Experimental Stark States

Since Vd(r) is only nonzero near r = 0 the matrix element of Eq. (6.51) reflects the amplitude of the wavefunction of the continuum wave at r 0. Specifically, the squared matrix element is proportional to C, the density of states defined earlier and plotted in Fig. 6.18. From the plots of Fig. 6.18 it is apparent that the ionization rate into a continuum substantially above threshold is energy independent. However, as shown in Fig. 6.18, there is often a peak in the density of continuum states just at the threshold for ionization, substantially increasing the ionization rate for a degenerate blue state of larger This phenomenon has been observed experimentally by Littman et al.32 who observed a local increase in the ionization rate of the Na (12,6,3,2) Stark state where it crosses the 14,0,11,2 state, at a field of 15.6 kV/cm, as shown by Fig. 6.19. In this field the energy of the... 

In our picture of microwave ionization the n dependence of the ionization fields comes from the rate limiting step between the bluest n and reddest + 1 Stark states. It would be most desirable to study this two level system in detail, but in Na this pair of Stark levels is almost hopelessly enmeshed in all the other levels. In K, however, there is an analogous pair of levels which is experimentally much more attractive [17,18]. The K energy levels are shown in Fig. 6. All are m = 0 levels, and we are interested in the 18s level and the Stark level labelled (16,3). We label the Stark states as (n, k) where n is the principal quantum number and k is the zero field state to which the Stark state is adiabatically connected. As shown in Fig. 6, the (16, k) Stark states have very nearly linear Stark shifts and the 18s state has only a very small second order Stark shift, which is barely visible on the scale of Fig. 6. The 18s and (16,3) states have an avoided crossing at a field of 753 V/cm due to the coupling produced by the finite size of the K-" core [19]. 

While we have examined calculated levels, as compared to experimental ones, we have not determined exactly how the Stark States arise. Let us now examine this phenomenon. 

The modification of the electronic potentials due to the interaction with the electric field of the laser pulse has another important aspect pertaining to molecules as the nuclear motion can be significantly altered in light-induced potentials. Experimental examples for modifying the course of reactions of neutral molecules after an initial excitation via altering the potential surfaces can be found in Refs 56, 57, where the amount of initial excitation on the molecular potential can be set via Rabi-type oscillations [58]. Nonresonant interaction with an excited vibrational wavepacket can in addition change the population of the vibrational states [59]. Note that this nonresonant Stark control acts on the timescale of the intensity envelope of an ultrashort laser pulse [60]. 

Even at high n s one needs to follow the system for many orbital periods if one is to mimic the experimental results. The difficulty is compounded if one measures the time in units of periods of the core motion. This suggests that the time evolution be characterized using the stationary states of the Hamiltonian rather than propagating the initial state. We have done so, but our experience is that in the presence of DC fields of experimental magnitude (which means that Stark manifolds of adjacent n values overlap), and certainly so in the presence of other ions that break the cylindrical symmetry and hence mix the m/ values, the size of the basis required for convergence is near the limit of current computers. In our experience, truncating the quan-... 

As shown by Fig. 8.14, in most Stark spectra above the classical ionization limit there is never one isolated resonance but, more often, an irregular jumble of them. For example, in Fig. 8.15 we show the observed22 and calculated23 Na spectra near the ionization limit in a field E = 3.59 kV/cm.22 The experimental spectrum of Fig. 8.15(a) was obtained by Luk et al.22 by exciting a Na beam with two simultaneous dye laser pulses from the 3s1/2 to 3p3/2 state and then to the ionization limit. Both lasers were polarized parallel to the field, and the ions... 

Fig. 8.15 (a) Experimental photionization spectrum from the Na 1 3/2 state in a field E = 3.59 kV/cm, vs photon energy hw, within 0.01 eV of threshold (from ref. 21). Both the laser populating the 3p3/2 state and the second scanned laser are polarized parallel to the static field. Note labeling of Stark resonances (n,/ ) for m = 0 and 1. (b) Theoretical cross section, from the density of states theory. Both m = 0 and 1 final states are present (from... 

Autoionization rates also decrease rapidly with (, a point first shown experimentally by Cooke etal.n who measured the autoionization rates of the Sr 5pl5 states of = 2-7. The t>2 states were populated using the Stark switching... 

The theoretical energy levels of the ground state 4Ig/2 are shown in table 13 together with the results of CF calculations and the experimental values. Among the irreducible representations of S4 symmetry, only I 5. Te, T7, Fg are possible for a three-electron system, where I 5 and 17, or F7 and Tg are degenerate. Comparing with the experimental values, the Stark splittings are somewhat overestimated. However, the order of irreducible representations of these five levels is consistent with both the experimental values and those obtained by CFT. 

In the "nonrigid symmetric-top rotors" (such as NH ), the second-order Stark effect is observed under normal circumstances. Indeed, field strengths of the order of 1 600 000 [V/m] are required to bring the interaction into the first-order regime in this case [18]. In contrast, very weak interactions suffice to make the mixed-parity states and appropriate for the description of optically active systems. Parity-violating neutral currents have been proposed as the interaction missing from the molecular Hamiltonian [Eq.(1)] that is responsible for the existence of enantiomers [14,19]. At present, this hypothesis is still awaiting experimental verification. 

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