Recoil momentum

Fig. 2.3 Recoil momentum and energy r imparted to a free nucleus upon y-ray emission...

For each pair of detected electrons the binding energy co and ion recoil momentum p are recorded. In a clean knockout, the recoil momentum p = -k, where k is the momentum of the bound electron when it is struck. Thus from energy and momentum conservation... 

Figure 39 shows angular distributions of Ar+ and HeAr+ for He (2 S) + Ar over a range of collision energies. The recoil momentum of the... 

This criterion is met for an atom bound (with a binding energy B greater than r°) in a collection of atoms, all of which share the required recoil momentum. Therefore, it becomes possible to observe the resonance in the solid state or viscous liquids where B is of the order of 1 eV. The effective value of M is thereby increased, resulting in a decrease in R. For example, chemical information may be obtained for atoms in an isolated particle several tens of nanometers in size, and for smaller particles where interactions with other particles or the catalyst support make the effective mass of the particle larger. The above condition, as will be shown below, is not sufficient for observation of the Mossbaucr effect. 

Gondolo, P. 2002c. Recoil momentum spectrum in directional dark matter detectors, Phys. Rev. D66, 103513... 

Modern MCP detectors permit the direct 3D measurement of LF recoil momentum vectors by measuring both spatial position (x,y) on-and time of... 

The nucleons inside a radioactive nucleus contained in a molecule interact with the electron-neutrino field and undergo the / transition—a transformation of a neutron into a proton accompanied by the emission of a / electron and a neutrino.5 The weak interaction does not affect the electron shell and the other nuclei of the molecule. For them the / decay is an instantaneous change (a jump) in the charge of the radioactive nucleus by unity. Besides this, the nucleus obtains a recoil momentum due to the emission... 

Thus, the molecular matrix element Eq. (13) is factorized into electron and vibrational-rotational matrix elements. The electron matrix element is independent of the recoil momentum, and, consequently, the electron degrees of freedom are excited only by the jump in the charge of the radioactive nucleus, whereas the excitation of vibrations and rotations is due to both the jump in the charge and the recoil of the radioactive nucleus. 

The vibrations and rotations of the daughter molecule may be excited owing both to the jump in the charge of the radioactive nucleus and to the recoil momentum of the latter. The electron excitations are due only to the jump in the charge. 

In order to perform the integration in Eq. (72), let us neglect the small recoil energy rec in the energy conservation law and perform the integration over the recoil momentum Prcc. Let us single out the kinematic factor in Mnucl (Zel dovich, 1955) ... 

Two types of kinematic range have been most-commonly observed in kinematically-complete experiments. In coplanar asymmetric kinematics 0 = 0, / Eg, Of is fixed at a value less than about 30° and Og is varied. An important subregion is known as the Bethe ridge. Here we are close to the billiard-ball kinematics of a free two-electron collision, for which the recoil momentum p of the ion, given by... 

Electron momentum spectroscopy (McCarthy and Weigold, 1991) is based on ionisation experiments at incident energies of the order of 1000 eV, where the plane-wave impulse approximation is roughly valid. The differential cross section is measured for each ion state over a range of ion recoil momentum p from about 0 to 2.5 a.u. Noncoplanar-symmetric kinematics is the usual mode. In such experiments the distorted-wave impulse approximation turns out to be a sufficiently-refined theory. Checks of this based on a generally-valid sum rule will be described. 

Fig. 11.12. The experimental and theoretical branching ratios for the 1000 eV ionisation of lead to the 6ps/2 and 6pi/2 states of Pb+, plotted against recoil momentum p (Frost et al, 1986). The calculations with target-state correlations in the plane wave impulse approximation are indicated by MCDF, multiconfiguration Dirac—Fock EAL, extended average level OL, optimal level. Cl indicates ion-state configuration interaction.

The geometry of the experiment is shown in fig. 11.14. The axis of quantisation z is the direction of the light beam. The atomic sodium beam is incident in the x direction and the electron beam in the y direction. The schematic diagram also shows the 3px and 3py lobes of the target charge cloud for the 3pi substate. The scattering plane is the zy plane so that the component px of the recoil momentum p is observed in noncoplanar-symmetric kinematics. Because of the finite angular resolution of the spectrometer the components py and pz are of the order of 0.06 a.u. rather than zero. 

Mossbauer effect Resonance absorption of gamma radiation by specific nuclei arranged in a crystal lattice in such a way that the recoil momentum is shared by many atoms. It is the basis of a form of spectroscopy used for studying coordinated metal ions. The principal application in bioinorganic chemistry is 57Fe. The parameters derived from the Mossbauer spectrum (isomer shift, quadrupole splitting, and the hyperfine cou-... 

Fig. 9.4 Recoil momentum of an atom for a fixed direction of the absorbed photons but different directions of the emitted fluorescence photons...

The absorbed photons, however, all come from the same direction. Therefore, the momentum transfer for q absorptions adds up to a total recoil momentum p = qhk (Fig. 9.4). This changes the velocity v of an atom which flies against the beam propagation by the amount Au = hk/M per absorption. For q absorption-emission cycles we get... 

Fig. 9.68 Momentum transfer and recoil momentum in a stimulated Raman transition...

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