3 Results

Figure 3: Population change of the $^2\Pi_{3/2}(J=7/2,~A')$ state under interaction with microwaves in the vicinity of the $F=4 \rightarrow F=4'$ and the $F=4 \rightarrow F=3'$ transition detected with LIF via Q1(3)

Figure 4: Population change of the $^2\Pi _{3/2}(J=7/2,A')$ state under interaction with microwaves in the vicinity of the $F=3 \rightarrow F=3'$ and the $F=3 \rightarrow F=4'$ transition detected with LIF via Q1(3)

The relative population change of the LIF signal was measured as a function of the stimulating microwave frequency. Figure 3 shows the $F=4\rightarrow F'=4$ line together with the $F=4\rightarrow F'=3$ line. Figure 4 shows the $F=3\rightarrow F'=3$ line together with the $F=3\rightarrow F'=4$ line. The incoupled microwave power was +6.5 dBm which leads to saturation in the main lines and in the satellite lines. The interaction time between the OH molecules and the microwave field is given by the delay between the OH production by the VUV-laser and the detection by the LIF excitation which terminates the interaction relevant for the results. The interaction time was 10 $\mu$s. Because of the higher dipole transition moment the main lines show a stronger saturation broadening than the satellite lines. The fitting includes saturation broadening, Doppler broadening and lifetime broadening (Wurps et al. 1996).

Population distribution of the hyperfine states

The LIF excitation does not resolve the hyperfine splitting of the $\Lambda$-doublet states. Nevertheless it is possible to calculate the population be the relative population change between th $\Lambda$-doublets. Thus the observable which is dealt with is the relative population change of the upper $\Lambda$-doublet in case of an interaction of the ensemble of OH fragments with microwave radiation of the $F\rightarrow F'$ transition (P_FF'). The measured P_FF' are shown in Table 1. The P_FF' are given by

$$P_{FF'}=\frac {S_0-S_{FF'}}{S_0}$$ (1)

with S₀ = LIF intensity of the Q₁(3) line without microwave stimulation and S_FF'= LIF intensity of the Q₁(3) after microwave stimulation. The LIF transistion is saturated. Thus the LIF intensity is proportional to the population of the $\Lambda$-doublets. Figure 5 shows the two experimental cases for the $F=3 \rightarrow F=4'$ transition. In the first case the LIF signal S₀is proportional to the nascent population of the upper $\Lambda$-doublet

$$S_{0}=c\cdot \left(N_4[4]+N_3[3]\right)$$ (2)

Figure 5: Schematic diagram of the two experimental cases in our experiment. The nascent LIF signal S0 is proportional to the population of the upper $\Lambda$-doublet. In the second case the microwave radiation couples two hyperfine levels (e.g. $F=3 \rightarrow F=4'$transition). If the microwave transition is saturated in our experiment,thus the population of each magnetic state ( NF,NF') of the two coupled hyperfine states is equalised. The change in the LIF signal can be measured. The relative LIF signal change is related to the nascent population of the hyperfine levels

with N_F being the population of each magnetic state of the hyperfine levels, [x]=2x+1 the multiplicity of each hyperfine level and c a constant factor. In the case of saturated microwave stimulation the population of the magnetic states of the two coupled hyperfine levels are equalised. In our example the N₃ is equal N_4'. The population of the upper F=3 hyperfine level after stimulation ( $N_3^{{\rm stim}}$) is then given by

$$N_3^{{\rm stim}}=\frac{N_3[3]+N_{4'}[4']}{[3]+[4']}.$$ (3)

The LIF signal S_34' is

$$c\times \left(N_4[4]+N_3^{{\rm stim}}[3]\right)$$ S_34' = (4)

$$c \times\left(N_4[4]+\frac{N_3[3]+N_{4'}[4']}{[3]+[4']}[3]\right)\cdot$$ = (5)

This leads to four linear equations one for each microwave transition:

  

$$c\times \left(\frac{N_4[4]+N_{F'}[F']}{[4]+[F']}[4]+N_3[3]\right)$$ S_4F' = (6)

$$c\times \left(\frac{N_3[3]+N_{F'}[F']}{[3]+[F']}[3]+N_4[4]\right)$$ S_3F' = (7)

with F'=4 or F'=3. Equations (2), (6), (7) put in Eq. (1) gives a system of four linear equations which connects the observable P_FF' to the population of the hyperfine levels:

$$P_{FF'}=\frac{[F][F']}{[F]+[F']}\ \frac{\left(N_F-N_{F'}\right)}{N_4[4]+N_3[3]}\cdot$$ (8)

The solution of the equation system for the values of P_FF' in Table 1 is shown in Table 2. The measured distribution of the hyperfine levels corresponds to a statistical distribution of [F]/([4]+[3]) per hyperfine level for each $\Lambda$-doublet.

  

Table 1: Fitting parameters for Fig. 3 and Fig. 4. The resonance frequency, the FWHM and the P_FF' are taken from the figures. The dipole moment is taken from Destombes et al. (1977). The main lines with $\Delta F=0$ show a stronger saturation broadening than the satellite lines with $\Delta F=1$

   

Table 2: Measured population of the hyperfine levels in the $^2\Pi _{3/2}(J=7/2)$ state of OH out of the photodissociation of water. The measured distribution corresponds well with the statistical distribution

$\Lambda$-doublet	hyperfine level F	measured distribution [%] NF[F]	statistical distribution[%] $$\frac {[F]}{[4]+[3]}$$
upper	F=4	$56.2\pm 1.14$	56.25
	F=3	$43.8\pm 0.86$	43.75
lower	F=4	$58.3\pm 1.19$	56.25
	F=3	$41.7 \pm 0.82$	43.75