Kernfysica: quarks, nucleonen en kernen Outline lecture (HL-4) HL-4 May 2004 Structure of nuclei Shell structure Deformation Nuclear reactions Stripping reaction DWBA Literature: PR 16, 17 HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

energy of 1. exc. state of even-even nuclei typ. JP=2+ shell and level structure determined by depth/shape of central potential, spin-orbit force, residual interaction (pairing correlations) j=l-1/2 j=l+1/2 HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

single-particle levels nlj shell gaps and intruder states HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

particle- and hole-states and excitations HL-4 May 2004 mirror pair, hole mirror pair, nucleon isospin independence of nuclear force HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

deformed nuclei: quadrupole moments prolate partially occupied p- and n-shells polarized the nucleus deformation oblate HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

regions of large deformation half-full shells  deformation Hund rule for atom shells: nl subshell filling: first different orbitals l next substates ml repulsive Coulomb force favours separate orbitals HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

pairing and polarization HL-4 May 2004 attractive NN force favours: pairing: l1 = l2; m1 = -m2; j = 0; JP = 0+ adjacent m-substate filling overlapping adjacent m-orbitals  deformation Nilsson Parameters:  = lz  = jz energy levels of deformed nuclei  ellipsoidal potential shape HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen

extended SPSM: Nilsson model [Nn3] single-particle motion in anisotropic oscillator field: quantum numbers N = n3 + n   deformation   - 3 HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

deformation parameters: exp. and calc.  = exp. A even  = exp. A uneven  = calc. A uneven HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

spectroscopy through nuclear reactions stripping reaction 16O(d,p)17O Proton spectrum at 45 and Ed = 25.4 MeV (n-1d5/2)1 (n-1d3/2)1 (n-2s1/2)1 HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

single-particle levels nlj shell gaps, intruder states level sequence in sd shell (n-1d3/2)1 (n-2s1/2)1 (n-1d5/2)1 HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

stripping cross section for Ed (vd)  binding of d and binding of n in A+1 nucleus A A+1 Fermi´s Golden Rule for weak d-A and p-(A-1) interaction: Born approx.: likely final state with n in outer shell: with shell-model w.f. for n and short-range stripping interaction: q-transfer to nucleus! HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

DWBA for stripping reaction X(a,b)Y proton angular distribution for 16O(d,p)17O at Ed = 25.4 MeV l=2 plane waves  scattered waves: solutions for complex optical potential V(r) + iW(r) taking into account absorption by W(r) q=0 is Y=X+(a-b) a single-particle state ?? initial-state spin l=0 l=2 spectroscopic factors Sl,j measure single-particle character excellent agreement for small q HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen

Kernfysica: quarks, nucleonen en kernen HL-4 May 2004 Summary lecture (HL-4) Nuclear structure Shell structure and shell gaps appear due to ls term Deformations in half-filled shells and polarization Nuclear reactions Stripping reactions study level structure DWBA approximation for transfer: spectroscopic factors Sl,j measure single-particle character HL-4 May 2004 Kernfysica: quarks, nucleonen en kernen Kernfysica: quarks, nukleonen en kernen