1 Coulomb Scattering b d r min v o v min • Elastic or inelastic. • Elastic Rutherford scattering. • At any distance: V = 0 T a = ½mv o 2 l = mv o b 0 4 1 2 a o T d zZe V r zZe mv mv o o 2 2 2 1 2 2 1 4 1 No dependence on Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
1 Coulomb Scattering b d r min vovo v min Elastic or inelastic. Elastic Rutherford scattering. At any distance: V = 0 T a = ½mv o 2 l = mv o b No dependence.
Mar 26, 2015
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1
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 Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).
2
• Closest approach “d”.• E = ECoulomb d = 2kZe2/E
• What about the recoil nucleus?• HW 9HW 9 Show that
where mN : mass of the nucleus m : mass of alpha
What are the values of d for 10, 20, 30 and 40 MeV on Au?How does this explain … ?
)(
2 2
mmE
mkZed
N
N
Coulomb Scattering
3
Coulomb Scattering
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
4
Coulomb Scattering
bdbnxdf
bnxf
2)(
)( 2
n target nuclei / cm3 x target thickness (thin).nx target nuclei / cm2
b < b > db d
b
HW 10HW 10Show thatand hence 2
cot2
db
24
222
sin
1
4
1
4
)(
ao T
zZe
d
d
Rutherford cross sectionAccelerator Physics, JU, First Semester, 2010-2011
(Saed Dababneh).
5
Coulomb ScatteringStudy Fig. 11.10 (a,b,c,d) in Krane
HW 11HW 11Show 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.
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
6
Coulomb Scattering
• RBS – Channeling.• Ion implantation.• Occupational or substitutional impurities.
7
Coulomb Scattering
• Elastic Rutherford scattering.• Inelastic Coulomb excitation.
See the corresponding alpha spectrum of Fig. 11.12 in Krane.
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
8
Coulomb Scattering
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
Excitation Ionization ion-pair, suppress recombination in detectors.
Energy loss
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
9
Interaction of heavy charged particles
• Electronic or nuclear (Rutherford, nuclear reactions, …) or radiative (Bremsstrahlung).
• Depletion layer.• Delta rays and secondary electrons.• Electron suppression for charge integration in accelerators.• Faraday Cup.• Tracks.
Detectors mainly designed to make use of electronic interactions.
SRIMhttp://www.srim.org
Principles of Spectrometry
Al in Al
?
24
222
sin
1
4
1
4
)( Rutherford
ao T
zZe
d
d
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
10
2
2
2
220
20
24
1ln2
ln4
c
v
c
v
I
vmNZ
vm
ze
dx
dE
Stopping power Stopping power Bethe-Bloch formula
Minimum ionizing particles (mip).
~1/E
Principles of Spectrometry
~1/E
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
11
eV / Å keV / m MeV / mm keV / (g/cm2) MeV / (mg/cm2) keV / (mg/cm2) eV / (1x1015 atoms/cm2)
UnitsUnits
(conversion)(conversion) You will encounter this when you run SRIM
Principles of Spectrometry
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
12
Electron pick-up. ~1/E
What about fission fragments?????What about fission fragments?????
Bragg curve
• Energy loss is a stochasticstochastic process, thus energy straggling.energy straggling.
Principles of Spectrometry
Target
Acc
eler
ated
be
am
Accelerator Physics, JU, First Semester, 2010-2011 (Saed Dababneh).
13
Hadrontherapy
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