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Electric quadrupole radiation

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 [Pg.183]

The quantum-mechanical expressions for dipole radiation transition probabilities were derived from the classical expressions for the power radiated, or, by the relation [Pg.184]

The ratio of the electric quadrupole to the electric dipole transition probability is given by equations (7.1) and (7.10) as [Pg.184]

Again the effect of forbidden electric quadrupole transitions on the lifetime of a given level will be negligible if any electric dipole transitions from that level are allowed. [Pg.184]

The lifetimes of levels which can decay only by the emission of electric quadrupole radiation are expected to be very long, of the order of 10 s or more (Problem 7.3). [Pg.184]


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. [Pg.68]

Similar substitution into the expression for k (El) with 1 = 2 for electric quadrupole radiation will eventually yield... [Pg.229]

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. [Pg.288]

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. [Pg.309]

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... [Pg.119]

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 ... [Pg.137]

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... [Pg.322]

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... [Pg.43]

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... [Pg.46]

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-... [Pg.47]

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. [Pg.180]

When higher-order transitions between the Is and 2s states are considered, we find that electric quadrupole radiation is strictly forbidden since both levels have J =... [Pg.190]

Using the fact that the electric quadrupole moment operator is a symmetric second rank tensor and t.he magnetic dipole moment operator transforms as an axial vector, derive the selection rules for magnetic dipole and electric quadrupole radiation given in Table 7.1. [Pg.224]


See other pages where Electric quadrupole radiation is mentioned: [Pg.443]    [Pg.54]    [Pg.567]    [Pg.68]    [Pg.39]    [Pg.92]    [Pg.351]    [Pg.131]    [Pg.118]    [Pg.173]    [Pg.9]    [Pg.14]    [Pg.212]    [Pg.226]   
See also in sourсe #XX -- [ Pg.16 , Pg.67 ]

See also in sourсe #XX -- [ Pg.16 , Pg.67 ]




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