S O V I E T P H Y S I C S J O U R N A L 99

COLORATION CENTERS IN CRTSTALS AS MODELS OF POSITRONIUM ATOMS AND MOLECULES OF POSITRONIUM AND POSITRON CHElvIICAL COMPOUNDS

A. A. Vorob'ev, S. A. Voreb'ev and E. K. Zavadovskaya

Izv. VUZ. Fizika, Vol. 10, No. 7, pp. 156-15q, 1967

The irradiation of ionic compounds is accompanied by the form- ation in them of radiation defects in the form of electron and hole

coloration centers.

The simplest electron center is the F-center. It is an electron

local ized on a vacant anion la t t ice point, L e . , B - + e-- --~ F. After

the addition of another electron the F-center forms an F '-center . Con- - - - - m

sequently F + e-- -~ F' or B + e + e "-~ F'. Two neighboring

F-centers form an M-center, i . e . , F+ F = 2B- + 2e- --~ M.

The subsequent more complex electron R- and N-centers may

be represented as compounds consisting of several neighboring F-cen-

ters in the ground or excited states. The other system of coloration

centers in crystals which causes the system of absorption V-bands ac-

cording to the Seitz models has been represented as formed from cation

vacancies and holes. Now other models have been proposed for color-

ation V-centers, basing them on haloid molecules in the la t t ic and the

holes local ized in them. In the classical representation of the pair

e - e + forming an atom of positronium II rotates about the general mass

center [1]. The positronium is a stable structure in the sense that a

certain amount of energy has to be expended in order to separate the e - and e + of which it is formed.

There is a difference between positronium and hydrogen atoms

in the fine structure of their levels; the explanation is the difference

in mass between the positron and the proton.

The ionizat ion energy of the positronium is half the ionization

energy of the hydrogen atom, i. e . , 6.78 eV. Each energy level of the

positronium is half of the corresponding level of the hydrogen atom.

The radius of the positronium atom in the ground state is twice the

radius of the hydrogen atom and is r n = 1.08 x 10- s cm.

A part icle of such dimensions cannot take up a position between

ions in the la t t ice of a lkal ine-haloid compounds. A positronium can

take up a position in an anion vacancy. It has been shown that it is pos-

sible for positrons P and positronium I1 to exist in defective lat t ices of

a lkal ine-haloid crystals, and their l i fe has been determined [2, 3].

In a la t t ice of the NaC1 type a positronium and a haloid can

form chemical compounds. An a n o n vacancy has an effective positive

charge of e +. When an electron e - is local ized in an anion vacancy

and an E- center is formed at a distance of the order of the dimensions

of the positronium radius the charges e + and e - are separated. A

steady state is possible for them provided they both rotate together

about the common center. Thus an F-center can be regarded as a

model of a positsonium existing in a steady state in a crystal lat t ice.

The conditions for the stable existence of an F-center or a

quasipositronium in a la t t ice may be defined in the following way [2].

The sum of the electron and positron affinity in the positronium

minus the affinity of the positmnium with the crystal must be less

than the binding energy in the positronium, i . e . , 6.78 eV.

The electron affinity in a lkal ine-haloid crystals is determined

by the electron affinity towards the haloid and is 3.94 eV for F and

3.3 eV for I. The energy of the positron affinity towards the haloid

ion can be estimated from the condition for motion of the positron in

the la t t ice field by describing it by means of a Hartree-Eock function.

When they approach one another at a distance of an ion radius the

magnitude of the positron affinity may be estimated at 1 - 2 eV. The

energy of the positsonium affinity towards the crystal may be estim-

ated as a large negative quantity. The estimates which have been

given justify the conclusion that the condition for stability of a posi-

tronium in an ideal la t t ice is not realized. F-centers in a la t t ice are

stable formations. This enables one to conclude that the effective

mass and charge possessed by an anion vacancy forms a more stable

complex with an electron than is obtained in the case of a positronium

formed in the manner II -~ e - + e +. In a la t t ice a positron has a

short life. An F-center is a stable formation, and its life can be arbi-

trarily long. The concentration of F-centers in a la t t ice can exceed

1019 cm -s. It is of interest to establish what is common and what is

different in the properties of the positronium and the F-center and the

l imits of modeling the positronium atom by means of the F-center and to

study the properties of the positronium in high concentration, by using the F-center. The F-center can also have an excited state, which

corresponds to the excited state of the positronium atom.

An F-center, having captured an electron, forms an F ' -center

in accordance with the condition F + e-- --* F' --~ 1I--. This center is

a model for a negative positronium ion in the lat t ice.

Correspondingly an M-center consisting of two F-centers can be represented as a positronium molecule, i . e . , M --~ 2F --~ II s. Complex R- and N-centers can be represented as molecules of more complex

compounds consisting of F-centers in the ground and excited states.

The model of a hole center on the basis of a quasipositronium atom

may be represented as consisting of a positron and fictitious negative

charge of a cation vacancy. Correspondingly these radiation defects

in a la t t ice can be models for chemical compounds of positronium

atoms if such compounds are possible. The positronium atom forms compounds with haloids, for example (C1 e - ) e+, etc. [4]. In a l a t -

t ice any pair II + F can be considered as a molecule of a compound

of a positronium with an anion.

The colored crystal is a body containing models of positronium

atoms and molecules of some of its compounds and is a topic for posi-

tronium chemistry.

Consequently radiation processes make it possible to obtain

in crystals chemical compounds of known compositions, quasiehemi-

cal elements of the type of isolated positronium atoms, and their

chemical compounds. It is assumed that some V-centers contain a

hole in their composition. It is possible to assume models of V-centers

with positrons but not with holes. Chemical compounds in a solid body formed with the participation of a positron P or a positronium 1I type

( p F - ) or ( I I F - ) possess interesting peculiarities. Their life, deter-

mined by the life of the positron P, is not long. The decomposition

of such a formation because of annihilation must be accompanied by

fluorescence with the escape of two quanta, each at 501 keV. These

centers can be obtained if one introduces into the la t t ice impurities

which form a solid solution with the main compound and can provide

induced activity with the emission of a positron.

REF ERENCES

1. A. G. Razumnikov, Trady Novocherkasskogo politekhniches-

kogo instituta, 47/61, 159, 1958.

2. R. Ferrel, Rev. Mod. Phys., 9.8, 308, 1956.

3. G. Fabri and E. Germagnoli, Nuovo cimento, 28, 572, 1962

4. A. Bisi, A. Fiorentinia, and L. Zappa, Phys. Rev., 181,

1023, 1963.

7 December 1966 Tomsk Polytechnic Institute