Hideki Yukawa and Nuclear Physics

Akito Arima

Japan Science Foundation

Musashi Gakuen

1 Professor Hideki Yukawa has encouraged Japanese, especially young Japanese, 　

　　 just after the Second World War.

2 Professor Hideki Yukawa’s creation of a new academic system for research in fundamental science: The inter-university research institutes.

3 Pions, nuclear interaction and nuclear structure.

1 Professor Hideki Yukawa has

encouraged Japanese, and

especially young Japanese,

just after the Second World War.

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2 Professor H. Yukawa’s creation of a new academic system to research fundamental sciences; inter-university research institutes

Institute of Fundamental Physics

in Kyoto University

The first inter-university research institute

Examples of inter-university research institutes

Cosmic ray laboratory (super Kamiokande)

Institute of Nuclear Study

KEK

etc.

The most important driving forces to develop research of fundamental sciences and technologies in Japan

Workshops, Winter and summer schools

have been organized in Institute of

Fundamental Physics.

3 Pions, nuclear interaction and nuclear structure

3-1 　 Nuclear magnetic moments

A difficult problem in 1950 was

the magnetic moment of 209Bi.

Ⅰ Nuclear Shell Model

1 Magic Number

Z=2(He), 10(Ne), 18(Ar), 36(Kr), 54(Xe), 86(Rn)

They are rare gases.

Nuclear magic numbers

Z=2,8,20,50,82

N=2,8,20,28,50,82,126

Nuclear radius(10-15m)

Har

tree

-Fo

ckp

ote

nti

al

(MeV

)

2g9/2

3p3/2

1i13/2

2d3/2

2s1/2

1f7/2

1d6/2

1d3/2

1p3/2

1p1/2

1s1/2

126

0

-10

82

50

20

2

8

-20

-30

-40

-50

0 102 84 6

1f5/2

2p3/2

2p1/2

1g9/2

1g7/2

2d6/2

1h11/2

2f7/2

3s1/2

1h9/2

2f5/2

3p1/2

1i11/2

-60

2g9/2

3p3/2

1i13/2

2d3/2

2s1/2

1f7/2

1d6/2

1d3/2

1p3/2

1p1/2

1s1/2

126

0

-10

82

50

20

2

8

-20

-30

-40

-50

0 102 84 6

1f5/2

2p3/2

2p1/2

1g9/2

1g7/2

2d6/2

1h11/2

2f7/2

3s1/2

1h9/2

2f5/2

3p1/2

1i11/2

-60

208Pb is very stable, because Z=82 and

N=126 which are magic numbers.

Pb20882 126 Very stable

Pb208

Pb+b208Bi209

This proton in h9/2 -shell is expected to rotatefreely about the center of 208Pb.

The operator of magnetic moment

s +gsg

The Schmidt value

( ) ( )2 1s

sg g

j j g

12

j

1

0

g

g

5.585 for protonsg - 3.826 for neutronsg

unit n.m.

μs （ h9/2 ）＝２．６２　 n.m.

（ 209Bi ）＝４．１１ n.m.

δμ ＝ μobs － μs

　　　＝１．５　 n.m. Very large.

A 　 serious problem in 1950.

μobs

Pi-meson exchange currentPi-meson(π)was Predicted byYukawa in 1935.π meson was discovered experimentallyby C.F.Powell.π +, π 0,and π -Pi-meson exchange currents H.Miyagawa 1951 Villars1952

2 Nuclear Shell ModelMean field theory with strong spin-orbit force

Mayer and Jensen 1949 Shell model level scheme

(mean field approximation)

s

A strong spin-orbit interaction

is necessary to explain the magic numbers

the jj-coupling shell model of Jensen and Mayer!

l

magic number

× × j<=ℓ －１２

× × × ×

16O 　 , 　 40Ca

j>=ℓ ＋１２

× ×

× × × ○

Impossiblebecausej<-orbit is closed.

M1-Giant Resonance

208Pb 　（ The Ground state O+ ）

××××××××××××

magic number

j<=ℓ －１２

j>=ℓ ＋１２

××× ○××××××××

× Possiblej< is vacunt

208Pb 　（ M1-Giant 1+ ） h11/2 → 　 h9/2 protons i13/2 → 　 h11/2neutrons

209 208

83 126 9 / 2

+ ;9 9( Bi ) ( Pb(0 ) )2 2h

208

9 / 2

+ ; 9( Pb(1 ) )2h

( ) 0

Configuration Mixing

= Core-Polarization (Bohr and Mottelson)

2099 / 2 9 / 2

9 9( Bi) ( Bi) 0 , 0 ,2 2h h

29 / 2 9 / 2

9 92 0 , 1 , ( )2 2 sh h

9 / 2 9 / 29 92 0 , 1 , 02 2h h

CM 0.8 n.m.

17O 0 0.0217F 0 -0.08

41Ca 0 0.3241Sc 0 -0.37209Bi 0.8 1.5

cm obsNucleus

Chemtob in 1967 found that the pi-meson exchange current modifies .g

g 0.10 for proton

g 0.10 for neutron

MEC 9/ 2( ) 0.5 n.m.h

theory CM MECBi)

0.8 0.5

1.3 n.m.

209obs ( Bi) 1.5 n.m.

0

0.5

1

1.5

1st orderC.P.

MEC2nd order

C.P.

CrossingC.P. × MEC

OBS

Magnetic moment of Bi12620983

0.79

1.37

1.49

1.05

Ref. ： A.Arima, K.Shimizu, W.Bentz, H.HyugaAdv. Nucl.Phys. 18 (1987) 1.

δ

Most important contributions to the magnetic moment of 209Bi :

(1) first order configuration mixing=first order core-polarization CP CM

(2) one pi-meson exchange current

Yamazaki, Nagamiya, Nomura and Katou in 1970confirmed experimentally

g 0.1 for protons

and

g 0.09 for neutrons

The contribution of pi-meson current is experimentally confirmed.

17O, 17F, 41Ca and 41Sc

obs are small, and CM 0

But are not zero.obs

Therefore higher order corrections, such as secondorder configuration mixings, must be considered:Shimizu, Ichimura and Arima in 1974,Towner and Khanna in 1979.

GT transition rates deviate from theirshell model values.

ISOSCALAR MOMENT

ISOVECTOR MOMENT

17 39 41-11/2p 5/2d

-13/2d 7/2

f

2ndCROSSMEC

-hole

Ref. : I.S.Towner, F.C.Khanna, Nucl.Phys. A339 (1983) 334.

δδ

GAMOW - TELLER

17 39 41-11/2p 5/2d

-13/2d 7/2f

2ndCROSSMEC

0.2

-0 .2

0

REL

-hole

Ref. : I.S.Towner, F.C.Khanna, Nucl.Phys. A399 (1983) 334.

δ

GT transition rates2s

2

obs2

shell model

12

s

s

2

obss are observed by using the (p,n) reaction.

(Goodman et al (1980))

This quenching has been explained by hole effect.

is the isobar of nucleon. ( )300MeV excitationenergy

The effect of the second order configuration mixing(= 2 particle -2 hole mixing) was not believed.

Why is quenched ?

Simple shell model

2p-2h or2p-1h mixings(second order configuration mixing)

hole mixing

h states( 300MeV)2p-2h

or2p-1h states

strength spread 50%of

over 20 50 MeV

50%of

strength

1p-1h or 1p statesBertsch, HamamotoShimizu et alTowner, Khanna

100%of

strength

1p-1hor

1p states

0p-0hor 1p

0p-0hor 1p

0p-0hor 1p

1p-1hor

1p states

Dang,Arima et al .

Rijsdijk,Dickhoff et al .

exp (K.Yoko,　 　 　 H.Sakai et al.)

Zr(p,n)90

Zr(n,p)90

IVSM

Ref. : K.Yoko, H.Sakai et al, Phys.Lett.B615 (2005) 193.

Comparison between experimental and theoretical results for GT strength

distributions

IVSM should be subtracted to evaluate GT quenching Q

IVSMIVSM

IVSM

• (p,n) Calc. with 2p2h• Bertsch,Hamamoto PRC 26 1323 (1982)

• Dang, Arima et al. PRL 79, 1638 (1997)

– Fairly good agreement with experimental results in contituum

– Exp. > Theory → IVSM

• (p,n) and (n,p) Calculations• DRPA by Rijssijk et al.PRC 48, 1752 (1993)

– Good agreement in low (GT)– Exp. > Theory in high → IVSM

• Final Values (Up to 50 MeV of 90Nb)– Total GT strengths

• •

– GT sum rule•

– Quenching Factor•

GT Quenching Factor Q after Subtraction of IVSM

)ˆ(7.1)IVSM(9.0)MDAstat(6.06.28 GT S

)ˆ(2.0)IVSM(3.0)MDAstat(5.08.2 GT S

)ˆ(5.1)IVSM(7.0)MDAstat(7.05.82 GT SS

)ˆ(05.0)IVSM(02.0)MDAstat(02.086.0 GTQ

)ˆ(15.0 .....)MDAstat(05.090.0 GTQPreviousInaccessible errors in TRIUMF data

07.086.0 Q (quadratic sum of uncertainties)Our final(latest) result

One- + two- exchange potential

M. Taketani, S. Machida, and S. Onuma:Prog. Theor. Phys. 7 45 (1952)

Central

Tensor

One-exchange

Two-exchange

One-exchange

Two-exchange

Tensor Operator

Summary:Most important parts of the nuclear force

ShortInter-mediate Long range

Tensor force

Spin-orbit force

Central force

(2) (2)12 12 12

0

12 12( ) , ( )TV S Y f r r

where

2(2)12

(2)

12

1 2

12

, spherical harmonics

( ) a function of relative distance r

S s s

Y

f r

(0)(2) (2) 223( ) ( ) /S Y r 1 1 2s r s r s s

The deuteron wave function has the form

(1)(0) (1) (2) (1)( ) ( ) ( ) ( )N u r Y r Y

where N is a normalization constant, u(r) andare radial wave functions , and 　　 are the spin wave functions of the two nucleons:

(1)

1 2

1 2 1 2 / 2

1 2

(1)( )r

The quadrupole moment of the deuteron confirms that the deuteron is not spherical.

This is the best evidence of the tensor force.

observed

OPEP

Deuteron

z-axis

z-axis

+ 0.03×

Deformed rotor

z-axis

=

03 22)2( rzQ

3S1 state 3D1 state

03 22)2( rzQ

Tensor force mixes 3S1 and 3D1 states

The first order effect of the tensor force is zero between a valence nucleon and the core16O or 40Ca, in which both j j and are closed.

This is because

magicnumber

1

0

0

ii

ii

S s

L

1 12 2

j j l lwhen both and are closed, and therefore

3( )( ) ( ) 0 .i ik k ik i ki

s r s r s s0 0

The second order effect of the tensor force suggested by Wigner in 1950.

Arima and Terasawa calculated the second order effect of the tensor foce in OPEP.

in 17O

-meson weakens the tensor force.

The second order effect of the tensor force could be 1/3 ～ 1/4 of the spin-orbit interaction.

51Sb isotopes (Proton SPE)J. P. Schiffer et al., Phys. Rev. Lett. 92 162501 (2004)

1h11/2

1g7/2

64 70 82Neutron number

En

erg

y [

MeV

]

The first order effect of tensor force on :sV s ( < 0 in shell model)

change of

1

2j

orbit is being occupied

0, 0S L

1

2j

orbit is being occupied

0, 0S L

j isclosed

after two orbitsj j and areclosed

0, 0S L

occupation

Shell model requires 0, where is the strength

of the spin-orbit interaction :

sV s

The first order effect of the tensor force weakensthe spin-orbit interaction when valence nucleon levels are being occupied.

j

is being occupied

11/ 2his being occupied

9 / 2h

Single particleenergy of protons

j

jj

’

1h11/2

1g7/2

1h9/21h11/2

Sb isotopes (Proton SPE)T. Otsuka, T. Matsuo, and D. Abe, Phys. Rev. Lett. 97 162501 (2006)J. P. Schiffer et al., Phys. Rev. Lett. 92 162501 (2004)

Summary:Most important parts of the nuclear force

ShortInter-mediate Long range

Tensor force

Central force

Spin-orbit force

In summary, I discussed the contributions of

Professor Hideki Yukawa in fostering and

encouraging young researchers and this

contributions to promote fundamental

sciences, especially by establishing inter-

university research institutes in Japan.

I then discussed nuclear magnetic moments where the one pi-meson exchange current plays a veryessential role together with the configuration-mixingeffect. The tensor force is of the most importantConsequences of the pion exchange potential. The best evidence is provided by the deuteron. The g7/2-h11/2 spacing of proton levels in the Sbistopes also provides an evidence of the tensorforce. Thus pions predicted by Professor H.Yukawa still plays important role in nuclear physicstoday.