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Outline lecture (HL- 4 )

Outline lecture (HL- 4 ). Structure of nuclei Shell structure Deformation Nuclear reactions Stripping reaction DWBA Literature: PR 16, 17. energy of 1. exc. state of even-even nuclei. typ. J P =2 + shell and level structure determined by depth/shape of central potential ,

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Outline lecture (HL- 4 )

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

  2. 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 Kernfysica: quarks, nucleonen en kernen

  3. single-particlelevels nlj shell gaps and intruder states Kernfysica: quarks, nucleonen en kernen

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

  5. deformed nuclei: quadrupole moments prolate • partially occupied p- and n-shells • polarized the nucleus • deformation oblate Kernfysica: quarks, nucleonen en kernen

  6. regions of large deformation half-full shells  deformation Hund rulefor atom shells: nl subshell filling: first different orbitals l next substates ml repulsive Coulomb force favours separate orbitals Kernfysica: quarks, nucleonen en kernen

  7. pairing and polarization 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 Kernfysica: quarks, nucleonen en kernen

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

  9. deformation parameters: exp. and calc.  = exp. A even  = exp. A uneven = calc. A uneven Kernfysica: quarks, nucleonen en kernen

  10. 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 Kernfysica: quarks, nucleonen en kernen

  11. single-particlelevels nlj shell gaps, intruder states level sequence in sd shell (n-1d3/2)1 (n-2s1/2)1 (n-1d5/2)1 Kernfysica: quarks, nucleonen en kernen

  12. A A+1 stripping cross section for Ed (vd) binding of d and binding of n in A+1 nucleus 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! Kernfysica: quarks, nucleonen en kernen

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

  14. 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 Kernfysica: quarks, nucleonen en kernen

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