Interactions of High Energy Particles with Nuclei |
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Page 3
One can also use some arguments based on approximate solutions of the wave equation of the incident particle interacting through potentials with the target particles . For instance , in the case of the Schrödinger equation E ↓ = 2m ...
One can also use some arguments based on approximate solutions of the wave equation of the incident particle interacting through potentials with the target particles . For instance , in the case of the Schrödinger equation E ↓ = 2m ...
Page 4
Take at + iq • ▽ — eV ¥ ° + 1⁄2 Koμ » F » — m ) 4 : + ir • -eVy ° + 1⁄2Ko1Fμm ) = 0 Ο ~ [ - ] - [ 1- απ 8 0 to get ( i — + ia • ▽ ―eV + ß1⁄41⁄2Kσ „ F “ — ßm ) = 0 . με at This equation was worked out in ref . [ 8 ] .
Take at + iq • ▽ — eV ¥ ° + 1⁄2 Koμ » F » — m ) 4 : + ir • -eVy ° + 1⁄2Ko1Fμm ) = 0 Ο ~ [ - ] - [ 1- απ 8 0 to get ( i — + ia • ▽ ―eV + ß1⁄41⁄2Kσ „ F “ — ßm ) = 0 . με at This equation was worked out in ref . [ 8 ] .
Page 5
... i → E and we have at E ¥ = [ − α • ▽ + ßm− Kß ( Σ • B − ia · E ) + eV ] ↓ = eik2 = exp ( iz√E2 — m2 ) ❤ → eiEzq , Inserting this into the Dirac equation and noting · i eiE EeiEz + eEz a Əz = a - ❤ we get Əz ( E → ∞ ) .
... i → E and we have at E ¥ = [ − α • ▽ + ßm− Kß ( Σ • B − ia · E ) + eV ] ↓ = eik2 = exp ( iz√E2 — m2 ) ❤ → eiEzq , Inserting this into the Dirac equation and noting · i eiE EeiEz + eEz a Əz = a - ❤ we get Əz ( E → ∞ ) .
Page 6
Let us consider this case in more detail . a From the equation - i Əz :) ] + eV - Kẞ ( Σ1 · В1 - iα · E ) = 0 we can eliminate the ' trivial ' dependence on V by substituting ❤ = f - F exp ( -ie [ ' _ dz'V ( z ...
Let us consider this case in more detail . a From the equation - i Əz :) ] + eV - Kẞ ( Σ1 · В1 - iα · E ) = 0 we can eliminate the ' trivial ' dependence on V by substituting ❤ = f - F exp ( -ie [ ' _ dz'V ( z ...
Page 9
When = 0 the equations of motion of such a particle are the so - called Proca equations . If , however , # 0 some additional terms appear ( as in the case of the Dirac equation with anomalous magnetic moment ) .
When = 0 the equations of motion of such a particle are the so - called Proca equations . If , however , # 0 some additional terms appear ( as in the case of the Dirac equation with anomalous magnetic moment ) .
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