8 Positronium and Positron Reactions i n
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Positron Radiation Spur S. J. TAO The New England Institute, Ridgefield, CT 06877
The study of positronium and positron reactions provides an alternative means to investigate hot radical reactions in the radiation spur. Positron and positronium react with radicals or others in the radiation spur created by the energetic positron itself. The positron may compete with other electron acceptors for electrons to form positronium. The positron also may be captured by a positron acceptor. The positronium formed may react with a radical or others to form a positronium compound. These reactions can be investigated by using the methods of positron annihilation, e.g. lifetime, angular correlation, and Doppler broadening measurements.
p h e experimental results b y Shearer and Deutsch, who observed the lifetime of positrons from N a i n various gases, first suggested an appreciable amount of positronium (Ps) formation i n these gases ( J ) . Then Ore followed the suggestions by F e r m i and made a thorough theoretical study on annihilation of positrons i n gases (2). D u r i n g this study, Ore described the possible formation of Ps i n gases on the basis of the law of conservation of energy and the general aspects of collision theory. This is the well-known Ore Gap model. The statistical weights of triplet and singlet states indicate that three-fourths of these Ps atoms formed w i l l be i n triplet ortho state with lifetimes of 140 nsec decaying into three coplanar gamma quanta and one-fourth of them in singlet para state w i t h lifetimes of 0.125 nsec decaying into two colinear gamma quanta ( 3 ) . The conversion of a Ps atom from ortho to para and para to ortho during a collision with a gas molecule and b y radiation has been disr
2 2
0-8412-0417-9/79/33-175-165$05.00/l © 1979 American Chemical Society
Ache; Positronium and Muonium Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1979.
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cussed by Ore (4). The probability of conversion per collision w i t h a paramagnetic molecule is only of the order 10~ . Obviously, if orthopositronium (o-Ps) is converted to para-positronium (p-Ps) because of the shorter lifetime of p-Ps, the lifetime of o-Ps is reduced, or o-Ps is quenched, and two-quantum instead of three-quantum annihilation takes place. This k i n d of reaction was observed by Deutsch i n his studies on three-quantum decay of positrons i n oxygen (5). Meanwhile, in order to explain the anomalous dependence of the lifetime of positrons on gas pressure in C C 1 F at pressures below 0.4 atm, Deutsch has made the hypothesis of positron attachment to C C 1 F (5). Ore studied the stability of the positron compound, indicated e C l " may be stable (6), and established a dynamical stability of a lower limit of 0.07 eV to the dissociation of e H " ( 7 , 8 ) . Positronium chloride ( P s C l ) was claimed to be stable in the calculation by Simons (9). If a Ps compound is formed the o-Ps lifetime w i l l be reduced considerably because of the availability of electrons of both spin state to positron in the positronium compound. 7
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2
2
2
2
+
+
W h e n an o-Ps atom collides with a molecule, the positron i n the o-Ps atom may sense electrons in the molecule in addition to its own electrons; therefore, more annihilation may occur through the twoquantum process. The possibility of this kind of pick-off quenching to o-Ps was mentioned by Garwin (JO) and Dresden (11), and discussed thoroughly by Ferrell (12). Pick-off quenching reduces o-Ps lifetime in liquid media to several nanoseconds or less. Positron and Ps reactions can be studied by using the common methods used i n positron annihilation studies, annihilation lifetime measurement, angular correlation, or Doppler broadening of the colinear two-gamma quanta. The quenching rate and fraction of o-Ps formed can be measured from the lifetime change and fraction intensity of the o-Ps component ( i n general, the longest lifetime component) i n lifetime spectrum. The fraction of p-Ps formed and certain information regarding the quenching rate of p-Ps can be estimated from the intensity and the shape of the p-Ps component (in general, the narrow component) in either angular correlation or Doppler broadening spectrum. The reaction-rate kinetic equation of conversion was considered some years ago by Dixon and Trainor (13). It has been studied by many workers. F o r a thorough discussion of the kinetic equations, including the chemical and other probable reactions, the reader is referred to the review by Goldanskii (14). The earlier works regarding Ps chemistry and positron annihilation were collected i n a monograph (15) and the proceedings of the first International Conference on Positron Annihilation (16). M a n y review articles have appeared during the last ten years and a partial list is
Ache; Positronium and Muonium Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1979.
8.
TAO
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referred to here (14-21). This article w i l l briefly review recent studies on Ps formation and Ps reactions i n the radiation spur created by the energetic positron.
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Positronium Formation Ore Gap Model. Using argon as an example, energetic positrons lose energy quickly by collisions with argon molecules (atoms) to several tens of electron volts (22). Then a positron may lose energy by ioniza tion either by inelastic and elastic collisions with argon, or it may pick up an electron from argon, e + A r - > P s (eV) + A r +
+
(1)
Since positron and Ps are both very light, during Reaction 1 the energies possessed by A r and A r can be neglected. F r o m the law of conservation of energy we have +
E(e ) + I(Ps) — E ( P s ) + I ( A r ) +
(2)
where Ε is the kinetic energy and I is the ionization potential. Since a l l the energies mentioned here can be only positive, we obtain the threshold energy for e at which it is able to carry out the above reaction, as +
E(e ) +
t h
= I(Ar) - I ( P s ) .
(3)
Because the ionization potential of most of the gases is higher than the ionization potential of Ps (6.8 e V ) i n most of the media an energy thresh old (E(e ) ) exists at which positron is able to form Ps through Reaction 1. From Reaction 2 we have +
th
E ( P s ) — E(e ) + I(Ps) - I ( A r ) . +
(4)
If the energy possessed by the formed Ps ( E ( P s ) ) is greater than the ionization potential of Ps ( I ( P s ) ), the Ps atom formed is not stable and is easily dissociated upon consequent collisions. Therefore, only when I ( A r ) > E ( e ) > ( I ( A r ) — I ( P s ) ) , is there a chance for a positron being able to form Ps through Reaction 1. Positrons possessing energies higher than the lowest excitation level of argon lose energy quickly through inelastic collisions and Ps formation is not favorable. Therefore, only positrons w i t h energies less than the +
Ache; Positronium and Muonium Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1979.
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lowest excitation level of the medium atoms, E x ( A r ) , and higher than the threshold energy, I( A r ) — I ( P s ) , stand a good chance of forming Ps. This was the argument given by Ore (2). The energy range was named E x ( A r ) > E ( e ) > [I(Ar) +
I(Ps)]
(5)
Ore Gap by Ferrell (12). F r o m the above considerations, the fraction of Ps formed ( I ) is roughly within the following limits: Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 24, 2017 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0175.ch008
2
I(Ps)/I(Ar)
> I > [Ex(AT) -
I(Ar) + I(Ps)]/I(Ar)
2
(6)
As summarized by Green and Lee (15) the above model provided a qualitative estimate of the fraction of positrons forming Ps i n some simple gases. The above theory was not expected to hold i n compound gases, dense gases, or liquids. Because of a lack of a satisfactory theory, it was modified i n order to provide a certain theoretical explanation for the formation of Ps i n media other than dilute simple gases. Goldanskii considered the two competing slowing down and Ps for mation processes and incorporated some parameters which assessed the effect of the slowing down process in the Ore Gap model (14). Tao and Green described the effect of hot Ps reactions on the final yield of Ps (22). As more experimental data are gathered, it becomes obvious that the formation of Ps i n condensed media is somewhat related to the positron or Ps reactions with the hot radicals i n the radiation spur produced by the positron itself. Ache and his colleagues pointed out that the change of free energy of electron-capturing reactions of many cations is related to the saturation intensity of the long lifetime component (o-Ps com ponent) in aqueous solutions of the cations (23). They explained this i n terms of the Estrup-Wolfgang theory (24,25) used for hot radical reac tions and obtained
Π_n /(τI // Iτ o \)J1 - l = 2
2
