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Using the Born approximation, the scattering amplitude $f(\theta)$ for a particle incident with momentum $\hbar k$ and scattered with momentum $\hbar k'$ by a potential energy $V(r)$ is given by: $$f(\theta) = -\frac{m}{2\pi \hbar^2} \int e^{i(\vec{k}-\vec{k'})\cdot\vec{r}} V(r) d^3r$$ where $\theta$ is the scattering angle between the incident and scattered momenta. For the Yukawa potential: $$V(r) = \alpha \frac{e^{-\mu r}}{r}$$ ($\alpha$, $\mu$ are constants) find the differential scattering cross-section $\frac{d\sigma}{d\Omega}$ and express the result in terms of the scattering angle $\theta$ and the energy $E = \frac{\hbar^2 k^2}{2m}$ of the particle.

Name: using the born approximation the scattering amplitude ftheta for a particle incident with momentum hbar k and scattered with momentum hbar k by a potential energy vr is given by ftheta fracm 65366
Uploaded: 2023-09-28T09:48:38-08:00
Duration: 2 min 59 s
Channel: Adi S
Description: using the born approximation the scattering amplitude ftheta for a particle incident with momentum hbar k and scattered with momentum hbar k by a potential energy vr is given by ftheta fracm 65366

          Using the Born approximation, the scattering amplitude $f(\theta)$ for a particle incident with momentum $\hbar k$ and scattered with momentum $\hbar k'$ by a potential energy $V(r)$ is given by:
$$f(\theta) = -\frac{m}{2\pi \hbar^2} \int e^{i(\vec{k}-\vec{k'})\cdot\vec{r}} V(r) d^3r$$
where $\theta$ is the scattering angle between the incident and scattered momenta.
For the Yukawa potential:
$$V(r) = \alpha \frac{e^{-\mu r}}{r}$$
($\alpha$, $\mu$ are constants)
find the differential scattering cross-section $\frac{d\sigma}{d\Omega}$ and express the result in terms of the scattering angle $\theta$ and the energy $E = \frac{\hbar^2 k^2}{2m}$ of the particle.

$using the born approximation the scattering amplitude ftheta for a particle incident with momentum hbar k and scattered with momentum hbar k by a potential energy vr is given by ftheta fracm 65366$

Added by Miguel -Ngel J.

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