Quadrupole 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. 

A) with respect to the operation of inversion about the origin of the system. The electric dipole operator is antisymmetric (A) with respect to inversion at a point of symmetry. The electric quadrupole operator is inversion symmetric (S). A transition is allowed if the product function in the expression for transition moment is symmetric for electric dipole radiation and antisymmetric for electric quadrupole radiation. 

Similar substitution into the expression for k (El) with 1 = 2 for electric quadrupole radiation will eventually yield... 

Prompt y-ray emission competes with or follows the last stages of prompt neutron emission. These photons are emitted in times from 10 15-10 7s. Typical y-ray multiplicities of 7-10 photons/fission are observed. These photons, as indicated earlier, cany away 7.5 MeV. This y-ray yield is considerably larger than one would predict if y-ray emission followed neutron emission instead of competing with it. Because of the significant angular momentum of the fission fragments ( 7-10 h) even in spontaneous fission, photon emission can compete with neutron emission. The emitted y rays are mostly dipole radiation with some significant admixture of quadrupole radiation, due to stretched El transitions (J/= 7, — 2). 

Rebane, V.N., Rebane, T.K. and Sherstyuk, A.I. (1981). Possibility of observing the relaxation of higher polarization moments in electric-quadrupole radiation, Optika i Spektroskopiya, 51, 753-755. 

In Section 3 a very brief discussion of the classical theory of the radiation of energy from accelerated charged particles has been given, in order to have a foundation for later discussions of this topic. Mention is made of both dipole and quadrupole radiation. 

J is the vector sum J = Ii + Iz, and m is the vector sum m = nti — ntz. /is also known as the multipolarity of the transition, and the smaller values of J give the larger intensities. / = 1 is a dipole transition and / = 2 is a quadrupole transition, etc. If there is no change in parity during the decay it is classified as magnetic dipole (Ml) or electric quadrupole (E2). Electric dipole (El) transitions with a change in parity also come within our scope. In some cases the y decay is a mixed dipole-quadrupole radiation, so that both must be included in the calculations. 

Accordingly, the transition cannot be vibrationally induced in the usual manner. The transition is not magnetic dipole allowed because A[ does not transform like a rotation. Nor is it allowed in electric quadrupole radiation since the matrix elements of the quadrupole moment transform like squared polar vectors, and E X E = a x +, 4 -H E . Since the transition is apparently observed, a most reasonable mechanism would involve a combination of two vibrations, say E and A z. The combination band symmetry is E", and A l X E" = E which is the rep of a polar vector. 

Transition probabilities for rotational levels. The excitation of a high member of the rotational spectrum in an even-even nucleus is followed by a cascade of 2 radiation. In an even-odd nucleus the cascade is less simple because E2 cross-over transitions are possible and the transition between one level and the next can consist of a mixture oi E2 and Mi radiation. If the transition probabilities were comparable with those to be expected of single particle transitions, E2 radiation at these energies (100 kev or less) would be far weaker than Mi radiation. The existence of strong E2 components and the successful competition of the E 2 components in the cross-over transitions is a clear indication of the collective nature of these processes where presumably the whole nuclear charge contributes to the emission of quadrupole radiation. 

Formulas for the line strengths for magnetic-dipole and electric-quadrupole radiation were included by Condon and Shortley (1935) in their classic text. Only minor modifications in the standard theory were necessary to allow for the presence of a lanthanide ion in a crystal. For electric-dipole radiation, on the other hand, the sequence of representations (69) has to be replaced by the product of matrix elements... 

The existence of many plausible sources for the contributions to the observed crystal-field parameters has an interesting parallel in the extraordinary sensitivity to the environment of certain lines in the absorption spectra of the lanthanides. These lines, the so-called hypersensitive transitions, satisfy the same selection rules as electric-quadrupole radiation that is, AJ < 2. This condition was first noticed when the absorption spectra obtained by Hoogschagen and Gorter (1948) for different kinds of aqueous solutions were compared. In going from solutions of the chlorides to those of the nitrates, the lines " Iis/2 Hn,2 of Er and 19/2 - Gs/ of Nd ... 

One may show that there is a contribution also from magnetic dipole and electric quadrupole radiation (and higher terms). The electric qnadrnpole term arises because the field is not uniform over the molecule. It is most important for wavelengths 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... 

It is apparent that the angular distribution of electric quadrupole radiation is generally a rather complicated function of 0,<(> but a simple example will serve to illustrate the main features. We consider an oscillating spheroidal charge distribution. In this case the off-diagonal elements of the electric quadrupole moment tensor vanish because of the symmetry of the system. If the z-axis is taken as the axis of symmetry we have = Q22 since the tensor is... 

Fig.2.7. Angular distribution of quadrupole radiation from an oscillating spheroidal charge distribution.

We are also interested in the total power radiated since this will enable us to derive an expression for the transition probability for electric quadrupole radiation in section 7.2. From equations ( 2.96) and (2.97) we see that we require integrals over products of the cartesian compo-... 

The transition probabilities for magnetic dipole and electric quadrupole radiation are important since they can be combined with measurements of the absolute and relative intensities of forbidden lines emitted by nebulae, the aurora, or the solar corona to yield estimates of the number density, composition, and temperature existing in these various sources. We therefore proceed to obtain explicit expressions for these transition probabilities, making use of the expressions for the power radiated from the corresponding classical current and charge distributions which we obtained in sections 2.10 and 2.11. 

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