Electric dipole moments enhancement factor

The summation runs over all the excited states s of the molecule, operators Dp, are components of the electric dipole moment operator and 7" is a damping factor which can be related to the width of the excited state vibrational levels. In the case of RRS, the first term in (2.3) is much smaller than the second one, which becomes only limited by the Efactor. Thus, under these conditions, RS is enhanced by factor 10 -10. ... 

Where po is the dipole moment, Eo the incident electric field, and M(cOl) the field enhancement at the fi-equency of the laser line. f[n,m) is the Frank-Condon factor, defined as ... 

To examine the role of the LDOS modification near a metal nanobody and to look for a rationale for single molecule detection by means of SERS, Raman scattering cross-sections have been calculated for a hypothetical molecule with polarizability 10 placed in a close vicinity near a silver prolate spheroid with the length of 80 nm and diameter of 50 nm and near a silver spherical particle with the same volume. Polarization of incident light has been chosen so as the electric field vector is parallel to the axis connecting a molecule and the center of the silver particle. Maximal enhancement has been found to occur for molecule dipole moment oriented along electric field vector of Incident light. The position of maximal values of Raman cross-section is approximately by the position of maximal absolute value of nanoparticle s polarizability. For selected silver nanoparticles it corresponds to 83.5 nm and 347.8 nm for spheroid, and 354.9 nm for sphere. To account for local incident field enhancement factor the approach described by M. Stockman in [4] has been applied. To account for the local density of states enhancement factor, the approach used for calculation of a radiative decay rate of an excited atom near a metal body [9] was used. We... 

As expected, the on-resonance enhancement factor decreases rapidly from 55 to 8 when the dye-particle separation increases from 1-5 nm. It is very interesting to note that the two equally strong absorption peaks at 311 nm and 407 nm of the bare N3 dye are not equally amplified by the presence of the silver sphere, with a notably heightened peak at 407 nm and a nearly invariant peak at 311 nm. The apparent difference in the light absorption efficiency can be ascribed to the relative directions of the silver sphere s scattered electric field and the N3 dye s transition dipole moment for the two resonant modes, showing the importance of including the dye molecule explicitly in many-body electronic structure theory in determining plasmon-enhanced response. 

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