Delta-hole effects on

the shell evolutionof

neutron-rich exotic nuclei

Takaharu Otsuka 　　 University of Tokyo / RIKEN / MSU

Chiral07Osaka

November 12 - 16, 2007

Outline

1. Motivations : Drip line of oxygen isotopes

(as an example)

2. 3-body force : Basically attractive effect

3. -hole effect on the shell evolution

4. Summary

リチウム１１ nuclei

(mass number)

stable

exotic

-- with halo

A

neutron skin

proton halo

Pro

ton

nu

mb

er

Stable Nuclei

Neutron number

Nuclear Chart- Left Lower Part -

neutronhalo

O (Z=8)

Drip Line (Existence Limit of Nuclei)

F (Z=9)

11Li

Why is the drip line of

Oxygen so near ?

This is because the neutron d3/2 orbit is high for Oxygen.

16O core

1d5/2

2s1/2

1d3/2

17O9 ~ 22O14

23O15 ~ 24O16

Neutron orbitsin Oxygen isotopes

16O core

Neutron orbitsin Fluorine isotopes

neutron threshold

Tensor-force contribution

due to a proton in d5/2

A reminder of

tensor-force effects on

the evolution of shell structure

One pion exchange ~ Tensor force

• Monopole part of the NN interaction

　　 Angular averaged interaction 　

(2 1)

(2 1)

JTababJ

J

Tab

JV

V

J

Isotropic component is extractedfrom a general interaction.

To see changes of single-particle energieswithin the shell model,

the monopole interaction is useful

• Effective single-particle energy (ESPE)

ESPE : Total effect on single-

particle energies due to interaction with other valence nucleons

Monopole interaction, vm

ESPE is changed by N vm

N particles

Monopole effects due to the tensor force

- An intuitive picture -

wave function of relative motion

large relative momentum small relative momentum

attractive repulsive

spin of nucleon

TO et al., Phys. Rev. Lett. 95, 232502 (2005)j> = l + ½, j< = l – ½

Tensorforce

d5/2

d3/2

Robust under-lying mechanism for the gap change

TO et al., Phys. Rev. Lett. 87, 082502 (2001) + Phys. Rev. Lett. 95, 232502 (2005)

16O core

1d5/2

2s1/2

1d3/2

17O9 ~ 22O14

23O15 ~ 24O16

Neutron orbitsin Oxygen isotopes

16O core

Neutron orbitsin Fluorine isotopes

neutron threshold

Why do those neutrons Why do those neutrons NOTNOTpull down dpull down d3/23/2 ? ?

Why do those neutrons Why do those neutrons NOTNOTpull down dpull down d3/23/2 ? ?

due to a proton in d5/2

Effective Single-Particle Energy for Oxygen isotopes

Kuo-BrownG-matrix

+ core-pol.

d3/2

d5/2

Neutron number

(N)

5 10

15 20

narrowing

Wrong drip line

Effective Single-Particle Energy for Oxygen isotopes

Less steep USD

Kuo-BrownG-matrix

+ core-pol.

d3/2

d5/2

Neutron number

(N)

5 10

15 20

narrowing

Empirical correction

5 10

15 20

Additionalrepulsion between

d5/2 and d3/2

Not enough

Neutron number (N)

Wrong drip line

Effective Single-Particle Energy for Oxygen isotopes

SDPF-M

Empirical correctionFinal correction

Less steep USD

Kuo-BrownG-matrix

+ core-pol.

d3/2

d5/2

Neutron number

(N)

5 10

15 20

narrowing

Neutron number (N)

Neutron number

(N)

Finally flat,d3/2 kept high correct drip

line

Y. Utsuno, T.O., T. Mizusaki, and M. Honma, Phys. Rev. C 60, 054315 (1999).

Question

What is the origin

of

the repulsive modification

to

T=1 monopole matrix elements ?

A solution within 2-body interaction is very unlikely

(more systematic studies for pf shell)

3-body interaction

Outline

1. Motivation : Drip line of oxygen

isotopes

(as an example)

2. 3-body force : Basically attractive effect

3. -hole effect on the shell evolution

4. Summary

Nucleons in valence orbits(of low momenta)

Nucleons in higher shell(of high momenta)

Nucleons in valence orbits(of low momenta)

3N force with short range produces basicallymore attraction from the 2nd order perturbation

Outline

1. Motivation : Drip line of oxygen

isotopes

(as an example)2. 3-body force : Basically attractive effect

3. -hole effect on the shell evolution

4. Summary

-hole excitation(Fujita-Miyazawa 3N mechanism)

is the key.

Oset, Toki and Weise

Pionic modes of excitation

Phys. Rep. 83, 281 (1982)

Renormalization of NN interaction Due to excitation in the intermediate state

T=1attraction

between NNeffectively

-hole excitation effect on single-particle energy and Pauli blocking

Pauli Forbidden-hole

contributionto single-particle

energies issuppressed

Renormalizationof single particle

energy due to core polarization

(attractive !)

T=1attraction

in NN interaction

m

m

m’ m’

m

m

m’

Possible origin of global T=1 repulsion

This involves excitation from the core

density-dependent long-ranged effect

Effective T=1 repulsionfor monopole

m

m m’

m’

Pauli forbidden(from previous page)

m

m

m’ m’

Relevant mechanismin Hypernuclei (Akaishi’s talk)

16O core

1d5/2

2s1/2

1d3/2

17O9 ~ 22O14

Neutron orbitsin Oxygen isotopes

neutron threshold

Back to the question of high-lying dBack to the question of high-lying d3/2 3/2 Back to the question of high-lying dBack to the question of high-lying d3/2 3/2

Central : attractive (generally)

Tensor : attractive - 0.9 MeV (next page)

-hole inducedrepulsion

( > tensor )Next page

Repulsive effective monopole interaction assuming 16O core

exchange with radial cut-off at 0.7 fm , ΔE =293 MeV f_{πNΔ ｝ /f_{πNN} = \sqrt{9/2}

Preliminary result Monopole interaction

j j' pion tensord5/2 d3/2 314 keV

Tensor -hole-inducedrepulsion

d3/2 single-particle energy relative to N=8

neutronnumber (N)

8 14

+1 MeV

S.P.E.

N

If another nucleon (X) is in state m’ and wave functions are coupled antisymmetric (T=1), the effect is vanished.

Repulsive T=1 force

No changes to T=0 monopole interaction

m

m’

Density dependent repulsive force in T=1 channel- Long-ranged due to exchange -

Suppression of renormalization of NN interaction

T=1interaction between valenceparticles

Pauliblocking

Particlein the

inert core

included in our results

Related effectwas discussed by Frisch, Kaiser andWeise for neutron matter(see next page).

See also Nishizaki,Takatsuka and HiuraPTP 92, 93 (1994)

-hole excitation may be crucial to neutron matter property

Chiral Perturbation incl. Frisch, Kaiser and Weise

Remark : Multipole interactions … different story

m4

m1 m2

m3

Multipole parts

Effective T=1 repulsionfor monopole

m

m m’

m’

T=1attraction

between NNeffectively

Effective point coupling ;The present effect

cannot be seen.

Explicit consideration of has been crucial

T=1repulsion

LikelyT=0 attraction

Modifications to effective NN interactionin the valence shell

- monopole channel -

Similar magnitudes of opposite sign

- Pions manifest themselves in the shell structure of exotic

nuclei

i) Tensor force changes the shell structure, including disappearance of magic numbers and appearance of new ones ii) Repulsive modification to T=1 channel

due to suppression of -hole effects (Fujita-Miyazawa 3N mechanism). drip line of Oxygen, neutron matter, etc.

Both should be considered in mean-field theories. - Explicit treatment of needed up to the derivation of effective NN interaction ( can be put aside at a later stage) a message to EFT (power counting may differ between bulk properties (order of magnitude = 100 MeV) and single-particle properties (order of magnitude = 100 keV) ).

- Related mechanism in Hypernuclei (Akaishi, Dote, et al.)

Summary

Collaborators

T. Suzuki Nihon U.Y. Akaishi RIKEN