1 / 29

A Review of The Nuclear Shell Model

A Review of The Nuclear Shell Model. By Febdian Rusydi. Why We Need the Model?. To describe and predict nuclear properties associated with the structure. This Review will focus on: Angular Momentum & parity, J  Ground and excited state configuration Magnetic moment, .

trella
Download Presentation

A Review of The Nuclear Shell Model

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A Review ofThe Nuclear Shell Model By Febdian Rusydi

  2. Why We Need the Model? • To describe and predict nuclear properties associated with the structure. • This Review will focus on: • Angular Momentum & parity, J • Ground and excited state configuration • Magnetic moment, 

  3. Presentation Overview • Historical development • Why Shell Model: The Evidences • How to develop the model • How to explain the ground and excited state configuration of an nucleus • How to determine the magnetic moment of the nucleus

  4. Historical Development • 1927-28: Statistical Law of Fermions developed by Fermi • 1932-33: Magic Number2, 8, 20, 28, 50, 82, 126 pointed out by Barlett & Elsasser • 1934: The nuclear structure model begun to discuss. Fermi Gas Model developed, then applied to nuclear structure. • 1935: Liquid Drop Model by Weizsäcker • 1936: Bohr applied LDM to nuclear structure The magic number remained mystery…

  5. Binding Energy per Nuclear Particle 4He and 12C  -cluster Solid Red  Experimental Dash Black  Semi-empirical

  6. Why Shell Model? • Old-fashioned thought: • nucleons collide with each other. No way for shell model. Nuclear scattering result: • that thought doesn’t fit the data! • Magic number even doesn’t look to support shell model! BUT Indication that nuclear potential can be approached by a Potential-Well  Experiment evidence Atomic physics  electron orbits around the core But, how is inside the core??? ?

  7. The Evidence #1:Excitation Energy of First 2+State N/Z=20/20 N/Z=126/82 Z=30 N/Z=50/40 N/Z=82/60 Z=50 Z=70 Review Physics Letter 28 (1950) page 432

  8. The Evidence #2:Neutron Absorption X-section (Logarithmic) E. B. Paul, “Nuclear & Particle Physics”, North Holland Pub. Comp., 1969, page 259

  9. The Evidence #3:Neutron Separation Energy Frauenfelder & Henley, “Subatomic Physics”, Prentice Hall, 1991, page 488

  10. Conclusion so far… • Nuclear structure BEHAVES alike electron structure • Magic number  a Closed Shell • Properties: • Spherical symmetric • Total angular momentum = 0 • Specially stable

  11. Presentation Overview • Historical development • Why Shell Model: The Evidences • How to develop the model • How to explain the ground and excited state configuration of an nuclei • How the determine the magnetic moment of the nuclei to

  12. Let’s Develop the Theory! • Keyword: • Explain the magic number • Steps: • Find the potential well that resembles the nuclear density • Consider the spin-orbit coupling

  13. Shell Model Theory:The Fundamental Assumption • The Single Particle Model • Interactions between nucleons are neglected • Each nucleon can move independently in the nuclear potential

  14. Various forms of the Potential Well Central potential Residual potential Cent. Pot >> Resd. Pot, then we can set   0. Finally we have 3 well potential candidates! Full math. Treatment: Kris L. G. Heyde, Basic Ideas and Concepts in Nuclear Physics, IoP, 1994, Chapter 9

  15. The Closed Shell:Square Well Potential The closed shell  magic number

  16. The Closed Shell:Harmonic Potential The closed shell  magic number

  17. The Closed Shell:Woods - Saxon Potential The closed shell  magic number But… This potential resembles with nuclear density from nuclear scattering

  18. The Closed Shell:Spin-Orbit Coupling Contribution • Maria Mayer (Physical Review 78 (1950), p16) suggested:, • There should be a non-central potential component • And it should have a magnitude which depends on the S & L • Hazel, Jensen, and Suess also came to the same conclusion.

  19. The Closed Shell:Spin-Orbit Coupling Calculation The non-central Pot. Energy splitting Experiment: Vls = negative  Energy for spin up < spin down Full math. Treatment: Kris L. G. Heyde, Basic Ideas and Concepts in Nuclear Physics, IoP, 1994, Chapter 9

  20. SMT: The Closed Shell Povh, Particle & Nuclei (3rd edition), Springer 1995, pg 255

  21. SMT: The Ground State • How to determine the Quantum Number J ?[1] • J (Double Magic number or double closed shell) = 0+. If only 1 magic number, then J determined by the non-magic number configuration. • J determined from the nucleon in outermost shell (i.e., the highest energy) or hole if exist. •  determined by (-1)l, where l(s,p,d,f,g,…) = (0, 1, 2, 3, 4, …). To choose l: consider hole first, then if no hole  nucleon in outermost shell.

  22. SMT: The Ground State (example)

  23. SMT: Excited State • Some conditions must be known: energy available, gap, the magic number exists, the outermost shell (pair, hole, single nucleon). • Otherwise, it is quite difficult to predict precisely what is the next state.

  24. SMT: Excited State (example) • Let’s take an example 18O with ground state configuration: • Z= 8 – the magic number • N=10 – (1s1/2)2 (1p3/2)4 (1p1/2)2 (1d5/2)2 or (d5/2)2 • If with E ~ 2 [MeV], one can excite neutron to (d5/2) (d3/2), then with E ~ 4 [MeV], some possible excite states are: • Bring 2 neutron from 1p1/2 to 2d5/2 (d5/2)4 0  J  5 • Bring 2 neutron from 2d5/2 to 2d3/2 (d3/2)2 0  J  3 • Bring 1 neutron from 2d5/2 to 1f7/2 (f7/2)1 1  J  6 • Some other probabilities still also exist

  25. Mirror Nuclei 15NZ=715OZ=8 If we swap protons & neutrons, the strong force essentially does not notice it Discrepancy The prediction of SMT fail when dealing with deformed nuclei. Example: 167Er Theory 7/2 - Exprm  7/2 + Collective Model!  SMT: Mirror & Discrepancy

  26. SMT: Mirror Nuclei (Example) Povh, Particle & Nuclei (3rd edition), Springer 1995, pg 256

  27. SMT: The Magnetic Moment • Since L-S Coupling  associated to each individual nucleon • SO   sum over the nucleonic magnetic moment Full math. Treatment: A. Shalit & I. Talmi, Nuclear Shell Model, page 53-59

  28. Conclusions • How to develop the model • Explain the magic number • Single particle model • Woods – Saxon Potential • LS Coupling Contribution • Theory for Ground & Excited State • Treat like in electron configuration • J can be determined by using the guide • Theory for Magnetic Moment •  is sum over the nucleonic magnetic moment

  29. Some More Left… • Some aspects in shell Model Theory that are not treated in this discussion are: • Quadruple Moment – the bridge of Shell Model Theory and Collective Model Theory. • Generalization of the Shell Model Theory – what happen when we remove the fundamental assumption “the nucleons move in a spherical fixed potential, interactions among the particles are negligible, and only the last odd particle contributes to the level properties”.

More Related