Physic 492 Lecture 6 - Michigan State Universitylynch/lecture_wk3.pdf · • Main points of...
Transcript of Physic 492 Lecture 6 - Michigan State Universitylynch/lecture_wk3.pdf · • Main points of...
• Main points of today’s lecture:– Born approximation for
electron scattering– Coulomb scattering.
• Main points of last lecture:– Radioactive dating– Sequential decay– Relation between width and
lifetime– Collisions and cross sections
Physic 492 Lecture 6
( )
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hwv
v
h
vv
h
/rqi3
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2
Ruth
int
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errdeZ
1qF
:Factor Form
qFdd
dd
:case scattering Coulomb
Verd2
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:ic)relativist-(nonion approximatBorn order 1st
fdd
:f Amplitude Scattering
EkVk2w
:RuleGolden s'Fermi
⋅−
⋅−
→
∫
∫
ρ⋅=
⋅Ωσ
=Ωσ
⋅π−
=θ
θ=Ωσ
θ
ρπ
=
Recall our discussion of radius determination from Coulomb scattering
What happens when there is no nuclear interaction?
Time dependent perturbation theory: (Fermi’s golden rule)Do we need to derive it?
( )EV2w
: to fromn transitioof rate for the RuleGolden s'Fermi2
iintffi
fi
ρΨΨπ
=
ΨΨ
→h
Assuming the validity of Fermi’s Golden Rule:
• What is ρ(E)?
Relating Fermi’s golden rule to a cross section
The scattering amplitude
• Main points of today’s lecture:– Born approximation for
electron scattering– Coulomb scattering.
– Charge distributions from electron scattering
– Isotope shifts– Muon and pionic atoms
• Main points of last lecture:– Born approximation for
electron scattering
Physic 492 Lecture 7
( )
( ) ( ) hvvv /rqi3
tgt
2
Ruth
errdeZ
1qF
:Factor Form
qFdd
dd
:case scattering Coulomb
⋅−∫ ρ⋅=
⋅Ωσ
=Ωσ
( )
( )
( )
( ) int
/rqi32Born
2
2
iintffi
Verd2
mf
:ic)relativist-(nonion approximatBorn order 1st
fdd
:f Amplitude Scattering
EkVk2w
:RuleGolden s'Fermi
hwv
h
vv
h
⋅−
→
∫ ⋅π−
=θ
θ=Ωσ
θ
ρπ
=
The Cross section in terms of form factor
Homework hint and result
• In the next homework, you will be asked to Show that the factor
is equal to :
• Replace , replace
and then take the limit.) • With this result:
( ) 23
2e
uuqiexpudk
2m
∫⋅−⋅
π
vv
h
RuthddΩσ
( ) ( )∫∫
δ−⋅−⋅⋅−⋅→δ u
uuqiexpudlimby u
uqiexpud 3
0
3 vvvv
The Form Factor
Simple models for nuclear charge distribution
• Assume a sharp spherical charge distribution.
What causes the deep diffraction minima.
• Diffraction occurs due to the interference of different parts of the wavefunction that traverse the nucleus
Real data – extraction of ρ(r).• Why no deep minima?
• What approach works?
• The results:
/d mb srd
qh
Some factual corrections
Other probes of the nuclear charge distributions
• Atomic lines of muonic or electonic atoms:• Shift is due to finite size of nuclei:
2
20
eZm4a
μ
πε=
h
• Main points of today’s lecture:– Isotope shifts– Hadronic scattering– Summary of nuclear sizes
and shapes– Nuclei as liquid drops-Semi-
empirical mass formula• Bulk• Surface• Symmetry• Coulomb
• Main points of last lecture:– Charge distributions from
electron scattering– Isotope shifts
Physic 492 Lecture 8
Muonic atom case
• Wavefunctions:
• Bohr radius is small:
• l value governs overlap and ΔE.
2
20
eZm4a :radiusBohr
μ
πε=
h
an interesting result
• One interesting trend is the dependence of the proton radii uponneutron number of a range of isotopes of the same element.
Hadronic scattering
• What happens when you scatter 14 MeV neutrons on 58Ni?
• Actual approach
Summary
Nuclear Masses and Binding Energies
• Definition of Binding energy
• Properties of nuclear binding energies– Average binding energy is approximately 8 – 9 MeV.
Liquid drop formula
• Bulk term.
• Surface term.