Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 1 The Deuteron Deuterium (atom). The only bound state of two nucleons  simplest bound state Neither di-proton nor di-neutron are stable. Why? Experimentally  MeV (Recoil..!). Also inverse ( ,n) reaction using Bremsstrahlung (Recoil…!).  mc 2 = 2.224…??…MeV  Very weakly bound. Compare n-p to n-n and p-p  Charge independence of nuclear force. Only ground state. (There is an additional virtual state).

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 2 The Deuteron V(r) = -V 0 r < R = 0r > R Oversimplified. HW 17 Show that V 0  35 MeV. (Follow Krane Ch.4 and Problem 4.6), or similarly any other reference. Really weakly bound. What if the force were a bit weaker…?

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 3 The Deuteron

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 4 The Deuteron Experiment  deuteron is in triplet state   = 1. Experiment  even parity.  = l + s n + s p parity = (-1) l Adding spins of proton and neutron gives: s = 0 (antiparallel) or s = 1 (parallel). For  = 1 parallels-stateeven parallelp-stateodd antiparallelp-stateodd paralleld-stateeven

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 5 Experiment   =  N  spins are aligned…..But.? Direct addition   N. Direct addition of spin components assumes s-state (no orbital component). Discrepancy  d-state admixture.  = a 0  0 + a 2  2  = a 0 2  0 + a 2 2  2 HW 18 HW 18 In solving HW 17 you assumed an s-state. How good was that assumption? The Deuteron

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 6 The Deuteron S-state  No quadrupole moment. Experiment  b. HW 18 Discuss this discrepancy. From  and Q, is it really admixture? What about other effects? Important to know the d-state wavefunction.

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 7 Nuclear Force Read Secs. 4.4 and 4.5 in Krane.

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 8 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.  others …..

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 9 Shell model Electron configuration…. 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 …. Atomic Atomic 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 Nuclear magic numbers: 2, 8, 20, 28, 50, 82,126, …

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 10 Shell modelEvidence: 1) End of radioactive series: thorium series 208 Pb uranium series 206 Pb actinium series 207 Pb neptunium series 209 Bi 2) At Z and N mn’s there are relatively large numbers of isotopes and isotones.

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 11 Shell model

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 12 Shell model

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 13 Shell model 3) Natural abundances.

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 14 Shell model NEUTRON NUMBER NEUTRON CAPTURE CROSS SECTION 4) Neutron capture cross section.

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 15 Shell model 5) Binding energy of the last neutron (Separation Energy). (The measured values are plotted relative to the calculations without  ).

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 16 Shell model Pb (even-A) isotopes. 6) Excited states.

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 17 Shell model HW 19 Work out more examples for the above evidences. For example, take part of a plot and work on a group of relevant nuclides. 7) Quadrupole moments ….. ?

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 18 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, 1 st Semester, (Saed Dababneh). 19 Shell model More realistic: Finite square well potential: Rounded well potential: Correction for asymmetry (n-p has more possibilities than n-n or p-p) and Coulomb repulsion.

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 20 Shell model 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. 1s1p1d2s1f2p1g2d3s 2(2 l +1) Total mlml msms

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 21 Shell model centrifugal potential

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 22 Shell model

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 23 Shell model Infinite spherical well (R=8F) Harmonic oscillator ? ? ? 2(2 l + 1) accounts correctly for the number of nucleons in each level. But what about magic numbers?

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 24 Shell model So far, 2(2 l + 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. Spherical Harmonics, Eigenfunctions of L 2 and L z.

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 25 Shell model 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, 1 st Semester, (Saed Dababneh). 26 Shell model Spin-Orbit Coupling M. G. Mayer and independently Haxel, Jensen, and Suess. Spin-Orbit term added to the Hamiltonian: Central, attractive No longer Spherically symmetric Orientation

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 27 Shell model LL antiparallel UL parallel LS J

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 28 Shell model 2(2x3 + 1) = 14 2j+1 1f 7/2 First time l = 3 j

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 29 Shell model HW 20