Potential energy magnetic dipole

In the presence of an external magnetic induction B this dipole Pm has a potential energy given by the laws of classical electromagnetism as... 

Atomic and molecular magnetic dipoles have to obey the angular momentum laws of quantum mechanics, since they are proportional to angular momenta. Each dipole can therefore make just a number of orientations with an applied magnetic induction B. Each allowed orientation corresponds to a different potential energy, and absorption of a photon with suitable energy may cause a change in orientation. 

In the MEG, we do not destroy the potentializing source dipole, which is the magnetic dipole of the permanent magnet. We include the vacuum interaction with the system, and we also include the broken symmetry of the source dipole in that vacuum exchange—a broken symmetry proved and used in particle physics for nearly a half century, but still inexplicably neglected in the conventional Lorentz-regauged subset of the Maxwell-Heaviside model. We also use the extended work-energy theorem, as discussed. 

Assume the particle is placed into an external magnetic field pointing along the z-direction (B = Bfz). The potential energy for a magnetic dipole in such a field is ... 

Assume that the magnetic moments ijl and in Eq (15.19) are both directed along the z-axis. Show that the angular dependence of the dipole-interaction potential energy then contains the factor (3 cos 6 — ). Show that this quantity vanishes when averaged over all orientations. 

A whole range of different properties can be obtained by choosing other interaction operators W t) and thus other V and A operators. Examples are given by Olsen and Jorgensen (1985) and include a diversity of properties such as derivatives of the dipole polarizability, the B term in magnetic circular dichroism, the first anharmonicity of a potential energy surface, two-photon absorption cross sections and derivatives of the dynamic hyperpolarizability. 

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