Exploring Physics: Is the Rutherford Scattering Formula Necessary?

[asdf1]

i'm interested in physics, but i don't major in it...
i look at physics in my free time, and i just came across the rutherford scattering formula and was wondering is it necessary to memorize it?

 

[Gokul43201]

Don't memorize it !

The important thing to take away from the formula is the $1/(1-cos \theta)^2$ dependence of the scattering cross-section which is a signature of scattering from point-like objects.

 

[asdf1]

@@a
the rutherford scattering formula is
N(cita)=(NntZ^2*e^4)/{[(8pi*epsilon)^2]*(E^2)sin^4(cita/2)} right?
because i don't see 1/[1-cos(cita)]^2...

 

[jtbell]

Hint: browse through a list of trig identities.

 

[asdf1]

so sin^4(cita/2)=[1-cos^2(cita)]/2={1-[1+cos(2cita)]/2}/2?

 

[Gokul43201]

Sorry, I didn't make this clear earlier. I was referring to the differential cross section. That's a more useful form of the scattering equation.

 

[asdf1]

differential cross section? what's that?
@@

 

[Gokul43201]

It's the number of scattering events that go through an elemental area on the surface of a unit sphere centered on the scattering center. In spherical co-ordinates, an area element on the unit sphere (or an element of solid angle) is given by $d \Omega = sin \theta d \theta d \phi$.

The differential cross-section is $dN/d \Omega$

 

[asdf1]

ok, thank you very much! :)