References - Bogoliubov Laboratory of Theoretical Physics - JINR

SPIN CORRELATIONS OF THE ELECTRON AND POSITRON
IN THE TWO-PHOTON PROCESS γγ → e + e −
V.L. Lyuboshitz and V.V. Lyuboshitz †
Joint Institute for Nuclear Research, 141980 Dubna, Moscow Region, Russia
† E-mail: Valery.Lyuboshitz@jinr.ru
Abstract
The spin structure of the process of electron-positron pair production by two
photons γγ → e + e − is theoretically investigated. It is shown that, if the primary
photons are unpolarized, the final electron and positron are unpolarized as well but
their spins are strongly correlated. Explicit expressions for the components of the
correlation tensor of the final (e + e − ) system are derived, and the relative fractions
of singlet and triplet states of the (e + e − ) pair are found. It is demonstrated that
in the process γγ → e + e − one of the incoherence inequalities of the Bell type for
the correlation tensor components is always violated and, thus, spin correlations of
the electron and positron in this process have the strongly pronounced quantum
character.
1. Let us consider the process of electron-positron pair production by two photons,
γγ → e + e − . The spin state of the electron-positron system is described, in the general
case, by the two-particle spin density matrix:
ˆρ (e−e + ) 1
�
(e
= Î
4
− )
⊗Î (e+ )
+Î (e− ) (e
⊗(ˆσ + ) (e
P + ) (e
)+( ˆσ − ) (e
P − )
)⊗Î (e+ )
+
3�
3�
i=1 k=1
Tikˆσ (e− )
i ⊗ˆσ(e+ �
)
k , (1)
where Î is the two-row unit matrix, P(e− ) (e and P + ) are the polarization vectors of the
electron and positron, respectively, Tik – components of the correlation tensor ( Tik =
〈ˆσ (e− )
i ⊗ ˆσ(e+ )
k 〉, i, k = {1, 2, 3} = {x, y, z} ). In the absence of correlations, we have:
Tik = P (e− )
i P (e+ )
k .
The process γγ → e + e − is described by two well-known Feynman diagrams [1]. Within
the first nonvanishing approximation over the electromagnetic constant ( Born approximation
), in case of unpolarized primary photons the final electron and positron prove to
be unpolarized as well, but their spins are correlated.
Thus, in the above formula for the spin density matrix ˆρ (e+ e − ) (1)
P (e− ) = P (e + ) =0.
The components of the correlation tensor of the electron-positron pair, generated in
the interaction of unpolarized γ quanta, may be calculated by applying the results of
paper [2]. Finally we obtain the following expressions:
Tzz =1− 2(1− β2 )[β2 (1 + sin 2 θ)+1]
1+2β2 sin2 θ − β4 − β4 sin4 , (2)
θ
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