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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 , - PowerPoint PPT Presentation
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HL-4 May 2005 Kernfysica: quarks, nucleonen en kernen 1
Outline lecture (HL-4)Structure of nuclei
•Shell structure•Deformation
Nuclear reactions•Stripping reaction•DWBA
Literature: PR 16, 17
HL-4 May 2005 Kernfysica: quarks, nucleonen en kernen 2
energy of 1. exc. state of even-even nuclei
typ. JP=2+
shell and level structuredetermined bydepth/shape of central potential,spin-orbit force,residual interaction(pairing correlations)
with )(2
1
0)()( with /)()()( 2
rVlE
rVdr
drVslrVrVrV
lsls
centrallslscentral
j=l-1/2j=l+1/2
HL-4 May 2005 Kernfysica: quarks, nucleonen en kernen 3
single-particlelevels nlj
shell gapsandintruder states
HL-4 May 2005 Kernfysica: quarks, nucleonen en kernen 4
particle- and hole-states and excitations
mirror pair, hole mirror pair, nucleon isospin independence of nuclear force
12/11 p
2/51d
HL-4 May 2005 Kernfysica: quarks, nucleonen en kernen 5
deformed nuclei: quadrupole moments
RRZeQ
baZe
xdxxzQ
zyx abbellipsoid
b-a with
5
45
2
3
2
22),,(
322
partially occupied p- and n-shellspolarized the nucleus deformation
prolate
oblate
HL-4 May 2005 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 2005 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 fillingoverlapping adjacent m-orbitals deformation
energy levels of deformed nuclei ellipsoidal potential shape
Nilsson Parameters: = lz
= jz
HL-4 May 2005 Kernfysica: quarks, nucleonen en kernen 8
extended SPSM: Nilsson model
single-particle motion inanisotropic oscillator field:
slV
ClV
xxxmV
ls
lll
eff
2
1
2
22
21
223
23
quantum numbersN = n3 + n
[Nn3]
deformation - 3
HL-4 May 2005 Kernfysica: quarks, nucleonen en kernen 9
deformation parameters: exp. and calc.
= exp. A even = exp. A uneven
= calc. A uneven
HL-4 May 2005 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-2s1/2)1(n-1d3/2)1
HL-4 May 2005 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
HL-4 May 2005 Kernfysica: quarks, nucleonen en kernen 12
stripping cross sectionfor Ed (vd) binding of d and binding of n in A+1 nucleus
A A+1
Fermi´s Golden Rule
ipnffi
dfi
UM
dEv
dppVM
d
d
,
2
3
22
2
2
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:
/exp /exp 1 ppAfdddAi xpixpi
nAA 1
pnU ,
pnpnpn xxUxxU 0, ,
xdxxppixUUM dpdnipnffi3*
0, 0/2/exp
)(2
1,0, pndnp xxxxxx q-transfer to nucleus!
HL-4 May 2005 Kernfysica: quarks, nucleonen en kernen 13
DWBA for strippingreaction X(a,b)Y
proton angular distribution for 16O(d,p)17O at Ed = 25.4 MeV
plane waves scattered waves:solutions for complexoptical potential V(r) + iW(r)taking into account absorption by W(r)
is Y=X+(a-b) a single-particle state ??initial-state spin
Y
ba
X JJ jl,
jljl jl
X
Y
jl
d
dS
J
J
d
d
d
d
,, ,
.exp
,
12
12
n transitioparticle singlefor
spectroscopic factors Sl,j measure single-particle character
l=0
l=2
l=2
q=0
excellent agreementfor small q
HL-4 May 2005 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