1. An  particle with initial kinetic energy K = 800 MeV
moves head on toward a gold (Z=29) nucleus.
It is slowed and then momentarily stopped at a distance of
closest approach r0 from the nuclear center before being reversed
(scattered by an angle  = 180o).
Find r0.
Because of the large energies involved we can
assume the closest approach will not be affected
by the presence of any atomic electrons.
The repulsive Coulomb force changes K → PE
279
800 MeV
= 1.44 MeV-fm
= 28.4 fm
The gold radius 6.4 fm so the  does not penetrate the gold nucleus.

2. rate particles are scattered out of beam
Recall the cross section is defined by the ratio
rate particles are scattered out of beam
rate of particles focused onto target material/unit area
a “counting” experiment
notice it yields a measure, in units of area
number of scattered particles/sec
incident particles/(unit area  sec)  target site density
how tightly focused or intense the beam is
density of nuclear
targets
With a detector fixed to record data from a particular location , 
we measure the “differential” cross section: d/d.

3. N number of scattering scattered particles
Incident mono-energetic beam
v D t A
d W
N = number density in beam
(particles per unit volume)
Solid angle d W represents
detector counting the dN
particles per unit time that
scatter through q into d W
N number of scattering
centers in target
intercepted by beamspot
FLUX = # of particles crossing through unit cross section per sec
= Nv Dt A / Dt A = Nv
Notice: qNv we call current, I, measured in Coulombs.
dN N F d W dN = s(q)N F d W dN = N F d s -

4. dN = FN s(q)d W  N F d s(q)
the “differential” cross section R  R R R R

5. the differential solid angle d for integration is sin d d
Rsind
Rd
Rsind
Rd
Rsin

6. Nscattered = N F dsTOTAL
Symmetry arguments allow us to immediately integrate  out
and consider
rings defined
by  alone R
Rsind  R R R
Nscattered = N F dsTOTAL
Integrated over all solid angles

7. Nscattered = N F dsTOTAL
The scattering rate
per unit time
Particles IN (per unit time) = FArea(of beam spot)
Particles scattered OUT (per unit time) = F N sTOTAL

8. we augmented with the specific example of
that general description of cross section
we augmented with the specific example of
Coulomb scattering

9.  q1 q2 Recoil of target q1   BOTH target and projectile
will move in response to
the forces between them. q1   q2 
Recoil of
target
But here we are
interested only
in the scattered
projectile q1

11.  When >0 The incoming projectile will not reach r0,
but a distance of closest approach rmin>r0
At that position
which of course:
Conservation of angular momentum guarantees:

12. impact parameter, b

13. A beam of N incident particles strike a (thin foil) target. b q2 d
A beam of N incident particles strike a (thin foil) target.
The beam spot (cross section of the beam) illuminates n scattering centers.
If dN counts the average number of particles scattered between and d
dN/N = n d
using
d = 2 b db
becomes:

14.  b q2 d
and so

15.  b q2 d