Parity of nucleons and fission

[CRGreathouse]

Can anyone explain this to me? It piqued my interest, especially since I nominally work with radioactive materials (though admittedly, not fissile material) and didn't know where this came from.

"It is not a coincidence, for example, that the three nuclei which are fissionable with slow neutrons, U233, U235, and Pu239, all contain an even number of protons and an odd number of neutrons."
- Shanks, Solved and Unsolved Problems in Number Theory (5th ed.), p. 137

[Useful nucleus]

As far as I know, the reason for this is the pairing force. For example when a U235 nucleus absorbs a neutron , it forms (as an intermediate stage before fission) U236. Now U326 is excited by an amount of energy equal to the binding energy of the neutron and its kinetic energy. But since U236 has even number of neutrons , the pairing force will lower its ground state so much which in turn renders the excitation energy due to the nuetron binding energy (without the kinetic energy part) high eneough to exceed the fission activation energy. So this nucleus can fission ,in principle, by absorping a zero kinetic energy neutron. This is actually why U235, U233 ,.. are called fissile.

On the other hand U238 is fissionable but non fissile. This because it cannot fission by a zero kinetic energy neutron. An explation based on the paring force is valid here also

[Morbius]

As far as I know, the reason for this is the pairing force.
Useful nucleus,

You are correct. Anyone can look up the semi-empirical mass formula - which actually gives
the binding energy

http://www.phys.washington.edu/users/savage/Class_560/lec560_5/node2.html

http://www.phy.uct.ac.za/courses/phy300w/np/ch1/node22.html

The pairing forces influence the binding energy.

Dr. Gregory Greenman
Physicist