Quantum Mechanical Properties of Nuclei Lecture 4 Sizes

Quantum Mechanical Properties of Nuclei Lecture 4

Sizes and Shapes of Nuclei • How big are nuclei? • 1 -10 fm • sharp cutoff model, R=r 0 A 1/3 fm r 0=1. 07 r 0=1. 2 r 0=1. 44

Nuclear Sizes (cont. ) • Diffuse surface model Lighter nuclei are mostly surface

Nucleus Fraction of nucleons in the “skin” 12 C 0. 90 24 Mg 0. 79 56 Fe 0. 65 107 Ag 0. 55 139 Ba 0. 51 208 Pb 0. 46 238 U 0. 44

The “Halo Nuclei” 11 Li 208 Pb

Nuclear Spin and Parity • Nuclei have an intrinsic angular momentum. This angular momentum is referred to as the “spin. ” • For odd A nuclei, the spin J is half integer. (1/2, 3/2, etc. ) For even A nuclei, the spin J is integer. (0, 1, 2, etc. ). The magnitude of the spin is multiple of hbar.

Parity (the symmetry properties of the nuclear wave function) For a central potential, V=V(r)

Nomenclature (J, π)=3/2+ (J, π)=7 -

Nuclear Shapes • Some nuclei are spherical. Many are not. • Instead they can be football shaped or frisbee shaped.

Electric and magnetic moments • Electric moments are measures of the distribution of electric charge. Magnetic moments measure the distribution of electric currents.

Electric Quadrupole Moments

Magnetic Moments Classical Analogy

Quantum mechanical view

Gyromagnetic ratios Find

Values of nuclear magnetic moments • Tables—Stone, http: //www. unidue. de/physik/wende/keune/deutsch/nucle ar-moments. pdf • Value of the n, p moments->Chap. 5 • Value of the isotopic moments->Chap. 6