Velocity, Larmor, angular

From equation (5.61), the Larmor angular frequency or velocity o l is equal to the velocity of the end of the vector L divided by the radius of the circular path shown in Figure 5.5... 

We have abstracted so far from the so-called Thomas precession. This originates in the relativistic transformations which account for the fact that the electron is moving in a curved path around a fixed nucleus. If an axis of the gyroscope obeys an own dynamical precession with the Larmor angular velocity coL = (e/m)B, then the corrected precession in the inertial system associated with the fixed nucleus is (o = (oL + o>r, the Thomas precession being... 

The fundamental magnetic properties of nuclei are well described elsewhere. I will begin with the bulk magnetization vector M for a series of nuclei of the same type. This is parallel to the external magnetic field Bq and is the resultant of individual magnetic moment vectors fi, precessing about Bq with the Larmor angular velocity... 

It cannot be emphasized too much that the resonant frequency in NMR is proportional to the magnetogyric ratio, y, and to the laboratory magnetic field strength, B0. This relationship forms the basis of nearly every phenomenon observed in NMR. There are two ways to measure the precession rate the angular velocity, co0, in units of radians per second and the frequency, v0, in units of cycles per second or hertz. In this book we will use frequencies in hertz. This frequency is sometimes called the Larmor frequency, and the zero subscript refers to this fundamental frequency, which results from the laboratory magnetic field interacting with the nucleus magnetic field. 

The precession frequency, also called the Larmor frequency, is represented as v0 ( new-zero, in hertz or cycles per second). The division by In is sometimes omitted because the units of y can be expressed in hertz per tesla rather than radians per seconds per tesla. When the Larmor frequency is represented in units of radians per second it is called the angular velocity or co0. These are related by a factor of In ... 

The first term represents the couple due to the electric field acting on an electron situated at the centre of gravity of the orbit the second term corresponds to Larmor s theorem, and signifies an additional rotation of the vector P about H with the angular velocity... 

In Chapter I, we introduced the angular velocity of the magnetization around Hj in the rotating frame as u)j=yHj, in analogy with the Larmor frequency in the laboratory frame. This physical picture of the effect of Hj breaks down for 1>% when the non-zero quadrupole interaction makes the energy levels unequal. The basic principles are treated in Chapter VII, Section II.B.(c) of Abragam, 1961 (Appendix A) but our discussion relies on some lecture notes by Schmidt (1972). 

The angular velocity can be converted to the frequency of precession Vn. known as the Larmor frequency, by dividing by lir. Thus,... 

---