Kern- und Teilchenphysik I Lecture 6: Nuclear fission

Kern- und Teilchenphysik I Lecture 6: Nuclear fission

Prof. Nico Serra

Dr. Patrick Owen, Dr. Silva Coutinho

http://www.physik.uzh.ch/de/lehre/PHY211/HS2016.html

Nuclear Fission and Fusion

We have seen that fission is the fragmentation of a heavy nucleus into 2

more stable components Usually requires to be triggered by a slow neutron

Nuclear Fission

Nuclides with Z>40 can in principle split, however the barrier is so high that the tunnelling effect is very improbable, so in practice

only nuclides with very large A split.

Nuclear Fission

Let’s consider an ✏ deformation of the sphere into an ellipsoid of axis a = R(1+✏) and b = (1 ✏/2)

• The surface energy becomes E_s = a_sA^2/3(1 + ²₅✏² + ...)

• The Coulomb energy becomes E_c = a_cZ²A ^1/3(1 ¹₅✏² + ...)

• The di↵erence in energy becomes E = ^✏₅² (2a_sA^2/3 a_cZ²A ^1/3)

In order for the deformation to be favourable E should be negative, which implies:

Induced Fission

If a large A material (e.g. ²³⁵U) breaks into smaller nuclei, close to the iron binding energy peak, it releases energy

Spontaneous Fission is rare because it is suppressed by the tunnelling of the Coulomb barrier

It is possible to perturbate the nucleus, such that it is in unstable state and breaks, this is called induced fission

Neutron Interaction

e le c tro n

ne utro n

p ro to n

Incident neutron, E1

Scattered neutron, E2

a EA

E1 = Eγ + E2

Inelastic Scattering:

e le c tron

ne utron

p roton

Elastic Scattering:

Incident neutron, E1

Scattered neutron, E2

E1 = EA + E2

e le c tron

Neutron Absorption:

Gamma Photon, Eγ

Gamma Photon, Eγ E γ ~ 7 MeV

• Scattering: the neutron bounces o↵, with or without the same energy

• Activation: the neutron is absorbed and the resulting nuclide is radioac- tive

– The nucleus emit a gamma ray – Fission follows absorption

Induced Fission

The energy appears mostly in the kinetic energy of the fission

products and in the beta and gamma radiation.

A neutron splits a uranium nucleus,

releasing energy (quickly turned to heat) and more neutrons, which can

repeat the process.

Outcome

• Energy is released (the quantity M(A, Z)^⇤ M(A₁, Z₁) M(A₂, Z₂) nM_n)

• One neutron triggers the reaction, 2 or 3 (on average) are produced and can induce more fission

• Depending on the fission material, the shape and the mass the reaction can be self-perpetuating (critical mass)

• Nuclear reactors are designed to have self-sustaining and controllable re- action

Fission

• Only a few nuclides can fission

• Nuclides that can fission for any incoming neutron are called fissile

• The only naturally occurring fissile nuclide is ²³⁵U

• Other fissile nuclides are ²³³U, ²³⁹P u and ²⁴¹P u, none of this is present naturally to any appreciable extent

• Nuclides that can be induced to fission only by neutrons of energy higher than a certain threshold are called fissionable, e.g. ²³⁸U and ²⁴⁰P u

Energy by fission

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Energy released per fission ~ 200 MeV [~ 3.2*10

J].

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This is hundreds of thousands, or millions, of times greater than energy produced by combustion, but still only ~0.09% of mass energy of uranium nucleus!

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The energy released appears mostly (85%) as kinetic

energy of the fission fragments, and in small part (15%) as the kinetic energy of the neutrons and other particles.

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The energy is quickly reduced to heat (random kinetic energy) as the fission fragments are stopped by the

surrounding atoms.

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The heat is used to make steam by boiling water,