Inelastic 14N(p,p/)14N* Radiative capture. Fission and fusion. Spallation. …..
• Reaction mechanism: Direct reactions. Compound nucleus reactions.
• More in what follows ….• What is a transfer reaction….?????
Stripping
Pickup
Reson
ant
Non-resonant
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
3
Reaction Cross Section(s) (Introduction)
• 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 33HW 33
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
4
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.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
5
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
2Doubly differential
Energy state in “Y”
dE
d
t for all “b” particles.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
6
Coulomb Scattering
b
d
rmin
vovmin
• Elastic or inelastic.• Elastic Rutherford scattering.• At any distance:V = 0
Ta = ½mvo2
l = mvob
0
4
1 2
a
o
T
d
zZeV
r
zZemvmv
oo
22
212
21
4
1
No dependence on
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
7
Coulomb Scattering
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
8
Coulomb Scattering
bdbnxdf
bnxf
2)(
)( 2
n target nuclei / cm3 x target thickness (thin).nx target nuclei / cm2
b < b > db d
b
HW 34HW 34Show thatand hence 2
cot2
db
24
222
sin
1
4
1
4
)(
ao T
zZe
d
d
Rutherford cross section
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
9
Coulomb ScatteringStudy Fig. 11.10 (a,b,c,d) in Krane
HW 35HW 35Show that the fraction of incident alpha particles scattered at backward angles from a 2 m gold foil is 7.48x10-5.
See also Fig. 11.11 in Krane.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
See the corresponding alpha spectrum of Fig. 11.12 in Krane.
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
11
Coulomb Scattering
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
12
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.
