Exotic Nucleiand

Yukawa’s Forces

Takaharu Otsuka 　　 University of Tokyo / RIKEN / MSU

INPCTokyo

June 4-8, 2007

T. Suzuki Nihon U.R. Fujimoto Hitachi Ltd.H. Grawe GSIY. Akaishi KEKP. Ring TUM

D. Abe TokyoT. Matsuo Hitachi Ltd.M. Honma U. AizuY. Utsuno JAEAG. Lalazissis Thessaloniki

Many experimentalists

Outline

1. Introduction - Past and present issues -

2. Shell structure and magic numbers of exotic nuclei

3. Deformation driven by tensor force

4. Relevant topics (neutrino, Lattice QCD, Superheavy)

5. Summary

Left-lower part of the Nuclear Chart

Studies on exotic nuclei in 1990’s

リチウム１１

neutron halo

nuclei

(mass number)

stable

exotic

-- with halo

A11Li

neutron skin

proton halo Stability line and drip

lines are not so far from

each other

　 Physics of loosely

bound

neutrons, e.g., halo

while other issues like 32Mg

Neutron number

Pro

ton

nu

mb

er

Neutron halo

11Li 208Pb

About sameradius

Strong tunneling of loosely bound excess neutrons

Breakup of 11Li

Nakamura et al.,Phys. Rev. Lett. 96, 252502 (2006)

F7-1 Nakamura

Drip line

Whathappenshere ?

中性子数　（同位元素の種類）Neutron

number

Pro

ton

nu

mb

er

In the 21st century, a wide frontier emerges between the stability and drip lines.

Stability line

A nuclei

(mass number)

stable

exotic

Riken’s work

1990’sneutron halo etc.

Phys. Rev. C 41, 1147 (1990), Warburton, Brown and Becker

Island of Inversion : Ne, Na, Mg with N=20-22

Island of Inversion Basic picture was

en

erg

y

intruder ground state

stable exotic

sd shell

pf shell

N=20gap ~constant

deformed 2p2h state

The Key : Tensor Force

meson (~ +) : minor (~1/4) cancellation

meson : primary source

Ref: Osterfeld, Rev. Mod. Phys. 64, 491 (92)

Multiple pion exchanges strong effective central forces in NN interaction (as represented by meson, etc.) nuclear binding

One pion exchange Tensor force

This talk : First-order tensor-force effect (at medium and long ranges)

Intuitive picture of monopole effect of tensor force

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

Example : Dripline of F isotopes is 6 units away from O isotopes

Sakurai et al., PLB 448 (1999) 180, …

Tensor

forced5/2

d3/2

N=16 gap : Ozawa, et al., PRL 84 (2000) 5493; Brown, Rev. Mex. Fis. 39 21 (1983)

only exchange term

78Ni42Si

Neutrinoreaction

51Sb

Island ofInversion

Superheavy

36Kr

Chart provided by Sakurai

50Sn

Nuclei or regionsto be discussed

R process

2. Shell structure and magic numbers of exotic nuclei

1h11/2 neutrons

1h11/2 protons

1g7/2 protons

Tensor bymeson

exchange

Exp. data from J.P. Schiffer et al., Phys. Rev. Lett. 92, 162501 (2004)

+ common effect (Woods-Saxon)

Z=51 isotopes

h11/2

g7/2

51Sb case

No mean field theory,(Skyrme, Gogny, RMF)explained this before.

Opposite monopoleeffect from tensor force with neutrons in h11/2.

Single-particle energies of exotic Ni isotopes

w/o tensor with tensorGogny-type

(finite-range)+

Tensor Force

TO, Matsuo, Abe, Phys. Rev. Lett. 97, 162501 (2006)

Hartree-Fock calculation including tensor force

N=28 Gap

Z=28 Gap

neutron g9/2neutron g9/2

Contributions of Kinetic+Central, 2-body LS, and Tensor components to the change of f7/2 – f5/2 gap

in going from N=40 to N=50 (g9/2 occupancy)

Kin+Cent and LS : almost the same among three calculations

Tensor : largest effect

TO, Matsuo, Abe, Phys. Rev. Lett. 97, 162501 (2006)

Kr

Sn

GT3GT3

EXPEXP

D1SD1S

h11/2g7/2

Heavy Sn and Kr aremore bound

Hartree-Fock-Bogoliubov calculation including tensor force

Two neutron separation energy

tensor

no tensor

Poster by Abe QW-048

16 O 40 Ca48 Ca

56 Ni90 Zr

132 Sn208 Pb

16 O 40 Ca48 Ca

56 Ni90 Zr

132 Sn208 Pb

Sp

in-o

rbit

sp

litt

ings

[M

eV]

1234567

2

4

6

8

pp

n n

1g1h

f7/2-f5/2

f7/2-f5/2

1g 1h1i

2g

d5/2-d3/2p3/2-p1/2

d5/2-d3/2p3/2-p1/2

SkPSkP T

Sk

P origin

alS

kP

Ten

sor + S

O*0.8

T

M.

Zale

wski,

W.

Satu

ła,

J. D

ob

aczew

ski,

(pre

lim

inary

)

Skyrme + Tensor’ : Many recent works An example by Dobaczewski et al. 　　　　　 Zero-range version of tensor force　　　　　　 (Skyrme 1956, Stancu et al. 1977)

Crucial for 42Si mentioned later

Dec. 22, 2006

April, 2007

October, 2006

February, 2007

F10-2

Full tensor

Half tensor

No tensor

NL3 is used

Lalazissis et al.

Long et al., Toki et al., …

Relativistic Mean Field

Relativistic Hartree-Fock

Proton 1h11/2 – 1g7/2 gap

Exchange terms

3. Deformation driven by Tensor-force

Effective shell-model interaction (refined empirically)

= central part

+ tensor ~

+ …

+ meson exchange (for medium- and long-range parts)

This feature is true also in G-matrix

A new shell-model interaction has been constructedfor the sd + pf shells.

Recent finding about the shell-model interaction

Chiral Perturbation of QCD

S. Weinberg, PLB 251, 288 (1990)

Tensor force is explicit

Short range central forceshave complicated origins andshould be adjusted.

proton

neutron

f7/2d3/2

d5/2

Potential Energy Surface

4214Si28

Tensor force can drive nuclei to (or from) deformation

Si isotopes Exp.

s1/2

full

Tensor force removedfrom cross-shell interaction

Z=28 gap is reduced also by tensor force

Strong oblateDeformation ?

Nature 435 (2005), MSU

PRL accepted (2007), GANIL

Debate over 42Si

deformed

44S -> 42Si cross section small

42Si oblate

44S 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

Modification to the Island of Inversion

Low-lying 3/2- level (0.765 MeV) in 27Ne

N=20 gap smaller

Terry et al, PLB 640 (2006) 86

Neyens et al. MgTripathi et al. NaDombradi et al. Ne

Ca

N=20 gap changes

O Ne Mg

~6MeV

~3MeV Expansionof the

territory

3. Intriguing relevant topics

Neutrino reaction cross section is enlargedby using interaction containing full tensor force

Relevance to Weak Processes

Temperaturte of supernovae explosion

Over Woosley

Over PSDMK2

Presented bySuzuki H4-2

accepted by PRL

central forcecalculated bya Lattice QCDcalculation

Presented byIshii D1-4

Tensor effective forces are close to bare ones.

Calculations for tensor and 3-body forces will be great

1k17/2

2h11/2

1h9/2

3p3/2

2f5/2

2f7/21i13/2

3p1/2

Neutron

Occupations of 1k17/2 and 2h11/2 reducesZ=114 gap to a half value

N=184

Z=114

Proton single-particle energiesby Woods-Saxon potential (A=300)

Modification of superheavy magic gap

by tensor force

Proton

En

ergy

(M

eV)

Story similar toZ=64 subshell closure

Summary

There are typically 20~100 isotopes between thestability and drip lines. They may give us a richfield of “harvest” from the NN interaction.By changing N (Z) so much, unknown or unrecognizedaspects of the NN interaction may emerge.This was the motivation of the project of the tensorforce.

The outcome so far are …

Summary - 2

- is a robust mechanism -- also for many classical cases --

- Shell evolution due to tensor force

- occurs from p-shell to superheavies developments in pf shell ex. N=34 new magic ANL, MSU, GANIL, REX-ISOLDE

- affects deformation (ex. Doubly-magic 42Si strongly oblate)

- Free tensor force (like +) many-body structure more input from ChP., eff. field th., lattice QCD

- Other cases … Weak processes, astrophysical implications, …. 11Li and tensor force Myo F3-3

mesons create variety and richness of exotic nuclei.

Thanks to Yukawa,