Recoil energy loss

Recoil Energy Loss in Free Atoms and Thermal Broadening of Transition Lines... 

The probability of the recoilless emission or absorption is given by the recoilless fraction f, meaning the fraction of all y rays of the Mossbauer transition that are emitted (fs) or absorbed (A) without recoil-energy loss. This is also commonly referred to as the Mossbauer fraction, Debye-Waller factor, Mossbauer-Lamb factor or, simply, the /-factor. 

If the Mossbauer atom is bound in a solid, the recoil energy may be taken up by the matrix via excitation of lattice vibrations. The recoil energy is then reduced by a factor given by the atom and the solid mass ratio. If the phonon energy is low enough, there will be a finite probability, f, that the emission (absorption) will take place with no creation or annihilation of phonon in the lattice, that is, with no recoil energy loss, and this is the Mossbauer effect. The / factor (recoil-free fraction, Debye-Waller factor, Lamb-Mossbauer factor) is given by... 

Similar to QSS, direct recoil (DR) of surface atoms produces energetic atoms that have a relatively narrow velocity distribution. DR particles are those species which are recoiled from the surface layers as a result of a direct collision of the primary ion. They escape from the surface with little energy loss through collisions with... 

The Mossbauer effect can only be detected in the solid state because the absorption and emission events must occur without energy losses due to recoil effects. The fraction of the absorption and emission events without exchange of recoil energy is called the recoilless fraction, f. It depends on temperature and on the energy of the lattice vibrations /is high for a rigid lattice, but low for surface atoms. 

Hence, nuclear resonance absorption of y-photons (the Mbssbauer effect) is not possible between free atoms (at rest) because of the energy loss by recoil. The deficiency in y-energy is two times the recoil energy, 2Er, which in the case of Fe is about 10 times larger than the natural line width F of the nuclear levels involved (Fig. 2.4). 

So far we have considered only the recoil-free fraction of photons emitted by the source. The other fraction (1 —/s), emitted with energy loss due to recoil, cannot be resonantly absorbed and contributes only as a nonresonant background to the transmitted radiation, which is attenuated by mass absorption in the absorber... 

Diffuse reflectance infrared Fourier transform spectroscopy deuterium triglycine sulphate energy compensated atom probe energy dispersive analysis energy-loss near edge structure electron probe X-ray microanalysis elastic recoil detection analysis (see also FreS) electron spectroscopy for chemical analysis extended energy-loss fine structure field emission gun focused ion beam field ion microscope... 

Non-occurrence of the inverse event was explained by Mossbauer in terms of the energy loss because of atomic recoil, during emission of the 7-ray photon. A simple calculation shows that a photon of frequency 1018 Hz has sufficient momentum to cause an Fe atom to recoil at a velocity of 102 ms-1. Alternatively, the photon is Doppler shifted because of the recoil by an amount... 

The stopping power of a material for a particular radiation is commonly expressed as the rate of energy loss (R.E.L.) or the linear energy transfer (L.E.T.) of the radiation in the material. These quantities are assumed to be proportional to the linear ion density and the specific ionization. Stopping powers range from approximately 106 e.v./cm. for fast electrons (1 Mev.) in water to 1011 e.v./cm. for fission recoils. The ranges of particles are frequently expressed in mg./cm.2, which when multiplied by the density of the material yields the range. 

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