1 / 8

Coulomb Scattering

Coulomb Scattering. The trajectory from an inverse square force forms a conic section. e < 1 ellipse e =1 parabola e >1 hyperbola. The force center is at a focus. Hyperbolic Orbits. q. attractive focus. a. r. a. ae. repulsive focus. Orient the incident axis to horizontal.

gefen
Download Presentation

Coulomb Scattering

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Coulomb Scattering

  2. The trajectory from an inverse square force forms a conic section. e < 1 ellipse e =1 parabola e >1 hyperbola. The force center is at a focus. Hyperbolic Orbits q attractive focus a r a ae repulsive focus

  3. Orient the incident axis to horizontal. Scattering mass forms a hyperbolic trajectory. Reoriented View q attractive focus a r a ae repulsive focus h v0 q m b x

  4. The potential is defined at infinity. The impact parameter would be closest approach for no force. Compare to angular momentum Impact Parameter h v0 q m x b

  5. Scattering cross section is based on the potential. Impact parameter Differential impact parameter The result is the Rutherford scattering cross section Rutherford Cross Section q b y

  6. Problem A spaceship of mass m moving with velocity v0 approaches the Moon. The impact parameter is b. The velocity v0 is perpendicular to the orbital velocity V of the moon. Show that if the spaceship passes behind the Moon it gains kinetic energy as it leaves the Moon. Lunar Miss q M b x m

  7. The moon is much more massive. Lunar frame is CM Incident and final energies same in CM Lunar Frame b m1 v0 q x b M

  8. In the Moon’s frame the velocity components come from the scattering angle. In the observer’s frame the velocity is boosted by the moon. Energy Boost next

More Related