Topics discussed in the Lectures 11/6-11/15 for
Graduate
Nuclear Physics
(PHYS722/822 Fall 2018)
Lecture 1
Nucleon-Nucleon Interaction Models
- 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 mp/mN
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 (S12) interaction.
- Each term occurs twice: once without isospin dependence, and
once with t1.t2
(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
Lecture 2
NN potentials and phase shifts continued
- 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 V18,...
- 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): 1S0, 3P0, 3P1,
3P2, 1D2, 3F2,
3F3, 3F4, e2
= 3P2 -> 3F2 (notation:
(2S+1)LJ)
- For total isospin I=0 (possible for pn scattering): 3S1,
1P1, 3D1, 3D2,
3D3, e1
= 3S1 -> 3D1 (see
homework)
- Shown example of NN scattering experiments (both cross section
and
polarization-dependent
variables - COSY)
Lecture 3
The deuteron - ground state properties
- 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.
If/as time permits:
- 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 ("T20") 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).
Lecture 4
Few body nuclei (A = 2,...,8) - ground state properties
- Most simple model: Shell model with "quasi-deuteron" coupling in
the
case
of 2 valence nucleons (p and n) outside a closed shell. Explains Jp
for all low A, e.g. 1/2+ for 3He and 3H,
0+ for 4He, 1+ for 6Li
and
3/2- for 7Li.
- 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.
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