Zeeman energy Hamiltonian, electronic

Sx, Sy, and Sz are the three components of the spin operator, D and E are the anisotropy constants which were determined via high-frequency electron paramagnetic resonance (D/kB 0.275 K and E/kB 0.046 K [10]), and the last term of the Hamiltonian describes the Zeeman energy associated with an applied field H. 

The spin Hamiltonian of a single electron (Hs) consists of two parts the Zeeman energy in a steady external field (Ho), and a random perturbation term due to local fieds (V(r)),... 

In a more detailed theory of magnetic susceptibilities, one has to ealculate the first and second order Zeeman energy, applying the approximate many-electron Hamiltonian for a eomplex ion in an external magnetic field... 

Consider the case of an isotropic, static (or time averaged) hyperfine interaction between the muon and the electron, that is represented by the following Hamiltonian, which includes the Zeeman energy terms of the electron and the muon. 

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... 

When magnetic fields are present, the intrinsic spin angular momenta of the electrons S (j) and of the nuclei I(k) are affected by the field in a manner that produces additional energy contributions to the total Hamiltonian H. The Zeeman interaction of an external magnetic field (e.g., the earth s magnetic field of 4. Gauss or that of a NMR... 

For a hydrogen atom in an external field of 10,000 G, draw a figure that shows the effect on the original 1 s energy level of including first the electron Zeeman term, then the nuclear Zeeman term, and finally the hyperfine coupling term in the Hamiltonian. 

In this appendix we collect together tables of matrix elements of r, r2, r3, z, z2, rz, and r(r2 — z2) in the scaled hydrogenic basis and perturbation corrections to the ground-state energy for the LoSurdo-Stark, Zeeman, screened Coulomb, and charmonium Hamiltonians and the one-electron diatomic ion. 

The through-space interaction is a dipolar coupling between the electron and nuclear magnetic moments. When the Zeeman interaction for both the electron and nuclear spins is the dominant term in the spin Hamiltonian of the system, the energy of the dipole-dipole interaction is inversely proportional to the third power of the dipole-dipole distance fis according to... 

The energy of an unpaired electron will now not only depend on the interactions of the unpaired electron (Zeeman level) and the nucleus (Nuclear Zeeman levels) with the applied external magnetic field, but also on the interaction between the unpaired electron and the magnetic nuclei. To explain how one derives the energy terms for such a system, a simple two-spin system (S = 1/2, I = 1/2) will be considered. The simplified spin Hamiltonian for this two-spin system (S = 1/2,... 

The isotropic g and a values are now replaced by two 3x3 matrices representing the g and A tensors and which arise from the anisotropic electron Zeeman and hyperfine interaction. Other energy terms may also be included in the spin Hamiltonian, including the anisotropic fine term D, for electron-electron interactions, and the anisotropic nuclear quadrupolar interaction Q, depending on the nucleus. Usually the quadrupolar interachons are very small, compared to A and D, are generally less than the inherent linewidth of the EPR signal and are therefore invisible by EPR. They are readily detected in hyperfine techniques such as ENDOR and HYSCORE. All these terms (g. A, D) are anisotropic in the solid state, and must therefore be defined in terms of a tensor, which will be explained in this section. 

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