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Electromagnetic moments

Electromagnetic moments. Electromagnetic interaction  information about nuclear structure. Charge  electric; current  magnetic. Electromagnetic multipole moments. Field  1/r 2 (zeroth, L=0) electric monopole moment. 1/r 3 (first, L=1) electric dipole moment.

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Electromagnetic moments

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  1. 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….!). • Higher order magnetic moments, we already discussed the magnetic dipole moment. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  2. 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, 1st Semester, 2006-2007 (Saed Dababneh).

  3. Electromagnetic moments • Electric monopole: net charge Ze. • Magnetic dipole: (already discussed). • g-factors. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  4. 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, 1st Semester, 2006-2007 (Saed Dababneh).

  5. 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. • Maximum  er02A2/3. • 6x10-30 to 50x10-30 em2. • 0.06 to 0.5 eb. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  6. Electric Quadrupole Moment • Closed shell  Spherically symmetric core. • Test for shell model • Strongly deformed nuclei…..! Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  7. Nuclear Force Recall Atomic Binding Energies for hydrogen like atoms: Dimensionless fine structure constant. Coulomb with Bohr radii: • Coupling constant  Strength. • Charge. • Mediators (Bosons). Other Forces ! Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  8. Nuclear Force Chromodynamics The deuteron: proton-neutron bound state. !!!!!!!!! !!!!!!!!! HW 16 Hydrogen: E1 = … eV r1 = …x10-10 m Positronium: E1 = … eV Deuteron: E1 = … MeV r1 = …x10-15 m Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  9. Nuclear Force Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  10. 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, 1st Semester, 2006-2007 (Saed Dababneh).

  11. Nuclear Force • Electrostatic and gravitational potential  long range (V1/r). • Near constancy of nuclear binding energy per nucleon B/A means that each nucleon feels only the effect of a few neighbors. This is called saturation. It implies also that the strong internucleon potential is short range. • Range is of order of the 1.8 fm internucleon separation. • Since volume A, nuclei do not collapse, there is a very short range repulsive component. • Exchange. • Some particles are immune. • Is nuclear physics just quark chemistry? • Charge independence. • Spin dependence. • Non-central (tensor) component  conservation of orbital angular momentum….? Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  12. Nuclear Force Mirror Nuclei Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  13. Strong Interaction If two charges, q and q' exchange photons, the Coulomb force occurs between them. What about forces between quarks? If pions are exchanged between two nucleons, the strong nuclear force occurs. Remember the weak nuclear force… Just for comparison. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  14. Strong Interaction • Only Hadrons. • Typical time: 10-24 s. (c, 10-15 m). • Exchange of light  140 MeV pions. • t = ħ/E = 4.7 x 10-24 s. (Why E?). • Range t c = ħ/mc = 1.4 x 10-15 m. • Range and time complicated by possibilities of heavier hadron exchange. • Isospin. Conservation of Isospin. Only relevant to hadrons. • Hadron multiplets: Doublet of nucleons and triplet of pions and … • The members of a multiplet have the same strangeness, hypercharge, spin, baryon number, electron family number, and muon family number, but differ in charge and differ slightly in mass. • Turn off electromagnetism …. !!! Scattering experiments. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  15. Strong Interaction • Isospin Magnitude • T3 can take T, T-1, T-2, ….., -T. • 1,2,3 not x,y,z (Isospin space). • Singlets (T = 0), Doublets (T = ½), Triplet (T = 1). • -T3 for antiparticles. • Isospin addition: for a collection of hadrons (e.g. in interaction) • Example: +-p scattering, Tmax = 3/2, T3 = 3/2T can only be 3/2. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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