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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

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fission and fusion

Fission and Fusion


Nuclear and Particle Physics

Ruben Saakyan


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

“Fissile” nuclei

“Non-Fissile” nuclei

(require an energetic neutron to induce fission)

238 u and 235 u
238U and 235U

Natural uranium: 99.3% 238U + 0.7% 235U



235U prompt neutrons: n  2.5. In addition decay products will decay

by b-decay (t  13s) + delayed component.

fission chain reaction
Fission chain reaction
  • In each fission reaction large amount of energy and secondary neutrons produced (n(235U)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
Fission chain reactions
  • Neutron mean free path
  • which neutron travels in 1.5 ns
  • Consider 100% enriched 235U. For a 2 MeV neutron there is a 18% probability to induce fission. Otherwise it will scatter, lose energy and Pinteraction. On average it will make ~ 6 collisions before inducing fission and will move a net distance of 6 ×3cm 7cm in a time tp=10 ns
  • After that it will be replaced with ~2.5 neutrons
fission chain reactions1
Fission chain reactions
  • From above one can conclude that the critical mass of 235U 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 tp
fission chain reactions2
Fission chain reactions
  • N(t)  if nq > 1; N(t)  if nq < 1
  • For 235U, N(t)  if q > 1/n  0.4 In this case since tp = 10ns explosion will occur in a ~1 ms
  • For a simple sphere of 235U the critical radius (nq=1) is  8.7 cm, critical mass  52 kg
nuclear reactors
Nuclear Reactors


  • To increase fission probability:
  • 235U enrichment (~3%)
  • Moderator (D2O, graphite)

Delayed neutron may be a problem

To control neutron density, k = 1

retractable rods are used (Cd)

Single fission of 235U ~ 200 MeV ~ 3.210-11 j

1g of 235U could give 1 MW-day. In practice efficiency much lower

due to conventional engineering

fast breeder reactor
Fast Breeder Reactor
  • 20% 239Pu(n3) + 80%238U used in the core
  • Fast neutrons are used to induce fission
  • Pu obtained by chemical separation from spent fuel rods
  • Produces more 239Pu 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
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=kBT  T~3×1010 K

Fortunately, in practice you do not need

that much

the solar pp chain






The solar pp chain

p+p  2H + e+ + ne

p+p+e-  2H + ne

+ 0.42 MeV



2H+p  3He + g

+ 5.49 MeV




3He+3He a+2p

3He+p a+ e+ + ne

+ 12.86 MeV

3He+a  7Be + g



7Be+e-  7Li + ne

7Be+p 8B + g

7Li +p  a+a

8B 2a+ e+ + ne


fusion reactors
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  3×108 K
  • The main problem is how to contain plasma at such temperatures
  • Magnetic confinement
  • Inertial confinement (pulsed laser beams)
fusion reactors1
Fusion reactors


Lawson criterion


Construction to start in 2008

First plasma in 2016

20 yr of exploitation after that