1. Kernfysica: quarks, nucleonen en kernen
Outline lecture (HL-3)
HL-3 May 2004
Structure of nuclei
NN potential
exchange force
Terra incognita in nuclear landscape
Neutron matter
Halo nuclei
Hypernuclei
Literature: PR 16, 17
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

2. nucleon-nucleon scattering
positive (negative) phase shift for attractive (repulsive) potential in
scattered
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

3. energy dependence of NN phase shifts
phase shift (degrees) 50
-50
s wave: short range repulsive
long range attractive
p wave: repulsive
Phys. Rev. 182 (1969)1714
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

4. NN potential shape and strength
attractive singlet/triplet s wave,
repulsive p wave scattering
attractive
non-central Tensor term,
and LS (spin-orbit) term
repulsive core r < 0.49 fm
Hamada, Johnston
Nucl. Phys. 34 (1962) 382
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

5. general form of NN potential
depends on NN separation
relative momentum
angular momentum
must be scalar, P and T invariant, 2N symmetric
central
spin-spin
Tensor
spin-orbit
Tensor term: non-central force mixes different L-states: 4% 3D1-state in d
LS term: induces polarized scattered beams
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

6. Kernfysica: quarks, nucleonen en kernen
polarized scattering
p wave (l=1) scattering: symmetric spin wf. (S=1); VLS < 0
repulsive,
scattered left
attractive,
scattered left
parallel
spins :
scattered
left ü ý
polarizati on
anti -
parallel
spins :
scattered
right þ
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

7. quark state for NN system
short distance repulsion: chromomagnetic spin-spin interaction
6 quarks in s-state (l=0): symmetric spin-isospin wf.
minimizing chromomagnetic energy
 minimizing parallel quark spins
 distorting wave function symmetry:
l = 0
l = 1 
=1/9
=8/9
required excitation energy  strong short range repulsion
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

8. covalent bonds and meson exchange force
energetic favourable
spin=0, isospin=0 di-quark
direct q exchange suppressed
by color restriction
virtual meson
exchange:
Yukawa
potential
color-neutral
(sea-quark) exchange:
relativistic form of
covalent strong force
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

9. nuclear equation-of-state
in-medium interactions and selfenergies determined in relativistic
Dirac-Brückner Hartree-Fock theory from realistic NN potential
pure neutron matter
is unbound
Z=0
-16 MeV
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

10. Kernfysica: quarks, nucleonen en kernen
terra incognita
spherical
shell closure
for Z>112?
100Sn
48Ni
78Ni
nuclei: strongly interacting quantum systems of finite size,
balanced by isospin-symmetric strong, -violating Coulomb force
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

11. Kernfysica: quarks, nucleonen en kernen
halo nuclei
quantum phenomenon: weakly bound valence neutrons
in classical forbidden region beyond potential barrier
with low l i.e. low centrifugal barrier,
single-particle structure and strong pairing correlations
2n-halo region of
11Li as large as
208Pb radius,
mixed
(p1/2)2 (s1/2)2
configuration
multi-nucleon
halos:
neutron-droplets?
N/Z=3
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

12. shell quenching at large N/Z
2n-separation
energies  shell gap
reduced from 6 MeV
(100Sn) to 2 MeV (78Ni)
n-potential changes
from WS- to
softer HO-shape
 reduced spin-orbit
splitting
high-l intruder
moved back
across shell gap
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

13. creating and detecting hypernucleiK-
 binding energy: -
()
0 by choice of kinematics
(=0)
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

14.  spectrum and levels of hypernuclei
-levels not restricted by Pauli principle
in neutron-like potential (shallower for weaker -N interaction)
11 MeV 
may sit in
occupied n-levels
n from below
the Fermi level
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

15. binding energy of  in nuclei
in discrete levels
V0  30 MeV
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

16. production of  hypernuclei (S=-2)
H dibaryon (uuddss) ??
study of
hyperon-hyperon interaction
c (-) = 4.91 cm,
long-lived enough
to be captured
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen

17. Kernfysica: quarks, nucleonen en kernen
HL-3 May 2004
Summary lecture (HL-3 )
Nuclear structure
Potential and phase shifts
NN potential: general form; spin-spin, spin-orbit, tensor part
exchange force: virtual di-quark (meson) exchange
Terra incognita in nuclear landscape
Tasks for exotic-beam facilities
Neutron matter: large N/Z for light nuclei
Halo nuclei observed
Hypernuclei: binding energy and structure
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen
Kernfysica: quarks, nukleonen en kernen

18. structure of nuclei: Fermi gas model
number of neutron (N) and proton (Z) states up to Fermi momentum:
V(r) r
average kinetic energy:
V0=EF+B´
HL-3 May 2005
Kernfysica: quarks, nucleonen en kernen