E2 radiation

As seen in Chapter 3, the relative proportions of Ml and E2 radiation in a /-decay can be determined from the relative intensities of hyperfine components. 

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. 

The accumulated evidence, then, is in good accord with the assumption that the 2.62 Mev y-ray is emitted by the first excited state with unit intensity. On the basis of measurements of the pair conversion coefficient (which is in agreement with that expected of E2 radiation) and of angular correlations, the spin of the 2.62 Mev state was assumed to be 2 with even parity, although the measured photoelectric internal conversion coefficient lies between that of Ml and E2 radiation. 

The multipole mixing ratio S of mixed M1+E2 radiation (d = IE2/M1I) as well as the phase angle between E2 and Ml components can be obtained from the relative areas of the corresponding peaks (Kistner 1968 Wagner et al. 1968 Atac et al. 1968). The value of the phase angle has a relevance in testing the time reversal in electromagnetic interaction. No violation of time reversal was found in Mossbauer experiments (Kalvius et al. 1968 Mullen 1986). 

An important experimental criterion to discriminate the various spectroscopic processes arising in Eq. (28) is the emission direction k of the polarization. Because the incident electric fields Ei, E2 radiate along their wave vectors ki, k2, the emission directions k of the thus induced polarization are given as linear combinations of ki and k2- In the most general case (i.e. when none of the assumptions above hold) it is clear that we get an enormous number of contributions and corresponding emission directions k in the expansion (28). Employing the RWA, however, it has been shown in Ref. 25 that the polarization of 2N + l)th order only radiates into the directions... 

Figure Bl.5.5 Schematic representation of the phenomenological model for second-order nonlinear optical effects at the interface between two centrosynnnetric media. Input waves at frequencies or and m2, witii corresponding wavevectors /Cj(co and k (o 2), are approaching the interface from medium 1. Nonlinear radiation at frequency co is emitted in directions described by the wavevectors /c Cco ) (reflected in medium 1) and /c2(k>3) (transmitted in medium 2). The linear dielectric constants of media 1, 2 and the interface are denoted by E2, and s, respectively. The figure shows the vz-plane (the plane of incidence) withz increasing from top to bottom and z = 0 defining the interface.

Since an atom of a given element gives rise to a definite, characteristic line spectrum, it follows that there are different excitation states associated with different elements. The consequent emission spectra involve not only transitions from excited states to the ground state, e.g. E3 to E0, E2 to E0 (indicated by the full lines in Fig. 21.2), but also transisions such as E3 to E2, E3 to 1( etc. (indicated by the broken lines). Thus it follows that the emission spectrum of a given element may be quite complex. In theory it is also possible for absorption of radiation by already excited states to occur, e.g. E, to 2, E2 to E3, etc., but in practice the ratio of excited to ground state atoms is extremely small,... 

We are interested in the transmission of y-quanta through the absorber as a function of the Doppler velocity. The radiation is attenuated by resonant absorption, in as much as emission and absorption lines are overlapping, but also by mass absorption due to photo effect and Compton scattering. Therefore, the number Tt E2)AE of recoilless y-quanta with energies EXo E + AE traversing the absorber is given by... 

Graphite will creep under neutron irradiation and stress at temperatures where thermal creep is normally negligible. The phenomenon of irradiation creep has been widely studied because of its significance to the operation of graphite moderated fission reactors. Indeed, if irradiation induced stresses in graphite moderators could not relax via radiation creep, rapid core disintegration would result. The observed creep strain has traditionally been separated into a primary reversible component (e,) and a secondary irreversible component (e2), both proportional to stress and to the appropriate unirradiated elastic compliance (inverse modulus) [69], The total irradiation-induced creep strain (ej is thus ... 

For energy to be absorbed, radiation of a frequency equivalent to E2-El must be supplied. Thus, using the Planck relation, the condition for absorption is defined as... 

When a polymer absorbs very strongly in the visible region, near IR incident radiation is used. In a very coloured solution the scattered intensity is reduced by a factor exp(—e)2) where e is the absorption coefficient of the solvent. Hence i0 must be multiplied by exp(+e ) in order to obtain the true scattered intensity undiminished by absorption effects. For small values of efi, the quantity exp(efi) approximates well to (1 + e2) so that Eq. (42) becomes38. ... 

This particular phenomenon is depicted by the solid-line in Figure 24.1 (a). In the case of Na atom E2 designates the highly energetic 4p state and the radiation X2 obtained therefrom will appear at a relatively shorter wavelength. 

Bohr s Equation If we consider two quantized energy levels e.g., higher as E2 and lower as Ex, the radiation given out during the transition from E2 to E, may be expressed by the following equation ... 

When we are far from sources in the radiation zone, the amplitudes of electric and magnetic fields verify the equality E2 = B2. 

If the electron is now brought from the first into the second orbit, then an amount of energy must be expended, equivalent to E2 — Ev If, on the other hand, the electron moves from state 2 to state 1, then an amount of energy E2 — Ex is set free, which, according to Bohr, is released as monochromatic radiation of a frequency given by the relationship v = E2 — Ej) jh, in which h is Planck s constant. 

As has been emphasized in Chapter 24 the probabilities of Ek- and Mfc-transitions are rapidly decreasing functions of k (see also Chapter 30). Therefore, we can usually restrict ourselves to examination of the radiation of the lowest multipolarity permitted by the appropriate selection rules. Between levels of one and the same configuration both E2- and Ml-transitions are allowed, that is why we must consider them together. 

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