Outline lecture (HL-4)

1
Outline lecture (HL-4)

• Structure of nuclei
• Shell structure
• Deformation
• Nuclear reactions
• Stripping reaction
• DWBA
• Literature PR 16, 17

2
energy of 1. exc. state of even-even nuclei
typ. JP2 shell and level structure determined
by depth/shape of central potential, spin-orbit
force, residual interaction (pairing correlations)
jl-1/2 jl1/2
3
single-particlelevels nlj
shell gaps and intruder states
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particle- and hole-states and excitations
mirror pair, hole
mirror pair, nucleon isospin
independence of nuclear force
5
deformed nuclei quadrupole moments
prolate

• partially occupied p- and n-shells
• polarized the nucleus
• deformation

oblate
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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
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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
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extended SPSM Nilsson model
Nn3??
single-particle motion in anisotropic oscillator
field
quantum numbers N n3 n?
? ?
deformation ? ?? - ?3
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deformation parameters exp. and calc.
? exp. A even ? exp. A uneven ?
calc. A uneven
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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
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single-particlelevels nlj
shell gaps, intruder states level sequence in
sd shell (n-1d3/2)1 (n-2s1/2)1 (n-1d5/2)1
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stripping cross section
for Ed (vd) ?? binding of d and binding of n in
A1 nucleus
Fermis 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!


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DWBA for strippingreaction X(a,b)Y
proton angular distribution for 16O(d,p)17O at
Ed 25.4 MeV
l2
plane waves ? scattered waves solutions for
complex optical potential V(r) iW(r) taking
into account absorption by W(r)
q0
l0
is YX(a-b) a single-particle state
?? initial-state spin
l2

excellent agreement for small q
spectroscopic factors Sl,j measure
single-particle character
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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