Fission and Fusion 3224 Nuclear and Particle Physics Ruben Saakyan UCL

Induced fission Recall that for a nucleus with A  240, the Coulomb barrier is 5-6 MeV If a neutron with E k  0 MeV enters 235 U, it will form 236 U with excitation energy of 6.5 MeV which as above fission barrier To induce fission in 238 U one needs a fast neutron with E k  1.2 MeV since the binding energy of last neutron in 239 U is only 4.8 MeV The differences in B E (last neutron) in even-A and odd-A are given by pairing term in SEMF.

Fissile materials “Fissile” nuclei “Non-Fissile” nuclei (require an energetic neutron to induce fission)

238 U and 235 U Natural uranium: 99.3% 238 U + 0.7% 235 U 235 U 238 U 235 U prompt neutrons: n  2.5. In addition decay products will decay by  -decay (t  13s) + delayed component.

Fission chain reaction In each fission reaction large amount of energy and secondary neutrons produced (n( 235 U)  2.5) Sustained chain reaction is possible If k = 1, the process is critical (reactor) If k < 1, the process is subcritical (reaction dies out) If k > 1, the process is supercritical (nuclear bomb)

Fission chain reactions Neutron mean free path which neutron travels in 1.5 ns Consider 100% enriched 235 U. For a 2 MeV neutron there is a 18% probability to induce fission. Otherwise it will scatter, lose energy and P interaction . On average it will make ~ 6 collisions before inducing fission and will move a net distance of  6 ×3cm  7cm in a time t p =10 ns After that it will be replaced with ~2.5 neutrons

Fission chain reactions From above one can conclude that the critical mass of 235 U corresponds to a sphere of radius ~ 7cm However not all neutrons induce fission. Some escape and some undergo radiative capture If the probability that a new neutron induces fission is q, than each neutron leads to (nq-1) additional neutrons in time t p

Fission chain reactions N(t)  if nq > 1; N(t)  if nq < 1 For 235 U, N(t)  if q > 1/n  0.4 In this case since t p = 10ns explosion will occur in a ~1  s For a simple sphere of 235 U the critical radius (nq=1) is  8.7 cm, critical mass  52 kg

Nuclear Reactors To increase fission probability: U enrichment (~3%) 2.Moderator (D 2 O, graphite) Core Delayed neutron may be a problem To control neutron density, k = 1 retractable rods are used (Cd) Single fission of 235 U ~ 200 MeV ~ 3.2  j 1g of 235 U could give 1 MW-day. In practice efficiency much lower due to conventional engineering

Fast Breeder Reactor 20% 239 Pu(n  3) + 80% 238 U used in the core Fast neutrons are used to induce fission Pu obtained by chemical separation from spent fuel rods Produces more 239 Pu than consumes. Much more efficient. The main problem of nuclear power industry is radioactive waste. –It is possible to convert long-lived isotopes into short- lived or even stable using resonance capture of neutrons but at the moment it is too expensive

Nuclear Fusion Two light nuclei can fuse to produce a heavier more tightly bound nucleus Although the energy release is smaller than in fission, there are far greater abundance of stable light nuclei The practical problem: E=k B T  T~3×10 10 K Fortunately, in practice you do not need that much

The solar pp chain p+p  2 H + e + + e p+p+e -  2 H + e 2 H+p  3 He +  3 He+ 3 He   +2p 3 He+p   + e + + e 3 He+   7 Be +  7 Be+p  8 B +  7 Be+e -  7 Li + e 7 Li +p   +  8 B  2  e + + e (99.77%) (0.23%) (84.92%) (~10-5%) (15.08%) (15.07%)(0.01%) pp pep hep 7 Be 8B8B MeV MeV MeV Overall:

Solar neutrino spectra

Fusion Reactors Main reactions: Or even better: More heat Cross-section much larger Drawback: there is no much tritium around A reasonable cross-section at ~20 keV  3×10 8 K The main problem is how to contain plasma at such temperatures Magnetic confinement Inertial confinement (pulsed laser beams)

Fusion reactors Tokamak Lawson criterion

ITER Construction to start in 2008 First plasma in yr of exploitation after that