Ionisation limit

Other series are present in the spectrum of the H atom, starting from different initial levels and undergoing transitions to higher levels. There is formally no limit to the value of n in the upper state but eventually in the limit the electron is so far from the nucleus that it is no longer confined by the attraction of the proton and it leaves the atom a process called ionisation. The ionisation event can be seen in any one of the series of the H atom when the separation between the lines of the series begins to converge towards zero - the ionisation limit at a fixed wavelength. 

Our new value for L2 of Au differs from our previous one by 0.17 per cent. The error in our previous work was due to the proximity of the bromine ionisation limit, which has a wave-length = 0.91796 X 10 8cm. In our new measurements it was unnecessary to have ethyl bromide in the ionization chamber. 

There are, of course, many other Rydberg states of H2 which could be studied, at least in principle. Perhaps enough has already been done, however, to show the trends to be expected as the ionisation limit of H2 is approached. 

The first ionisation limit of a many-electron atom corresponds to the ground state of the corresponding or parent ion. Higher thresholds correspond to excited states of the parent ion. Apart from the special case of He, which has a hydrogenic parent ion, they are not simply related to fundamental constants. The many-electron Schrodinger equation must also be solved for the parent ion in order to determine the energies of the thresholds. 

However, there is one important difference in this new situation the ionisation limits now correspond to highly excited states of the core. If these are fairly stable (as in fig. 2.9) then long series can be built on them. If, on the other hand, the parent ion states decay very rapidly, then Rydberg excitation can be quenched, especially for the highest Rydberg states which would have long natural lifetimes in the absence of core deexcitation. 

The conditions under which nonexponential decay of autoionising states might appear have been considered phenomenologically [281], and it was suggested that the crucial issue is how close a resonance lies above the ionisation limit. In fact, it is the ratio T/Eo, where Eq the resonance energy is measured from the threhold, which must be significant for effects to appear.4... 

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). 

This rule is only approximate because it misses out many important physical considerations. For example, e/ is taken as the field-free ionisation limit for a one-electron system, and the rule contains nothing explicit about pulse duration. Nevertheless, it has been found to work reasonably well. From this rule, we can see that a well-developed spectrum of high harmonics is only expected in species with a high ionisation threshold. 

If one continues the term diagram in Fig. 6.2 upwards, i.e. into a higher-energy region, it ends at the ionisation limit, that is with the emission of an electron from the crystal. For anthracene, the ionisation Hmit of the free molecule Hes at 7.5 eV and the work function for emission of an electron out of the crystal at 5.75 eV. 

With a sufliciently high total energy, this process can even cause the ejection of an electron from the crystal that is, the exciton annihilation leads to ionisation. In the case of anthracene, the ionisation limit of 5.75 eV lies lower than twice the Si energy, 2x3.15 = 6.30 eV. Measurement of the kinetic energy of the emitted photoelectrons permits the verification of the fusion process. In general, the fusion of two excitons allows higher excited states to be reached with smaller energy quanta. Table 6.4 contains numerical values of the rate constants for exciton annihilation processes. 

So it really follows that for lighter elements the radiationless transitions are by far the most probable. According to our formulae, this must be particularly true for terms of the optical spectra which lie beyond the normal ionisation limit E > 0). Indeed, the lifetimes of these states are by order of magnitude hardly larger than their oscillation times [see Eq. (10)] the spectral lines corresponding to these terms will be very weak and furthermore unsharp. In fact such spectral terms (for instance in the higher p -terms of Ca) have been observed only recently using special observational tricks. 

By comparison between spectroscopic values and the ab initio predictions of the relativistic parametric potential method, the first ionisation limit of the three ions has been estimated with an accuracy of about 10000 cm [4]. 

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