HL-3 May 2006Kernfysica: quarks, nucleonen en kernen1 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

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen2 nucleon-nucleon scattering positive (negative) phase shift for attractive (repulsive) potential in scattered

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen3 energy dependence of NN phase shifts phase shift (degrees) Phys. Rev. 182 (1969)1714 s wave: short range repulsive long range attractive p wave: repulsive

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen4 NN potential shape and strength Hamada, Johnston Nucl. Phys. 34 (1962) 382 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

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen5 general form of NN potential depends on NN separation relative momentum angular momentum must be scalar, P and T invariant, 2N symmetric Tensor term: non-central force mixes different L-states: 4% 3 D 1 -state in d LS term: induces polarized scattered beams central spin-spin Tensor spin-orbit

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen6 polarized scattering p wave (l=1) scattering: symmetric spin wf. (S=1); V LS < 0 repulsive, scattered left attractive, scattered left onpolarizati   right scattered :spins parallel-anti left scattered :spins parallel

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen7 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  required excitation energy  strong short range repulsion =1/9=8/9

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen8 covalent bonds and meson exchange force energetic favourable spin=0, isospin=0 di-quark direct q exchange suppressed by color restriction color-neutral (sea-quark) exchange: relativistic form of covalent strong force virtual meson exchange: Yukawa potential

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen9 nuclear equation-of-state in-medium interactions and selfenergies determined in relativistic Dirac-Brückner Hartree-Fock theory from realistic NN potential Z=0 pure neutron matter is unbound -16 MeV

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen10 terra incognita nuclei: strongly interacting quantum systems of finite size, balanced by isospin-symmetric strong, -violating Coulomb force spherical shell closure for Z>112? 48 Ni 100 Sn 78 Ni

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen11 single-particle levels nl j shell gaps and intruder states p: (s1/2) 2 (p1/2) 1 n: (s1/2) 2 (p3/2) 4 (p1/2) 2

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen12 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 11 Li as large as 208 Pb radius, mixed (p1/2) 2 (s1/2) 2 configuration multi-nucleon halos: neutron-droplets? N/Z=3

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen13 shell quenching at large N/Z 2n-separation energies  shell gap reduced from 6 MeV ( 100 Sn) to 2 MeV ( 78 Ni) n-potential changes from WS- to softer HO-shape  reduced spin-orbit splitting  high-l intruder moved back across shell gap

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen14 creating and detecting hypernuclei  binding energy: 0 by choice of kinematics (  =0  ) p K-K- -- ()()

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen15  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 2006Kernfysica: quarks, nucleonen en kernen16 binding energy of  in nuclei  in discrete levels V 0  30 MeV

HL-3 May 2006Kernfysica: quarks, nucleonen en kernen17 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 2006Kernfysica: quarks, nucleonen en kernen18 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 2006Kernfysica: quarks, nucleonen en kernen19 structure of nuclei: Fermi gas model number of neutron (N) and proton (Z) states up to Fermi momentum: average kinetic energy: V(r) r V 0 =E F +B´