Outline lecture (HL-3)

1
Outline lecture (HL-3)

• Structure of nuclei
• NN potential
• exchange force
• Terra incognita in nuclear landscape
• Neutron matter
• Halo nuclei
• Hypernuclei
• Literature PR 16, 17

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nucleon-nucleon scattering
positive (negative) phase shift for attractive
(repulsive) potential
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energy dependence of NN phase shifts
s wave short range repulsive long
range attractive p wave repulsive
Phys. Rev. 182 (1969)1714
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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
lt 0.49 fm
Hamada, Johnston Nucl. Phys. 34 (1962) 382
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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
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polarized scattering
p wave (l1) scattering symmetric spin wf.
(S1) VLS lt 0
repulsive, scattered left
attractive, scattered left
ü
left

scattered



spins

parallel
on
polarizati
ý
right

scattered


spins

parallel
-
anti
þ
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quark state for NN system
short distance repulsion chromomagnetic
spin-spin interaction 6 quarks in s-state (l0)
symmetric spin-isospin wf. minimizing
chromomagnetic energy ? minimizing parallel quark
spins ? distorting wave function symmetry
1/9
8/9
required excitation energy ? strong short range
repulsion
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covalent bonds and meson exchange force
energetic favourable spin0, isospin0
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
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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
Z0
-16 MeV
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terra incognita
spherical shell closure for Zgt112?
100Sn
48Ni
78Ni
nuclei strongly interacting quantum systems of
finite size, balanced by isospin-symmetric
strong, -violating Coulomb force
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single-particlelevels nlj
shell gaps and intruder states
p (s1/2)2(p1/2)1 n (s1/2)2(p3/2)4 (p1/2)2
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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 mul
ti-nucleon halos neutron-droplets?
N/Z3
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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

14
creating and detecting hypernuclei
p
K-
? binding energy
?-
(?)

0 by choice of kinematics (??0?)
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? 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
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binding energy of ? in nuclei

• in discrete levels
• V0 ? 30 MeV

17
production of ?? hypernuclei (S-2)
H dibaryon (uuddss) ?? study of hyperon-hyperon
interaction
c? (?-) 4.91 cm, long-lived enough to be
captured
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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

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structure of nuclei Fermi gas model
number of neutron (N) and proton (Z) states up to
Fermi momentum
V(r)
r
V0EFB
average kinetic energy