ABSTRACT

Up to the 1950s and in spite of the preceding advances in the field of spectroscopy, it was commonly considered as being impossible to determine the energy levels and transitions within the ground and excited states of nuclei. This had mainly two reasons:

Whereas transitions in the electronic shell of an atom can be easily measured by a common optical spectrometer due to the low lifetime of the excited state and, hence, the comparably broad line widths involved, this is not valid for the energy states of excited nuclei: Here, the lifetime of the excited state is comparably huge, the energy or frequency line width, on the other hand, comparably tiny. This effect is due to an uncertainty relation that may be written as Γ = ℏ τ , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315196640/6bf3e800-cc06-43be-adf8-892f8d78b5a4/content/eq7.tif"/>

12where Γ is the line width, τ the lifetime of the excited state and ħ Planck’s constant.

The frequency region of the electromagnetic wave here involved is X-ray, whereas the spectra of excited electrons are in the range of the visible light. Switching to the particle image, we may consider the X-ray wave as a γ-photon. Figure 3.1 illustrates the physical properties that are applicable to quantum resonance phenomena in general.

Γ is the halfwidth of the lorentzian frequency line of the γ-photon, E F the fundamental state, EI the excited one and E 0 the transition energy. Eγ is described as an energy distribution W(E) around E 0 that may be written as the famous Breit–Wigner formula: W ( E ) = Γ 2 / 4 ( E − E 0 ) 2 + Γ 2 / 4 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315196640/6bf3e800-cc06-43be-adf8-892f8d78b5a4/content/eq8.tif"/>

Due to the long lifetime of the excited energy state in the case of nuclei, the halfwidth of the lorentzian line of the γ-photon is incredibly small and uncompared to other effects in nature.

The second obstacle is the influence of the recoil. Whereas in the frequency range of electronic transitions in the shell and the subsequent emission of optical photons the hereby 13released recoil on the atom does not play any role; this is substantially otherwise in the case of excited nuclei: The influence of the recoil which decreases the energy of the emitted γ-photon is considerable. On the other hand, when such a photon is absorbed by an analogous nucleus, the recoil acts in the opposite direction, so that resonance at free nuclei cannot be observed. This is demonstrated by Fig. 3.2.

The energy levels of two neighbouring nuclei and the exchanged <italic>γ</italic>-photon. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315196640/6bf3e800-cc06-43be-adf8-892f8d78b5a4/content/fig3_1_OC.tif"/> Emission and absorption of a <italic>γ</italic>-photon regarding the recoil involved, schematically. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315196640/6bf3e800-cc06-43be-adf8-892f8d78b5a4/content/fig3_2_OC.tif"/>