1 Nuclear Scattering Elastic or inelastic. Analogous to diffraction. Alternating maxima and minima. First maximum at Minimum not at zero (sharp edge of.

1

Nuclear Scattering• Elastic or inelastic.• Analogous to diffraction.• Alternating maxima and minima.• First maximum at

• Minimum not at zero (sharp edge of the nucleus??)• Clear for neutrons.• Protons? High energy, large angles. Why?• Inelastic Excited states, energy, X-section and spin-parity.

31

ARR

p

h

o

R

Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).

2

Reaction Cross Section(s)• Probability.• Projectile a will more probably hit target X if area is larger.• Classically: = (Ra + RX)2. Classical = ??? (in b) 1H + 1H, 1H + 238U, 238U + 238U • Quantum mechanically: = 2.

• Coulomb and centrifugal barriers energy dependence of .• Nature of force: Strong: 15N(p,)12C = 0.5 b at Ep = 2 MeV. Electromagnetic: 3He(,)7Be = 10-6 b at E = 2 MeV. Weak: p(p,e+)D = 10-20 b at Ep = 2 MeV.• Experimental challenges to measure low X-sections..

CMaXaXaaX

Xa

EEmm

mm

22

HW 14HW 14

Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).

3

Reaction Cross Section(s) (Introduction)

d,Ia

Detector for particle “b”

NI

dRd

a

b

“X“ t

arge

t Nuc

lei /

cm2

“a” particles / s

“b” particles / scm2

Typical nucleus (R=6 fm): geometrical R2 1 b.Typical : <b to >106 b.

Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).

4

Reaction Cross Section(s) (Introduction)

Many different quantities are called “cross section”.Krane Table 11.1

NI

r

d

d

drdR

a

b

4

),(4

),(

Angular distribution

“Differential” cross section(,) or ( )or “cross section” …!!

Units … !

d

dddd

d

d

ddd

0

2

0

sin

sin

ddE

d

b

2

Doubly differential

Energy state in “Y”

dE

d

t for all “b” particles.

Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).

Spectroscopic Factor.

calcmeas d

dS

d

d

5

Compound Nucleus Reactions

Direct

CN decays

• Time.• Energy.

• Two-step reaction. • CN “forgets” how it was formed.• Decay of CN depends on statistical factors that are functions of Ex, J.• Low energy projectile, medium or heavy target.

QCN

EaCM

Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).

6

Compound Nucleus Reactions• Consider p + 63Cu at Ep

CM= 20 MeV.• Calculate Ep

CM + [m(63Cu) + m(p) – m(64Zn)]c2.• Divide by 64 available energy per nucleon << 8 MeV.• Multiple collisions “long” time statistical distribution of energy small chance for a nucleon to get enough energy EvaporationEvaporation.• Higher incident energy more particles “evaporate”.

See also Fig. 11.21 in Krane.

Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).

7

• Random collisions nearly isotropic angular distribution.• Direct reaction component strong angular dependence.

See also Fig. 11.20 in Krane.

Direct Reactions

Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).