HL-3 May 2006Kernfysica: quarks, nucleonen en kernen1 Outline lecture (HL-3) Structure of nuclei NN potential exchange force Terra incognita in nuclear.

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

qq

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´