Vector coupling constant

Undoubtedly the Chalk River ISOL will be used, as others are, in the identification and spectroscopy of exotic nuclei. The nuclear chart in figure 5 illustrates the scope for such studies. However, the extreme purity of isotopes separated by our ISOL has been essential in the past to precision studies of the weak interaction, in one case the lifetimes of superallowed 0+ 0+ transitions [K.OS83], in another 8-v-a triple correlation coefficients in the decay of 2( Na [CLI83] both yielded measurements of the weak vector coupling constant. These types of measurements will be extended to other nuclei, since they exploit the best qualities of the accelerator and separator. 

In the beta-decay allowed approximation, we neglect the variation of the lepton wave-functions over the nuclear volume and the nuclear momentum (this is equivalent to neglecting all total lepton orbital angular momenta L > 0). The total angular momentum carried off by the leptons is their total spin i.e. 5 = 1 or 0, since each lepton has When the lepton spins in the final state are antiparallel, se+s = stot = 0 the process is the Fermi transition with Vector coupling constant g = Cv (e.g. a pure Fermi decay 140(J r = 0+) —>14 N(JJ = 0+)). When the final state lepton spins are parallel, se + sv = stot = 1> the process is... 

There are other important properties tliat can be measured from microwave and radiofrequency spectra of complexes. In particular, tire dipole moments and nuclear quadmpole coupling constants of complexes may contain useful infonnation on tire stmcture or potential energy surface. This is most easily seen in tire case of tire dipole moment. The dipole moment of tire complex is a vector, which may have components along all tire principal inertial axes. 

Figure 1 The principal sources of structural data are the NOEs, which give information on the spatial proximity d of protons coupling constants, which give information on dihedral angles < i and residual dipolar couplings, which give information on the relative orientation 0 of a bond vector with respect to the molecule (to the magnetic anisotropy tensor or an alignment tensor). Protons are shown as spheres. The dashed line indicates a coordinate system rigidly attached to the molecule.

Table 2. Calculated energy gap due to an in-plane Kekul distortion for CNTs having chiral vector L/a = (m, 2m). The critical magnetic flux (p. and the corresponding magnetic field are also shown. The coupling constant is A, = 1.62.

Alternatively, one may attempt to estimate the integral over the derivative of the displacement field that entered in the expression for the coupling constant g= pc Jy cPr du/2. Since da is the divergence of a vector, the integral is reduced to that over a surface within the droplet s boundary ... 

Figure 5.7 (A) Pulse sequence for gated decoupled /-resolved spectroscopy. It involves decoupling only during the first half of the evolution period

Figure 5.10 (A) Selective spin-flip pulse sequence for recording heteronuclear 2D / resolved spectra. (B) Its effect on magnetization vectors. The selective 180° pulse in the middle of the evolution period eliminates the large one-bond coupling constants, /< ...

The relaxation theory used in the Appendix to describe the principle of TROSY clearly tells us what to expect, but it is always a little more satisfying if one can obtain a simple physical picture of what is happening. We consider a system of two isolated scalar coupled spins of magnitude %, 1H (I) and 15N (S), with a scalar coupling constant JHN. Transverse relaxation of this spin system is dominated by the DD coupling between spins XH and 15N and by the CSA of each individual spin. The relaxation rates of the individual multiplet components of spin 15N are now discussed assuming an axially symmetric 15N CSA tensor with the axial principal component parallel to the 15N-XH vector as shown in Fig. 10.2. 

Since the discovery of the nuclear Overhauser effect (NOE, see previous section) [4, 5] and scalar coupling constants [36, 37] decades ago, NMR-derived structure calculations of biomolecules largely depended on the measurement of these two parameters [38]. Recently it became possible to use cross-correlated relaxation (CCR) to directly measure angles between bond vectors [39] (see also Chapt 7). In addition, residual dipolar couplings of weakly aligned molecules were discovered to measure the orientation of bond vectors relative to the alignment tensor (see Sect 16.5). Measurement of cross-correlated relaxation was described experimentally earlier for homonuclear cases [40, 41] and is widely used in solid-state NMR [42 14]. 

All other factors are constants. The angle 9 is the projection angle between bond vectors and is the sole unknown in Eq. 1, and can be readily and precisely determined by measurement of the cross-correlated dipolar relaxation rate. It should be emphasized that 9 is measured directly, without the need of experimental calibration as in the Karplus curve for J-coupling constants for example. 

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