PHY982 3rd week
Scattering theory: single and multi channel
1
Classical Coulomb scattering
o Coulomb trajectories are hyperbolas
o the cross section for a pure Coulomb
interaction is
1
Coulomb scattering
oexamples
Coulomb functions
o Coulomb wave equation
PHY982 5th week
Scattering theory: identical particles
1
Identical particles: symmetrization
o if two groups of nucleons are far apart, their wfns do not overlap exchange
of nucleons cannot affect observables
o antisymmetrization tends to be less importan
many body structure
effective interactions
Solve the problem in a part of the Hilbert space (P)
where P+Q=1
1
structure models
Winning the (nobel) prize was not half as exciting as doing the work!
Maria Meyer
Ab-initio models
Variational monte carlo (VMC)
R-matrix method for solving eqs.
Solving equations: single channel
Single channel: Equation to solve
Boundary conditions
1
Solving equations: single channel
Equation to solve
Trial function: initialization for integration
Solution
Boundary conditions
Solv
PHY982 11th week
Transfer spectroscopy
Knockout spectroscopy
Breakup Spectroscopy
Charge exchange spectroscopy
DWBA 1st order
binding
potential
remnant term
1
Standard approach to transfer
d + A p+B
DWBA transition matrix element
M = (f ) I AB V I pd i(+
PHY982 12th week
Electromagnetic field and coupling with photons
1
Maxwells equations
o magnetic H and electric E fields are related
Charge current and
charge density
o radiative capture reactions: coupling of photons and the nucleus
one radiative photon
PHY982 12th week
Basic ideas on compound reactions
1
Compound versus direct
o fast direct reactions (forward-peaked)
o slow compound nucleus (symmetric contributions around 90 deg)
o usually possible to separate these contributions
1
Compound nucleus - de
Fitting data (ch15)
Comparing theory and experiment
cfw_pj inputs parameter set
exp(i) experimental data ( standard deviation)
Measure of discrepancy
If theory agrees exactly with experiment 2=0 (very unlikely!)
What is statistically reasonable th(i)- ex
PHY982 13th week
Reaction rates and networks
1
Types of reactions in astrophysics
o nuclear reactions
o examples (,n), (p,), (d,p), etc
o non-resonant, resonant, sub-threshold state
o S-factor range 1-108 MeV b
o electromagnetic reactions
o examples (p,),