Recoil line

An additional line ( Coulomb-recoil line) appears to be... 

An additional line ( two-transverse-photon-recoil line) appears to be ------------- ... 

Figure 4. a - Landscape and b - isocontour map representations of the incoherent neutron scattering function for the proton harmonic oscillator in one dimension. The intensity is a maximum along the recoil line labelled H. Recoil lines for oscillators with masses corresponding to D, C and O atoms are shown. For a fixed incident energy, only momentum transfer values inside the parabolic area (dashed lines) can be measured. 

The full spectral form is seen in the data obtained on a chopper spectrometer, see Figs. 9.18 and 9.19 [68]. The continuum is a very broad response that tracks the unit-mass recoil line and is by far the strongest spectral component. Especially since the unbound scattering cross section of hydrogen, 20 bam ( 2.1), should be used in calculations of this effect. Analysis of this spectmm has proved very difficult because the width of the response. Fig. 9.19, far exceeds conventional predictions. Since neutrons cannot determine the electrical nature of the scatterer directly H" ", H , or H are all possibly present. 

Fig. 37. Recoil line abc, and recoil energy (hatched area) for a given magnet material.

Islands of intensity are observed for the out-of-plane and in-plane bending modes at about 1000 and 1400 cm , respectively, for the overtone 2 x 7 OH at 1850 cm and for the broad stretching mode at 2800 cm. The maxima of intensity for all observed eigenstates are very close to the recoil line for the proton mass, with only one exception for the in-plane bending 8 CO3 at 650 cm . A more quantitative analysis... 

Figure 8.7 (Plate3) S(Q,u>) for powdered KHCO3 at 20 K measured with a fixed incident energy of 500 meV. The recoil line for protons is superimposed (white line).

Velocity recoils are measured at short times after tire initial ultraviolet excitation pulse by probing tire nascent Doppler profiles for tire different spectral lines probed in tliese last steps. 

The pay-off roll is unwound by the tension of the sheet, caused by the speed of the recoiler at the finishing line and the bridles positioned at different locations. The pay-off roll motors therefore operate in a regenerative mode and can feed-back the energy thus saved to the source of supply, if desired. This can be done by using a full-wave synchronous inverter, as shown in Figures 6.31 or 6.33. 

The recoiler is driven by motor M - that adjusts its speed and tension as calculated for the whole process line. It is this drive and the bridles that maintain the required tension throughout the process and make the pay-off reel drives operate as regenerative units. 

The absolute precision of ERS therefore depends on that of da/dfl (Ej, (t>). Unfortunately, some disagreement prevails among measurements of the recoil cross section. One recent determination is shown in Figure 4a for (t> = 30° and 25°. The convergence of these data with the Rutherford cross section near 1 MeV lends support to their validity. The solid lines are least squares fits to the polynomial form used by Tirira et al.. For (t> = 30°, the expression reads ... 

Fig. 3.64. H depth profile of an H-im-planted Si sample obtained with 6-MeV C projectile ions for different recoil angles 9. q gives the charge ofthe incident ions. The experimental depth profiles (full line) are compared with simulated spectra (dashed line-SIMNRA, dotted line - DEPTH) [3.177].

As a second example, results from a TOP ERDA measurement for a multi-element sample are shown in Fig. 3.65 [3.171]. The sample consists of different metal-metal oxide layers on a boron silicate glass. The projectiles are 120-MeV Kr ions. It can be seen that many different recoil ions can be separated from the most intense line, produced by the scattered projectiles. Figure 3.66 shows the energy spectra for O and Al recoils calculated from the measured TOF spectra, together with simulated spectra using the SIMNRA code. The concentration and thickness of the O and Al layers are obtained from the simulations. 

The tensile stresses acting in the direction of converging stream lines can ellipsoidally deform the big particles, but not so much as to form fine fibrils from small particles (region B). The matrix are also elongated in the converging section. As they pass the die exit (region C), recoil of the matrix occurs to release the stored energy... 

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

The recoil effect causes an energy shift of the emission line from Eq to smaller energies by an amount r, whereby the y-photon carries an energy of only Ey = Eq — Ep. However, a recoil effect also occurs in the absorption process so that the photon, in order to be absorbed by a nucleus, requires the total energy Ey = Eq+ r to make up for the transition from the ground to the excited state and the recoil effect (for which and Py will have the same direction). 

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). 

Fig. 2.4 Energy separation of y-emission and absorption lines caused by recoil of resting free nuclei (2 r lO T, note the three separate sections of the energy scale). Since there is virtually no overlap between emission and absorption line, resonant absorption is not possible...

The arguments seen in section 2.3 suggest that resonant y-absorption should decrease at very low temperatures because the Doppler broadening of the y-lines decreases and may even drop below the value of the recoil energy. In his experiments with solid sources and absorbers, however, R.L. Mossbauer ([1] in Chap. 1) observed on the... 

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