l24 - Nuclear shells Liquid drop model Curve of binding...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Nuclear shells Liquid drop model Curve of binding energy Fission and fusion Fission Fission reactors Nuclear shells We have seen how atoms have electron “shells” or sequential orbitals with different energies. The potential for nucleons is not the same as the Coulomb potential so the quantum mechanical solutions to energy states are not the same as what we’ve seen before. Here’s a picture of nuclear shells. See discussion of Maria Göppert-Mayer’s contributions to this on Serway p. 478 (Nobel Prize 1963). We can fit protons and neutrons into separate shell sequences. There exist magic numbers for closed shells: 2, 8, 20, 28, 50, 82, 126 Nuclear shells, from Geor- gia State’s Hyperphysics web site
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Nuclear shells Liquid drop model Curve of binding energy Fission and fusion Fission Fission reactors Magic numbers Again, the magic numbers refer to the top of energy state sequences before there is a gap, and they apply separately to neutrons and protons. The magic numbers are 2, 8, 20, 28, 50, 82, 126 Some nuclei are doubly-magic, in that both the proton number and the neutron number are magic. These nuclei are especially stable: 4 2 He, 16 8 O, 40 20 Ca, 48 20 Ca, 208 82 Pb Consider the two doubly-magic calcium nuclei: detailed calculations of the binding energy difference from the liquid-drop model trend (a trend we’ll discuss next) illustrate the extra stability: From Georgia State’s Hyperphysics web site
Background image of page 2
Nuclear shells Liquid drop model Curve of binding energy Fission and fusion Fission Fission reactors More magic Additional evidence for “magic” shells (again from Hyperphysics ): Enhanced abundance of those elements for which Z or N is a magic number. The stable elements at the end of the naturally occuring radioactive series all have a “magic number” of neutrons or protons. The neutron absorption cross-sections for isotopes where N is a magic number are much lower than surrounding isotopes. The binding energy for the last neutron is a maximum for a magic neutron number and drops sharply for the next neutron added. Electric quadrupole moments are near zero for magic number nuclei, indicating more symmetric charge distribution. The excitation energy from the ground nuclear state to the first excited state is greater for closed shells.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Nuclear shells Liquid drop model Curve of binding energy Fission and fusion Fission Fission reactors The liquid drop model This is discussed in Serway Sec. 13.3 but not in much detail. Origins of the model: von Weizsäcker, Z. Phys. 96 , 431 (1935); Bethe and Bacher, Rev. Mod. Phys. 8 , 82 (1936). Important additions to understand fission made by Frisch and Meitner and then by Bohr and Wheeler in 1939. Note that Frisch and von Weizsäcker were German which was of particular interest at that moment in history . . . Bethe was German, and Meitner was an Austrian Jew, but they both left Germany around this time. The main term in the liquid drop model is an average binding
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

l24 - Nuclear shells Liquid drop model Curve of binding...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online