Study of the tensor correlation with a beyond-mean-field method

1
Study of the tensor correlation with a
beyond-mean-field method

• ???
• ????

2
?????????

• ?????????????????????
• ?????(????)?????????????????????????
• ???????
• ls????????
• ??????????????????????????
• ??????????????????
• ??????(Shell evolution) (Otsuka, Suzuki, Abe et
  al.)
• ?????????????????????????????????
• ??????????????-?????????
• ?????????r?? etc.

3
1????????????
4
????????
2??2????
????????????????? -gt???????(jj???)?ls?????????????
??
?????????????
??????(?????????)???????????????? -gt?????????????
(?????????????????????)
?????????!
5
23F??????0d???ls???????????????????????

• S. Sugimoto, K. Ikeda, and H. Toki Phys. Rev. C
  76 (2007) 054310

6
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
7
ls??????????????

• ??????ls??????????????
• ??????????? jj??????ls?????????????Tarbutton
  et al.(HF), Bouyssy et al.(Relativistic HF),
  etc.
• ???(???)????????????Otsuka, Suzuki, Abe, Utsuno,
  etc
• 2p2h ?? Terasawa and Arima, Ando and Bando, Myo
  et al., etc.
• ls???????????????????????
• ????????(Michimasa et al. PLB 638 (2006)
  146)D(pd) in 17F(16Op) 5 MeV ? D(pd) in
  23F(22Op) 4 MeV
• 23F????ls?????????????????????????(Sugimoto et
  al. PRC 76 (2007) 054310)

8
Michimasa et al. (PLB 638 (2006) 146 NPA 787
(2007) 569)
5 MeV
3/2
23F
5/2
17F
Bohr Mottelson vol. 1
9
??????ls??????????????
jgtl1/2 jltl-1/2
VT?ls?????????????
VT?ls?????????????

• jgt-jgt or jlt-jlt ??
• jlt-jgt ??
• jgt?jlt????????????????VT??????
• ???-?????????(T0)
• cf. Bouyssy et al. PRC 36 (1987) 380
• Otsuka et al. PRL 95 (2005) 232502

VT??????
10
???????????
??????ls?????????????
11
Hartree-Fock calculationfor 15O, 16O, 17O, 22O,
and 23F

• 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 .
12
??????(HF??)

• ???Modified Volkov No.1, m0.59
• LS?d-LSW0115 MeV fm515O????D(0p3/2-1-0p1/2-1)
  ???????????? cf. Gogny force D1
• ?????G3RS (Tamagaki, PTP 39 (1968) 91)
• G3RS?????
• ?????G??????????????????????????????????????????

13
15,16,17,22O
ETOT VLS VT Rm
16O(0) -128.3 (-127.6) -1.0 0.0 2.58(2.54(02))
17O(5/2) -132.3(-131.8) -4.1 0.0 2.64 (2.59(05))
15O(1/2-) -110.2(-112.0) -4.9 -0.1 2.55 (2.44(04))
15O(3/2-) -104.5 0.9 0.0 2.59
D(15O(3/2-)- 15O(1/2-)) 5.7 (6.18) 5.8 0.1
22O(0) -161.8 (-162.0) -20.8 1.9 2.85 (2.88(06))

• 15O ????ls???????????LS????????????

exp G.Audi et al. NPA 729 (2003) 337.
Bohr Mottelson Vol. 1 Ozawa et al., NPA
693 (2001) 32.
14
Exp. 4.06MeV (Michimasa et al. PLB 638 (2006)
146)

• ??????ls?????????????

c.f. Otsuka et al. PRL 95 (2005) 232502
cf. D(0d5/2-0d3/2) 67.5 MeV in 40Ca
Sugimoto et al. PRC 76 (2007) 054310
15
(No Transcript)
16
??????????????????????

• S. Sugimoto, H. Toki, and K. Ikeda Phys. Rev. C
  75 (2007) 014317

17
????????
2??2????
????????????????? -gt???????(jj???)?ls?????????????
??
?????????????
??????(?????????)???????????????? -gt?????????????
(?????????????????????)
?????????!
18
?????????????????????(CPPHF)? 1

• 1????????????????????
• ?????(s??)
• ????????????????????????????????????????(over-shel
  l??)
• ???????(t)
• ??????????????????????????????????????????(??-????
  ?)
• ????????
• ???????????????????????????????-gt
  ????????????????????????(Charge and
  parity-projected Hartree-Fock equaiton)

cf. ?????????????(QQ?????????????????)
References Toki, Sugimoto, and Ikeda., Prog.
Theor. Phys. 108 (2002) 903(????) Sugimoto et
al., Nucl. Phys. A 740 (2004) 77 PRC 75 (2007)
014317(?????) Ogawa et al., Prog. Thoer. Phys.
111 (2004) 75 Phys. Rev. C 73 (2006)
034301(????)
19
CPPHF????????????
??????
????
??????????????2??2?????????????????????!
20
?????????????????????(CPPHF)? 2
??????????????????????(CPPHF)???
21
????????????????????????
H-F part
cf. PPHF??? (Takami et al., Prog. Theor. Phys. 96
(1996) 407)
22
?????????? (??????)
????????????????????????????
23
Couplings treated in the spherical CPPHF method

• Single particle states with the same j but
  different ls are mixed.
• Higher node states like 2s1/2, 1p3/2, 1p1/2, etc.
  are included.

24
?????? (CPPHF??)

• ???Modified Volkov No.1 (Ando et al, PTP 64
  (1980) 1608)
• LS???????G3RS (Tamagaki, PTP 39 (1968) 91)
• G3RS ?????
• ?????G??????????????????????????????????????????
• 23F??????0d???ls????????????

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CPPHF??(4He,16O)
xTE Etot KE Vtot VC VT Rm P(D)
HF 1.00 -27.9 49.7 -77.6 -77.6 0.0 1.45 0.00
PPHF 0.96 -28.3 52.5 -80.8 -75.1 -5.7 1.45 0.68
CPPHF 0.92 -28.7 57.8 -86.5 -73.2 -13.3 1.42 3.22
4He (Volkov No. 1 G3RS)
16O (MV1 G3RS)
Etot KE VC VT VLS VCoul V3B Rm
HF -123.4 228.9 -416.9 0.0 -0.2 13.4 51.5 2.57
PPHF -126.6 236.5 -423.6 -5.3 -0.2 13.5 52.5 2.55
CPPHF -133.3 256.5 -440.0 -17.8 -0.2 13.9 54.4 2.52

• ?????????????????????????2??2???????????????

Sugimoto et al., Nucl. Phys. A 740 (2004) 77 PRC
75 (2007) 014317
26
??????????(4He)
P(-)16 P(p)17
Wave function

• ??????????????????????????????????
• ????????????????????p??????s??????????????????????
  ??????

??????????????????????!
27
??????????(16O)
0s1/2 proton dominant
0p3/2 proton dominant
0p1/2 proton dominant
Opposite parity components mixed by the tensor
force have small spatial width. It suggests that
the tensor correlation needs high-momentum
components.
28
???????????????(14O, 16O, 22O, 24O, 28O)
2p2h??
d3/2
s1/2
p1/2
d5/2
p3/2

• ????????1?????????????????????????????
• sd????????????16O???????????????????2??2??????????
  ?????

29
????????????????
0d5/2
0p1/2
1s1/2

• ???????????????????????????
• n0d5/2??????????????????????????
• n1s1/2???????????16O????????????????????
• ????????????16O??????????????

30
???

• ??????23F??????0d???ls????????????????????????????
  ????????????
• ????????2??2?????????????????????????????????????
  ???????????
• ??????????????????????????????????????????
• ?????
• ??????????????
• ?????????2??2???????
• ?????????(????????????)