Presentation on theme: "Semi-Empirical Mass Formula Applications – II Nucleon Separation Energies and Fission [Sec. 4.4 + 12.1 Dunlap]"— Presentation transcript:
1Semi-Empirical Mass Formula Applications – II Nucleon Separation Energies and Fission [Sec Dunlap]
2The Semi-Empirical Mass Formula Let us see how this equation can be applied toNeutron Separation EnergiesAlpha Particle Decay EnergiesFission
3Single neutron separation energies Fig PULLING NEUTRONS OUT OF ODD-A NUCLIDESThe 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
4Single 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 energiesBto o-oEvenOddA1to e-eApply the SEMF assuming B(A,Z) is continuous in A.
5Single neutron separation energies Now apply the SEMF:This is an interesting result because it can give us an equation for the “neutron drip” lineby putting Sn=0
6Mass ParabolasZ=NProton numberNeutron drip lineNeutron number
7Alpha Particle Decay QWe saw in a previous lecture that the Q-value (energy released) in -decay is:whereFrom which:
9Energy 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.
10Energy released in Fission This figure shows the prediction of the SEMF for the energy released in FISSION when two equal fragments are formed.
12The 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.
13Understanding the Fission Barrier Consider the stability of an Ellipsoidal Deformation, =eccentricity of ellipseHow do BS and BC vary on deformation?
14Understanding the Fission Barrier SURFACE ENERGYThe surface area increases on deformation and so does BS. The nucleus becomes LESS boundSurface tenstionThe mass energy increases with deformation – This produces a potential that seeks to keep =0, I.E. the nucleus in SPHERICAL condition
15Understanding the Fission Barrier COULOMB ENERGYThe Coulomb energy has the opposite tendency. On deformation the charge in the nucleus is less condensed – the electrostatic “blow apart” energy is lessNuclear deformation makes the nucleus MORE BOUND.
17The 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.
18The FissionabilityThe Fissionability parameter Z2/A as a function of A. Note that the fastest decaying man-made transuranics still have F<45
19The rate of spontaneous fission NOTE log of the decay rate (period) is approximately proportional to the fissionability Z2/A