Positron annihilation in a strong magentic field.

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Differential cross section for two-photon <strong>annihilation</strong> <strong>in</strong> CM (n=0, lowest Landau level) 2 2 3 2 2 dσ αλC Em 0 0 1 ⎛ E0 2 ⎞ = 2 exp ⎜− 2 s<strong>in</strong> θ ⎟ dΩ π p E + b ⎝ bm0 ⎠ 2 2 ( 0 2bm0) CM E = p + m B e + e- 2 2 0 0 p p θ Dirac (Heitler) formula for free <strong>annihilation</strong>: . dσ αλC m ⎡ E + p + p s<strong>in</strong> θ 2p s<strong>in</strong> θ dΩ E p ⎣ E − p E − p 2 2 2 2 2 2 2 4 4 0 0 = ⎢ − 2 2 2 2 2 2 2 D,CM 16π 0 0 cos θ ( 0 cos θ) ⎤ ⎥ ⎦ 20/37
Differential cross section for two-photon <strong>annihilation</strong> <strong>in</strong> CM system. Free particles <strong>in</strong> CM (Dirac formula) direction of motion of positron and electron. b=0.1 direction of magnetic l<strong>in</strong>e E=1.5m 0 2m 0 3m 0 E=1.5m 0 2m 0 3m 0 21/37
Page 1 and 2: Positron a
Page 3 and 4: Outline 1. Introdu
Page 5 and 6: Pulsars and magnetars: Magnetic fie
Page 7 and 8: The Dirac equation in</stro
Page 9 and 10: Landau levels The transverse motion
Page 11 and 12: Single photon <str
Page 13 and 14: Differential cross section for s<st
Page 15 and 16: Total cross section for sin
Page 17 and 18: The single photon
Page 19: Total cross section for two-photon
Page 23 and 24: Differential cross section for two-
Page 25 and 26: Differential cross section for two-
Page 27 and 28: Comparison 1e+5 1e+4 E 0 =3m 0 c 2
Page 29 and 30: In „annihilation
Page 31 and 32: The case of small x 0 means the sma
Page 33 and 34: The case of large x 0 . The created
Page 35 and 36: Daugherty and Bussard suggested to
Page 37: Thank you for your attention 37/37

Positron annihilation in a strong magentic field.

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