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Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February 4 – 6, 2008 Marcella Grasso Nuclear structure far from stability

Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February 4 – 6, 2008

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Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February 4 – 6, 2008. Nuclear structure far from stability. Marcella Grasso. General interest: Correlations in finite fermion many-body systems. Adopted approaches: Microscopic mean field approaches and extensions. - PowerPoint PPT Presentation

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Page 1: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Atelier de l’Espace de Structure Nucléaire Théorique, Saclay

February 4 – 6, 2008

Marcella Grasso

Nuclear structure far from stability

Page 2: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

General interest: Correlations in finite fermion

many-body systems

Adopted approaches: Microscopic mean field

approaches and extensions

Page 3: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

DIFFERENT TOPICS:

Nuclear structure. Exotic nuclei (properties of exotic nuclei, pairing, continuum coupling, shell structure evolution along isotopic chains,…)

Mean field, HF, HFB + QRPA

Collaborations: Elias Khan, Jerome Margueron, Nguyen Van Giai, IPN-Orsay

Nicu Sandulescu, Bucarest

Nuclear astrophysics. Neutron star crusts (pairing, excitation modes, specific heat,…)

Mean field, HFB + QRPA

Collaborations: Elias Khan, Jerome Margueron, Nguyen Van Giai, IPN-Orsay

Extensions of RPA (avoiding the quasi-boson approximation)

Collaborations: Francesco Catara, Danilo Gambacurta, Michelangelo Sambataro, Catania

Interdisciplinary activity: ultra-cold trapped Fermi gases

Mean field, finite temperature HFB and QRPA

Collaborations: Elias Khan, Michael Urban, IPN-Orsay

Page 4: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Second meeting:

May 21 2007

Next meeting: to be fixed (2008)

Page 5: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Noyaux riches en neutrons – Approche self-consistante champ moyen + appariement Hartree – Fock – Bogoliubov (HFB)

Etats du continuum: comportement asymptotique (états de diffusion) et largeur des résonances

Isotopes of Ni

Drip line

A

S2n (MeV)

Neutron drip line position?

S2n(N,Z)=E(N,Z)-E(N-2,Z)

Microscopic mean field approach. Pairing is included in a self-consistent way (Bogoliubov quasiparticles): Hartree-Fock-Bogoliubov (HFB)

Two-neutron separation energy

Last observed isotope

Boundary conditions of scattering states for the wave functions of continuum states

Exp. values

Grasso et al, PRC 64, 064321 (2001)

Page 6: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Pairing and continuum coupling in neutron-rich nuclei. What to

look at?

Direct reaction studies: pair transfer? (LoI GASPARD for Spiral2)

Page 7: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Reduction of spin-orbit splitting for neutron p states in 47Ar

Gaudefroy, et al. PRL 97, 092501 (2006)

Transfer reaction 46Ar(d,p)47Ar: energies and spectroscopic factors of neutron states p3/2, p1/2 and f5/2 in 47Ar. Comparison with 49Ca: reduction the spin – orbit splitting for the f and p neutron states

Page 8: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Energy difference between the states 2s1/2 and 1d3/2

Grasso, Ma, Khan, Margueron, Van Giai, PRC 76, 044319 (2007)

Page 9: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Effect due to the tensor contribution with SLy5

Grasso, Ma, Khan, Margueron, Van Giai, PRC 76, 044319 (2007)

Page 10: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

HF proton density in 46Ar with SkI5

Khan, Grasso, Margueron, Van Giai, NPA 800, 37 (2008)

INVERSION

Page 11: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Perspectives

• Particle-phonon coupling

• Extensions of RPA (to include correlations that are not present in a standard mean field approach). Applications to nuclei

Page 12: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

B(E2;0+ g.s. -> 21

+) (e2fm4)

Riley, et al. PRC 72, 024311 (2005)

Raman, et al., At. Data Nucl. Data Tables 36, 1 (2001)

218 31 e2 fm4

SkI5 SLy4

Inv. No inv.

B (E2) (e2 fm4) 256 24

Khan, Grasso, Margueron, Van Giai,

NPA 800, 37 (2008)

Page 13: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Inversion of s and d proton states

Theoretical analysis. Relativistic mean field (RMF). 48Ca et 46Ar

48Ca Z=20

1d3/2 2s1/2

2s1/2 1d3/2

1d5/2 1d5/2

46Ar Z=18

1d3/2 2s1/2

2s1/2 1d3/2

1d5/2 1d5/2

Todd-Rutel, et al., PRC 69, 021301 (R) (2004)

Page 14: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Kinetic, central and spin – orbit contributions to the energy difference between the states 2s1/2 and 1d3/2

Grasso, Ma, Khan, Margueron, Van Giai, PRC 76, 044319 (2007)

Page 15: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Extension of RPA: starting from the Hamiltonian a boson image

is introduced via a mapping procedure (Marumori type)

Approximation:

Degree of expansion of the boson Hamiltonian (quadratic -> standard RPA)

If higher-order terms are introduced the RPA equations are non linear (the matrices A and B depend on the amplitudes X and Y)

Page 16: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Test on a 3-level Lipkin modelGrasso et al.

Diag. of HB in B

RPA

Extension

Page 17: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

'00 222 qqq

qSO

WWV

q, q’ -> proton or neutron

Spin – orbit potential

Non relativistic case and standard Skyrme forces

Relativistic case

The potential is proportional to 'qq

Page 18: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Hartree-Fock equations with the equivalent potential.

rrrVrr

llr

dr

d

mljeq

,

1

2 22

22

rU

m

rmm

rm

rmm

rm

rmm

rmrU

m

rmrV

ljso

ljeq

)(

)(1

22

)(

22,

*

*''

*

2*

2'

*

2

2

2*

0

*

Equivalent potential:

Central term

Page 19: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Veqcentr

m

rmVVT so

centreq

)(*1

rU

m

rmm

rm

rmm

rm

rmm

rmrU

m

rmrV

ljso

ljeq

)(

)(1

22

)(

22,

*

*''

*

2*

2'

*

2

2

2*

0

*

Page 20: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

dso

d

d

centreq

ds

centreq

s

dd

ss

ds

Vmrm

Vmrm

Vmrm

Tmrm

Tmrm

/)(*

1

/)(*

1

/)(*

1

/)(*

1

/)(*

1

Kinetic contribution

Central contribution

Spin-orbit contribution

Page 21: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Important contributions of the HF potential

qxxt 000 2122

1

2213

133 21222

24

1npqxxt

Central term

Density-dependent term

It favors the inversion

Against the inversion

Page 22: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

…and the tensor contribution?

• Shell model : T. Otsuka, et al., PRL 95, 232502 (2005)

• Relativistic mean field: RHFB : W. Long, et al., PLB 640, 150 (2006)

• Non relativistic mean field:• Skyrme : G. Colò, et al., PLB 646, 227 (2007)• Gogny : T. Otsuka, et al., PRL 97, 162501

(2006)

Page 23: Atelier de l’Espace de Structure Nucléaire Théorique, Saclay February  4 – 6, 2008

Variation of the energy density (dependence on J)

pnpn JJJJH 22

2

1

)(4

31112

4

1)( 2

3rvlljjj

rrJ iiiii

iiq

''0 22 qq

qqqSO JJ

dr

d

dr

dWU

TC TC

221121 8

1

8

1xtxtttC 22118

1xtxtC

J -> spin density

The spin – orbit potential is modified: