Foundation of Physics 3A (Nuclear Physics part 2)

Scattering in Particle Physics

Rutherford scattering
:




demzl1212
la Ruth
=


16 Ei sin * If/2)


is some measure




=
T


of scattering


eZ
1

-
In classic mechanics :



j
&
gravity




- anything in this area
------




will

hit the earth
↑




·

Rutherford scattering :




1) non-relativitic /i .
e no
spin)
2) charged point particles
3) no recoil



Rutherford scattering is not a
complete model ,




we need to modify .
it

, 1)
Introducing relativity
:




· In
Rutherford model , we have
neglected the


spins of the particle and the
target .




ISE is a non-relativistic &M a it does not involve
spin)

At relativistic energies , Rutherford cross-


section is modified by spin effects .




Mott's scattering describes electron
·

scattering
and includes effects electron
due to the
spin :




It matt =
Inlaut11-B-sin 1612)) .




where p=


When /
·
& >
-




It matt =
Int Cos
Helicity :




- normalized
So values : #
only have
2



·
Particles with
spin pointing in the direction of their

have
motion
helicity +1
J

, spin
> F
1
-




& > => n =




Particles direction
with
spin pointing in the
opposite
their have
of motion
helicity -1

pin F
>
= n = -
1
&




·
Helicity is conserved
.

H-momentum , spin momentum are conserved ,
then

So is
helicity .




·


Backscattering a
particle off of a nucleus :



spin
>
#
IIII
-




Before :
& 7
spin
= = h =
1

2- Proton


After
:




case I : Spin I
>
#
IIII
-




= h=
spin
=
& E


2- Proton

Not allowed , as
helicity should be conserved


spin
Lase 2 :

- E IIII = = h 1
spin
=




2- Proton


momentum should be conserved
Not allowed , as
spin
=> We need to involve the
spin of the
proton
both and
we can Conserve
helicity momentum

by flipping proton spir

, spin Spin
&
>
-

F
Before :
IIII spin
0 = h 1
= =
& 7


2-
Proton


After
:



spin
. spin >
t #
& E 1//I Spin
= o => h=

2- Proton