Electronic Zeeman energy

The first temi describes the electronic Zeeman energy, which is the interaction of the magnetic field with the two electrons of the radical pair with the magnetic field, Bq. The two electron spins are represented by spin... 

I. Electronic Zeeman energy with the spin-orbit interaction incorporated in the anisotropic g value... 

The energy spacing A is essentially given by the electronic Zeeman energy split 0 with some reduced mass /x of the order of magnitude of one. If we assume N l we arrive at the following estimate of the quotient (k/A) ... 

Energies are given to 1st and 2nd order assuming that the electronic Zeeman energy is the dominating one, i.e. the high field approximation holds. The principal axes of the coupling tensors need not coincide with the (X, Y, Z) axes. The principal axes of the different tensors need not coincide. 

A numerical method for arbitrary nuclear spin values has been described [54] using a similar procedure as applied in the original treatment by Mims [82]. The method is thus applicable for all values of the hyperfine, nuclear Zeeman and quadrupole terms smaller than the electron Zeeman energy. The frequencies are obtained as for ENDOR in Appendix A3.3.2. The modulation amplitudes depend on the elements of a matrix denoted M by Mims. The elements are calculated as the dot product Mile = F- [83] between the nuclear state eigenvectors i for electronic level... 

The high field condition with the electron Zeeman energy gf sB hfc does not apply. 

If a proton is situated near the unpaired spin (at the broken site of a molecule), each electron Zeeman energy state will split into two (for nuclear spin I = f2) or three (for nuclear spin 1=1) states. For each nuclear spin, electron spin energy level splits into 21+1 levels. The magnetic field positions of the resonance lines for I = 1 are given by... 

The transition between levels coupled by the oscillating magnetic field B corresponds to the absorption of the energy required to reorient the electron magnetic moment in a magnetic field. EPR measurements are a study of the transitions between electronic Zeeman levels with A = 1 (the selection rule for EPR). 

Thus both the (/-factor and the Upvalues affect Tq-S mixing. In general, the two radicals comprising the radical pair will have different gr-values and therefore different Zeeman energies [the first term in equation (12)]. Likewise the upvalues and hyperfine energies [the second term in equation (12)] will differ. The difference between the LPFs for two radicals is then given by equation (13), where gx and are the electronic y-factors... 

When the Zeeman energy is large compared to the crystal field interaction, the electronic wave functions are approximately the 5z) states with energy... 

Energy level splitting in a magnetic field is called the Zeeman effect, and the Hamiltonian of eqn (1.1) is sometimes referred to as the electron Zeeman Hamiltonian. Technically, the energy of a... 

Figure 7.2 Schematic representation of coherent oscillations between states 0) and 1) of a qubit. For an electron spin placed in a dc magnetic field, oscillations can be induced via the application of an external radio frequency (rf) pulse resonant with the Zeeman energy. The amplitude 8 of the...

A major effect of the introduction of static ZFS is that of reducing the amplitude of the cosic dispersion, because the energy of most electronic spin transitions increases and can be much larger than the Zeeman energy, and larger than so that for those transitions at all magnetic fields... 

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