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