Positron annihilation in a strong magentic field.

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Solution for positrons ψ E + m ( x) exp( iE t) v ( x) ( −) ( −) n 0 ( −) ↑↓ = ( −) n n 2En v ⎛ ⎜ E ⎜ ⎜ − ( −) n − p + m 0 n−1 2nb m I ↑ 0 n ( x) = ⎜ , ( −) n ⎟ En + m0 ⎜ ⎜ ⎜ ⎝ I n−1 0 I ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ v ⎛ ⎞ ⎜ 2nb m ⎟ ⎜ 0 − ( ) I ⎟ ⎜ − n−1 ⎟ ⎜ En + m0 ⎟ ⎜ ⎟ ⎜ ⎟ ↓ ⎜ p ⎟ n ( x) ⎜ I ( −) n ⎟ ⎜ En + m ⎟ ⎜ 0 ⎟ ⎜ ⎟ ⎜ 0 ⎟ ⎜ ⎟ ( −) ⎜ I ⎝ n ⎟⎠ = , n 2 i ⎡ b( x−a) ⎤ ⎛ x−a⎞ ⎛ iayb⎞ In = exp ⎢− H exp exp( ) 1/4 2 ⎥ n ipz n ⎜ ⎟ ⎜− 2 ⎟ L( πλ / b) 2 n! ⎣ 2λC ⎦ ⎝ λ ⎠ ⎝ λC ⎠ C 8/37
Landau levels The transverse motion of the positron (e+) and electron (e‐) is quantized, they energy obeys the relation : m0 1+ 4b m0 1+ 2b ∆ E > m 0 E = m + ( p ) + 2 n bm ( ± ) 2 ( ± ) 2 2 n 0 ± 0 n ± = 0,1,2,... is the number of the Landau level, m 0 p - is the longitud<strong>in</strong>al momentum, along the magnetic field l<strong>in</strong>e. In calculations it is sufficient to assume: n=0 9/37
Page 1 and 2: Positron a
Page 3 and 4: Outline 1. Introdu
Page 5 and 6: Pulsars and magnetars: Magnetic fie
Page 7: The Dirac equation in</stro
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 and 20: Total cross section for two-photon
Page 21 and 22: 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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