(PHYS722/822 Fall 2018)

Lecture 1

- Gluon and Quark exchange, plus Pauli-repulsion between like quarks in overlapping nucleons
- Gluon exchange based on Constituent Quark model plus 1-gluon exchange potential - not a good description for reasonable distances (because of confinement of non-color singletts)
- Pauli repulsion related to minimum energy to excite a nucleon (i.e. to move a quark into a different state) of 300 MeV
- Quark exchange between nucleons can change their charge (p->n and at the same time n->p)
- Gives reasonable (semi-quantitative) description of short range repulsive part of the nucleon-nucleon potential (plus maybe intermediate range)
- Quark-antiquark pair (= meson) exchange
- Similar to quark exchange (just reverse direction of one quark in time)
- Very good description of many aspects of NN potential
- Preferred because meson states are color-neutral and have relatively low mass (longer range)
- E.G.: pion mass = 140 MeV corresponds to range of 1.4 fm
- Will study one-pion exchange potential (OPEP) and generalizations to other mesons - so far only model that gives perfect agreement with data, especially long range part
- Chiral Symmetry and ChPT
- Based on chiral symmetry of QCD Lagrangian (quarks of opposite helicity are indistinguishable and don't couple to each other except for their masses)
- Chiral symmetry is spontaneously broken (because QCD prefers quark-antiquark pairs with negative parity over quark-quark pairs with positive ones). Consequence: Low (theoretically, zero) mass modes of the "quark condensate" called Goldstone bosons (pions, kaons and etas). This constrains the Lagrangian for processes involving nucleons and pseudoscalar mesons.
- Chiral symmetry is also violated by the (small) quark masses,
so
Goldstone
bosons are not totally massless. But one can expand the interaction in
small parameters like m
_{p}/m_{N}to make definite predictions (Chiral Perturbation Theory). - Effective Field Theory (EFT) approaches
- Describe Nature on different, separate length and mass scales without using underlying theory except for its symmetries
- Example: Chiral symmetry, see above
- In the context of NN interaction, EFT means applying all symmetries (including chiral symmetry) of the QCD lagrangian but not explicitely taking into account underlying degrees of freedom like pions or quarks. This gives a most general lagrangian which contains many parameters one can constrain with data.
- General form of potential allowed by symmetries like rotation, translation, isospin,... (see Wong)
- Somewhat in the same spirit as EFT, but much older and restricted to space-time and isospin symmetries
- 4 important terms: Central potential V(r), spin-spin (ss)
interaction,
spin-orbit (Ls) interaction and tensor (S
_{12}) interaction. - Each term occurs twice: once without isospin dependence, and
once with
**t**_{1}^{.}t_{2}(which measures total isospin of NN combination). The latter terms are responsible for charge-changing pion exchange etc. - Tensor term is important for long-range part of potential and arises "naturally" from pion exchange. QED analogy: magnetic dipole-dipole interaction

- Derived one-pion exchange potential (see Homework and also Wong)
- Described several high-precision phenomenological potentials:
- Everything described via one- and two- meson exchange (pi, rho, omega, sigma, ...): CD-Bonn
- Short- and medium range described via purely phenomenological
fit:
Nijmegen
I and II, Paris, Argonne V
_{18},... - Have 16 scattering amplitudes instead of 1, for each possible combination of incoming and outgoing spin orientation for both nucleons.
- Explained necessity of having more "labels" for phase shifts, involving S, L and J for each channel:
- For total isopin I=1 (only possibility for pp and nn
scattering):
^{1}S_{0},^{3}P_{0},^{3}P_{1},^{3}P_{2},^{1}D_{2},^{3}F_{2},^{3}F_{3},^{3}F_{4}, e_{2}=^{3}P_{2}->^{3}F_{2}(notation:^{ (2S+1)}L_{J}) - For total isospin I=0 (possible for pn scattering):
^{3}S_{1},^{1}P_{1},^{3}D_{1},^{3}D_{2},^{3}D_{3}, e_{1}=^{3}S_{1}->^{3}D_{1}(see homework) - Shown example of NN scattering experiments (both cross section and polarization-dependent variables - COSY)

- Discuss simple-most picture of dominant S-wave (square well potential)
- D-state: Origin, form, and consequences for magnetic moment, quadrupole moment and momentum distribution
- A complete writeup of today's lecture (actually much, much more!) can be found in Wally van Orden's beautiful summary paper.

- Discuss "higher order" corrections to simple picture:

- Meson Exchange currents (MEC) - lead to corrections of magnetic moment and cross sections because charged meson (esp. pion) exchange contributes to the overall electromagnetic current density in d
- Other "non-nucleonic" components in the wave function (somewhat speculative): Delta-Delta components (must occur in pairs because of Isospin), overlapping quark bags -> six-quark bags
- Discuss experiments on deuterium:
- Electromagnetic Form Factors. There are 3 (charge, magnetic,
quadrupole),
2 of which can be seperated via Rosenbluth, while one needs to measure
tensor analyzing powers or polarizations ("T
_{20}") to separate out all 3. - Photo-disintegration of deuterium and quark counting rules
- Quasi-elastic scattering to extract information on momentum distribution (including directional dependence due to D-state) and final state interaction
- Inclusive scattering on neutron with a spectator proton in the backward hemisphere (to suppress final state interactions).

- Most simple model: Shell model with "quasi-deuteron" coupling in
the
case
of 2 valence nucleons (p and n) outside a closed shell. Explains J
^{p}for all low A, e.g. 1/2^{+}for^{3}He and^{3}H, 0^{+}for^{4}He, 1^{+}for^{6}Li and 3/2^{-}for^{7}Li. - Can again have D-state components and more complicated correlated p-waves even in A=3.
- More precise approach: Use "exact" NN potentials fitted to NN data in Schroedinger equation
- Use either "exact" analytic methods (Fadeev, Hyperspherical Harmonics) or high-precision Monte Carlo method (Green's function MC, variational MC) to solve Schroedinger equation
- Calculate Ground state properties of A=3-8 nuclei, like mass (binding energy), energies of excited states, magnetic moments, form factors etc.
- Most potentials give too little binding energy. Can be cured (partially) using non-local potentials (sensitive to off-shell effects) like the CD-Bonn, by "relativizing" the Hamiltonian (both kinetic energy and potential due to length contraction), and by adding 3-body terms (e.g. Urbana IX 3-body potential).
- In addition, need Meson Exchange Currents (and maybe non-nucleonic components like Delta in the wave function) to fit magnetic properties.
- See the write-up by Rocco Schiavilla et al.