Spins external magnetic field

B BLi T spins external magnetic field (n H) effective molecular field acting on M A/r sublattice magnetization magnetization of the R sublattice... 

Electrons and most other fiindamental particles have two distinct spin wavefunctions that are degenerate in the absence of an external magnetic field. Associated with these are two abstract states which are eigenfiinctions of the intrinsic spin angular momentum operator S... 

While all contributions to the spin Hamiltonian so far involve the electron spin and cause first-order energy shifts or splittings in the FPR spectmm, there are also tenns that involve only nuclear spms. Aside from their importance for the calculation of FNDOR spectra, these tenns may influence the FPR spectnim significantly in situations where the high-field approximation breaks down and second-order effects become important. The first of these interactions is the coupling of the nuclear spin to the external magnetic field, called the... 

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

FIGURE 13 3 (a) In the absence of an external magnetic field the nuclear spins of the protons are randomly oriented (b) In the presence of an external magnetic field Xq the nuclear spins are oriented so that the resulting nuclear magnetic moments are aligned either parallel or antiparallel to Xq The lower energy orientation is the one parallel to Xq and more nuclei have this orientation... 

FIGURE 13 4 An external magnetic field causes the two nuclear spin states to have different energies The difference in energy AE is proportional to the strength of the applied field... 

Section 13 3 In the presence of an external magnetic field the +j and —5 nuclear spin states of a proton have slightly different energies... 

Section 13 4 The energy required to flip the spin of a proton from the lower energy spin state to the higher state depends on the extent to which a nucleus is shielded from the external magnetic field by the molecule s electrons... 

No energy difference in nuclear spin states in absence of external magnetic field... 

There are in principle also energy levels associated with nuclear spins. In the absence of an external magnetic field, these are degenerate and consequently contribute a constant term to the partition function. As nuclear spins do not change during chemical reactions, we will ignore this contribution. 

The energy 7i(S) of a given configuration of N spins is made up of two parts (1) a contribution that arises solely from the inter-spin molecular forces (= Hst s), and (2) a contribution that is due to the interaction between the spins and any external magnetic fields (= Since 5, is effectively the magnetic moment... 

Figure 13.1 (a) Nuclear spins are oriented randomly in the absence of an external magnetic field but (b) have a specific orientation in the presence of an external field, B0. Some of the spins (red) are aligned parallel to the external field while others (blue) are antiparallel. The parallel spin state is slightly lower in energy and therefore favored. 

Before being placed in a magnetic field, the nucleus is spinning on its axis, which is stationary. The external magnetic field (like that generated... 

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