Study of the tensor correlation with a beyondmeanfield
Study of the tensor correlation with a beyond-mean-field method 杉本聡 京都大学
ls splitting in nuclei • “Is there any indication of spin-orbit coupling? ” Enrico Fermi in Mayer PR 75 (1949) 1969 • “There is not yet a quantitative understanding of the microscopic origins of the spin-orbit term in the nuclear Hamiltonian. ” in Schiffer et al. PRL 92 (2004) 162501 • Origins of the ls splitting – – – Spin-orbit force Tensor force 3 -body force Central force and kinetic term Mean field or correlation? Schiffer et al. PRL 92 (2004) 162501 Warner NATURE 430 (2004) 519
Michimasa et al. (PLB 638 (2006) 146 NPA 787 (2007) 569) 5 Me. V 3/2+ 23 F 5/2+ 17 F Bohr & Mottelson vol. 1
Hartree-Fock calculation for 15 O, 16 O, 17 O, 22 O, and 23 F • Spherical symmetry is not assumed – A valence particle breaks the shperical symmetry – Each jm orbit has a different radial dependece. – Resulting wave function has almost good angular momentum. Radial wave function depends on m
15, 16, 17, 22 O ETOT 16 O(0+) VT Rm -128. 3 (-127. 6) -1. 0 0. 0 2. 58(2. 54(02)) 17 O(5/2+) -132. 3(-131. 8) -4. 1 0. 0 2. 64 (2. 59(05)) 15 O(1/2 -) -110. 2(-112. 0) -4. 9 -0. 1 2. 55 (2. 44(04)) 15 O(3/2 -) -104. 5 0. 9 0. 0 5. 7 (6. 18) 5. 8 0. 1 -161. 8 (-162. 0) -20. 8 D(15 O(3/2 -)- 15 O(1/2 -)) 22 O(0+) • VLS 15 O 2. 59 1. 9 2. 85 (2. 88(06)) においてlsスプリッティングは主にLS力によって生み出される。 exp: G. Audi et al. NPA 729 (2003) 337. Bohr & Mottelson Vol. 1 Ozawa et al. , NPA 693 (2001) 32.
Exp. 4. 06 Me. V (Michimasa et al. PLB 638 (2006) 146) • テンソル力はlsスプリッティングを狭める。 c. f. Otsuka et al. PRL 95 (2005) 232502 cf. D(0 d 5/2 -0 d 3/2)= 6~7. 5 Me. V in 40 Ca Sugimoto et al. PRC 76 (2007) 054310
酸素同位体におけるテンソル力に よる相関の研究 S. Sugimoto, H. Toki, and K. Ikeda Phys. Rev. C 75 (2007) 014317
Couplings treated in the spherical CPPHF method l. Single particle states with the same j but different l’s are mixed. l. Higher node states like 2 s 1/2, 1 p 3/2, 1 p 1/2, etc. are included.
CPPHF計算(4 He,16 O) x. TE HF 4 He 1. 00 (Volkov No. 1 PPHF 0. 96 +G 3 RS) CPPHF 0. 92 16 O HF (MV 1 +G 3 RS) PPHF CPPHF Etot KE Vtot VC VT Rm P(D) -27. 9 49. 7 -77. 6 0. 0 1. 45 0. 00 -28. 3 52. 5 -80. 8 -75. 1 -5. 7 1. 45 0. 68 -28. 7 57. 8 -86. 5 -73. 2 -13. 3 1. 42 3. 22 VT VLS KE VC VCoul V 3 B Rm -123. 4 228. 9 -416. 9 0. 0 -0. 2 13. 4 51. 5 2. 57 -126. 6 236. 5 -423. 6 -5. 3 -0. 2 13. 5 52. 55 -133. 3 256. 5 -440. 0 -17. 8 -0. 2 13. 9 54. 4 2. 52 • パリティ、荷電射影を行うことによりテンソル力に よる2粒子2空孔相関を取り込むことが可能。 Sugimoto et al. , Nucl. Phys. A 740 (2004) 77; PRC 75 (2007) 014317
単一粒子軌道波動関数(16 O) 0 s 1/2 proton dominant 0 p 3/2 proton dominant Opposite parity components mixed by the tensor force have small spatial width. It suggests that the tensor correlation needs high-momentum components. 4 He case P(-)=16% P(p)=17%
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