20- nuclear reactions
elastic deflects projectile, inelastic other changes occur, e.g. projectile loses energy (gamma emission)
Notation
shorthand eg
N(α,p)O
α + N -> o + p
can classify types of reaction which are similar
(α,n) reactions
Alpha-n reactions
main source of background neutrons in the environment
use to make neutron source, AmBe
chances of a particular type of reaction occurring will likely depend on the kinetic energy of projectile
elastic scattering can occur at any energies by inelastic scattering can't
reaction has to be energetically possible
compound reactions
general
projectile and target merge together to form a single new nucleus
nucleons will try to rearrange themselves to find a stable state, passing through several configurations
falls apart by emitting one or more nucleons or possibly splitting it apart completely
relatively slow reaction
time taken at least longer than it would take for the projectile to cross the diameter of the target nucleus
~10^-16 s
intermediate state nucleus lifetime is at least as long as the reaction time, can be much longer
activation reaction- activated a nucleus, unstable isotope later decays
characteristics
2-stage process comprising the formation of a relatively long-lived intermediate nucleus followed by decay
Once intermediate state is formed, decay is independent of the mode of formation
decay probability to a particular final state does not depend on the creating reaction, just the amount of excitation energy it has
generally happen at low projectile energies <50MeV
evidence
resonances in the interaction cross section vs energy plot
when uncertainty relation applied, a lifetime of ~10^-16 is implied, long
QM treatment of compound nuclei
consider simplified potential for the nucleus as before
3 types of energy levels
filled, where nucleons mainly live
excited unfilled sTATES
virtual bound states
have positive energy and this is where the projectile particles are momentarily trapped
while trapped nucleon shares its energy, raising nucleons to excited states and dropping into an excited state
called a many particle excited state nucleus, compound nucleus
Now have unstable wobbling existing between formation and decay, and complicated nucleon motions occur and origional mode of excitation forgotten
decay happens when the excitation energy is concentrated back into a single few particle virtual state, with enough energy for the particles to escape
at this point many decay configurations may occur before the products are released
Branching ratios and widths
independence hypothesis
many independent reaction channels and exit channels
no good for direct reactions
think of cross sections as partial widths
cross section for the object a ending up at object b
could also end up at c, or something else
maths
total width is the aum of all the possible Partial widths
total decay probability is the sum of all the decay probabilities of individual decay channels
can link partial width to the observed behaviour of how the xsection for an interaction behaves vs energy. Get peaks like resonance
therfore are able to invoke uncertainty principle
wqidth of resonant peaks are directly related to the xsection for that state
Breit-Wigner formula
for particles of short lifetime there will be uncertainty in the measured energy
the shape of the uncertainty is the breit-wigner formula
maths
resonance
low e scattering
high e scattering
when most likely to get compound reactions, showiing up as peaks in xsection vs energy coresponding to compound states.
small energies compared the virtual bound states
smoother continuum, varies slowly with energy
effective energies large compared to energy separation
at A~20 10MeV, A~200 100keV transition