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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.
毎日新聞社提供
毎日新聞社提供
出典: TIME アーカイヴス
出典:毎日新聞の好意による
毎日新聞社提供
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.