Nuclear Magnetic Moment

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Presentation transcript:

Nuclear Magnetic Moment Remember, for electrons Revise: Torque on a current loop. Gyromagnetic ratio (g-factor) Z component ?? Experiment, applied magnetic field. Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Nuclear Magnetic Moment For Nuclei For free protons and neutrons Proton: g = 5.5856912 ± 0.0000022  3.6  Neutron: g = -3.8260837 ± 0.0000018  3.8  The proton g-factor is far from the gS = 2 for the electron, and even the uncharged neutron has a sizable magnetic moment!!!  Internal structure (quarks). Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Nuclear Magnetic Moment Nuclide Nuclear spin Magnetic moment  (in N) n 1/2 -1.9130418 p +2.7928456 2H (D) 1 +0.8574376 17O 5/2 -1.89279 57Fe +0.09062293 57Co 7/2 +4.733 93Nb 9/2 +6.1705 Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Nuclear Parity (r)  (-r) Even. (r)  -(-r) odd. For a nucleon  is either of even ( = +) or odd ( = -) parity. For the nucleus  = 1 2 3 … A. Practically not possible. Overall  can be determined experimentally. Overall  for a nucleus (nuclear state). Transitions and multipolarity of transitions (-emission). Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Electromagnetic moments Electromagnetic interaction  information about nuclear structure. Charge  electric; current  magnetic. Electromagnetic multipole moments. Field1/r2 (zeroth, L=0) electric monopole moment. 1/r3 (first, L=1) electric dipole moment. 1/r4 (second, L=2) quadrupole moment. ……… 1/r2 magnetic monopole (questionable….!). Magnetic Dipole (familiar). Higher order magnetic moments. Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Electromagnetic moments Expectation value of the moment. Each multipole moment has a parity, determined by the behavior of the multipole operator when r  -r. Parity of  does not change the integrand. Electric moments: parity (-1)L. Magnetic moments: parity (-1)L+1. Odd parity  vanish. electric dipole. magnetic quadrupole. electric octupole. ………… Vanishing moments Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Electromagnetic moments Electric monopole: net charge Ze. Magnetic dipole: (already discussed). g-factors. Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Electromagnetic moments The nucleus has charge (monopole moment). No dipole moment since it is all positive. But if the nucleus is not spherically symmetric, it will have a quadrupole moment. Classical moments Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Electric Quadrupole Moment For a point charge e: eQ = e(3z2 - r2). Spherical symmetry  x2 = y2 = z2 = r2/3  Q = 0. For a proton: In the xy-plane: Q  - r2. r2 is the mean square radius of the orbit. Along z: Q  +2 r2. Expected maximum  er02A2/3. 6x10-30 to 50x10-30 em2. 0.06 to 0.5 eb. Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Electric Quadrupole Moment Nuclide Q (b) 2H (D) +0.00288 17O -0.02578 59Co +0.40 63Cu -0.209 133Cs -0.003 161Dy +2.4 176Lu +8.0 209Bi -0.37 Closed shell  Spherically symmetric core. Test for shell model Strongly deformed nuclei…..! Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Nuclear Force (Origin of Binding) Recall Atomic Binding Energies for hydrogen like atoms: =1 Dimensionless fine structure constant. Coulomb with Bohr radii: Coupling constant  Strength. Charge. Mediators (Bosons). Other Forces ! Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Nuclear Force The deuteron: proton-neutron bound state. Chromodynamics !!!!!!!!! QCD Color charge! !!!!!!!!! QFT HW 17 Hydrogen: E1 = … eV r1 = …x10-10 m Positronium: E1 = … eV Deuteron: E1 = … MeV r1 = …x10-15 m Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Nuclear Force Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Nuclear Force Repeated Attractive but repulsive core. At what separation? Repeated Saturation? Get an estimate for nuclear density and thus inter-nucleon distance. Have you done that? Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Nuclear Force Repeated Is the nucleon bounded equally to every other nucleon? C ≡ this presumed binding energy. Btot = C(A-1)  A  ½ Bave = ½ C(A-1) Linear ??!!! Directly proportional ??!!! Clearly wrong … !  wrong assumption  finite range of strong force, and force saturation. Repeated Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

Nuclear Force Rate of decay or interaction R  (E). Coupling constant . Vertices in the diagrams. For decays R  1/T. (T  Lifetime). The density of states  is a measure of the number of quantum mechanical states per unit energy range that are available for the final products. The more states that are available, the higher the transition rate. The coupling constant  can be interpreted as an intrinsic rate. Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).