Spin Zeeman interaction

The spin-Zeeman interaction is Mi-independent 1"vLSMlMs 1MBge(-B- ) lnv LS ... 

Analogously, the spin-Zeeman interaction involves the matrix element... 

Electron spin Zeeman interaction with relativistic correction. 

These represent the nuclear spin Zeeman interaction, the rotational Zeeman interaction, the nuclear spin-rotation interaction, the nuclear spin-nuclear spin dipolar interaction, and the diamagnetic interactions. Using irreducible tensor methods we examine the matrix elements of each of these five terms in turn, working first in the decoupled basis set rj J, Mj /, Mi), where rj specifies all other electronic and vibrational quantum numbers this is the basis which is most appropriate for high magnetic field studies. In due course we will also calculate the matrix elements and energy levels in a ry, J, I, F, Mf) coupled basis which is appropriate for low field investigations. Most of the experimental studies involved ortho-H2 in its lowest rotational level, J = 1. If the proton nuclear spins are denoted I and /2, each with value 1 /2, ortho-H2 has total nuclear spin / equal to 1. Para-H2 has a total nuclear spin / equal to 0. 

From the treatment described in chapter 4 the nuclear spin Zeeman interaction may be written as the sum of two terms, one for each nucleus,... 

The matrix elements of the anisotropic spin Zeeman interaction are ... 

The second additional term is an anisotropic correction to the electron spin Zeeman interaction, which in a molecule-fixed axis system is given by... 

The first term of Eq. 4.34 is easily recognized as the Boltzmann average of the orbital NMR shielding tensor the second term accounts for the interaction of the nuclear magnetic moment with the average spin density, induced by orbital- and electron spin-Zeeman interactions. 

The magnetic dipole operator describes the magnetic moment induced by the angular momentum of the electrons arising from the orbital motion, in contrast to the magnetic moment arising from the electron spin which we discuss when we consider the spin-Zeeman interaction. 

The second term in O Eq. 11.239, is the electron spin-Zeeman interaction describing the interaction between the spin-magnetic moment of the electron and the external magnetic field induction... 

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