, n has the values 1.127, 1.056, and 1.036 respectively. The deviation of n from the expected value of unity arises from the instability in the escape configuration discussed above. 

---

We now address the question how much atomic physics needs to be included in order to account for ATI In fig. 9.6, we show experimental data for ATI from [493], obtained at several laser intensities. One of the important properties of ATI peaks, referred to as peak suppression, is that the relative intensity of the first ATI peaks above threshold does not increase uniformly with laser field strength, but actually begins to decrease in intensity relative to higher energy peaks as the laser field strength increases. Such behaviour cannot be explained in a perturbative scheme, in which interactions must decrease monotonically order by order as the number of photons involved increases, but can be accounted for in terms of the AC Stark shift of the ionisation potential in the presence of the laser field. In ATI experiments, the ionisation potential appears to shift by an average amount nearly equal to the ponderomotive potential, so that prominent, discrete ATI peaks are seen despite the many different intensities present during the laser pulse. However, ATI peaks closest to the ionisation limit become suppressed as the amplitude of the laser field oscillations increases and the ionisation threshold sweeps past them (a different effect which also suppresses ionisation near threshold is discussed in section 9.24.1). 

The method works particularly well for ATI spectra excited by circularly polarised light. The reason for this is as follows an atom which absorbs N photons then acquires Nh units of angular momentum. The emerging electron is then subject to a repulsive centrifugal barrier (see chapter 5) and does not therefore penetrate into the core. Consequently, most atomic effects are suppressed, and a final state representation as a Volkov wavefunction is a reasonable approximation. This is also why intensity suppression occurs near threshold in this case the effect is very similar to delayed onset in single-photon ionisation to continua of high angular momentum. 

Another effect is found near and above the photodissociation thresholds. Just as in the case of ionisation, molecules may continue to absorb excess photons over and above the minimum required, and this results in extra peaks in the spectra this effect is called ATD by analogy with ATI. 

In contrast to 3d and 4d levels 4p and 4s core levels have received less attention up to now either from EELS or from other core level spectroscopies. The case of 4p excitation is complicated by breakdown of the one-electron approximation for 4p core holes, which in this part of the Periodic Table may decay by 4p <—>4d f giant Coster-Kronig coupling, leading to broad ill-defined peaks in photoemission (Wendin 1981). In the rare earths (except Yb) such processes are allowed for 4pi/2 holes but not for 4p3/2- In electron loss the unstable 4p /2 excitations lead to ill-defined structure in the corresponding energy region, but sharp peaks are observed near the 4p3/2 ionisation threshold (Strasser et al. 1984). 

In a laser desorption/photoionisation (LD/PI) experiment a number of experimental variables needs to be defined (i) desorption parameters (requirement minimal fragmentation) (ii) photoionisation parameters (resonant or non-resonant near UV, far UV, VUV single or multiple step laser shot laser power) and (Hi) mass analyser. By fine-tuning of the laser diminished fragmentation can be achieved by setting the laser power to produce ions near the threshold value for ionisation ( soft ionisation). 

---