The laser system that has been used in this work is tunable over a range of
numbers in parentheses are the vibrational quantum numbers of the (upper, lower) states of the transition. “X” refers to the ground electronic state; “A” refers to the first excited electronic state. All of the transitions considered herein involve exciting molecules from the ground electronic, ground vibrational state X(v"=0) to the first excited electronic,
ground vibrational state A(v'=0) via single photon absorption. Note that single
apostrophes label quantities associated with the upper state, double apostrophes label
those associated with the lower state. This convention is derived from emission
spectroscopy terminology, since the upper level is taken to be the initial state, and the lower level, the end state. These transitions are indicated by the notation: A<-X(0,0). The more specific notation for these transitions is given by A2E+<-X2IIn(0,0). See Palma (1999) and Herzberg (1950) for a more thorough explanation of the spectroscopic notation of nitric oxide.
Once molecules are electronically excited, fluorescence can occur at the same wavelength as the excitation, returning molecules to the state they occupied prior to excitation, or it can occur at longer, less energetic wavelengths. It is also possible that higher energy levels may be populated through collisions, resulting in fluorescence at shorter wavelengths than that of the laser. The temperatures (less than 600 K) and pressures (less than 16 psi, 110 kPa, 1.1 atm) that exist in the jet flows of this investigation are low enough that such collisions may populate higher rotational levels, but non-quenching vibrational excitation of the electronically-excited state is rare. However, vibrational excitation of the electronic ground state may result from
but more energy than the probed state. The ground and first excited electronic energy levels of nitric oxide are separated by approximately 5.5 eV, whereas the ground and first excited vibrational levels differ by about 0.3 eV. The vibrational quantum number of the lower level in the fluorescence transition may be non-zero, and so the observed fluorescence will occur via the A->X(0,0-5) transitions. As discussed in Chapter 2, the fact that a large part of the fluorescence is spectrally distinct from the frequency of the laser allows a filter to be used that transmits fluorescence but blocks elastic scatter at the frequency of the laser. Such a filter blocks the majority of the fluorescence from the A->X(0,0) transition.
Rotational quantum numbers of the states are also involved. As the frequency of the laser is varied, so is the rotational quantum number of the state that is being probed. The rotational quantum number of the ground state is not being varied directly, but rather, the energy difference between the upper and lower states is the variable quantity. If one considers all pairs of rotational quantum numbers in the upper (J') and lower (J") state and sorts all such allowed transitions by the energy difference between them, one finds that transitions with the same AJ tend to have similar energies. Transitions are seen to form groups based on their associated AJ. These groups (or bands) are labeled P, Q, and R, corresponding to AJ = -1, 0, +1, respectively.
But it is, of course, more complicated than this. The effect of electronic spin parity, that is, whether the spin of the electron is aligned or antialigned with the total angular momentum (excluding electronic and nuclear spin) of the molecule, also plays a role in splitting these transitions into groups. After the capital letter indicating the value of AJ for the transition, two subscripts—a and p—indicate the parity of the upper (a) and
lower
((3)
states involved in the transition. States with positive parity are labeled with a subscript of 1. Positive parity states are those in which the spin of the electron is aligned with the total angular momentum of the molecule N (excluding electronic and nuclear spin), such that J=N+l/2. Those with negative parity—where the spin of the electron is antialigned with the total angular momentum such that J=N-l/2— are labeled with a subscript of 2. By convention, repeated indices are dropped (e.g., Q2 2 becomes simplyQ2) (Herzberg 1950).
There exist four classes of transitions as distinguished by the spin parity of the upper and lower states: those in which the parity is positive in both the upper and lower state (and so the subscripts a P = ll-M ), those in which it is negative in both the upper and lower state (a|3=22->2), those in which it is positive in the upper but negative in the lower state (ap=12), and those in which it is negative in the upper but positive in the lower state (aP=21).
Transitions with the same parity in the upper and lower state (i.e., with a = P) are considered to be the main branches in the spectrum of the molecule, while those involving a parity flip are considered satellite branches. The primary selection rule for these transitions is AJ =0,±1. For every value of J” (the rotational quantum number of the lower state), there are 3 possible values of AJ and 4 possible parity cases, resulting in 12 possible branches—6 main branches (Pi, P2, Qi, Q2, Ri, R2) and 6 satellite branches (P1 2,
P2 1, Q12, Q2 1, R12, R2 1) (Palma 1999). Table 3.1 summarizes the notation most commonly
AJ AN
a P A/aptfO Atf«p (AO
-1
-2
1
2
Pll
^12
°P11
-1
1
O
Pi
Pi
2
2
Pi
Pi
Pi
0
1
Pll
021
QPn
0
-1
1
2
Qn
Pll
pQii
0
1
Qi
0 i
01
2
2
02
02
02
+1
1
021
^21
*021
1
0
1
2
^12
012
QRn
1
1
Pi
Pi
Pi
2
2
Pi
Pi
Pi
+2
1
Pll
Pll
SP11
Table 3.1: Different notations for the branches of the NO A2Z+<-X2n transition. The first two columns list the change in rotational quantum number between the upper state and the lower state of each transition, where the 7s are half-integer valued and the Ns are integer valued. The next two columns list the spin parity of the upper (a) and lower (3) state of the transition, with 1 corresponding to positive parity and 2 corresponding to negative parity. The notations listed in the last three columns denote entire branches, where the rotational quantum number would need to be specified to refer to a particular spectral line. This text uses the ANa$(N") notation listed in the center of these three columns.
Alternative notations involve a change of basis and use the quantum number N to label states instead of J. This is sometimes more convenient, as J values are half-integers, whereas N values are integers. For the selection rule-allowed values of AJ = 0,±1, possible values of AN are 0,±1, ±2. For branches labeled in this manner, O corresponds to AN = -2 and S corresponds to AN = +2. The six main branches are labeled the same as in the AJ notation, but the six satellite branches are labeled O1 2, P12, Q1 2, Q2 1, R2 1, S2 1.
Of course, in order to fully specify a selected transition, one must define not only the
changes in the quantum numbers, but also the specific quantum number of either the
upper or lower level. It is conventional to use the quantum number of the lower level— either J" or N"—for this purpose.