VMI Calibration

The recorded images simply give an array of pixels of varying intensity. To calibrate the spectrometer, i.e. to relate the pixel radius to the kinetic energy of the ion, a well studied system, giving distinct kinetic energy products was examined. HBr was identified as an ideal candidate, since both photoproducts formed are atomic in nature, essentially eliminating broadening of their velocity distributions due to population of vibrational and rotational states.

The photodissociation of HBr and indeed HI following population of the A-band has been extensively studied by both theory161-163 and experiment164-165. The dissociation energy (D0) of HBr has been measured as 30210 cm-1 (3.75 eV) experimentally165, corresponding to dissociation forming H and Br (2P3/2). The splitting between the ground state Br (2P3/2) and spin excited Br (2P1/2) is known

to be 3685 cm-1(0.46 eV). Following excitation at 200 nm, equation 1.14 can be re-written to equate the theoretical kinetic energies observed on the H photoproduct following dissociation into the 2P3/2 and 2P1/2 Br channels. With the reduced mass taken into account, the theoretical maximum kinetic energies in the H photoproduct are 19546 cm-1 and 15906 cm-1for the 2P3/2 and 2P1/2 channels respectively. Following excitation at 243.1 nm (which also excites the A-band) kinetic energies of 10790 cm-1and 7151 cm-1 for these two channels should also be seen. The signal from pumping with 243.1 nm and subsequent probing with 243.1 nm is expected to be small, due to the four photon nature of the overall process.

Figure 2.10, raw image of H+ following photodissociation of HBr, with a time delay

between pump (200 nm) and probe (243.1 nm) of 2000 fs, enabling the propagated wavepacket to dissociate. Laser polarization shown on right.

Calibration runs were completed, pumping at 200 nm and probing the H at 243.1 nm. An individual image of H from HBr is shown in Figure 2.10. It is worth noting that this image is a convolution of the entire Newton sphere, so dissociation events from outside of the plane of the detector (  0) are convolved upon the true mapping of velocity vectors. Ion optic voltages were

manually optimised toVA = 5000 V andVR= 3575 V (VA/VR= 0.715) to yield the

sharpest (and hence best focussed) images.

F i g u r e 2 . 1 1 , ( l e f t )

H+ signal vs. pixel radius from the photodissociation of HBr. Assignment to different spin state product channels shown. (right) H+signal vs. kinetic energy after calibration.

Figure 2.12, plot of kinetic energy vs. pixel radius squared. A calibration factor of 0.4441 is obtained

Processing of the raw image using the POP program153 yields a deconvoluted plot of intensity vs. pixel radius (R), as shown in Figure 2.11. Assignment of these observed maxima to the calculated theoretical maximum kinetic energy values of the photoproducts yields the calibration plot shown in Figure 2.12.

200 nm 2 P3/2 200 nm 2 P1/2 243.1 nm 2 P1/2 243.1 nm 2 P3/2

The measured anisotropy parameters for dissociation following excitation at 200 nm for the spin excited and ground state Br channels of β2=0 and β2 =-1

respectively match excellently with previous measurements listed in the literature164. Due to the small signal from the probe, the anisotropy parameters at this wavelength are less accurate.

Fitting the observed peaks with Gaussian functions (G) of the form illustrated in equation 2.20, where R0 is the peak maximum reveals the resolution of the

VMI set-up to be ≈ 4 % of the pixel radius. The resolution is limited by the

optical bandwidth of the laser pulses used in these experiments.

   2 2 0 04 . 0 ) 2 ln 4 ( R R R e G      (2.20) 2.8.3 TR-VMI of HBr

Integration of the two kinetic energy regions (now separated via VMI) following excitation at 200 nm over a range of different time delays allows the assignment of timescales to these two individual channels, which without the energy resolving ability lent from VMI would not have been possible.

An illustrative example of this is given in Figure 2.13 which shows the H+ transients for the two dissociation channels. It is clear to see that dissociation into the two distinct product channels occur on different timescales. The appearance time of the 2P3/2product channel is longer than the 2P1/2channel. Physical interpretation of this is difficult, given that the channel with the highest

kinetic energy (lowest level of energy deposited as internal energy of photoproducts) is dissociating slower than the lowest kinetic energy channel.

Figure 2.13, (Top) integrated H+ signals for 2P1/2 (red) and 2

P3/2 (blue) Br channels

following photodissociation at 200 nm. Error bars shown correspond to a 95 % confidence limit. (Bottom) Comparison of rise times of H+ signals for 2P1/2 and 2P3/2

channels at 200 nm, displacement of half maxima fromτ0 indicated.

The fitted timescales for dissociation, are both < 50 fs, so confident assignment of these timescale is not possible, due to the short dissociation timescales

compared to the cross correlation of the two laser pulses (≈ 170 fs). Although

we are unable to assign timescales to these two channels with any confidence, it is very clear that the low KE channel occurs on a faster timescale than the

high KE channel. The reasoning to this is still a matter of debate, and ongoing calculations with theoretical collaborators aim to clarify this.