Quantum Theory of Coherent Raman and Coherent Hyper-Raman Scattering |
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Page 70
... transition . resonant contribution to the transition rate is due to the ground level term in the sum over R " . We shall thus discuss in detail only the term R " = 0 and treat the rest as background contributions to the rate . 1 Now ...
... transition . resonant contribution to the transition rate is due to the ground level term in the sum over R " . We shall thus discuss in detail only the term R " = 0 and treat the rest as background contributions to the rate . 1 Now ...
Page 76
... transition polarizability of a molecule in its own ( molecule fixed ) coordinate system . We now define b ̄ = <a> - <a> a = ( 1/3 ) ( 2 ( a ) + ( a >> 11 1 [ 3.29a ] [ 3.296 ] and observe that the ensemble average of âlab in the ...
... transition polarizability of a molecule in its own ( molecule fixed ) coordinate system . We now define b ̄ = <a> - <a> a = ( 1/3 ) ( 2 ( a ) + ( a >> 11 1 [ 3.29a ] [ 3.296 ] and observe that the ensemble average of âlab in the ...
Page 77
Jón Örn Bjarnason. fact that the laboratory frame ensemble average of the transition polarizability is d I and notice that ( B ) = 0 since ĝis traceless . We substitute Eq . [ 3.30 ] into the correlation function , [ 3.27 ] . Since b and ...
Jón Örn Bjarnason. fact that the laboratory frame ensemble average of the transition polarizability is d I and notice that ( B ) = 0 since ĝis traceless . We substitute Eq . [ 3.30 ] into the correlation function , [ 3.27 ] . Since b and ...
Common terms and phrases
aabb abab abcd background contribution CARS band center of mass circularly polarized coherent hyper-Raman scattering coherent Raman process coherent Raman scattering components correlation function CSRS defined density matrix derived difference dipole and electric Doppler line shape Doppler profile Doppler width double Raman e₁ eigenstates eigenvalues electric quadrupole interactions electronic energy eigenvalues ensemble average evaluate evolution operator factor fully quantum mechanical Hamiltonian ideal gas integral isotropic isotropic tensor k₁ k₂ beam k₂ photon Kronecker deltas linear lineshape lowest order magnetic dipole matrix elements molecular molecule momentum conservation condition N-molecule neglected nonzero obtain one-molecule perturbation photon polarizability polarizability approximation polarization vectors quantity quantum mechanical Raman transition rate expression RCARS replace resonance denominator rotational sample spectrum symmetric tion transition amplitude transition polarizability Ursell function VHH experiment vibrational VVV experiment w₁ w₂ wave vectors αα Σ Σ