The field ionization Coulomb explosion model (Codling et al, 1987) predicts that the kinetic energies of the dissociating ionic fragments should depend on the risetime of the pulse. The scenario of dissociative ionization begins with a molecule ionizing and expanding. During the expansion the laser intensity increases with the risetime of the pulse until the intensity is high enough to cause another ionization. This process of ionization followed by expansion continues until the intensity no longer increases or until the molecule has completely dissociated. It follows that the steeper the risetime of the pulse the less the molecule will have been able to dissociate before the laser intensity is high enough to cause a further ionization. Thus, the model predicts that the kinetic energies of the resulting highly charged fragment ions are greater for a steeper laser pulse risetime.
Table 1.1: Comparison of the kinetic energy releases of fragment ions released in the dissociative ionization of the nitrogen molecule from Lavancier etal, 1991 (Ref 1), Codling et al, 1990 (Ref 2) and Cornaggia et al, 1991 (Ref 3).
Atomic Ion kinetic energy release (eV) Fragmentation
channel 2 ps pulse duration (Refi) 600 fs pulse duration (Ref 2) 1 0 0 fs pulse duration (Ref 3) 3.5 3 3.4 N^ + N^ 5.8 6.5 6.3 6 . 2 6.5 6 . 8 N+ + 1 0 1 1 1 1 9 1 0 9.5 N^ + N^ 14 15 16
Cornaggia at al, 1991, compared their results to those of Lavancier at al 1991, and Codling at al, 1990, and found that the kinetic energy releases for the dissociative ionization of N2 did not appear to depend on the risetime of the pulse, as shown in
Table 1.1. Similar conclusions were drawn from their comparisons of O2 and CO
from the same groups.
Results from Stankiewicz at al, 1993, also seemed to suggest the independence of kinetic energy release of the fragmentation channels on laser pulse risetime when they investigated the dissociative ionization of N2 using 248 nm wavelength laser
light and pulse durations of 1 to 4 ps. Schmidt at al, 1994, experimenting on CI2
the kinetic energy releases of I2 dissociatively ionizing using 750 nm wavelength
laser light of 2 0 0 fs and 400 fs pulse durations. They found that there was indeed a
dependence of kinetic energy releases with pulse risetime but that dependence was much less than was predicted by the field ionization Coulomb explosion model (Codling et a/, 1987). An accurate experiment (GHes et al, 1995) was carried out using the technique of laser interferometry which allowed the modification of the pulse risetime without the alteration of any of the other laser parameters. The careful measurement of the kinetic energy releases of I2 led the authors to believe
that, as suggested by Hatherly et ai, 1994, there is a small dependence of kinetic energy release on the laser pulse risetime.
1.4
Bond Softening and Bond Hardening
Bond softening is an above threshold dissociation (ATD) process which occurs after an initial ionization of a molecule when further absorption of photon energy leads to dissociation. The kinetic energies of the fragment ions are typically much smaller than the kinetic energies of the fragment ions produced by Coulomb explosion processes. Bond softening, first postulated by Giusti-Suzor et ai, 1990, predicted multiphoton absorptions occurring in the dissociation continuum of the product ion H2^. In this model repulsive states are field-dressed, which is a term to describe the
virtual absorption of /i-photons by a molecule (where »^1). This dressed state can be presented on a potential energy curve diagram, as shown in Figure 1.6, such that it crosses a bound molecular state. Due to the non-crossing rule the dressed states of the same parity do not cross and an avoided crossing ensues. When a state is dressed by a photon the parity of the state changes by (-1).
If the molecule is promoted to the g, n=0 state it can dissociate via tunneling of the atomic fragment ion/neutral through the potential barrier lowered by the avoided crossing of the bound state and the dressed repulsive curve, as shown in Figure 1.6. Bond softening also occurs where the molecular ion is promoted to the g, n=2 curve and tunnels adiabatically onto the u, n=3 curve dressed with three photons. During dissociation some of the photons used in the dressing of the potential curves can be returned to the laser field via stimulated emission.
g.n=o Tunneling u,n=1 (eV) g,n=2 Adiabatic path -10 u,n=3 -12 R
Figure 1.6: The avoided crossing of a bound state and a repulsive dressed molecular state, resulting in tunneling and low energy dissociation.
The modification of the potential curves results in a very small kinetic energy for the dissociated atomic fragment ions/neutrals for both of the bond softening processes described above, due to the fact that the energy difference between the asymptote of the repulsive curve and the height of the barrier formed by the avoided crossing of the bound and repulsive state is small.
The first experimental verification of this theoretical model was presented by Bucksbaum et al, 1990. Using 532 nm, 100 ps laser pulses on laser produced molecular ions the measured kinetic energies were compatible with bond softening. The process of production of the H2* ion from the H2 molecule occurs on the rising
edge of the laser pulse and the bond softening dissociation occurs later within the same pulse. As in ATD they found that there were peaks in the proton spectrum separated by "hw/2 and as in ATD they interpreted this as a sharing of the photon energy by the neutral and ionic products of dissociated H2^. For higher laser
intensities the avoided crossing gap opened up and they concluded that the lower kinetic energy fragments detected were due to lower vibrational states participating in the dissociation.
Unperturbed v" 3 4 5 6 1.0 ■■---' r - f— — »---—1— O'® [' : : 0 . 61 : . / ! ' ' X i , [■
/ j 4 i %
U
L
0.2 0.4 0.6 0.8 1.0 Proton energy <eV)Figure 1.7: Intensity dependence of the proton spectra for 355 nm laser light. The lower spectra, A, collected with I = 5 x 10^^ W/cm^ and the upper spectra, B, with I =1 x 10^'^ W/cm^. The expected proton energies for the different unperturbed vibrational levels of the H2* ground state
are marked on the bottom of the figure. At the higher laser intensity the relative amount of protons coming from the dissociation of the ions in the lower vibrational levels increases (Zavriyev et al, 1990).
Zavriyev at al, 1990, were also able to detect protons produced by the bond softening process and claimed to be able to distinguish protons liberated from different vibrational levels, as shown in Figure 1.7, for 355 nm laser light. Figure 1.8 shows how Zavriyev at al, 1990, explained that lower kinetic energy fragments were detected for higher laser intensity due to the unbinding of the lower vibrational levels with increasing laser intensity.
Giusti-Suzor and Mies, 1992, investigated theoretically the dissociation of H2"’ from
different vibrational states by solving the time dependent Schrodinger equation. They found that for vibrational levels less than v=4 the molecule dissociates at earlier and earlier times in the laser pulse for increasing vibrational level. Figure 1.9 shows that this is due to the crossing point of the bound and repulsive states that occur at this vibrational level of the bound state. The non-crossing gap widens with increasing intensity. However, they found that there was a reluctance for the molecule to dissociate in vibrational levels higher than v=4. They named this phenomenon bond hardening. Figure 1.9 shows a bond hardening process occurring for v=10 due to the intensity-modified upper curve c. The vibronic wave packet, originally in the vibrational level v=1 0, is trapped in the upper well produced by the avoided crossing between the
bound (g,n=0) and repulsive (u,n=1) state. As the laser intensity decreases and the non-crossing gap narrows lower vibrational levels to v=4 will be trapped in this upper level.
Potential Energy (eV) 19 18 no light 17 R (Bohr)
Figure 1.8: One photon crossing for 532 nm light. Solid lines show the unperturbed 1s<Pg
state and the 2p0u state lowered by one photon. The component of the laser field parallel to the internuclear axis perturbs the states. A s the laser polarization increases the gap between the states opens, and more vibrational states become unbound. (Zavriyev et al,
1990)
6
5 7 8
3 A
2
Interatomic distance (au)
Figure 1.9: Field dressed IsOg and 2p0u states of H2*. Curve a: I = 5x 10^^ W/cm^, curve
b: I =2.5 X 10^^ W/cm^ and curve c: I =1 x 10'^^ W/cm^. yi is the total kinetic energy for bond softening dissociation and yo is the kinetic energy for the bond hardening dissociation (Giusti-Suzor and Mies, 1992).
A significant population could be trapped in these light induced vibrational bound states and is a possible mechanism for stabilization against dissociation, discussed in Section 1.6, since it means that the dissociation could be postponed to later in the
Zavriyev et al, 1993, continuing the work of Zavriyev et ai, 1990, investigated the intense laser field dissociative ionization of H2* and 0 2^ using 160 fs 769 nm laser
light. They found structure within the kinetic energy spectra of the deuteron and the proton which they attributed to the vibrational structure of the ATD and population trapping (bond hardening) The paper describes the bond hardening process temporally through the pulse, as shown in Figure 1.10.
ionisertion 14TW /cm 2 20 19 Inter- "I® nuclear ^ y potential (® V ) 1 6 15 14 lOfe 2pcr„ -IV 29TW /cm 2 90TW /cm 2trapping 15fs 40fs 4 5 1 2 3 4 5 1 2 3 4
internuclear distance (Bohr)
Figure 1.10: A possible population trapping scenario. During the second vibrational cycle the vibrational wave packet becomes trapped in the adiabatic well above the three-photon avoided crossing t>etween the Isog and 2pou states of the molecular ion. The fine lines show the Isog ground state as well as the 2pou state shifted down by integer numbers of photons (Zavriyev et al, 1993).
At low intensities the vibrational wavepacket is bound within the Isog state modified by the avoided crossing of the 2pou state dressed with 1%w. Within the pulse duration vibrations of the molecule are possible even as the laser intensity increases. When the intensity is high enough the 2pou dressed with 3),w forms an avoided crossing with the Isog state and trapping of the vibrational wavepacket occurs in the potential well created by the 2pou-3},w repulsive curve and the Isog bound state. At the peak of the pulse the ion ionizes for a second time from the trapped state. Zavriyev et al, 1993, concluded that this is the first experimental verification of light induced trapped states that are stable against dissociation but can be detected by the photoionization of the molecular ion.
u, n-1
O, n»2
- 6.0
R ( a u )
Figure 1.11: The trapping of v=12 for H2*. The population is trapped in an adiabatic weii
formed by the avoided crossing (Giusti-Suzor et ai, 1995).
Giusti-Suzor et al, 1995, continuing the theoretical interest in the processes of bond hardening and bond softening for different vibrational states shows how complicated the dissociation of H2* is due to the number of possible processes
there are, as shown in Figure 1.11. Wunderlich et al, 1996, theoretically investigated Arg^ and found that increasing the laser frequency moves the avoided crossing to smaller internuclear distances. All of these discoveries show how dramatically the dynamics of dissociative ionization of molecules can be affected by the characteristics of the laser pulse.