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8-Element production in thermonuclear reactions (pp chain (pp1 (pp1 rate…
8-Element production in thermonuclear reactions
Binding energy
nucleus is more energetically stable than the sum of its constituents
Features of binding energy curve
Roughly the same for all A (roughly same energy needed to free a nucleon regardless of size of the nucleus)
short range forces dominate
broad maximum at A=60 separates nuclei that will release energy when undergoing fusion and those who undergo fission
peaks at A=4n at low A are bound states of alpha particles
strong nuclear force much stronger than EM
fission and fusion
Q binding energy maths
if Q positive there is net energy release
Liquid drop model
implied that nucleon only interacts with its nearest neighbours
relatively constant central density
analogy with drop of charges fluid, liquid drop model
can be used along with shell model
r proportional to A^(1/3)
different terms maths
Physics of fusion
thermal energy to trigger thermonuclear fusion comres from gravitational contraction
hindered by coulomb repulsion
electrostatic barrier must be overcome
QM required to explain penetration of coulomb barrier to reach strong interaction egion
wavefunction can go to places classically forbidden
Reaction Rates
Maths:
Cross section for fusion like reaction will rise with E as coulomb barrier more easily overcome
cross section written as gamow expression
Explosive Burning
Maths:
Reactions are occuring between a realatively small number of nuclei in the tail of boltzman dist, and this number changes rapidly with temperature
pp chain
pp1
pp1 rate determining step
pp1 has never been seen in a lab
two protons form diproton
then beta decay into deuterium
2 protons cannot form a bound state of 2H, otherwise hydrogen burning would be very fast
scale factor for pp2 10^18 greater than for i
EM vs weak force
Dominent hydrogen burning mechanism in the sun
Only was to synthesise Helium in pop 3 stars, which do not contain preprocessed material
pp1 chain dom for stars of solar mass and lighter
hydrogen burning process
starts around 4x10^6K
CNO cycle
Especially in hot stars, heavier than sun which already contain some CNO
Net result is the same as the pp chain
CNO act as catalysts
4th step is slowest, so 14 N build up
Cycles which envolve F-17 and O-17 also exist
hydrogen burning process
coulomb barriers are higher
starts around 1.3x10^7