Precession Larmor

A qualitative explanation of these abnormally large diamagnetic susceptibilities as arising from the Larmor precession of electrons in orbits including many nuclei3 has come to be generally accepted. With the aid of simple assumptions, I have now developed this idea into an approximate quantitative treatment, described below. 

In order for relaxation to occur through Wj, the magnetic field fluctuations need to correspond to the Larmor precession frequency of the nuclei, while relaxation via requires field fluctuations at double the Larmor frequency. To produce such field fluctuations, the tumbling rate should be the reciprocal of the molecular correlation time, i.e., f), so most efficient relaxation occurs only when voT, approaches 1. In very small, rapidly tumbling molecules, such as methanol, the concentration of the fluctuating magnetic fields spectral density) at the Larmor frequency is very low, so the relaxation processes Wj and do not occur efficiently and the nuclei of such molecules can accordingly relax very slowly. Such molecules have... 

A unique situation is encountered if Fe-M6ssbauer spectroscopy is applied for the study of spin-state transitions in iron complexes. The half-life of the excited state of the Fe nucleus involved in the Mossbauer experiment is tj/2 = 0.977 X 10 s which is related to the decay constant k by tj/2 = ln2/fe. The lifetime t = l//c is therefore = 1.410 x 10 s which value is just at the centre of the range estimated for the spin-state lifetime Tl = I/Zclh- Thus both the situations discussed above are expected to appear under suitable conditions in the Mossbauer spectra. The quantity of importance is here the nuclear Larmor precession frequency co . If the spin-state lifetime Tl = 1/feLH is long relative to the nuclear precession time l/co , i.e. Tl > l/o) , individual and sharp resonance lines for the two spin states are observed. On the other hand, if the spin-state lifetime is short and thus < l/o) , averaged spectra with intermediate values of quadrupole splitting A q and isomer shift 5 are found. For the intermediate case where Tl 1/cl , broadened and asymmetric resonance lines are obtained. These may be the subject of a lineshape analysis that will eventually produce values of rate constants for the dynamic spin-state inter-conversion process. The rate constants extracted from the spectra will be necessarily of the order of 10 -10 s"F... 

Unlike these conventional techniques, NSE measures the neutron velocities of the incident and scattered neutrons using the Larmor precession of the neutron spin in an external magnetic field, whereby, the neutron spin vector acts like the hand of an internal clock, which is linked to each neutron and stores the result of the velocity measurement at the neutron itself. The velocity measurement is thus performed individually for each neutron. For this reason, the... 

Larmor precession The motion describing the rotation of the axis of the spin of a nucleus in a magnetic field. 

Our discussion has so far ignored the effect of relaxation, namely spin flip of electrons in a time comparable to the Larmor precession period ( 1 ). The apparent low field (weak bonding) component in the analysis above might be the result of relaxation. However, the decrease in relaxation time is also considered to reflect the decrease in the strength of chemical bonds between the adsorbed metal species and the substrate. Therefore, the conclusion described above is considered to remain valid. 

When the anisotropy energy is large enough it prevents any precession of the magnetic moment of super-paramagnetic crystals. The magnetic fluctuations then arise from the jumps of the moment between different easy directions. The precession prohibition is introduced into the Freed equations in order to meet that requirement every time the electron Larmor precession frequency appears in the equations, it is set to zero 12). 

The torque is simply the rate of change of angular momentum and since magnetic moment is related to angular momentum by Equation (1), one may solve Equation (6) to find the motion of the spin vector. The spin precesses about H and the angular frequency of this precession, known as the Larmor precession, is yH. This situation is illustrated in Fig. 2. 

Fig. 2. Illustration of the Larmor precession of a magnetic moment m in a field H with the rf field Hi perpendicular to H as in magnetic resonance.

The mechanics of EPR spectroscopy as to Larmor precession and the nteraction of the spin S in the applied radiation are exactly similar to that... 

The precession observed in a plane of an electron orbit of an atom when that atom hes within a uniform magnetic field. The plane will precess about the direction of the field such that a cone is traced out having an axis normal to the direction of the field. The frequency of this precession is usually symbolized by j l and is equal to eBI (Aimtc) where e is the electron charge, B is the field strength, m is the mass, and c is the velocity of the electron. Larmor precession is also important in NMR studies of enzymes. 

LANGMUIR TROUGH AND BALANCE LAPLACE TRANSFORM LARMOR PRECESSION LASER-FLASH KINETIC ANALYSIS LATENT ACTIVITY LATENT HEAT Latent heat of fusion LATENT HEAT Latent heat of vaporization LATENT HEAT Lateral binding proteins,... 

LARMOR PRECESSION MAGNETICALLY ANISOTROPIC GROUP MAGNETOTACTIC Magnetic field strength,... 

NUCLEAR MAGNETIC RESONANCE LARMOR PRECESSION LIGAND BINDING ANALYSIS LINE-SHAPE ANALYSIS LOW-BARRIER HYDROGEN BONDS ROLE IN CATALYSIS MAGNESIUM ION (INTRACELLULAR) MAGNETIZATION TRANSFER Nuclear pores,... 

The radiofrequency, or frequency with which the spin vector rotates around the central axis Oz that induces a change in states, is called the Larmor precession frequency. The Irish physicist Larmor, whose work preceded NMR, has shown independently that to, the angular rotation frequency around a central axis Oz, has a value of ... 

Fig. 1.2. Larmor precession of a spinning nucleus in a static magnetic field.

In contrast to bar magnets, the magnetic moments of spinning nuclei do not align in the direction of B0, no matter how strong this field is. Instead, the Larmor precession is accelerated by increasing the strength B0 of the field vector B0 ... 

Maximum induction current due to resonance between rf field and Larmor precession corresponds to maximum absorption of energy. Thus, the plot of the induction current in the v direction (n/2 ahead of the vector Bl i ) as a function of frequency is the NMR... 

Only those molecular motions whose frequencies lie in the region of the 13C Larmor precession lead to rapid 13C dipolar relaxation. The 13C nuclei are known to precess with a frequency of v0 % 2.26 x 107 Hz or a>0 = 2 n v0 1.42 x 108 rad/s at a field strength of... 

---