A New Method to Solve the Diffusion Equations under Approximation B in Electron-Photon Cascade Theory : By Using Suzuki-Trotter Formula : Astrophysics and Relativity

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概要

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• A new method of calculation is studied, and the analytical solutions of the diffusion equations under Approximation B in electron-photon cascade theory is obtained. In this method, we rewrite the inhomogeneous diffusion equations as a homogeneous equation in a matrix form and apply the Suzuki-Trotter formula for non-commutable two exponential operators describing the cascade process and the collision loss process. The calculation is simpler and more straightforward than former calculations. Our transition curves agree very well with ones obtained by Rossi and Greisen under Approx. B or obtained by Greisen's approximate formula. Integral energy spectrum we obtain is given for any depth and is represented by a single expression from low energy region to high energy region. The matrix calculus developed here can be applied to other problems in the cascade theory.

• 理論物理学刊行会の論文
• 1992-04-25

著者

• Nii Nobuhiko

  Department Of Physics Saitama University:ashikaga Institute Of Technology

• NII Nobuhiko

  Department of Physics, Saitama University:Ashikaga Institute of Technology

関連論文

• A New Method to Solve the Diffusion Equations under Approximation B in Electron-Photon Cascade Theory : By Using Suzuki-Trotter Formula : Astrophysics and Relativity

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