Positron states transitions

Simultaneous measurement of positron lifetime and the momentum of the annihilating pair can give information on thermalisation and transitions between positron states (and hence on chemical reactions of positrons or Ps). The most recent version uses MeV positron beams [35]. A full description of AMOC can be found elsewhere in this volume. 

AMOC allows time-dependent observations of the occupations and transitions of different positron states tagged by their characteristic Doppler broadening. Chemical reactions of positronium have been studied by beam-based AMOC as well as bound states between positrons (e+) and halide ions (cf. Sect. 2). 

For free particles this point of view has indeed some attractive features. There are, however, situations where the sign of the energy does not distinguish between electronic and positronic behavior. Consequently, transitions from electronic to positronic states cannot be excluded. A famous example is the Klein paradox, where a potential step divides space into two regions with a different interpretation of particles and antiparticles. If the step size is larger than twice... 

All that then needs to be done is to collect the individual terms to obtain the total transformed two-electron term, i.e., transformed Coulomb plus transformed Breit terms. Then, the reduction to twoelectronic states (for the positronic states one would have to replace them by (—Ij) and through a transition from the (4 x 4)-dimensional Dirac matrices a to the (2 x 2)-dimensional Pauli matrices a. Although we skip all these steps, we discuss the result in the next section. 

In practical situations any intermediate case is possible. In the case of the transition-limited regime, the link between positron states in the specimen and the experimental positron lifetime spectrum is provided by the simple trapping model (STM) [103]. Let m t) denote the probability that positron will be present in the specimen at time t. In the case of an ideal crystal i.e., if no defect is present in the specimen), positrons will be delocalised in the material. The time when positron thermalisa-tion is accomplished is chosen as t = 0, so m t = 0) = 1. The probability m t) decreases exponentially with time ... 

We have briefly covered some of the important developments in structural characterization techniques. There are many other techniques such as Mossbauer spectroscopy, positron annihilation and Rutherford backscattering which have wide applications. Mossbauer spectroscopy is specially useful to investigate different oxidation states, spin-states and coordinations of metal ions, phase transitions, magnetic ordering. 

Table 2.1 Isotopes of arsenic (Audi et al., 2003 Holden, 2007 Lindstrom, Blaauw and Fleming, 2003).15As is the only stable arsenic isotope. The possible decay modes include electron capture (EC), electron emission (P ), positron emission (P+), proton decay (p), internal transition (IT), and neutron emission (ne). Superscripts on some of the arsenic isotope mass numbers designate excited-state isomers. The first (lowest energy) excited state is designated with an m and a second excited state is designated with an n. ...

In the case of the positronium spectrum the accuracy is on the MHz-level for most of the studied transitions (Is hyperfine splitting, Is — 2s interval, fine structure) [13] and the theory is slightly better than the experiment. The decay of positronium occurs as a result of the annihilation of the electron and the positron and its rate strongly depends on the properties of positronium as an atomic system and it also provides us with precise tests of bound state QED. Since the nuclear mass (of positronium) is the positron mass and me+ = me-, such tests with the positronium spectrum and decay rates allow one to check a specific sector of bound state QED which is not available with any other atomic systems. A few years ago the theoretical uncertainties were high with respect to the experimental ones, but after attempts of several groups [17,18,19,20] the theory became more accurate than the experiment. It seems that the challenge has been undertaken on the experimental side [13]. 

The techniques used in the three measurements of the 23S —23Pj, J = 0,1,2 intervals are summarized in Figure 8. In all of these experiments the initial state is the 23S i state formed from positrons striking a metal target with about 100 eV kinetic energy. The first two measurements [15] [16] detected the transition as a 243 nm Lyman-a photon in delayed coincidence with a detected 7 ray from the annihilation of orthopositronium. The most recent and most precise experiment [17], which we detail below, uses only the Lyman-a detection. 

The wavelength dependence of laser-stimulated recombination could be used to perform spectroscopy. The recombination rate is closely related to the distribution of positrons in energy and also to the population of bound levels close to the ionization threshold [17]. The spectral resolution for the first step of laser-stimulated recombination is thus limited by the energy distribution of the positrons. Laser-induced two-step recombination, first into a high-lying state with the subsequent stimulation of a bound-bound transition into a lower lying state, offers a first possibility for precise laser spectroscopy [18]. 

Decay mode (emission), and energy (MeV ( if to ground state)), separated by / if several modes if in parentheses, mode produces a shortlived daughter, or occurs <10% Emissions a=alpha =2He4++ P"=electron P+=positron gamma, n=neutron EC=electron capture from K or L-shell (n,2a) =nucleus absorbs neutron and emits 2a IT=internal transition SF=spontaneous fission... 

Studies on other high-temperature superconductors Positron annihilation measurements across Tc, coupled with the calculations of PDD have been carried out in a variety of hole-doped superconductors that include YBa2Cu40g [48], Bi-Sr-Ca-Cu-0 [49], and Tl-Ba-Ca-Cu-0 [50, 51] systems. We will not labor with the details here, except to state that a variety of temperature dependencies are seen and these can be rationalized when the results are analysed in terms of positron density distribution and the electron-positron overlap function [39]. These calculations show that the positron s sensitivity to the superconducting transition arises primarily from the ability to probe the Cu-O network in the Cu-0 layer. The different temperature dependencies of lifetime, i.e., both the increase and decrease, can be understood in terms of a model of local electron transfer from the planar oxygen atom to the apical oxygen atom, after taking into account the correct positron density distribution within the unit cell of the cuprate superconductor. 

In most cases the emission of nucleons, electrons or positrons leads to an excited state of the new nucleus, which gives off its excitation energy in the form of one or several photons (y rays). This de-excitation occurs most frequently within about 10 s after the preceding or P decay, but in some cases the transition to the ground state is forbidden resulting in a metastable isomeric state that decays independently of the way it was formed. 

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