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HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 1
Outline lecture (HL-3)Structure of nuclei
•NN potential•exchange force•Terra incognita in nuclear landscape•Neutron matter•Halo nuclei•Hypernuclei
Literature: PR 16, 17
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 2
nucleon-nucleon scattering
positive (negative) phase shift for attractive (repulsive) potential
in
scattered
RkRkkk
l
RkkRkk
RrVEmk
211
20
2211
01
tanarctan)0(
)cot()cot(
for /)(2
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 3
energy dependence of NN phase shiftsphase shift (degrees)
50
-50
0
Phys. Rev. 182 (1969)1714
s wave: short range repulsive long range attractivep wave: repulsive
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 4
NN potential shape and strength
Hamada, JohnstonNucl. Phys. 34 (1962) 382
attractive singlet/triplet s wave,repulsive p wave scattering
attractive non-central Tensor term,and LS (spin-orbit) term
repulsive core r < 0.49 fm
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 5
general form of NN potential
depends on NN separation relative momentum angular momentummust be scalar, P and T invariant, 2N symmetric
Tensor term: non-central force mixes different L-states: 4% 3D1-state in dLS term: induces polarized scattered beams
central
spin-spin
Tensor
spin-orbit
xp
21,, ssL
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 6
polarized scattering
1s
2s ts
1l
2l
p wave (l=1) scattering: symmetric spin wf. (S=1); VLS < 0
01 SlVLS
02 SlVLS
repulsive,scattered left
attractive,scattered left
onpolarizati
right scattered :spins parallel-anti
left scattered :spins parallel
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 7
quark state for NN systemshort distance repulsion: chromomagnetic spin-spin interaction6 quarks in s-state (l=0): symmetric spin-isospin wf. minimizing chromomagnetic energy minimizing parallel quark spins distorting wave function symmetry:
l = 0
l = 1
required excitation energy strong short range repulsion
=1/9 =8/9
0b r
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 8
covalent bonds and meson exchange force
energetic favourablespin=0, isospin=0 di-quark
direct q exchange suppressedby color restriction
color-neutral (sea-quark) exchange:relativistic form ofcovalent strong force
virtual mesonexchange:Yukawa potential
r
rmc
gV
exp
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 9
nuclear equation-of-statein-medium interactions and selfenergies determined in relativisticDirac-Brückner Hartree-Fock theory from realistic NN potential
Z=0pure neutron matteris unbound
-16 MeV
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 10
terra incognita
nuclei: strongly interacting quantum systems of finite size,balanced by isospin-symmetric strong, -violating Coulomb force
sphericalshell closurefor Z>112?
48Ni
100Sn
78Ni
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 11
single-particlelevels nlj
shell gapsandintruder states
8113Li
p: (s1/2)2(p1/2)1
n: (s1/2)2(p3/2)4 (p1/2)2
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 12
halo nucleiquantum phenomenon: weakly bound valence neutrons in classical forbidden region beyond potential barrierwith low l i.e. low centrifugal barrier,single-particle structure and strong pairing correlations
2n-halo region of 11Li as large as208Pb radius,mixed(p1/2)2 (s1/2)2
configuration
multi-nucleonhalos:neutron-droplets?
N/Z=3
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 13
shell quenching at large N/Z2n-separation energies shell gapreduced from 6 MeV(100Sn) to 2 MeV (78Ni)
n-potential changesfrom WS- to softer HO-shape reduced spin-orbit splittinghigh-l intruder moved back across shell gap
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 14
creating and detecting hypernuclei
sA
AAK
nK
1010
binding energy:
energy-recoil
2
cMM
EEBB
n
Kn
0 by choice of kinematics(=0)
p
K-
-
()
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 15
spectrum and levels of hypernuclei
-levels not restricted by Pauli principlein neutron-like potential (shallower for weaker -N interaction)
11 MeV
may sit inoccupied n-levelsn from below
the Fermi level
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 16
binding energy of in nuclei
KAA
in discrete levelsV0 30 MeV
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 17
production of hypernuclei (S=-2)
H dibaryon (uuddss) ??
study ofhyperon-hyperon interaction
%5p
c (-) = 4.91 cm,long-lived enoughto be captured
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 18
Summary lecture (HL-3 )Nuclear structure•Potential and phase shifts•NN potential: general form; spin-spin, spin-orbit, tensor part•exchange force: virtual di-quark (meson) exchange•Terra incognita in nuclear landscape•Tasks for exotic-beam facilities•Neutron matter: large N/Z for light nuclei•Halo nuclei observed•Hypernuclei: binding energy and structure
HL-3 May 2006 Kernfysica: quarks, nucleonen en kernen 19
structure of nuclei: Fermi gas model
MeVm
pEA/ZNcMeV
Rp
dppv
Zdppv
N
N
FFF
pp pF
nF
332
and 2for /2508
9
42
2 and 42
2
23/1
0
2
0 32
0 3
number of neutron (N) and proton (Z) states up to Fermi momentum:
average kinetic energy:
A
ZNA
ZN
m
pZ
m
pNEZENZNE
N
pF
N
nF
pnkin
2
3/2
3/53/522
Z-N termasymmetry volume
at min. with 225
3),(
V(r)
r
V0=EF+B´