1. 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

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
HL-4 May 2004
Kernfysica: quarks, nucleonen en kernen

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

4. 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

5. 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

6. 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

7. 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

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

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

11. 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

12. 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

13. 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

14. 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