Positron angular distribution

Fig. 3.9. Angular distributions of positrons elastically scattered by helium. The model H5 phase shifts were used to obtain these results.

Fig. 4.5. The angular distribution of positronium formation in positron-hydrogen scattering at various incident positron wavenumbers in the Ore gap.

Fig. 4.11. The angular distribution of positronium formation in positron-helium collisions at various energies in the Ore gap (Van Reeth and Humberston (1999b). The results for E = 17.8 eV, just above the positronium formation threshold, have been multiplied by a factor of 30.

As an example, the angular distribution function for positrons annihilating in atomic hydrogen, obtained using the accurate variational wave function for zero energy positron-hydrogen scattering described in section... 

The positron-trap technique has been used by Surko and coworkers to measure the Doppler broadening of the 511 keV line for positrons in helium gas. This method does not have the drawback of the experiment described above, in which both positronium and free-positron events overlap on the angular distribution curves here the positrons are thermalized prior to the introduction of the gas and therefore cannot form positronium. A comparison of the theoretically predicted and experimentally measured Doppler spectra (Van Reeth et al., 1996) is shown in Figure 6.16. The theoretical results were obtained from the variational wave functions for low energy positron-helium scattering calculated by Van Reeth and Humberston (1995b) see equations (3.75) and (3.77). 

The author and A. Robatino have pointed out that the sharp positron spectrum resembles electron spectra found in atomic collisions by Niehaus and coworkers. [21),25] The quantum mechanics in both cases is analogous. In our point of view, the sharpness of the spectra arises from interferences arising at avoided crossings of potential curves of the molecules formed by the collision partners. In particular, such a model is consistent in a natural way with the multiple summed energies found by the G. S. I. experimenters. [15,16,19] The molecular model predicts very different angular distributions than those of the particle model. [26] The more recent discovery of electron positron pairs is equally consistent with the molecular model, as with more exotic explanations. [26]... 

A recent analysis of the G. S. I. experiments shows that the design of the experiments did not decide between the particle explanation [18,19] and the conventional, atomic physics model of the collisions. [27] Furthermore, the kinematic data of these experiments is incomplete. The sharpness in the summed energy of the electron positron pair is not unambiguous evidence of a back-to-back decay mechanism of a particle or other entity. Neither the equality of the e+, e energies nor the equal but opposite momenta are directly observed. These experiments give too little information about the angular distributions or the relative energies of the electron-positron pair. 

It seems to the author that a conventional explanation, which follows the principle of scientific parsimony, is preferable as a point of departure, before postulating new entities, involving totally new principles of physics. As experimenters still pursue with undiminished enthusiasm the possibility of a new physics, the investigation of the atomic alternative awaits the definitive test. Such a test would involve a study of the angular distribution of the electrons and/or positrons with a different geometry than that used by the. G. S. I. EPOS group. [15]... 

Hsu, F.H., Wu, C.S. (1967) Correlation between decay lifetime and angular distribution of positron annihilation in the plastic scintillator naton . 

The mean lifetime of the is 2.1974 /iS. The angular distribution of decay positrons is anisotropic. This can be understood most easily for the case where the neutrino (vq) and antineutrino (v ) are emitted exactly opposite the positron, which then exits with the maximum possible energy (m /2 = 52.3 MeV). In this case, since and i have opposite helicities, angular momentum conservation forces the positron (which at high energies acts like an antineutrino and must have positive helicity) to exit along the original muon spin direction. 

C E) is the energy distribution function and W E, ) is the angular distribution function of the decay positrons. The latter can be expressed as... 

Fig. 3. Polar diagram of the angular distribution of positrons from muon decay. The pattern with Oq 1 results if only positrons near are counted the pattern Oq = when aU positron energies are sampled with equal probability. The distributions are rotationally symmetric around the muon spin direction (z-axis).

Now the field is turned on. Using the coordinate system presented in fig. 8, we have Sy, II (-z) and By, x (since By is assumed to be the external field only). It follows that Sy processes in the ( v,z)-plane. The angular distribution W(0) of the emitted positrons is coupled to the motion of At time zero, Sy points away from Dp and Nf (t) oc (1-ao). Half a precession period later, Sy points towards Dp and Nf(t) oc (1 -I- ao). The count rate Nf(t) will thus be modulated with the amplitude ao and the muon spin precession frequency fy. One finds... 

Fig. 3.21. The angular distribution of positron and annihilation y rays for Y (Williams et al., 1966). The dashed curve is the calculated angular distribution in the free election approximation.

Fig. 3.22. The angular distributions of positron annihilation y rays for Ho in two different directions at two different temperatures (Williams and Mackintosh, 1968). The dashed curves are the calculated angular distributions in the free electron approximation.

The macrostructure of pyrolytic a-BN of density 2.19 g/cm has been studied by electron-positron annihilation. The annihilation photon angular distributions have been measured with and without superposition of a static magnetic field (B = 10 kG) at 85 K. The total concentration of point defects has been found to be about 10 cm" [11, 12]. 

The angular distribution can be understood as follows. At high energies the vector coupling 7 will only permit electrons and positrons of opposite helicity to annihilate. (See Section 1.3. This is true also of the axial-vector coupling 7 75.) The helicity amplitudes axe of the form... 

Fig. 11.16. Angular distribution in two baryon production. Polar angle distribution of (a) proton, (6) A, and (c) E with respect to the positron direction. (Kdpke and Wermes, 1989).

Annihilation of a positron by combination with an electron in a solid results in the emission of a pair of photons (for singlet states) in opposite directions (i.e. 180 degrees apart) in the zero momentum case. The electrons in a solid have a momentum distribution, however, and the photons will, therefore, be separated by an angle 180 degrees , where 0 depends on the momentum of the electrons. By measuring the angular distribution of the emitted photons the momentum distribution of electrons in the solid may be obtained and this, in turn, may lead to information on the electronic structure. 

Fig. 6.15. Cylindrically averaged angular correlation of annihilation radiation (ACAR) distributions for positron annihilation in the noble gases, (a) helium, (b) neon, (c) argon, (d) krypton and (e) xenon, from the work of Coleman et al. (1994). Reprinted from Journal of Physics B27, Coleman et al, Angular correlation studies of positron annihilation in the noble gases, 981-991, copyright 1994, with permission from IOP Publishing.

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