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