Nuclear Force Spin dependent difference in neutron scattering cross sections of ortho- and para-hydrogen. Compare n-p to n-n and p-p Charge independence of nuclear force. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 1
Nuclear Force Mirror Nuclei Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 2
Nuclear Force If two charges, q and q' exchange photons, the Coulomb force occurs between them. Krane 4.5 What about forces between quarks? Color? If pions are exchanged between two nucleons, the strong nuclear force occurs. Remember the weak nuclear force _ n p + e +ν Boson? Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 3
Nuclear Force Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 4
Nuclear Force 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, etc, but differ in charge and differ slightly in mass. Relationship between ee particle and nuclear physics. Accelerators and large accelerators. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 5
Isospin Isospin Magnitude T ( T +1) T 3 can take TT-1 T, T 1, T-2 2,.., -T. 1,2,3 not x,y,z (Isospin space). Singlets (T = 0), Doublets (T = ½), Triplet (T = 1), Quartet (??). -TT 3 for antiparticles. Isospin addition: for a collection of hadrons (e.g. in interaction) T = max T ( i ) i ( T = T3( i ) T T T 3 3 i Example: π + -p scattering, T = 3 = 3 3 max / 2, T 3 / 2 T can only be / 2. Read Krane 11.3. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 6
The Deuteron Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 7
The Deuteron Deuterium (atom). The only bound state of two nucleons simplest bound state. Neither di-proton nor di-neutron are stable. Why? 1 2 n + H H + γ Experimentally 2.224 MeV (Recoil..!). Also inverse (γ,n) reaction using Bremsstrahlung (Recoil!). Mass spectroscopy mass of D (or deuterium atom). mc 2 = 2.224?? MeV224 Very weakly bound. Mass doublet method all results are in agreement. Compare 2.224 MeV to 8 MeV (average B/A for nuclei). Only ground state. (There is an additional virtual state). HW 18 Problems 4.1-4.5 in Krane. Nuclear and Radiation Physics, BAU, 1 st Semester, 2006-2007 8
The Deuteron V(r) = -V 0 r < R = 0 r > R Oversimplified. HW 19 Assuming l = 0,, 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 e a bit weaker? Nuclear and Radiation Physics, BAU, 1 st Semester, 2006-2007 9
The Deuteron Nuclear and Radiation Physics, BAU, 1 st Semester, 2006-2007 10
The Deuteron Experiment deuteron is in triplet state Ι = 1. Experiment even parity. Ι = l + s n + s p Adding spins of proton and neutron gives: s = 0 (antiparallel) or s = 1 (parallel). For Ι = 1 parallel s-statestate even parallel p-state odd antiparallel tpa a p-state odd parallel d-state even parity = (-1) l Nuclear and Radiation Physics, BAU, 1 st Semester, 2006-2007 11
The Deuteron Experiment µ = 0.8574376 µ N spins are aligned..but.? Direct addition 0.8798038 µ N. Direct addition of spin components assumes s-state (no orbital component). Discrepancy d-state admixture. ψ = a 0 ψ 0 + a 2 ψ 2 µ =a 2 +a 2 0 µ 0 2 µ 2 HW 20 In solving HW 19 you assumed an s-state. How good was that assumption? Nuclear and Radiation Physics, BAU, 1 st Semester, 2006-2007 12
The Deuteron S-state No quadrupole moment. Experiment +0.00288 00288 b. HW 21 Discuss this discrepancy. From µ 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, 2006-2007 13
Nuclear Force Nuclear and Radiation Physics, BAU, 1 st Semester, 2006-2007 14