Chemistry Reference
In-Depth Information
Fig. 13.3
The Feynman diagrammatical sum of interactions entering the Raman effect by con-
necting the single and double photonic particles' events in absorption (
incident wave light q
0
,
υ
0
)
and emission (
scattered wave light q
,
υ
) induced by the quantum first
H
(1)
and second
H
(2)
order
, final
B
f
, and virtual
interaction Hamiltonians of Eqs. (13.1) and (13.2) through the initial
|
B
i
|
bondonic states. The first term accounts for absorption (
A
)-emission (
E
) at once, the second
term sums over the virtual states connecting the absorption followed by emission, while the third
terms sums over virtual states connecting the absorption following the emission events. (Putz
2010a
,
2012a
)
B
v
molecules, crystals,
etc
.) by modeling the inelastic interaction between an incident
IR photon and a quantum system (here the bondons of chemical bonds in molecules),
leaving a scattered wave with different frequency and the resulting system in its fi-
nal state (Freeman
1974
; Thomas
1991
; Sutton
2009
). Quantitatively, one firstly
considers the interaction Hamiltonian as being composed by two parts (Putz
2010a
)
r
j
,
t
)
e
B
m
B
p
Bj
·
A
(
H
(1)
=−
(13.1)
j
e
B
2
m
B
H
(2)
A
2
(
=
r
j
,
t
)
(13.2)
j
accounting for the linear and quadratic dependence of the light field potential vector
A
(
r
j
,
t
) acting on the bondons “
j
”, carrying the kinetic moment
p
Bj
=
m
Bj
v
Bj
,
charge
e
B
and mass
m
B
. Then, noting that, while considering the quantified incident (
q
,
υ
) light beams, the interactions driven by
H
(1)
and
H
(2)
model
the changing in one- and two- occupation numbers of photonic trains, respectively.
In this context, the transition probability between the initial
q
0
,
υ
0
) and scattered (
and final
B
f
bondonic states writes by squaring the sum of all scattering quantum probabilities
that include absorption (
A
, with
n
A
number of photons) and emission (
E
, with
n
E
number of photons) of scattered light on bondons, see Fig.
13.3
.
Analytically, one has the
initial-to-final
total transition probability (Heitler
1954
)
dependence here given as
|
B
i
δ
E
|
B
i
+
hυ
0
−
E
−
hυ
υ
2
dυdΩ
h
π
fi
1
¯
2
d
2
fi
∼
|
B
f
h
1
¯
H
(2)
=
f
;
n
A
−
1,
n
E
+
1
|
|
n
A
,
n
E
;
i
