A presentation supported by the JSPS Core-to-Core Program

“

International Research Network for Exotic Femto Systems (EFES)” 7 th CNS-EFES summer school Wako, Japan August 26 – September 1, 2008

Structure of exotic nuclei

Takaharu Otsuka

Day 3

University of Tokyo / RIKEN / MSU

Summary of Day2-1

Single-particle properties (shell structure) are one of the most dominant elements of nuclear structure.

Example : The deformation (of low-lying states) is a Jahn-Teller effect to a good extent.

We discussed on how single-particle levels change ( shell evolution ) as functions of Z and N in exotic nuclei due to various components of the nuclear force.

1. Tensor force 2. Central force

Summary of Day2 - 2 Some components of NN interactions show characteristic patterns of the shell evolution Tensor force : - variation of spin-orbit splitting - strong 

unexpected oblate deformation of a doubly-magic 42 Si

Central force : - differentiates different radial nodal structure of single-particle orbits - stronger (< tensor) Tensor + Central combined (typically in the ratio 2:1)  lowering of neutron f5/2 in Ca-Cr-Ni inversion of proton f5/2 and p3/2 in Cu for N~46

54

Ca,

78

Ni,

100

Sn Day-One experiments of RIBF

Outline

Section 1: Basics of shell model Section 2: Construction of effective interaction and an example in the pf shell Section 3: Does the gap change ? - N=20 problem Section 4: Force behind Section 5: Is two-body force enough ?

Section 6: More perspectives on exotic nuclei

From Day 2 lecture

T=1 monopole interaction

j = j’ j = j’ T=1 monopole interactions in the pf shell GXPF1A G-matrix (H.-Jensen) Tensor force ( p + r exchange)

Basic scale ~ 1/10 of T=0 Repulsive

corrections to G-matrix

j = j’ j = j’ T=1 monopole interactions in the sd shell SDPF-M (~USD) G-matrix (H.-Jensen) Tensor force ( p + r exchange)

Basic scale ~ 1/10 of T=0 Repulsive

corrections to G-matrix

Origin and implication of repulsive modification of T=1 monopole components

Nuclear Chart - Left Lower Part -

proton halo Stable Nuclei

Why is the drip line of Oxygen so near ? Li F (Z=9) O (Z=8) Drip Line (Existence Limit of Nuclei) Neutron number

 neutron skin neutron halo

A nuclei

(mass number)

stable exotic -- with halo

This is because the neutron d 3/2 orbit is high for Oxygen.

in Neutron orbits Oxygen isotopes Neutron orbits in Fluorine isotopes 1d 3/2 neutron threshold 2s 1d 1/2 5/2 16 O core 23 O 15 ~ 24 O 16 17 O 9 Proton-neutron force, Incl. strong tensor force, due to a proton in d

5/2

16 O core

in Neutron orbits Oxygen isotopes 1d 3/2 2s 1/2 1d 5/2 neutron threshold 23 17 O 15 ~ 24 O 16 O 9 ~ 22 O 14

Why do those neutrons NOT pull down d 3/2 ?

Neutron orbits in Fluorine isotopes 16 O core

Effective Single-Particle Energy for Oxygen isotopes

Kuo-Brown G-matrix + core-pol.

d3/2 d5/2 5 10 15 20 Neutron number (N) narrowing Wrong drip line

Effective Single-Particle Energy for Oxygen isotopes

Empirical correction USD Less steep Kuo-Brown G-matrix + core-pol.

d3/2 5 10 15 20 Neutron number (N) Additional repulsion between d 5/2 and d 3/2 Not enough d5/2 5 10 15 20 Neutron number (N) narrowing Wrong drip line

Effective Single-Particle Energy for Oxygen isotopes

Final correction SDPF-M Empirical correction USD Less steep Kuo-Brown G-matrix + core-pol.

d3/2 d5/2 

Finally flat, d3/2 kept high correct drip line

Neutron number (N) 5 10 15 20 Neutron number (N) narrowing Neutron number (N) 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 bare 2-body interaction is very unlikely (considering efforts made so far)  3-body interaction

However

3NF -> attractive effects systematics in results of GFMC, NCSM CC (Hagen et al., Phys. Rev. C76, 034302 (2007)

GFMC (Green Function Monte Carlo) by Argonne group 3-body force 3-body force included

3-body force increases binding energies

One reason : 3N force with short range produces basically more attraction from the 2 nd order perturbation Nucleons in valence orbits (of low momenta) Nucleons in higher shell (of high momenta) Nucleons in valence orbits (of low momenta)

The key : Fujita-Miyazawa 3N mechanism

(D

-hole excitation)

D

particle m=1236 MeV S=3/2, I=3/2

D N p N p N

Renormalization of NN interaction due to

D

excitation in the intermediate state

D Modification to bare NN interaction (for NN scattering) T=1 attraction between NN effectively

D

-hole excitation effect on single-particle energy

N N

D N N core valence particle

N

D D

N N

Renormalization of single particle energy due to D -hole excitation  attractive (more bound)

Pauli blocking effect on the renormalization of single-particle energy

m m single particle states m’ D m’ m’ D m  Renormalization of single particle energy due to D -hole excitation more binding (attractive) m Another valence particle in state m’ Pauli Forbidden 

The effect is suppressed

m

Inclusion of Pauli blocking

m m’ m’ m’ D m Pauli forbidden (from previous page) D m’ m This Pauli effect is included automatically by the exchange term.

m

Realization in terms of 3-body interaction

m m’ m’ m D Renormalization of single particle energy + D m m’ m Pauli blocking

same

A part of Fujita-Miyazawa 3-body force m’ D m’ m

Fujita-Miyazawa 3N mechanism

(D

-hole excitation)

D

particle m=1236 MeV S=3/2, I=3/2

D N p N p N

Incorporation of this effect into effective interaction m m’ We look at this effect as an effective interaction between states m and m’. m m’ D

v eff

m’ m m’ m This effect is monopole , because it is about single-particle energies.

This effect is repulsive of more binding.

, because it is suppression Effective monopole repulsive interaction reproduces the effect.

|v eff |

mm’>

> 0

Particle in the inert core

Other diagram included

Pauli blocking D T=1 interaction between

valence particles

Related effect was discussed by Frisch, Kaiser and Weise for neutron matter See also Nishizaki, Takatsuka and Hiura PTP 92, 93 (1994)

D -hole excitation may be crucial to neutron matter property

Chiral Perturbation incl.

D :

Frisch, Kaiser and Weise

1d 3/2

Back to the question of high-lying d 3/2

in Neutron orbits Oxygen isotopes neutron threshold Central : attractive (generally) 2s 1d 1/2 5/2 17 O 9 ~ 22 O 14 Tensor : attractive - 0.9 MeV (next page) 16 O core D -hole induced repulsion ( > tensor ) Next page

Repulsive effective monopole interaction assuming 16 O core p exchange with radial cut-off at 0.7 fm , ΔE =293 MeV f_{πNΔ ｝ /f_{πNN} = \sqrt{9/2} Monopole interaction j j' pion tensor d 5/2 d 3/2 250 keV 8 d 3/2 single-particle energy relative to N=8

+1 MeV +2 MeV

Tensor D 14 -hole-induced repulsion neutron number (N)

More binding by 3NF Is this always true ?

EFT (V low-k ) result for D ~ conventional p -N D calculation Contact terms can be evaluated as well Pairing cases 2-body

Effects may be larger with higher order diagrams.

empirical fit (~SDPF-M)

From EFT (Effective Field Theory) sd shell pf shell

j = j’ j = j’ T=1 monopole interactions in the pf shell GXPF1A G-matrix (H.-Jensen) Tensor force ( p + r exchange)

Basic scale ~ 1/10 of T=0 Repulsive

corrections to G-matrix

new magic numbers ?

(Effective) single-particle energies

n-n

34

KB3G

p-n

32

Lowering of f5/2 from Ca to Cr : ~ 1.6 MeV = 1.1 MeV (tensor) + 0.5 MeV (central) Rising of f5/2 from 48 Ca to 54 Ca : p3/2-p3/2 attraction p3/2-f5/2 repulsion

KB interactions : Poves, Sanchez-Solano, Caurier and Nowacki, Nucl. Phys. A694, 157 (01)

KB3 interaction and its family By Strasbourg – Madrid group Started from Kuo-Brown’s G-matrix Monopole part and pairing part are empirically adjusted Recent versions : KBF, KB3G , ....

good for lighter pf-shell nuclei

m Density dependent repulsive force - Long-ranged due to

p

exchange m’ N

 D p p If another nucleon ( antisymmetric ,  X ) is in state m’ and wave functions are coupled the effect is vanished.

Repulsive force

Remark : Multipole interactions … different story

m’ m m 3 m 4 D m m’ Effective repulsion for monopole D m 1 m 2 Multipole parts

Contact terms in 3N force Back-ground attraction : still not completely known

Effect of higher order diagram Effective monopole repulsive interaction

|v eff |

mm’>

> 0

Important next order diagram m m’ D Other terms of 3-body force cancel this effect to a certain effect Cancellation strong for T=0 weak T=1 included in EFT calc.

Tensor force m’ m Larger correction to T=0

Outline

Section 1: Basics of shell model Section 2: Construction of effective interaction and an example in the pf shell Section 3: Does the gap change ? - N=20 problem Section 4: Force behind Section 5: Is two-body force enough ?

Section 6: More perspectives on exotic nuclei

Can the shell evolution change the deformation ?

If so, how much ?

Application to controversial 42 Si Nature 435 (2005), Florida/MSU 44 S -> 42 Si cross section small deformed

PRL accepted (2007), GANIL

42 Si oblate 44 S prolate

Cauier et al. Shell Model, Werner et al. Skyrme model, Lalazissis et al. RMF, Peru et al. Gogny model, Rodriguez-Guzman et al. Gogny model

d 3/2 f 7/2 neutron s 1/2 proton Strong oblate Deformation ?

Potential Energy Surface full 42 14 Si 28 New SM Exp.

Otsuka, Suzuki and Utsuno, Nucl. Phys. A805, 127c (2008) Tensor force removed from cross-shell interaction

Z=28 gap is reduced also by tensor force

S isotopes

Potential Energy Surface of 44 S (triaxial)

Tensor force may not be so crucial for S isotopes. full Tensor removed from cross shell int.

Effect of tensor force on (spherical) superheavy magic numbers

Proton single particle levels Occupation of neutron 1k17/2 and 2h11/2

1k17/2 2h11/2 N=184

Woods-Saxon potential

Neutron

Tensor force added Otsuka, Suzuki and Utsuno, Nucl. Phys. A805, 127c (2008)

Mean field theories Skyrme, Gogny, RMF, … - Inclusion of tensor Stancu, Brink and Flocard, Phys. Lett. 68B, 108 (1077) d -func. Tensor into Skyrme, no prospect for systematic effect Otsuka, Matsuo and Abe, Phys. Rev. Lett. 97, 162501 (2006) Tensor force with Gogny interaction First systematic studies along with the shell evolution idea due to the tensor force, new parameter being searched Brown, Duguet, Otsuka, Abe and Suzuki, Phys. Rev. C 74, 061303, (2006).

Re-visit to SBF, systematics, strange T=1 tensor from fit + many other works afterwards e.g. Zalewski, Satula and Dobaczewski, Phys. Rev. C (2008) - Inclusion of 3-body force open for Fujita-Miyazawa type

Does the shell evolution remain in continuum ?

Tsukiyama has given a short presentation.

The nuclear force shifts resonance-type peaks of neutron spectra. The width changes also.

More to be done in a close connection to the nuclear force. (Some works have been done with simpler forces.)

1 + and 2 states of to be seen in charge exchange from 24 + F 24 O Tsukiyama, Otsuka, Fujimoto 2008

Summary of Day-3 Three-body force : - repulsive monopole modification for T=1 channel - suppression of D -hole excitation (monopole part of Fujita-Miyazawa force) - effect seen in single-particle energies (Ca) and drip lines (O) in neutron-rich exotic nuclei with high T (isospin)

same physics as neutron matter (through NNN force)

- features consistent with modern nuclear forces, e.g. EFT (Effective Field Theory)  oxygen drip line closer to the b stability line new magic N=34 in (or maybe only around) Ca

Summary Nuclear force is rich Although it is known to a good extent, - some properties are still uncertain for instance, 3-body force - many-body effects unknown aspects More is different

Collaborators

T. Suzuki

R. Fujimoto U. Tokyo (Hitachi)

M. Honma

Nihon U.

U. Aizu

Y. Utsuno

JAEA Y. Akaishi RIKEN H. Grawe GSI A. Schwenk TRIUMF B. Holt TRIUMF