266
F. Chaussard et al.
transition, which can be described by the usual linear mixing rule for a mixture of n
molecules
γ J i =
n
k=1
c k γ
k−i
J i
(11.4)
where c k are the mole fractions of molecules k, γ
i−i
J i
are the self-perturbed
linewidths, and γ
k−i
J i
are the linewidths of molecule i perturbed by molecule k.
As it can be seen in Eq. (11.3), the signal measured in a gas mixture is the sum of
each component contributions (consisting in series of transients) whose amplitudes
are proportional to the square anisotropy polarizability α J i and their concentrations N i . The latter can thus be deduced from the experimental total signal, as soon
as the anisotropy polarizabilities α i are known, whereas the temperature can be
determined thanks to the signal dependence versus the population distribution and
linewidth parameters.
Accidental temporal coincidences between transients of two or more molecules
due to the value of their molecular constants can exist and lead to macroscopic interferences, which exhibit a more sensitive shape with respect to the concentration [6].
When no such overlaps occur, it is still possible to induce them by using a multiple
pump pulses sequence and tuning the delay between these pulses so as to improve
the concentration dependence on the resulting transient [7].
In order to calculate the RIPS signal using Eqs. (11.1)–(11.3), the values of collisional linewidths γ J are needed. These ones are the diagonal elements of the real
part of the relaxation matrix W, whereas the off-diagonal elements k J J describe the
coupling of the lines through rotational energy transfer. Such transfers are important
when the pressure is increasing and one observes then the so-called line-mixing effect, which results in the fact that in the frequency domain the lineshape is not the
sum of individual lines. The relaxation matrix is usually obtained by inversion of experimental or calculated linewidths with fitting or scaling laws. There exist several
relaxation models to do so, but one of the most suitable is based on the energy corrected sudden (ECS) formalism [8]. Following this formalism, the relaxation matrix
is written as
k J J = Re(W J J ) =
2J
+ 1
ρ J >
ρ J
L
(2L + 1)
J L J
0 0 0
2 Φ L (ω J J ) 2
Φ L (ω L0 ) 2 Q L ,
(11.5)
with
γ J = Re(W J J ) = −
J =J
Re(W J J ),
(11.6)
where (11.6) is known as the sum rule. In this expression, ρ J is the population of the
J level, J > is the upper value of (J, J ), L is the coupled angular momentum between J and J , Φ L is an adiabatic correction term accounting for the finite collision
duration [8], and
· · ·
· · ·
is a 3J -symbol.
F. Chaussard et al.
transition, which can be described by the usual linear mixing rule for a mixture of n
molecules
γ J i =
n
k=1
c k γ
k−i
J i
(11.4)
where c k are the mole fractions of molecules k, γ
i−i
J i
are the self-perturbed
linewidths, and γ
k−i
J i
are the linewidths of molecule i perturbed by molecule k.
As it can be seen in Eq. (11.3), the signal measured in a gas mixture is the sum of
each component contributions (consisting in series of transients) whose amplitudes
are proportional to the square anisotropy polarizability α J i and their concentrations N i . The latter can thus be deduced from the experimental total signal, as soon
as the anisotropy polarizabilities α i are known, whereas the temperature can be
determined thanks to the signal dependence versus the population distribution and
linewidth parameters.
Accidental temporal coincidences between transients of two or more molecules
due to the value of their molecular constants can exist and lead to macroscopic interferences, which exhibit a more sensitive shape with respect to the concentration [6].
When no such overlaps occur, it is still possible to induce them by using a multiple
pump pulses sequence and tuning the delay between these pulses so as to improve
the concentration dependence on the resulting transient [7].
In order to calculate the RIPS signal using Eqs. (11.1)–(11.3), the values of collisional linewidths γ J are needed. These ones are the diagonal elements of the real
part of the relaxation matrix W, whereas the off-diagonal elements k J J describe the
coupling of the lines through rotational energy transfer. Such transfers are important
when the pressure is increasing and one observes then the so-called line-mixing effect, which results in the fact that in the frequency domain the lineshape is not the
sum of individual lines. The relaxation matrix is usually obtained by inversion of experimental or calculated linewidths with fitting or scaling laws. There exist several
relaxation models to do so, but one of the most suitable is based on the energy corrected sudden (ECS) formalism [8]. Following this formalism, the relaxation matrix
is written as
k J J = Re(W J J ) =
2J
+ 1
ρ J >
ρ J
L
(2L + 1)
J L J
0 0 0
2 Φ L (ω J J ) 2
Φ L (ω L0 ) 2 Q L ,
(11.5)
with
γ J = Re(W J J ) = −
J =J
Re(W J J ),
(11.6)
where (11.6) is known as the sum rule. In this expression, ρ J is the population of the
J level, J > is the upper value of (J, J ), L is the coupled angular momentum between J and J , Φ L is an adiabatic correction term accounting for the finite collision
duration [8], and
· · ·
· · ·
is a 3J -symbol.