1. Semi-Empirical Mass Formula Applications – II Nucleon Separation Energies and Fission
[Sec Dunlap]

2. The Semi-Empirical Mass Formula
Let us see how this equation can be applied to
Neutron Separation Energies
Alpha Particle Decay Energies
Fission

3. Single neutron separation energies
Fig PULLING NEUTRONS OUT OF ODD-A NUCLIDES
The arrows show the transitions from the odd A parabola to the even (A-1) parabolas for the two cases of
(e,o)(o,o) breaking pairing on neutron side
(o,e)(e,e) breaking no pairing bond

4. Single neutron separation energies
In an earlier lecture we found that the separation energy for a neutron was:
This can be written in terms of mass of constituents and binding energies B
to o-o
Even
Odd A 1
to e-e
Apply the SEMF assuming B(A,Z) is continuous in A.

5. Single neutron separation energies
Now apply the SEMF:
This is an interesting result because it can give us an equation for the “neutron drip” line
by putting Sn=0

6. Mass Parabolas
Z=N
Proton number
Neutron drip line
Neutron number

7. Alpha Particle Decay Q
We saw in a previous lecture that the Q-value (energy released) in -decay is:
where
From which:

8. Alpha Particle Decay Q

9. Energy released in Fission
The diagram shows the Q (energy released) from the fission of 236U as a function of the A of one of the fragments (as obtained from the SEMF). Note that maximum energy release is 210MeV/Fission for the nucleus splitting into equal fragments.

10. Energy released in Fission
This figure shows the prediction of the SEMF for the energy released in FISSION when two equal fragments are formed.

11. Energy released in Fission

12. The Fission Barrier Fission barrier
The origin of the fission barrier can be seen by reversing the fission process. Two fission fragments approach with (1/r) potential – consider the fragments equal. When r decreases until the two fragments are nearly touching the nuclear attractive strong force takes over – the potential energy is less than that calculated by Coulomb law.

13. Understanding the Fission Barrier
Consider the stability of an Ellipsoidal Deformation, =eccentricity of ellipse
How do BS and BC vary on deformation?

14. Understanding the Fission Barrier
SURFACE ENERGY
The surface area increases on deformation and so does BS. The nucleus becomes LESS bound
Surface tenstion
The mass energy increases with deformation – This produces a potential that seeks to keep =0, I.E. the nucleus in SPHERICAL condition

15. Understanding the Fission Barrier
COULOMB ENERGY
The Coulomb energy has the opposite tendency. On deformation the charge in the nucleus is less condensed – the electrostatic “blow apart” energy is less
Nuclear deformation makes the nucleus MORE BOUND.

16. Understanding the Fission Barrier

17. The fission barrier on the SEMF
To calculate the height of the fission barrier using the SEMF is fairly complex, but can be done as seen in this study – Fig12.3 Dunlap.
The dotted lines show variations that are understood on the shell model.
Note that the barrier is only small ~3MeV for A>250.

18. The Fissionability
The Fissionability parameter Z2/A as a function of A. Note that the fastest decaying man-made transuranics still have F<45

19. The rate of spontaneous fission
NOTE log of the decay rate (period) is approximately proportional to the fissionability Z2/A