Quantum number Raman scattering

Quantum effects are observed in the Raman spectra of SWCNTs through the resonant Raman enhancement process, which is seen experimentally by measuring the Raman spectra at a number of laser excitation energies. Resonant enhancement in the Raman scattering intensity from CNTs occurs when the laser excitation energy corresponds to an electronic transition between the sharp features (i.e., (E - ,)" type singularities at energy ,) in the ID electronic DOS of the valence and conduction bands of the carbon CNT. 

Hydrogen is the most abundant chemical element in the universe, and in its various atomic and molecular forms furnishes a sensitive test of all of experimental, theoretical and computational methods. Vibration-rotational spectra of dihydrogen in six isotopic variants constituting all binary combinations of H, D and T have nevertheless been recorded in Raman scattering, in either spontaneous or coherent processes, and spectra of HD have been recorded in absorption. Despite the widely variable precision of these measurements, the quality of some data for small values of vibrational quantum number is still superior to that of data from electronic spectra [106], almost necessarily measured in the ultraviolet region with its concomitant large widths of spectral lines. After collecting 420... 

Figure 1. Rotational—vibrational line strength correction factors for pure rotational Raman scattering (fM)0 and for O-, S-, and Q-branch vibrational Raman scattering (foh fots, and folQ). The value J is the rotational quantum number of the initial level (O), Stokes (A), anti-Stokes.

In Eq. (6), is the energy of the zero-zero electronic transition (t oo) in cm, (Oj and Aj are respectively the wavenumber in cm and the displacement of the /clh normal mode, and is the vibrational quantum number of the kth normal mode in the ground electronic state (nj = 0,1,2 etc.). Equation (6) is composed of two parts. Note that the exponential term in square brackets is the same as the overlap of the absorption (A) and the new feature in the overlap for the Raman is the other term, the Raman factor (R). The contribution of each part to the overlap for the Raman scattering will be discussed later. Equation (6) is used to calculate the cross-sections for the fundamentals, overtones, and combination tones. For example, in order to calculate the cross-section of the combination band (v, + Vj) in a three mode case, n, = 1, tid /ij = 0. 

This review is largely concerned with vibrational Raman scattering in which the states G> and F> differ only in the possession of one or more quanta of vibrational energy. In systems with electronically degenerate ground states it is impossible to avoid entirely the effects of simultaneous changes in the electronic and vibrational quantum numbers This latter point is discussed briefly later on with respect to the Jahn-Teller effect as well as the electronic Raman effect. 

The carrier multiplication (CM) process generated as a result of a single photon absorption in a spherical quantum dot (QD) is explained as due to multiple,virtual band-to-band electron-photon quantum transitions. Only the electron-photon interaction is used as a perturbation without the participation of the Coulomb electron-electron interaction. The creation of an odd number of electron-hole (e-h) pairs in our model is characterized by the Lorentzian-type peaks, whereas the creation of an even number of e-h pairs is accompanied by the creation of one real photon in the frame of combinational Raman scattering process. Its absorption band is smooth and forms an absorption background without peak structure. It can explain the existence of a threshold on the frequency dependence of the carrier multiplication efficiency in the region corresponding to the creation of two e-h pairs. 

The considered model is based on the use as a perturbation only the electron-photon interaction, on introduction of the photon states as virtual and real states along with the states of many e-h pairs. Only the e-h pairs with the same quantum numbers I, n, m for both partners were considered. The combinational Raman scattering process with the creation of an even number of e-h pairs is the main treasure of the presented model. The influence of the Coulomb electron-electron interaction must be also taken into account. 

To the extent that we can trust the harmonic approximation, each level of vibrational excitation (each increment in vibrational quantum number v) costs one vibrational constant in energy. As Table 8.2 shows, the vibrational constants of typical stretching motions place vibrational excitation energies in the infrared region of the spectrum. We can measure vibrational transitions that occur by absorption or emission or by scattering. Section 6.3 introduced the concept of Raman scattering, which in principle can be applied to the spectroscopy of any degree of freedom, but which is most commonly used for spectroscopy of vibrational states. 

One way to directly measure rotational transitions in non-polar molecules such as these is by rotational Raman spectroscopy, which operates on the same principle as other Raman techniques (see Section 6.3). A rotational Raman transition connects initial and final rotational levels within the same vibrational state, so only the rotational quantum number changes. However, this technique is limited in precision by the uncertainties in the photon energies of the incident and scattered light. The scattering intensity increases dramatically with photon energy. 

This scattered photon gives rise to a Stokes line in the Raman spectrum. According to quantum mechanics the allowed change in the vibrational quantum number for a Raman transition is Jp = 1 for a harmonic vibration. The final possibility is that the molecule initially is in the excited state... 

---