Zeeman interactions quantum

This corresponds to an EPR-silent sample that gives no detectable ESR spectrum at X-band frequencies because it possesses a zero-field splitting larger than the Zeeman interaction (see Chapter 6), and the energy spacing between the two lowest levels is too large to be spanned by a microwave quantum at X-band. Nevertheless, higher frequencies are able to induce transitions. Since... 

The principal interaction experienced is the Zeeman interaction (Hz), which describes the interaction between the magnetic moment of the nucleus and the externally applied magnetic field, B0 (tesla). The nuclear magnetic moment, p (ampere meter2) is proportional to the nuclear spin quantum number (/) and the magnetogyric ratio (y, radian telsa-1 second-1) ... 

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. 

We are interested in what happens when a magnetic moment fJt interacts with an applied magnetic field B0—an interaction commonly called the Zeeman interaction. Classically, the energy of this system varies, as illustrated in Fig. 2.1a, with the cosine of the angle between l and B0, with the lowest energy when they are aligned. In quantum theory, the Zeeman appears in the Hamiltonian operator... 

The classical Zeeman interaction between a magnetic moment and an applied magnetic field was defined above. In a quantum mechanical description the operators for the quantities need to be used, such as the nuclear spin I. With an externally applied magnetic field B the Zeeman Hamiltonian is given by... 

The above has adopted a classical picture for describing the interaction between an rf field and the magnetisation. However, just as for the interaction with the main static applied magnetic field there is an analogous quantum mechanical description. The interaction between the rf magnetic field and the nuclear spins is simply another Zeeman interaction. The difference for this field is that it is time-dependent. In practice, the sample is irradiated with a linearly polarised rf-field of strength 2Bj, frequency corf and phase a. 

Slight modification of the electron g-factor is due to the radiative corrections introduced through quantum electrodynamics. The magnetogyric factor is different for the Zeeman interaction and the spin-orbit term. 

The observation of a signal in NMR spectroscopy necessitates a nucleus with a nonzero spin quantum number, that is. a nucleus with either an odd mass number or an even mass number and an odd atomic number. The resulting nuclear spin produces a magnetic moment. When the nucleus is placed inside a static magnetic field, Bq the magnetic moment of the nucleus interacts with the external field, the Zeeman interaction, yielding different energy levels for the nucleus. 

---