Magnetic dipole radiation

For quadrupole radiation, they estimate P 2x 10-9, whereas for magnetic-dipole radiation their result was P 2 x 10-8. The experimental values lie in the range of 10 7 to 10 5. From these estimates, one concludes that the probability of significant electric-quadrupole and higher-order-multipole radiation is very small indeed. The magnetic-dipole radiation is weak but probably is of some importance, particularly in cases where the electric-dipole emission is strictly prohibited. 

One-electron submatrix elements of the spherical functions operator occur in the expressions of any matrix element of a two-electron energy operator and the electron transition operators (except the magnetic dipole radiation), that is why we present in Table 5.1 their numerical values for the most practically needed cases /, / < 6. 

The 3-j symbol represents the coupling of the angular momenta le — f and Ig = i through the magnetic dipole radiation field for which L — 1. 

Two mechanisms have been proposed to explain the appearance of an asymmetric doublet in randomly oriented substances with no magnetic ordering. One mechanism is based on the combination of the directional quantities — the angular distribution function of the magnetic dipole radiation and the Debye-Waller factor which becomes anisotropic in systems of lower than cubic symmetry. This mechanism predicts an asymmetry which should decrease as the temperature is lowered, in contradiction to the experimental observations in hemoglobin. The second mechanism is based on magnetic interactions described by the general Hamiltonian Eq. (234). 

There are, of course, other types of radiation which may also be important, for example, electric quadrapole and magnetic dipole radiation. The ratio of their intensities is given by Idipole Iquad Imag = 1 (16). Therefore in... 

Recently, the theoretical aspects of magnetic dipole radiation have been very exhaustively discussed by DeWaard and Ger-HOLM , who have, in addition, remeasured the lifetimes of some of the Z-forbidden M1 transitions included in Fig. 62, (e.g. 

The appropriate perturbative terms to add to the Hamiltonian for electric-dipole and magnetic-dipole radiation are proportional to E-D and H (L + 2S), respectively, where D is the sum over all the electrons i of r,. The vectors and H characterize the radiation field, whose direction of propagation, k, makes no appearance in the dipolar perturbations. As for the quadrupolar term, we can take advantage of a very useful notational device introduced by Innes and Ufford (1958) whereby two tensors T and t/ , when coupled to a resultant of rank w, are written as (j " (/( >)< " . We get, for the term in question, an expression proportional to where the quadrupole tensor is given by the sum over i of the... 

So far we have only treated electric dipole radiation. In a more detailed treatment the radiation field can be described by electric and magnetic multipole fields" i.e. magnetic dipole radiation, electric quadrupole radiation etc. Magnetic dipole radiation is analogous to electric dipole radiation and it depends on the magnetic dipole moment of the atom... 

Situations will be encountered where the electric-dipole transition between two levels is allowed, and others where such a transition is forbidden. It will be seen that in the latter case, apart from magnetic-dipole radiation, electric-dipole radiation is nevertheless frequently observed, albeit very much weaker. We shall look at the conditions in which a forbidden transition partly ceases to be forbidden. 

Since the Zeeman levels are equally spaced, the transitions between the levels, governed in NMR by the magnetic dipole radiation selection rule, Ami = 1, are all identical and have the value... 

The Clebsch-Gordon coefficients CG (J, M, J, M ) also contain a selection rule on AJ = J - J, For electric or magnetic dipole radiation El or Ml the evaluation of the CG coefficients yields... 

Comparing equations (2.66) and (2.84), we see that the vector potential for magnetic dipole radiation, pro-... 

It follows that the magnetic field for magnetic dipole radiation can be obtained directly from equation (2.67)... 

This, of course, means that the plane of polarization is different in the two cases. For electric dipole radiation the electric vector lies in the plane defined by r and p, while for magnetic dipole radiation it is perpendicular... 

The second term in the expansion of the classical vector potential for an oscillating distribution of current and charge, equation (2.81), contains contributions from both magnetic dipole and electric quadrupole distributions, as shown in sections 2.10 and 2.11, We therefore expect these different distributions to radiate at similar rates. Thus, whenever the electric dipole transition probabilities from a given level are identically zero we must consider the possibility of decay by electric quadrupole radiation in addition to the magnetic dipole radiation discussed in... 

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