Ortho spin positronium

Positron annihilation lifetime spectroscopy (PALS) provides a method for studying changes in free volume and defect concentration in polymers and other materials [1,2]. A positron can either annihilate as a free positron with an electron in the material or capture an electron from the material and form a bound state, called a positronium atom. Pnra-positroniums (p-Ps), in which the spins of the positron and the electron are anti-parallel, have a mean lifetime of 0.125 ns. Ortho-positroniums (o-Ps), in which the spins of the two particles are parallel, have a mean lifteime of 142 ns in vacuum. In polymers find other condensed matter, the lifetime of o-Ps is shortened to 1-5 ns because of pick-off of the positron by electrons of antiparallel spin in the surrounding medium. 

Positronium can exist in the two spin states, S = 0, 1. The singlet state (5 = 0), in which the electron and positron spins are antiparallel, is termed para-positronium (para-Ps), whereas the triplet state (5 = 1) is termed ortho-positronium (ortho-Ps). The spin state has a significant influence on the energy level structure of the positronium, and also on its lifetime against self-annihilation. 

A positron in an electronic media can pick up an electron and form a neutral atom called Positronium (Ps) [9], The existence of Ps and its chemical reaction with molecules was detected from annihilation photons in 1951 [10], Ps is formed in most molecular systems. Due to the different combinations of positron and electron, there are two states of Ps the para-Ps (p-Ps) from the anti-parallel spin, and the ortho-Ps (o-Ps) from the parallel spin combination. The lifetime and the annihilation events for p-Ps and o-Ps are very different from each other, as given by electromagnetic theory. Figure 1.1 shows basic physical properties of Ps and compares them with the H atom, although it should not be considered an isotope of H (see problems 1.5 and 1.6 and answers at the end of this chapter). 

Positrons emitted for a radioactive source (such as 22Na) into a polymeric matrix become thermalized and may annihilate with electrons or form positronium (Ps) (a bound state of an electron and positron). The detailed mechanism and models for the formation of positronium in molecular media can be found in Chapters 4 and 5 of this book. The para-positronium (p-Ps), where the positron and electron have opposite spin, decays quickly via self-annihilation. The long-lived ortho positronium (o-Ps), where the positron and electron have parallel spin, undergo so called pick-off annihilation during collisions with molecules. The o-Ps formed in the matrix is localized in the free volume holes within the polymer. Evidence for the localization of o-Ps in the free volume holes has been found from temperature, pressure, and crystallinity-dependent properties [12-14]. In a vacuum o-Ps has a lifetime of 142.1 ns. In the polymer matrix this lifetime is reduced to between 2 - 4 ns by the so-called pick-off annihilation with electrons from the surrounding molecule. The observed lifetime of the o-Ps (zj) depends on the reciprocal of the integral of the positron (p+(rj) and electron (p.(r)) densities at the region where the annihilation takes place ... 

Positroniums (Ps) have two spin states ortho (o-Ps) (triplet) and para (p-Ps) (singlet). In condensed matter 75% of the Ps formed will be o-Ps and 25% p-Ps and their existence will depend on the existence of regions with low electron density [4]. The lifetime of positrons depends on the overlap integral of the wave functions of the positron and local electrons and, thus, it is related with the electronic structure of the material [5]. Since the positrons thermalize after a few ps, and the subsequent lifetime is roughly two orders of magnitude higher than the thermalization time, the lifetime of positrons within the matter will effectively depend upon the local electron density [5]. Thus, PALS implies the measurement of the lifetime, t, which is the inverse of the annihilation rate, X, defined by [ 1 ] C p r)p r)dr (1)... 

The spin value of both the electron and the positron is 1/2. (The absolute value of the magnetic moment of the positron agrees with that of the electron, i.e., 1 Bohr magneton, but its sign is positive and hence its direction is parallel with the spin.) Accordingly, depending on whether the spins of the electron and the positron in the positronium display antiparallel or parallel orientations, the resultant spin value of the Ps may be 0 or 1 (h/27r). The name of the former is singlet or para-Ps ( Sq. Ps), and that of the latter is triplet or ortho-Ps ( Sji Ps). The former decomposes by 2y- and the latter by 3y-annihilation. 

The most general interaction, which occurs in all materials, is pick-ofT interaction. The essence of this is that positron of the positronium atom in the triplet state is annihilated not by its own electron, but undergoes 2y-annihilation with some antiparallel-spin electron of a molecule encountered during collision with the molecules of the medium. As a result of the interaction, the lifetime of the ortho-positronium is shortened, although, because of the shielding effect of its own electron, not to the extent that it would have been if it had been destroyed in free annihilation. Pick-off interaction occurs to a significant extent particularly in the condensed phase. 

Another important type of positronium interactions is ortho-para conversion. This can take place if the medium includes paramagnetic species containing unpaired electrons. On collision with such a species, the direction of one of the parallel spins in the orrfco-positronium is reversed, and at the same time the direction of the spin of the unpaired electron in the colliding molecule also reverses. In accordance with its lifetime, the resulting para-positroniunr is then rapidly annihilated. Hence, this effect also leads to a decrease in the lifetime of the positronium. 

A certain fraction of these positrons, however, may enter the bound state of the positronium (Ps), by combining with an electron. Ps can be formed in two ground states either in the triplet or ortho state, with parallel spin orientation and an intrinsic average annihilation lifetime of 1.4 x 10" s, or in the singlet or para state with antiparallel spin orientation, which has an intrinsic average lifetime of 1.25 x 10"l s (Fig. 3). 

Positron Annihilation Lifetime Spectroscopy (PALS) provides a measure of free volume holes or voids, free volume, and free volume distribution, at an atomic scale. The technique exploits the fact that the positively charged positron (e" ), the antiparticle to the electron, preferentially samples regions of low positive charge density. When injected in a polymer matrix, thermalized positrons can combine with an electron to form a bound state, known as positronium (Ps). This species can only exist in a void and it rapidly annihilates on contact with the electron cloud of a molecule. For polymer studies using PALS, it is ortho-positronium (oPs, a triplet state) which is of interest. The oPs spin exchanges with electrons of opposite spin on the walls of the cavity and it is annihilated. Thus, the oPs lifetime, 13, gives a measure of the mean free volume cavity radius, whereas the relative intensity of... 

In the case of positronium atoms the spin plays a more significant role and distinguishes ground states much more significantly. Determined hy the relative orientation of the spins of the constructing electron and positron, the spin of a Ps atom is either 0 or 1 i. The former is called singlet or para-Ps Ps), while the latter is the triplet or ortho-Ps ( Si, Ps). According... 

Another important interaction of positronium is the ortho-para conversion. It occurs when the substance contains paramagnetic particles with unpaired electrons. When colliding with such a particle, the orientation of one of the parallel spins of ortho-positronium may be reversed, simultaneously with the reversion of the spin of the unpaired electron of the colliding molecule. This interaction takes place via electron exchange between the molecule and o-Ps. The pflra-positronium formed by this process annihilates very rapidly, according to its short mean lifetime. Consequently, this effect also leads to the decrease of the lifetime of positronium. Ortho-para conversion can be demonstrated by the following reaction scheme (vertical arrows show the directions of the spins) ... 

Molecular free volume (distribution) of a sample probed by the ortho positronium (o-Ps) formed by the parallel spin interaction of injected positron atom with the electron of the sample Second order nonlinear optical imaging of chiral crystals (SONICC)... 

Figure 23 Spin orientation for ortho- and para-positronium.

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