Physics 492 Lecture 17 - Michigan State Universitylynch/lecture_wk7.pdf · Physics 492 Lecture 18....
Transcript of Physics 492 Lecture 17 - Michigan State Universitylynch/lecture_wk7.pdf · Physics 492 Lecture 18....
• Main points of today’s lecture:– Direct Reactions: Summary– Resonances – Compound nucleus– Relativistic kinematics
• Main points of last lecture:– exam
Physics 492 Lecture 17
Same technique can be used for inelastic scattering
• Measurement of inelastic scattering on 26Mg
26Mg
These were examples of “direct reactions”What are properties of direct reactions?
Compound nuclear reactions
• important at low incident energies E<30 MeV
Example of CN reactions
• Inelastic proton scattering on 50Cr
Branching ratios in CN decay
Resonance shape reflects interference with direct background
• Left side shows destructive interference. Right side does not.
Consider simple case p+4He
Breit-Wigner resonance formula
• If there is no direct background and only one decay channel, theresonance scattering amplitude is given by.
Relationship to lifetime
Lifetimes of short lived states
• Two ways to measure lifetime:– Focus on exponential decay law:
– Measure width of state:
Consider simple case p+4He
Resonances with multiple decay channels
• Need to consider Branching Ratios
Summary of Compound nuclear reactions
• Main points of today’s lecture:– Relativistic transformations– Four vectors– Invarients,
• Proper time• Inner products of vectors
– Momentum– Example: Photon-electron
scattering
• Main points of last lecture:– Compound nucleus– extrance and exit channel– Symmetries and selection rules
Physics 492 Lecture 18
Relativistic Kinematics
• When is it necessary?
• Review: Special relativity is based upon– Laws of Physics are independent of the inertial frame– Speed of light=c in all frames
Lorentz transformations
• Consider two inertial frames S and S’ whose velocities differ by Δvz= vt.
Matrix formulation
• In matrix form
• Inverse transformation
Identity
• If we transform and then transform back, we should get the same 4 vector.
Time dilation
• Consider the transformation of the point at the origin of S’
Inner Products
• What is an inner product?
• What are the properties of an inner product?
What is the correct 4-vector inner product
• Add time-like component with the opposite sign as the space-like component. Check whether it is an invariant
→It is an invariant!
Formal expressions
• The metric:
Other metrics
• You have used metrics without knowing it
Other 4 vectors
• “4-velocity” and 4-momentum
value for inner product