Zeeman energy spin states

When nuclei with spin are placed in a magnetic field, they distribute themselves between two Zeeman energy states. At thermal equilibrium the number (N) of nuclei in the upper (a) and lower (j8) states are related by the Boltzmann equation (1) where AE=E — Ep is the energy difference between the states. In a magnetic field (Hq), E = yhHo and... 

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...

VP-16 phenoxyl radicals [detection, 234, 632-637 reduction reactions in aqueous solution, 234, 638-640 reduction reactions in cell and nuclear homogenates, 234, 641-642] Zeeman energy of spin states, 246, 538, 593 zero-field splitting, 246,550-551. 

Transitions between the two spin states (+1/2 and -1/2) can be induced by oscillating electromagnetic radiation (v in the microwave region) applied perpendicularly to 77. The energy-level splitting is referred to as the Zeeman effect, illustrated in Figure 16.1. Normally in the EPR measurements, v is maintained at a fixed value and 77 is permitted to vary until the resonance is matched. 

Since nuclear Zeeman energies are so small, the populations of the a and f spin states differ very slightly. For protons in a 1-T field, AN/N 3x 10 . Althougli... 

The Zeeman Hamiltonian can be used to calculate the energy difference between the nuclear spin states. For a nucleus the energy eigenvalues can be obtained by taking the Hamiltonian operator given in Eq. 2.11 so that... 

This splitting into multiple states has been called the Zeeman effect. By convention, we shall assign the lower energy E to the state with /- = - 5. The difference in energy between the two spin states then is given by... 

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