Positron spectra

The unitary transformation U can be determined as the product of two ttansfor-mations f/of/i- The first transformation f/o is the free-particle Fouldy-Wouthuysen transformation and leads to the approximate separation of the electronic and positronic spectra = U HqUq. The second unitary transformation is... 

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]... 

The nuclei of mass 39 are analogous to 0 in that single particle (actually hole) levels are expected to occur in Ca. There is no evidence on this point. The decay to appears from the positron spectrum end-point to be governed by the Coulomb energy, and in this case the T =— nucleus is again stable. A also decays, by a forbidden transition, to the 3/g+ ground state of Analysis of the shape of the beta spectrum classifies the transition as Zl/ = 2, yes, so that... 

A typical 19F NMR spectrum of a compound with a trifluorovinyl group is given in Fig. 6.20. This compound is the chemical precursor of the drug known as EF5, which is used in positron emission tomography imaging to detect hypoxic tissue. 

If the kinetic balance condition (5) is fulfilled then the spectrum of the L6vy-Leblond (and Schrodinger) equation is bounded from below. Then, in each case there exists the lowest value of E referred to as the ground state. In effect, this equation may be solved using the variational principle without any restrictions. On the contrary, the spectrum of the Dirac equation is unbounded from below. It contains the negative ( positronic ) continuum. Therefore the variational principle applied unconditionally would lead to the so called variational collapse [2,3,7]. The variational collapse maybe avoided by properly selecting the trial functions so that they fulfil the boundary conditions specific for the bound-state solutions [1]. 

Figure 2a, b. Antineutrino number distribution function for the 1.64 Hq core evolved with the soft EOS. The maximum is normalized to unity, as only the shape of the curve is being considered. Also shown is the shape of the expected positron number spectrum that would be produced by electron antineutrino capture on protons taking into account detector characterestics. 

After a large number of composite slices, when all positrons are expected to have > relative intensity I, of a certain lifetime r, in the spectrum is... 

Fig. 1.7. Comparison of the energy spectrum of / + particles from a radioactive source with that for moderated positrons.

Additional, but rather less direct, evidence for the accuracy of the variational results for models H5 and H14 is provided by the excellent agreement between the theoretical and experimental lifetime spectra for positrons diffusing in helium gas, where calculation of the theoretical spectrum requires a knowledge of the momentum transfer and annihilation cross sections, both of which are derived from the wave functions generated in the calculations of the elastic scattering phase shifts. A detailed discussion of positron lifetime spectra is given in Chapter 6. 

Traditionally, experimental values of Zeff have been derived from measurements of the lifetime spectra of positrons that are diffusing, and eventually annihilating, in a gas. The lifetime of each positron is measured separately, and these individual pieces of data are accumulated to form the lifetime spectrum. (The positron-trap technique, to be described in subsection 6.2.2, uses a different approach.) An alternative but equivalent procedure, which is adopted in electron diffusion studies and also in the theoretical treatment of positron diffusion, is to consider the injection of a swarm of positrons into the gas at a given time and then to investigate the time dependence of the speed distribution, as the positrons thermalize and annihilate, by solving the appropriate diffusion equation. The experimentally measured Zeg, termed Z ), is the average over the speed distribution of the positrons, y(v,t), where y(v,t) dv is the number density of positrons with speeds in the interval v to v + dv at time t after the swarm is injected into the gas. The time-dependent speed-averaged Zef[ is therefore... 

Fig. 6.5. Examples of positron lifetime spectra for (a) argon and (b) xenon gases. The argon data are for a density of 6.3 amagat at 297 K. The channel width is 1.92 ns. In (a), (i) shows the raw data, (ii) shows the signal with background removed, (iii) shows the free-positron component and (iv) shows the fitted ortho-positronium component. In (b), the spectrum for xenon is for room temperature and 9.64 amagat and has a channel width of 0.109 ns. The inset shows the fast components as extracted and discussed by Wright et al. (1985).

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