Positron annihilation in a strong magentic field.

The case of small x 0
means the small distances
between the centers of Landau orbits <strong>in</strong> the plane
orthogonal to the magnetic field, then the effective
2
potential reads:
e
V00
( z)
≅
2b
z +
2
π m
0
( δ )
(0,0) 2
f( z) ≡ f ( z,0) = δ exp − z
↓↑
ρ( P, P , P ) =Φ ˆ ( P, P , P ) =
x y u x y u
2 2 2
( − Px
+ Py
m b)
4δα
exp 2( ) /
π b (( P mα) + δ )
2
6 2
0
2 2 4 2
u
m ⎛
0
22 b ⎞
δ ≡ α ln
2 ⎜
π α ⎟
⎝ ⎠
The momentum spectrum of <strong>annihilation</strong> radiation
∫
∫
N( P) = dP dP ρ( P, P , P ); i, j, k∈{ x, y, z}
i j≠i, k k≠i,
j i j k
2 6
2 ⎧⎪
2P
⎫
xy , ⎪
2δ
N( Pxy
,
) = exp , ( ) .
2 ⎨− 2 ⎬ N Pz
=
4 2 2
πmb 0 ⎪⎩
mb
0 ⎪⎭
π( δ + Pz
)
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