Annihilation parameters

Physical chemistry of the positron and Ps is unique in itself, since the positron possesses its own quantum mechanics, thermodynamics and kinetics. The positron can be treated by the quantum theory of the electron with two important modifications the sign of the Coulomb force and absence of the Pauli exclusion principle with electrons in many electron systems. The positron can form a bound state or scatter when it interacts with electrons or with molecules. The positron wave function can be calculated more accurately than the electron wave function by taking advantage of simplified, no-exchange interaction with electrons. However, positron wave functions in molecular and atomic systems have not been documented in the literature as electrons have. Most researchers perform calculations at certain levels of approximation for specific purposes. Once the positron wave function is calculated, experimental annihilation parameters can be obtained by incorporating the known electron wave functions. This will be discussed in Chapter 2. 

The different temperature dependencies of positron annihilation parameters... 

While the above-mentioned physical picture may appear too simplistic, at least at the present stage of development in the theory of superconductivity in HTSC [4], we must mention that it provides a broad qualitative framework to account for the observed temperature dependence of annihilation parameters, even in other high-temperature superconductors [39], provided the correct positron distribution within the unit cell is taken... 

Table 14. 2 Annihilation parameters of PsF, PsCI, PsBr, PsI, and Ps yield.

Muramatsu, H., Matsumoto, K., Minekawa, S., Yagi, Y., Sasai, S. ortho-Positronium annihilation parameters in polyvinyl alcohol with various degree of polymerization, saponification and crystallinity . Radiochim acta, 89,119. 

Thus an attempt was made to correlate (liquid scintillation) counting efficiency determined as a function of the composition of the solution with structural changes occurring in the solution as reflected in positron annihilation parameters. 

In order to determine the effect of the microstructure of the solution on the beta counting efficiency in toluene -Triton mixtures in a first series of experiments the positron annihilation parameters were determined in toluene - Triton mixtures containing various amounts of water. As can be seen from Eigs. 11 and 12, where the Parameter l2 which is correlated to the formation probability of thermal positronium, is plotted as a function of Triton (in the presence of 0 and 2 % water) concentration, increasing amounts of Triton reduce I2 to a semi-plateau value, while X2, the annihilation rate of the thermal positronium, changes only slightly. A more detailed plot of I2 at lower Triton concentration reveals that I2 remains constant up to 20 mM or 10 mM Triton in solutions containing 0 or 2 % water, respectively. 

In Fig. 21 the positron annihilation parameters are shown for a solution of 70% toluene and 30% Triton X-100 containing increasing amounts of water. Again a distinct discontinuity is observed at about 3% H2O (region I) followed by a plateau (Il)and an intermediate maximum in region III before and I2 increase abruptly at about 26% followed by a slighter monotonous increase from 30% to 50%. 

Another positron state is formed when free volume-type crystal defects are present in the metal crystal. The positively charged ionic cores are missing from these defects, so, usually they are effective traps for any positive particle, including the positron in our case. Thus, in most metals, vacancies, vacancy clusters, dislocations, and grain boundaries localize some or all of the free positrons and produce another positron state, the trapped positron. These localized positrons still can meet conducting electrons, but ionic cores are out of their reach. Accordingly, their annihilation characteristics differ from those of free positrons significantly. Different kinds of traps all have their own characteristic annihilation parameters but these parameters are very close to each other. 

On the other hand, without this trapping, Ps diffuses from one free-volume site to another in amorphous materials (Brandt et al. 1960) or gets into Bloch-state in crystalline materials (Brandt et al. 1969). In these cases the annihilation parameters are determined by a larger volume of the substance. 

I. Kanazawa, P. Sferlazzo and A.R. Moodenbaugh, 1988, Temperature and depth dependence of positron annihilation parameters in YBajCujO,, and La, gjSro ijCuOj, in Proc. American Vacuum Soc. Topical Conf (American Institute of Physics, New York) pp. 435-442. 

Early experiments with positrons were dedicated to the study of electronic structure, for example Fermi surfaces in metals and alloys [78,79], Various experimental positron annihilation techniques based upon the equipment used for nuclear spectroscopy underwent intense development in the two decades following the end of the Second World War. In addition to angular correlation of the annihilation of y quanta, Doppler broadening of the annihilation line and positron lifetime spectroscopy were established as independent methods. By the end of the 1960s, it was realised that the annihilation parameters are sensitive to lattice imperfections. It was discovered that positrons can be trapped in crystal defects i.e., the wavefunction of the positron is localised at the defect site until annihilation. This behaviour of positrons was clearly demonstrated by several authors (e.g., MacKenzie et al. [80] for thermal vacancies in metals, Brandt et al. [81] in ionic crystals, and Dekhtyar et al. [82] after the plastic deformation of semiconductors). The investigation of crystal defects has since become the main focus of positron annihilation studies. 

The lifetimes of positrons trapped in small vacancy clusters were calculated using the LDA approach. As the lattice relaxation around the cluster has a relatively small influence on positron annihilation parameters, it was not included in the calculations. The results show that the lifetime of a positron trapped by a divacancy does not differ a lot from that trapped by a monovacancy (it increases by about 10 ps for Fe and 20 ps for Al). However, the lifetime increases rapidly when the cluster grows into a two-dimensional trivacancy and then into a three-dimensional tetravacancy [72]. For large clusters, the lifetime saturates at around 500 ps. The dependence of the positron lifetime in vacancy clusters on the free volume of the cluster expressed as the number of vacancies comprising the cluster is shown in Figure 4.32. 

Positron annihilation can cause an increase in vacancy type defects due to irradiation [149,157-168,180], but the loads used during the RPV s operational lifetime (10 n/m ) are too small to produce large changes in positron annihilation parameters. Irradiation temperatures of around 300 °C cause the partial annealing of small (vacancy) defects, so that the positron lifetime remains practically unchanged or decreases after the initial period (this probably occurs after Cu, P and/or carbide precipitation, and is connected to restructuring). For more information, see [181] and Figure 4.50. 

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