Secular width

Figure 6.37. The teinperature dependence of the motional narrowed secular width (y7 2 ) (O) [6,82] and the phase memory time Tm (taken at X-band) in irans- CD), obtained by (I) Shiren et al ( ) [159-161] and (2) Isoya ( ) [193], The solid curve shows typical behaviour for (yTj ) 4- A// p...

The best resolution of Q-branch rotational structure in a N2-Ar mixture was achieved by means of coherent anti-Stokes/Stokes Raman spectroscopy (CARS/CSRS) at very low pressures and temperatures (Fig. 0.4). A few components of such spectra obtained in [227] are shown in Fig. 5.9. A composition of well-resolved Lorentzian lines was compared in [227] with theoretical description of the spectrum based on the secular simplification. The line widths (5.55) are presented as... 

We digress to point out that secular usually means worldly or of things which exist through the ages and in the specialized usage here describes those terms in the Hamiltonian operator (which describe the interactions of the spins) which commute with the Zeeman term. A simply stated consequence is that secular terms do not cause nuclear transitions but do contribute to line positions and widths. ]... 

The described phenomenon is analogous to the wave function eigenstates of a particle in a one dimensional quantum potential well. Infinitely strong orientational interaction with the surface (infinite anchoring) corresponds to an infinitely deep potential well, and a finite anchoring to a finite one (Fig. 4.6), where the width of the well corresponds to the thickness d of the planar sample. The fluctuation modes are of sinusoidal shape and the perpendicular wave vector components are determined by secular equations ... 

The relative accuracy of the transition frequencies, which can be achieved within a sympathetically cooled ensemble, is in principle better than with buffer gas cooled ions or with fast ion beams. Molecular dynamics simulations of the motion of the trapped HD+ ions lead to an estimate of a Doppler broadening of only 10 MHz under ideal conditions, whereas a thermal 10K ion ensemble leads to a Doppler width (FWHM) of 280 MHz. In reality the reported line broadening was 40 MHz indicating an effective temperature of 0.2 K. Note that this temperature describes only the axial motion of the HD+ ions, the radial motion does not lead to a first-order Doppler effect. The explanation given by the authors is based on a non-linear coupling between the axial and radial motion of the ions via Coulomb interaction. In a more detailed analysis, Koelemeij et a/. ° distinguish between translational (secular) temperature of 50 mK resulting... 

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