Positronium molecule

A bound system containing a positron may be considered either as positronium bound to a positive ion or an atom or as a positron bound to the corresponding atom or negative ion. It is therefore appropriate to consider here all bound states containing positrons. Bound systems containing more than one positron, however, such as e+e+e (the anti-system of the positronium negative ion Ps ) and the positronium molecule Ps2, are considered in more detail in sections 8.1 and 8.2. 

Although positron plasmas can be considered to be systems containing many positrons, and as such technically fall within the scope of this section, we will not consider them here. Rather, we will concentrate on the theory of, and the possibilities of observing, assemblages of particles containing both positrons and electrons. These include the positronium molecule and a Bose-Einstein (BE) condensate of positronium atoms. 

Fig. 8.5. The coordinate system for the positronium molecule. Particles a and b are the two positrons and particles 1 and 2 are the two electrons.

Apart from the system consisting of two positrons and one electron, which is merely the charge conjugate of Ps, the simplest bound system containing two positrons is the positronium molecule, Ps2- In order that binding can take place, the two electrons must be in a singlet spin state, and the two positrons likewise. The wave function is therefore symmetric under the interchange of the spatial coordinates of the electrons and the positrons separately. 

Tisenko, Yu. A. (1981). Decay of the positronium molecule into a positronium atom and photons. Russian Physics J. 24 99-102. 

The calculated annihilation rate of Ps2Li+ is close to twice the spin-averaged rate, suggesting a structure in which a relatively well-defined diatomic positronium molecule is bound to the Li+ core. 

The most extensive use of the analytical formulas for four-hody wavefunctions has been by Rebane and associates in 1992 Rebane and Yusupov [27] presented a preliminary study on model problems there followed a detailed study of the positronium molecule Ps2 (e e e e ) hy Rebane et al. [28] and an application to a number of four-particle mesomolecules by Zotev and Rebane [29]. These authors then refined the branch-tracking procedure so as to make it applicable to complex parameter sets [30,31]. At this point, the use of multiconfiguration exponential wavefunctions has produced results of a quality similar to that from more extensive Gaussian expansions, hut with what appears to be a comparable amount of effort. There are at present insufficient data to indicate whether the exponential wavefunctions have significant superiority over the Gaussian functions for short-range (e.g., delta-function) properties. 

The positronium atom (Pos) was introduced in Problem 2.7. In this problem, we are concerned with the positronium molecule, (Pos)2. Indirect experimental evidence [D. B. Cassidy and A. P. Mills, Jr., The production of molecular positronium. Nature 449,195-7 (2007) ] for (Pos)2 was reported in 2007,61 years after the prediction of its existence from... 

These traps, (Fig. 6) and similar effects in the motion of holes and other charges through polymers, would eventually be correlated also with such structural probes as positron lifetimes in macromolecular solids. Extensive recent studies of positron lifetime are based on positronium decay. In this, the lifetime of o-positronium (bound positron-electron pair with total spin one) is reduced from about 140 nanoseconds to a few nanoseconds by "pick-off annihilation" in which some unpaired electron spins in the medium cause conversion quenching of orthopositronium to para-positronium. The speed of the t2 effect is supposed, among other things, to represent by pick-off annihilation the presence of defects in the crystalline lattice. In any case, what amounts to empty space between molecules can then be occupied by orthopositronium.(14,15,16) It is now found in linear polyethylene, by T. T. Wang and his co-workers of Bell Laboratories(17) that there is marked shift in positron lifetimes over the temperature range of 80°K to 300°K. For... 

During the last several years, much advance has been made concerning the smdy of bound states of the positron with small systems. The ability of various atoms, ions, and molecules to bind a positron is now well established and represent a popular subject of research. However, most of the calculations performed were done on atomic systems (or those containing just one particle significanly heavier than the positron). For example, there has been considerable interest to the positronium hydride, HPs and its isotopomers (see Refs. 128-130... 

Of most relevance to us here is the production of positronium atoms in gases or at the surface of solids, and we restrict our discussion to these situations. In gases, positronium can be created in the collision of a positron with an atom or molecule according to... 

The physical basis of the interactions of positrons and positronium with atoms and molecules... 

The threshold for positronium formation in collisions of positrons with atoms and molecules is an example of a general class of thresholds in collision processes where there is no residual long-range Coulomb interaction between the constituent subsystems in either the initial or final states. Since the original work of Wigner (1948), there has been much discussion of the effect of the opening of a new channel on those already... 

Another model of positronium formation, the so-called spur model, was originally developed by Mogensen (1974) to describe positronium formation in liquids, but it has found some applications to dense gases. The basic premise of this model is that when the positron loses its last few hundred eV of kinetic energy, it creates a track, or so-called spur, in which it resides along with atoms and molecules (excited or otherwise), ions and electrons. The size of the spur is governed by the density and nature of the medium since these, loosely speaking, control the thermalization distances of the positron and the secondary electrons. It is clear that electrostatic attraction between the positron and electron(s) in the spur can result in positronium formation, which will be in competition with other processes such as ion-electron recombination, diffusion out of the spur and annihilation. 

Table 4.1. Ore model parameters for both standard and modified Ore approaches (Fmin, / max, F °d and F °d), and the experimental fractions F for the noble gases and a variety of molecules. Note that when Eex < EPS, the minimum predictions have been set to zero see equation (4.38). See Charlton (1985a) for the origin of the measurements. In general, the fractions for the molecular gases have been found to be both density and temperature dependent. The value quoted here is for low densities and is thus expected to be the Ore contribution to the overall positronium fraction in these gases at higher densities...

Before the advent of low energy beams, the only means of investigating positron interactions with atoms and molecules was to study their annihilation. Information could thereby be obtained directly on the annihilation cross section but only indirectly for other processes such as elastic scattering. In this chapter we consider the annihilation of so-called free positrons in gases. The fate of positrons which have formed positronium prior to annihilation is treated in Chapter 7. 

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