Nuclear Models Nuclear force is not yet fully understood.

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Presentation transcript:

Nuclear Models Nuclear force is not yet fully understood. No absolutely satisfying model, but models. Specific experimental data  specific model. Model  success in a certain range. Some are: Individual particle model. (No interaction, E. states, static properties, …). Liquid drop model. (Strong force, B.E., Fission, …). Collective model. -particle model. Optical model. Fermi Gas model. others ….. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Electron configuration…. 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 …. Atomic Electron magic numbers: 2, 10, 18, 36, 54, … Common center of “external” attraction. Well understood Coulomb force. One kind of particles. Clear meaning for electron orbits. … Nuclear magic numbers: 2, 8, 20, 28, 50, 82,126, … (for Z or N). Chemistry! Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Evidence: End of radioactive series: thorium series 208Pb uranium series 206Pb actinium series 207Pb neptunium series 209Bi At Z and N mn’s there are relatively large numbers of isotopes and isotones. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Natural abundances. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Neutron capture cross section. NEUTRON CAPTURE NEUTRON NUMBER Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Binding energy of the last neutron (Separation Energy). (The measured values are plotted relative to the calculations without ). Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Excited states. Pb (even-A) isotopes. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model All are even-even. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Quadrupole moments ….. ? HW 22 Work out more examples for the above evidences. For example, take part of a plot and work on a group of relevant nuclides. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Nucleons are in definite states of energy and angular momentum. Nucleon orbit ?? Continuous scattering expected ..!! No vacancy for scattering at low energy levels. Potential of all other nucleons. Infinite square well: Harmonic oscillator: Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Infinite spherical well Shell model ? ? 2(2l + 1) accounts correctly for the number of nucleons in each level. But what about magic numbers? ?    Infinite spherical well (R=8F) Harmonic oscillator Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model More realistic! (Can it solve the problem?) Finite square well potential: Rounded well potential: Correction for asymmetry and Coulomb repulsion. Adjusted by the separation energies. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model HW 23 Coulomb repulsion? Vc(r) = ?? Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model HW 24 Separation of variables: For a given spherically symmetric potential V(r), the bound-state energy levels can be calculated from radial wave equation for a particular orbital angular momentum l. Notice the important centrifugal potential. HW 24 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model centrifugal potential Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

What about other magic numbers? 1p 1d 2s 1f 2p 1g 2d 3s 2(2l +1) 2 6 10 14 18 Total 8 20 34 40 58 68 70 ml ms 2, 8, 20 ok. What about other magic numbers? Situation does not improve with other potentials. Something very fundamental about the single-particle interaction picture is missing in the description…..!!!!! Spin-orbit coupling. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model So far, 2(2l + 1) accounts correctly for the number of nucleons in each level, since we already considered both orbital angular momentum, and spin, but still not for closed shells. Separate. Spherical Harmonics, Eigenfunctions of L2 and Lz. But this representation does not solve the problem. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Spherically symmetric Shell model Spin-Orbit Coupling M. G. Mayer and independently Haxel, Jensen, and Suess. Spin-Orbit term added to the Hamiltonian: Orientation No longer Spherically symmetric Central, attractive Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model L S J LL antiparallel UL parallel Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model 2j+1 1f7/2 2(2x3 + 1) = 14 l = 3 j First time Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model HW 25 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Notes: 1. The shell model is most useful when applied to closed-shell or near closed-shell nuclei. 2. Away from closed-shell nuclei collective models taking into account the rotation and vibration of the nucleus are more appropriate. 3. Simple versions of the shell model do not take into account pairing forces, the effects of which are to make two like-nucleons combine to give zero orbital angular momentum. The pairing force increases with l. 4. Shell model does not treat distortion effects (deformed nuclei) due to the attraction between one or more outer nucleons and the closed-shell core. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Fermi Gas EF  n2/3 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Transition probability? Shell model Nuclear reactions? Transition probability? Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Ground state: (near closed shells) 1. Angular momentum of odd-A nuclei is determined by the angular momentum of the last nucleon that is odd. 2. Even-even nuclei have zero ground-state spin, because the net angular momentum associated with even N and even Z is zero, and even parity. 3. In odd-odd nuclei the last neutron couples to the last proton with their intrinsic spins in parallel orientation. Provided that the ordering is known….!! A < 150 190 < A < 220 Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Harmonic oscillator Near drip line No spin-orbit coupling Near valley of  stability Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model 17 p, 21 n. p in 1d3/2 l  s   = + n in 1f7/2 l  s   = - Rule 3  sp  sn   lp  ln  ½ + ½ + 3 – 2 = 2  total  = - Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

Shell model Excited states: Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).