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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出典：TIMEｱｰｶｲｳﾞｽ
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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
0
2g9/2
1i11/2
3p1/2
2f5/2
2f7/2
1h9/2
3s1/2
1h11/2
2d6/2
1g7/2
1g9/2
2p1/2
2p3/2
1f5/2
1f7/2
2s1/2
126
Hartree-Fock potential (MeV)
-10
82
-20
50
-30
20
1i13/2
2d3/2
1d3/2
1d6/2
-40
8
1p1/2
1p3/2
2
-50
-60
3p3/2
1s1/2
0
2
4
6
Nuclear radius(10-15m)
8
10
208Pb
is very stable, because Z=82 and
N=126 which are magic numbers.
Pb
208
82
Bi
209
126
Pb
Very stable
208
208
Pb+b
This proton in h9/2 -shell is expected to rotate
freely about the center of 208Pb.
The operator of magnetic moment
  gs s + g
The Schmidt value
 s ( j)  j( g 
j 
gs  g
2 1
)
1
2
g 1

g  0
g s  5.585
for proton
g s  - 3.826 for neutron
unit n.m.
μs（h9/2）＝２．６２ n.m.
μobs （209Bi）＝４．１１ n.m.
δμ＝μobs－μs
＝１．５ n.m.
Very large.
A serious problem in 1950.
Pi-meson exchange current
Pi-meson(π)was Predicted by
Yukawa in 1935.
π meson was discovered experimentally
by C.F.Powell.
π +, π 0,and π Pi-meson exchange currents
H.Miyagawa 1951
Villars 1952
2 Nuclear Shell Model
Mean field theory with strong spin-orbit force
 s
Mayer and Jensen 1949
Shell model level scheme
(mean field approximation)
A strong spin-orbit interaction
is necessary to explain the magic numbers
the jj-coupling shell model of Jensen and Mayer!
l
magic number
××
１
j<=ℓ－ ２
××××
１
j>=ℓ＋ ２
16
O
,
40
Ca
M1-Giant Resonance
××
××× ○
Impossible
because
j<-orbit is closed.
１
j<=ℓ－ ２
magic number
××××××××××××
208
１
j>=ℓ＋ ２
Pb （The Ground state O ）
+
×
Possible
j< is vacunt
×××××××××××○
208
Pb （M1-Giant 1+）
h11/2 → h9/2 protons
i13/2 → h11/2 neutrons
(
9
i
B
126
83

209
2
)  (
208
P b(0 ) h 9 / 2 ; 9
+
2
208
+
   ( P b(1 ) h 9 / 2 ; 9

)

2
)

 ( )  0
Configuration Mixing
= Core-Polarization (Bohr and Mottelson)
(
209
B i)   (



B i)
0  h9/2

 2 0  h 9 / 2
 

,9

2
 2 0  h 9 / 2
,9
, 9

 0  h 9/2 , 9
2

 1 h

2
9/2
,9

2

 1 h
  0.8 n.m .
CM


9/2
,9
2
  ( )   s   
2

2

0

 

 cm
 obs
17O
0
0.02
17F
0
-0.08
41Ca
0
0.32
41Sc
0
-0.37
209Bi
0.8
1.5
Nucleus
Chemtob in 1967 found that the pi-meson exchange
current modifies g .
 g  0.10
for proton
 g   0.10
for neutron
 M EC ( h 9 / 2 )  0.5 n.m .
 theory 

B i)   C M   M E C
 0.8  0.5
 1.3
 obs (
209
Bi)  1.5
n.m .
n.m .
δ
Magnetic moment of
209
83
Bi126
1.49
1.5
1.37
MEC
2nd order
C.P.
1
1.05
Crossing
C.P. × MEC
0.79
0.5
1st order
C.P.
0
Ref.： A.Arima, K.Shimizu, W.Bentz, H.Hyuga
Adv. Nucl.Phys. 18 (1987) 1.
OBS
Most important contributions to the magnetic
moment of 209Bi :
(1) first order configuration mixing
=first order core-polarization   C P   C M 
(2) one pi-meson exchange current
Yamazaki, Nagamiya, Nomura and Katou in 1970
confirmed experimentally
 g  0 .1
fo r p ro to n s
an d
 g   0 .0 9 fo r n eu tro n s
The contribution of pi-meson current
is experimentally confirmed.
17O, 17F, 41Ca
and
41Sc
 obs are small, and  C M  0
But  obs are not zero.
GT transition rates deviate from their
shell model values.
Therefore higher order corrections, such as second
order configuration mixings, must be considered:
Shimizu, Ichimura and Arima in 1974,
Towner and Khanna in 1979.
δ
ISOSCALAR MOMENT
2nd
CROSS
MEC
-hole
δ
ISOVECTOR MOMENT
-1
p 1/2
17
d 5/2
39
-1
d 3/2
41
f 7/2
Ref. : I.S.Towner, F.C.Khanna, Nucl.Phys. A339 (1983) 334.
GAMOW - TELLER
δ
0.2
0
(GT)
-0 .2
REL
2nd
CROSS
MEC
-hole
-1
p 1/2
17
d 5/2
39
-1
d 3/2
Ref. : I.S.Towner, F.C.Khanna,
Nucl.Phys. A399 (1983) 334.
41
f 7/2
GT transition rates   s
s
s
s
2
obs
2
obs
2
shell m odel

2
1
2
are observed by using the (p,n) reaction.
(Goodman et al (1980))
This quenching has been explained by   h o le e ffe c t.
 is the isobar of nucleon. (  300 M eV excitation energy )
The effect of the second order configuration mixing
(= 2 particle -2 hole mixing) was not believed.
Why is  quenched ?
  hole m ixing
2p-2h or
2p-1h mixings
(second order
configuration mixing)
Simple
shell model
  h s ta te s
(  300 M eV )
2p-2h
or
2p-1h states
50 % of 
strength spread
over 20  50 M eV
0p-0h
or
1p
100 % of
 stre n g th
1p-1h
or
1p states
0p-0h
or
1p
50 % of
 stre n g th
1p-1h or 1p states
Bertsch, Hamamoto
Shimizu et al
Towner, Khanna
0p-0h
or
1p
1p-1h
or
1p states
90
Zr(p,n)
exp (K.Yoko,
H.Sakai et al.)
Rijsdijk,
Dickhoff et al .
Dang,
Arima et al .
IVSM
90
Zr(n,p)
IVSM
Ref. : K.Yoko, H.Sakai et al, Phys.Lett.B615 (2005) 193.
Comparison between experimental and
theoretical results for GT strength
distributions
• (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)
IVSM
IVSM
IVSM
– Good agreement in low w (GT)
– Exp. > Theory in high w → IVSM
IVSM should be subtracted to evaluate GT quenching Q
GT Quenching Factor Q after
Subtraction of90IVSM
• Final Values (Up to 50 MeV of
– Total GT strengths
Nb)
• S   28 . 6  0 . 6 ( stat  MDA )  0 . 9 ( IVSM )  1 . 7 (ˆ GT )
• S   2 . 8  0 . 5 ( stat  MDA )  0 . 3 ( IVSM )  0 . 2 (ˆ GT )


– GT sum rule
•
S    S    2 5.8  0 . 7 ( stat  MDA )  0 . 7 ( IVSM )  1 . 5 (ˆ GT )
– Quenching
Factor
Q  0.86  0.02(stat  MDA)  0.02(IVSM )  0.05(ˆ
•
Inaccessible errors in TRIUMF data
Previous Q  0 . 90  0 . 05 ( stat  MDA )  .....
GT
)
 0 . 15 (ˆ GT )
Our final(latest) result
Q  0 . 86  0 . 07 (quadratic sum of uncertainties)
One-p + two-p exchange potential
Central
One-p exchange
Two-p
exchange
Tensor
One-p exchange
Two-p exchange
Tensor Operator
M. Taketani, S. Machida, and S. Onuma:
Prog. Theor. Phys. 7 45 (1952)
Summary:
Most important parts of the nuclear force
Short
Central force
Tensor force
Spin-orbit force
Intermediate
Long range
VT ( r 12 )   S 12  Y
(2)
(2)
  12 ,  12  
0
f ( r12 )
where
(2)
S 12
Y
(2)
  s1  s 2 
2
  ,    spherical harm onics
f ( r12 )  a function of relative distance r 1 2
 S
(2)
Y
(2)

(0)
  3( s 1  r )  ( s 2  r ) / r  s 1  s 2
2
The deuteron wave function has the form

  N u (r )Y
(0)
(  ) 
(1)
  w ( r )  Y
(2)
(  )  
(1)

(1)

where N is a normalization constant, u(r) and w ( r )
(1)

are radial wave functions , and
are the spin
wave functions of the two nucleons:

(1)
 1    2 


    1    2    1    2   /

 1    2 

2
observed
OPEP
The quadrupole moment of the deuteron
confirms that the deuteron is not spherical.
This is the best evidence of the tensor force.
Deuteron
Q
 3z  r
(2)
2
2
0
z-axis
3S
1
3D
1
state
state
z-axis
=
+ 0.03×
Deformed rotor
Tensor force mixes 3S1 and 3D1 states
z-axis
Q
(2)
 3z  r
2
2
0
The first order effect of the tensor force is zero
between a valence nucleon and the core
16O or 40Ca, in which both j a n d j a re clo se d .


This is because
m agic num ber

S
si  0
i 1
L

i
0
i
w h e n b o th j   l 
1
2
a n d j  l 
0
   3 (s
i
i
1
a re clo se d , a n d th e re fo re
2
0
 rik )( s k  rik )  ( s i  s k )  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 spinorbit interaction.
51Sb
isotopes (Proton SPE)
Energy [MeV]
J. P. Schiffer et al., Phys. Rev. Lett. 92 162501 (2004)
1h11/2
1g7/2
64 70
Neutron number
82
The first order effect of tensor force on
V
s

s
(  < 0 in sh e ll m o d e l) :
change of 
occupation
j   2
orbit is being
occupied
1
S  0,L  0
j   2
orbit is being
occupied
1
S  0,L  0
j  is c lo s e d
after two orbits
j  a n d j  a re clo se d
S  0,L  0
Shell model requires   0 , w here  is the strength
of the spin-orbit interaction :
V
s

s
The first order effect of the tensor force weakens
the spin-orbit interaction when valence nucleon
levels are being occupied.
j
1h11/2 j 
’
Single particle
energy of
protons
1g7/2 j 
j
h 11 / 2
h9/2
is being
occupied
is being
occupied
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)
1h11/2
1h9/2
Summary:
Most important parts of the nuclear force
Short
w

Intermediate

Central force
Tensor force
Spin-orbit force
p

w
Long range
p
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 interuniversity research institutes in Japan.
I then discussed nuclear magnetic moments where
the one pi-meson exchange current plays a very
essential role together with the configuration-mixing
effect. The tensor force is of the most important
Consequences of the pion exchange potential.
The best evidence is provided by the deuteron.
The g7/2-h11/2 spacing of proton levels in the Sb
istopes also provides an evidence of the tensor
force. Thus pions predicted by Professor
H.Yukawa still plays important role in nuclear physics
today.