Transition frequencies

Rotational transition frequencies acquired in the THz region expand upon and complement those acquired in the microwave. Two types of molecules undergo rotational transitions that fall in the FIR molecules witli rotation about an axis having a small moment of inertia, and molecules in high-J states. FIR spectra of the first type of molecules are... 

Figure Bl.4.5. The Lamb dip spectrum of the CO 6-5 transition obtained with the Cologne THz BWO spectrometer. The dip is of order 30-40 kHz in width and the transition frequency is detennined to 0.5 kHz [M].

A-B relative or external motion undergo free-free transitions (E., E. + dE.) (Ej Ej+ dE within the translational continuum, while the structured particles undergo bound-bound (excitation, de-excitation, excitation transfer) or bound-free (ionization, dissociation) transitions = (a, 3) ->/= (a, (3 ) in their internal electronic, vibrational or rotational structure. The transition frequency (s ) for this collision is... 

The differential cross section da.j-/ dj for — /transitions from any one of the g-initial states is defined as [dR-j-/ / gjj, the transition frequency per unit incident current. Since current is the number of particles... 

In equations (Cl. 4.4) and (Cl. 4.5) Acoj = cu - coj is the detuning of the optical field from the atomic transition frequency Q is the natural width of the atomic transition and m is tenned the Rabi frequency and reflects the... 

Figure Cl.4.9. Usual cooling (carrier) and repumping (sideband) transitions when optically cooling Na atoms. The repumper frequency is nonnally derived from the cooling transition frequency with electro-optic modulation.

Dashed lines show tliat lasers are timed about one natural linewidtli to tire red of tire transition frequencies. 

Most molecular vibrations are well described as hannonic oscillators with small anlrannonic perturbations [5]. Por an hannonic oscillator, all single-quantum transitions have the same frequency, and the intensity of single-quantum transitions increases linearly with quantum number v. Por the usual anhannonic oscillator, the single-quantum transition frequency decreases as v increases. Ultrashort pulses have a non-negligible frequency bandwidth. Por a 1... 

The reason that non-adiabatic transitions must be included for protons is that fluctuations in the potential for the quantum degrees of freedom due to the environment (e.g. solvent) contain frequencies comparable to the transition frequencies between protonic quantum states. In such cases pure quantum states do not persist. 

Here, I(co) is the Fourier transform of the above C(t) and AEq f is the adiabatic electronic energy difference (i.e., the energy difference between the v = 0 level in the final electronic state and the v = 0 level in the initial electronic state) for the electronic transition of interest. The above C(t) clearly contains Franck-Condon factors as well as time dependence exp(icOfvjvt + iAEi ft/h) that produces 5-function spikes at each electronic-vibrational transition frequency and rotational time dependence contained in the time correlation function quantity <5ir Eg ii,f(Re) Eg ii,f(Re,t)... 

A simple method for predicting electronic state crossing transitions is Fermi s golden rule. It is based on the electromagnetic interaction between states and is derived from perturbation theory. Fermi s golden rule states that the reaction rate can be computed from the first-order transition matrix and the density of states at the transition frequency p as follows ... 

If an atom or molecule is travelling towards the detector with a velocity v, then the frequency at which a transition is observed to occur is related to the actual transition frequency v in a stationary atom or molecule by... 

Identification of a molecule known in the laboratory is usually unambiguous because of the uniqueness of the highly precise transition frequencies. However, before frequencies detected in the interstellar medium can be compared with laboratory frequencies they must be corrected for the Doppler effect (see Section 2.3.2) due to the motion of the clouds. In Sagittarius B2 the molecules are found to be travelling fairly uniformly with a velocity of... 

Fig. 52. (a) The frequency swept dipole-dipole driven NMR spectra of thioanisole recorded at a variety of magnetic fields, (b) The NMR and sideband transitions observed in the thioanisole data presented as a plot of magnetic field versus transition frequency. The transitions are defined in fig. 51. 

V (in Hz) by w = l-nv, comparison of Eqs. (4-43) and (4-44) shows that the Larmor precessional frequency is identical to the transition frequency that was calculated earlier. 

The quantum mechanical view of Raman scatering sees a radiation field hvo inducing a transition from a lower level A to a level n. If vnlc is the transition frequency, then the inelastically scattered light has frequency v0 — v t. That is, the molecule removes energy hv k from an incident photon. This process corresponds to Stokes scattering. Alternatively, a molecule under-... 

The validity conditions of the models given in (1.5) and (1.6) are also of great importance [4], though seldom taken into account. Transition between rotational states j and j + 1 is induced only when the product of the transition frequency and the collision time rc is less than 1 ... 

The origin of the rotational structure of the isotropic Q-branch (Av = 0, Aj = 0) is connected with the dependence of the vibrational transition frequency shift on rotational quantum number j [121, 126]... 

Here te, tc are the correlation times of rotational and vibrational frequency shifts. The isotropic scattering spectrum corresponding to Eq. (3.15) is the Lorentzian line of width Acoi/2 = w0 + ydp- Its maximum is shifted from the vibrational transition frequency by the quantity coq due to the collapse of rotational structure and by the quantity A due to the displacement of the vibrational levels in a medium. 

We do not possess detailed information on the transition amplitudes however, they should be on the order of the transition frequencies themselves, just as is the case for those two-level systems that are primarily responsible for the phonon... 

Assignments. - Electric modulation of vibrational rotational bands of polar molecules included a study of phosphine.120 Ringbending (puckering) transition frequencies have been measured for the phospholene (42) for the ground and excited states.121 The PD deformation band for the sulphide (43) has been assigned.122... 

Again the energy E2p(ls) is minimized by varying p and the optical transition frequency is given by... 

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