ボルン近似

Born approximation

[目次：理論(電子の散乱／回折／結像)]

結晶のポテンシャルエネルギーが電子線のエネルギーに比べて小さい場合、結晶に入射する電子線は結晶中で散乱されるが、散乱は一回のみで入射波は弱まらないとして、散乱波の振幅を求める近似のこと。
結晶による入射電子の散乱振幅をシュレーディンガー方程式の積分方程式の解として求めるとき、散乱波の振幅は結晶中の各点でのクーロンポテンシャルとその点での入射電子波の振幅に比例する。結晶中の電子波を入射波で置き換えて一回散乱した散乱波の振幅を求める。電子線の散乱振幅は結晶ポテンシャルのフーリエ係数で与えられる。

If the potential energy in a crystal is much smaller than the incident electron energy, the scattering event can be assumed to occur only one time in the crystal and the amplitude of the incident electron wave is not attenuated in the crystal. To calculate the amplitude of the scattered wave under such an approximation is called Born approximation.
When the scattered wave in a crystal is calculated as the solution of the integral form of Schroedinger equation, the scattering amplitude is proportional to Coulomb potential at the point where the scattering event occurs, and the amplitude of the electron wave incident at the point. Under Born (the 1st Born) approximation, the scattering amplitude is calculated by replacing the amplitude of the electron wave falling on the point with that of the incident electron wave to the crystal. The scattering amplitude of the electron wave is given by the Fourier coefficient of the crystal potential.

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