1. May the Strong Force be with you

2. Origin of the nucleon-nucleon force
The simplest contributions to the force between nucleons, as viewed from QCD. Here, the exchange of two colored gluons causes two quarks in each nucleon to change their colors (blue changes to green and vice versa in the case illustrated). This process produces a force without violating the overall color neutrality of the nucleons. The strength of the force depends on the separation of the different quark colors within each nucleon. On the other hand, low-energy nuclear physics measurements show clearly that the longest-range part of the force arises from the exchange of a single pi meson between two nucleons, as in In this low-energy view, the internal structure of each nucleon is generally attributed to three pseudo-quarks, which somehow combine the properties of the valence quarks, sea quarks, and gluons predicted by QCD.

3. The challenge and the prospect: physics of nuclei directly from QCD
Nuclear Force from Lattice QCD
Inoue et al. PRL 111, (2013); HALQCD/HPCI
The interaction between two nucleons is effected by the exchange of a particle. However, because the nucleon interactions appear to be short-ranged, the particle must have a finite mass. In fact, one can correlate the range and mass roughly by the quantum uncertainty principle, r ∼ 1/m, therefore, the mass of the quanta exchanged is about 1/fm which is about 200 MeV.

4. A realistic nuclear force force: schematic view
Nucleon r.m.s. radius ~0.86 fm
Comparable with interaction range
Half-density overlap at max. attarction
VNN not fundamental (more like inter-molecular van der Waals interaction)
Since nucleons are composite objects, three-and higher-body forces are expected.
OPEP: One-pion-exchange potential (at large distances)
Yukawa force

5. Realistic nuclear force
QCD!
Repusive core
attraction
There are infinitely many equivalent nuclear potentials!
OPEP
Reid93 is from V.G.J.Stoks et al., PRC49, 2950 (1994).
AV16 is from R.B.Wiringa et al., PRC51, 38 (1995).
quark-gluon structures
overlap
heavy mesons

6. Nucleon-nucleon scattering
pp, np, nn scattering in T=0, 1 channels
pp scattering easy
neutron beams (np,nn) and neutron targets (pn,nn) difficult
7Li(p,n), reactors
short neutron lifetime (~10min); deuteron - a substitute (pp and 3N effects have to be subtracted) k’ k z
Elastic scattering (the same value of k) valid for short-ranged potentials (V=0 at large r); Coulomb contribution must be removed

7. Partial-wave decomposition
For scattering off a short-ranged potential, it is useful to carry out a partial-wave decomposition.
phase shift
The probability current density in each partial wave is conserved - unitarity (valid only for elastic scattering!). The partial wave decomposition is very convenient at low energies since only a few terms enter the expansion.
potential range

8. Phase shift
hard core
attractive square well

9. 2S+1LJ Partial wave analysis
For pn scattering (potential range 2fm) and low momenta (<400 MeV/c), the s-waves dominate. The phase shift d0 is decisive for nuclear binding.
For momenta > 400 MeV/c the phase shift is negative. This indicates that the
nuclear force is repulsive at short distances!
2S+1LJ
V (MeV)

10. NN potentials from partial wave analysis
CD-Bonn potential
Paris potential

11. Scattering length and effective range
At very low energies, the l=0 total cross section remains finite for NN scattering
S-wave scattering length
is positive if there is a bound state
effective range

12. Consider a simplified deuteron potential of the form:
(i.e., a square well potential where the depths become different for the spin triplet and singlet wave functions). Scattering data show that Vtriplet ≈ 2Vsinglet. Determine the constant a.
Remember:

13. Resolution and Effective Field Theory
multipole expansion
of electrostatic potential

15. If system is probed at low energies, fine details not resolved
Use low-energy variables for low-energy processes
Short-distance structure can be replaced by something simpler without distorting low-energy observables
Physics interpretation can change with resolution!

16. The Hierarchy of Nuclear Forces in Chiral-EFT
2N forces
3N forces
4N forces
Leading Order
The Hierarchy of Nuclear Forces in Chiral-EFT
Next-to Leading Order
Next-to-Next-to Leading Order
derived 2002
optimized 2014
derived 2000
Next-to-Next-to-Next-to Leading Order
R. Machleidt
derived 2003
derived 2011
derived 2007

17. three-nucleon interactions
Three-body forces between protons and neutrons are analogous to tidal forces: the gravitational force on the Earth is not just the sum of Earth-Moon and Earth-Sun forces (if one employs point masses for Earth, Moon, Sun) 17

18. nucleon-nucleon interactions from chiral EFT
Effective-field theory potentials
Renormalization group (RG) evolved nuclear potentials
Vlow-k unifies NN interactions at low energy
N3LO: Entem et al., PRC68, (2003)
Epelbaum, Meissner, et al.
Bogner, Kuo, Schwenk, Phys. Rep. 386, 1 (2003)

19. Deuteron rms radius=1.963 fm D-wave produced by tensor force!
Binding energy
2.225 MeV
Spin, parity 1+
Isospin
Magnetic moment
m=0.857 mN
Electric quadrupole moment
Q=0.282 e fm2
rms radius=1.963 fm
D-wave produced by tensor force!

20. Deuteron Shapes with V18
Jlab data

21. Short Range Correlations and Tensor Force
Dominance of proton–neutron pairs at intermediate range (c.o.m. momenta around 400 MeV/c)
Science 320, 1475 (2008)
Two-nucleon knockout
The distinctive experimental features of two-nucleon SRCs are the large back-to-back relative momentum and small centre-of-mass momentum of the correlated pair, where large and small are relative to the Fermi-sea level of about 250 MeV/c.
Theory explains the pn pair dominance in terms of the tensor force:
Phys. Rev. Lett. 98, (2007)