References - Bogoliubov Laboratory of Theoretical Physics - JINR

the two-photon system equaling 1). If both the photons are unpolarized, then the relative
fraction of such photon pairs amounts to 1/4.
Meantime, triplet electron-positron pairs (S = 1) are produced, in the process γγ →
e + e − , in the states with odd orbital momenta and positive space parity. In doing so, total
angular momenta may take both even and odd values . The contribution into generation
of triplet (e + e − ) pairs is provided only by states of two photons with positive space parity,
being symmetric over polarizations, which correspond to the total spins of the two-photon
system equaling 0 and 2. If both the photons are unpolarized, then the relative fraction
of such photon pairs amounts to 3/4.
3. Now let us consider the particular cases θ =0 andθ = π. In accordance with the
formula for the differential cross section dσ
dΩ
(5), here we obtain :
dσ
dΩ
= 1
4 r2 0 β (1 + β2 ) . (9)
In the ultrarelativistic limit formula (9) turns to dσ
dΩ = r2 0
2 .
According to the general expressions (2)–(4) for the correlation tensor components, at
θ =0andθ = π we have:
Tzz =1− 2(1+β2 )(1 − β2 )
1 − β4 = −1;
1 − β2
Txx = Tyy = − .
1+β2 (10)
In doing so, the “trace” of the correlation tensor (6) takes the value
T =1− 4
1+β
− β2
= −3 , (11)
2 1+β2 and the relative fractions of the triplet states Wt (7) and the singlet state Ws (8) amount
to
Wt =
T +3
4
= β2
1+β 2 , Ws =
1 − T
4
1
= . (12)
1+β2 At nonrelativistic velocities Wt ≈ 0, Ws ≈ 1, in accordance with the general case ;
meantime, in the ultrarelativistic limit (β → 1) we have: Wt = Ws = 1
2 .
Let us remark that in the process γγ → e + e− we observe the violation of the “incoherence”
inequalities, established previously at the classical level , according to which
for incoherent “classical” mixtures of factorizable two-particle spin states the sum of any
two ( or three ) diagonal components of the correlation tensor cannot exceed unity [3].
Indeed, at θ =0 andθ = π, in particular, we obtain:
|Tzz + Txx| = |Tzz + Tyy| = 2
> 1, (13)
1+β2 since β