Resonant absorption cross section

In a Mdssbauer transmission experiment, the absorber containing the stable Mdssbauer isotope is placed between the source and the detector (cf. Fig. 2.6). For the absorber, we assume the same mean energy q between nuclear excited and ground states as for the source, but with an additional intrinsic shift A due to chemical influence. The absorption Une, or resonant absorption cross-section cr( ), has the same Lorentzian shape as the emission line and if we assume also the same half width , cr( ) can be expressed as ([1] in Chap. 1)... 

Note as the discussion proceeds, the near total independence of the functional absorption spectra of the Rhodonines, based on their resonant absorption cross section, from the nature of the ionone ring and whether the chromogen was Vitamin Al, A2 or A3. While the dipole-molecular absorption of the Rhodonines in the visual spectrum may reflect a small change relative to the parent chromogen, the enhancement related to resonant-molecular absorption does not. 

The resonant absorption cross section for radiation at Lyman-a can be as high as 3A /27r [39]. Consider a volume of 1 mm diameter being illuminated with InW resonant radiation at Lyman-a. The excitation rate for an atom is then 5s-1. Suppose that we would like to cool antihydrogen atoms in a magnetic... 

Equation (5) gives the maximum value of the resonance absorption cross-section, which varies as follows with the energy ... 

The theoretical interpretation of the effect was done by R. L. Mossbauer himself, using the theory of W. E. Lamb, Jr. (8), for neutron capture by atoms in a crystal. According to this theory the resonance-absorption cross section is given by... 

Position of the emitting atom Resonance-absorption cross section Mass attenuation coefficients Line width Isotope abundance... 

The resonant absorption cross-section a(E) can be similarly expressed as... 

In these and the above equations, the a are cross sections per imit volume, the a in (8) is scattering cross section, the average loss in r per collision. The are used because the material may contain different types of atoms. The (Ta is the thermal absorption cross section r(r) the resonance absorption cross section per unit volume. The = qef is the multiplication constant divided by the resonance escape probability. The product of thermal utilization / and (Ta is the effective cross section of uranium per unit volume, i.e., its cross section per unit volume multiplied by the thermal neutron density in it and divided by the average thermal neutron density. One can write, therefore, (Tu for f(Ta- If one multiplies this with rj the result is the same as crfU where fission cross section for thermal neutrons per unit volume, p the number of fast neutrons per fission. As a result, the third term in (7) can be written also as e is the multiplication by fast effect)... 

G. I. Bell, A simple treatment for effective resonance absorption cross sections in dense lattices. Nuclear Sci. and Eng. vol. 5 (1959) p. 75. 

G. L BeU, "A Simple Treatment for Effective Resonance Absorption Cross Sections in Dense Lattices, Nwcleer Sci.a Eng.,S 1959),p.75. ... 

Fractional abundance of atoms which can absorb resonantly Absorption cross section at resonance in square centimeter Thickness of absorber in centimeter... 

The energy distribution of the emitted radiation and that of the resonant absorption cross section have identical lineshapes. Both are Lorentzian lines centered at the nuclear transition energy E, with fullwidth at half height given by the uncertainty principle energy width of the nuclear excited state. This width, the natural linewidth, is defined by... 

In addition to the preparation of a solid sample, one should also notice that the content of iron as well as the natural abundance of its Mossbauer isotope Fe is manifestly low. Thus, the intensity of Mossbauer resonance may have difficulty in meeting the requirement since the resonance absorption cross-section is relatively low. More often, samples containing iron have to be enriched with the isotope If the samples are purified from bacteria or cells in... 

The density reactivity coefficients tend to increase with bumup. This is due to plutonium buildup in the fuel Pu has a larger thermal neutron absorption cross section, fission cross section, and the resonance absorption cross section than U. Although the density reactivity coefficient decreases with increasing water density, it is kept positive for all density region (i.e., the void reactivity coefficient is negative). Hence, the core can secure the inherent safety characteristics. 

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