1. Hideki Yukawa and Nuclear Physics Akito Arima Japan Science Foundation Musashi Gakuen

3. 1Professor Hideki Yukawa has encouraged Japanese, especially young Japanese, just after the Second World War. 2Professor 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.

4. 1Professor Hideki Yukawa has encouraged Japanese, and especially young Japanese, just after the Second World War.

5. 毎日新聞社提供

8. 出典： TIME ｱｰｶｲｳﾞｽ

9. 出典：毎日新聞の好意による

10. 毎日新聞社提供

11. 2Professor H. Yukawa’s creation of a new academic system to research fundamental sciences; inter-university research institutes

12. Institute of Fundamental Physics in Kyoto University The first inter-university research institute

13. 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

14. Workshops, Winter and summer schools have been organized in Institute of Fundamental Physics.

15. 3 Pions, nuclear interaction and nuclear structure 3-1 Nuclear magnetic moments A difficult problem in 1950 was the magnetic moment of 209 Bi.

16. 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

18. 208 Pb is very stable, because Z=82 and N=126 which are magic numbers.

19. Pb 208 82 126 Very stable Pb 208 Pb+b 208 Bi 209 This proton in h 9/2 -shell is expected to rotate freely about the center of 208 Pb.

20. The operator of magnetic moment The Schmidt value unit n.m.

21. μs （ h 9/2 ）＝２．６２ n.m. （ 209 Bi ）＝４．１１ n.m. δμ ＝ μ obs － μs ＝１．５ n.m. Very large. A serious problem in 1950. μ obs

22. 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.Miyagawa1951 Villars1952

23. 2 Nuclear Shell Model Mean field theory with strong spin-orbit force Mayer and Jensen 1949 Shell model level scheme (mean field approximation)

24. A strong spin-orbit interaction is necessary to explain the magic numbers the jj-coupling shell model of Jensen and Mayer! l

25. magic number × × j < = ℓ － １２１２ × × × × 16 O, 40 Ca j > = ℓ ＋ １２１２

26. × × × × × ○ Impossible because j < -orbit is closed. M1-Giant Resonance

27. 208 Pb （ The Ground state O + ） ×××××××××××× magic number j < = ℓ － １２１２ j > = ℓ ＋ １２１２

28. ××× ○ ×××××××× × Possible j< is vacunt 208 Pb （ M1-Giant 1 + ） h 11/2 → h 9/2 protons i 13/2 → h 11/2 neutrons

29. Configuration Mixing = Core-Polarization (Bohr and Mottelson)

31. 17 O00.02 17 F0-0.08 41 Ca00.32 41 Sc0-0.37 209 Bi0.81.5 Nucleus

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

33. 0 0.5 1 1.5 1st order C.P. MEC 2nd order C.P. Crossing C.P. × MEC OBS Magnetic moment of Bi 126 209 83 0.79 1.37 1.49 1.05 Ref. ： A.Arima, K.Shimizu, W.Bentz, H.Hyuga Adv. Nucl.Phys. 18 (1987) 1. δ

34. Most important contributions to the magnetic moment of 209 Bi : (1) first order configuration mixing =first order core-polarization (2) one pi-meson exchange current

35. Yamazaki, Nagamiya, Nomura and Katou in 1970 confirmed experimentally The contribution of pi-meson current is experimentally confirmed.

36. 17 O, 17 F, 41 Ca and 41 Sc are small, and But are not zero. Therefore higher order corrections, such as second order configuration mixings, must be considered: Shimizu, Ichimura and Arima in 1974, Towner and Khanna in 1979. GT transition rates deviate from their shell model values.

37. ISOSCALAR MOMENT ISOVECTOR MOMENT 173941 1/2 p 5/2 d 3/2 d 7/2 f 2nd CROSS MEC -hole Ref. : I.S.Towner, F.C.Khanna, Nucl.Phys. A339 (1983) 334. δ δ

38. GAMOW - TELLER 173941 1/2 p 5/2 d 3/2 d 7/2 f 2nd CROSS MEC 0.2 -0.2 0 REL -hole (GT) Ref. : I.S.Towner, F.C.Khanna, Nucl.Phys. A399 (1983) 334. δ

39. GT transition rates are observed by using the (p,n) reaction. (Goodman et al (1980)) This quenching has been explained by is the isobar of nucleon. The effect of the second order configuration mixing (= 2 particle -2 hole mixing) was not believed.

40. Why is quenched ? Simple shell model 2p-2h or 2p-1h mixings (second order configuration mixing) 2p-2h or 2p-1h states strength spread 1p-1h or 1p states Bertsch, Hamamoto Shimizu et al Towner, Khanna 1p-1h or 1p states 0p-0h or 1p 0p-0h or 1p 0p-0h or 1p 1p-1h or 1p states

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

42. Comparison between experimental and theoretical results for GT strength distributions IVSM should be subtracted to evaluate GT quenching Q 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

43. Final Values (Up to 50 MeV of 90 Nb) –Total GT strengths –GT sum rule –Quenching Factor GT Quenching Factor Q after Subtraction of IVSM Previous Inaccessible errors in TRIUMF data (quadratic sum of uncertainties) Our final(latest) result

46. 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

47. Summary: Most important parts of the nuclear force Short Inter- mediate Long range Tensor force Spin-orbit force Central force

48. where

49. The deuteron wave function has the form where N is a normalization constant, u(r) and are radial wave functions, and are the spin wave functions of the two nucleons:

50. The quadrupole moment of the deuteron confirms that the deuteron is not spherical. This is the best evidence of the tensor force. observed OPEP

51. Deuteron z-axis + 0.03× Deformed rotor z-axis = 3 S 1 state 3 D 1 state Tensor force mixes 3 S 1 and 3 D 1 states

52. The first order effect of the tensor force is zero between a valence nucleon and the core 16 O or 40 Ca, in which both This is because 00

53. 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 17 O

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

55. 51 Sb isotopes (Proton SPE) J. P. Schiffer et al., Phys. Rev. Lett. 92 162501 (2004) 1h 11/2 1g 7/2 6470 82 Neutron number Energy [MeV]

56. The first order effect of tensor force on orbit is being occupied orbit is being occupied after two orbits occupation

57. Shell model requiresis the strength of the spin-orbit interaction : The first order effect of the tensor force weakens the spin-orbit interaction when valence nucleon levels are being occupied. is being occupied Single particle energy of protons ’ 1h 11/2 1g 7/2

58. 1h 9/2 1h 11/2 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)

59. Summary: Most important parts of the nuclear force Short Inter- mediate Long range Tensor force Central force Spin-orbit force

60. 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.

61. 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.