1. P461 - Nuclei I1 Properties of Nuclei Z protons and N neutrons held together with a short-ranged force  gives binding energy P and n made from quarks. Most of the mass due to the strong interactions binding them together. Recent JLAB results show masses inside nucleus might be slightly smaller than free particles P and n are about 1 Fermi in size and the strong force doesn’t compress. Size ~ range of strong force  all nuclei have the same density and higher A nuclei are bigger (unlike atoms)

2. P461 - Nuclei I2 Nuclei Force Strong force binds together nucleons Strong force nominally carried by gluons. But internucleons carried by pions (quark-antiquark bound states) as effective range too large for gluons Each p/n surrounded by virtual pions. Strong force identical p-p, p-n, n-n (except for symmetry/Pauli exclusion effects) Range of 1 F due to pion mass p n n p 

3. P461 - Nuclei I3 Nuclear Sizes and Densities Use e + A -> e + A scattering completely EM Pe = 1000 MeV/c  wavelength = 1.2 F now JLAB, in 60s/70s SLAC up to 20 GeV( mapped out quarks) Measurement of angular dependence of cross section gives charge distribution (Fourier transform) Can also scatter neutral particles (n, Klong) in strong interactions to give n,p distributions Find density ~same for all but the lowest A nucleii

4. P461 - Nuclei I4 P461 Model of Nuclei “billiard ball” or “liquid drop” Adjacent nucleons have force between them but not “permanent” (like a liquid). Gives total attractive energy proportional to A (the volume) – a surface term (liquid drop) Repulsive electromagnetic force between protons grows as Z 2 Gives semi-empirical mass formula whose terms can be found by fitting observed masses Pauli exclusion as spin ½  two (interacting) Fermi gases which can be used to model energy nd momentum density of states Potential well is mostly spherically symmetric so quantum states with J/L/S have good quantum numbers. The radial part is different than H but partially solvable  shell model of valence states and nuclear spins

5. P461 - Nuclei I5 Semiempirical Mass Formula M(Z,A)=f0 + f1 +f2 + f3 + f4 + f5 f0 = mpZ + mn(A-Z) mass of constituents f1 = -a 1 A A ~ volume -> binding energy/nucleon f2 = +a 2 A 2/3 surface area. If on surface, fewer neighbors and less binding energy f3 = +a 3 Z 2 /A 1/3 Coulomb repulsion ~ 1/r f4 = +a 4 (Z-A/2) 2 /2 ad hoc term. Fermi gas gives equal filling of n, p levels f5 = -f(A) Z, N both even = 0 Z even, N odd or Z odd, N even = +f(A) Z., N both odd f(A) = a 5 A -.5 want to pair terms (up+down) so nuclear spin = 0 Binding energy from term f1-f5. Find the constants (ai’s) by fitting the measured neclei masses

6. P461 - Nuclei I6 Fermi Gas Model p,n spin ½ form two Fermi gases of indistinguishable particles  p n through beta decays (like neutron stars) and p/n ratio due to matching Fermi energy In finite 3D well with radius of nucleus. Familiar: Fermi energy from density and N/A=0.6 Slightly lower proton density but shifted due to electromagnetic repulsion

7. P461 - Nuclei I7 Fermi Gas Model II V = depth of well = F(A) ~ 50 MeV Fermi energy same for all nuclei as density = constant Binding energy B = energy to remove p/n from top of well ~ 7-10 MeV V = E F + B Start filling up states in Fermi sea (separate for p/n) Scattering inhibited 1 + 2  1’ + 2’ as states 1’ and 2’ must be in unfilled states  nucleons are quasifree If ignore Coulomb repulsion, as n p through beta decay, lowest energy will have N=Z (gives (N-Z) term in mass formula) vs n p V B