??????????????? fss2 ???

1

• ??????????????? fss2 ???
• ?????? nd ????
• K. Fukukawa Y. Fujiwara (Kyoto Univ.)
• Y. Fujiwara and K.F. , Prog. Theor. Phys. 124
  (2010), 433-469.
• K. F. and Y. Fujiwara, arXiv1010, 2024.
• Contents
• 1.Introduction
• 2.Formalism
• 3. Results
• 3.1 The J-averaged nd central phase shift
• 3.2 Scattering lengths
• 3.3 Coulomb correction to differential cross
  sections
• 4. Summary

2

• 1. Introduction
• ?????? (NN) ??????????
• ??? ????????????????
• ????3 ????? 2 ??? 3 ????????????????
• ????? 2N3N potential ????????????????????
• (Nd ???? Nucleon analyzing power (Ay) puzzle ??
• breakup process ???? space star anomaly ??)

Ay puzzle
Space star anomaly
nd
pd
A. Deltuva, A.C. Fonseca, and P.U. Sauer, PRC 72
(2005), 054004.
A. Kievsky, M .Viviani and S. Rosati, PRC 64
(2001), 024002.
3

• ?????????NN???????
• ?????? meson ? exchange ????
• ????? ??? nonlocal ? quark exchange kernel
  ??????
• (cf??????? ?????????????)
• 3??????????? nonlocal effect ?????????
• The (3q)-(3q) RGM (Resonating group method)
• ?????????????????

Y. Fujiwara, Y. Suzuki and C. Nakamoto, Prog.
Part. Nucl. Phys. 58 439 (2007). QMPACK homepage
http//qmpack.homelinux.com/qmpack/index.php
4
NN phase shifts by fss2
Y. Fujiwara, M. Kohno, C. Nakamoto and Y.
Suzuki Phys. Rev. C64, 054001 (2001).
5

• 3H binding energy predicted by fss2

NN ???????????binding energy
Meson exchange 0.5 MeV1 MeV fss2 (Quark
model ) 0.35 MeV
350 keV
2 ?????????????3???? ?????????3????????? ?????????
?? How about the scattering state? (
)
Deuteron D-state probability Y. Fujiwara et al.
PRC77 (2008) 027001
?????????????? (red line) ?????????????????
(blue line) (190 keV ??????????????)
R. Machleidt, Adv. Nucl. Phys. 19 (1989) 189
6

• 2. Formalism
• AGS equation
• Channel-spin formalism
• Channel spin (Sc) deuteron spin (I1)
  neutron spin (s1/2)
• Sc3/2 (quartet channel) Pauli principle
• Sc1/2 (doublet channel) deuteron distortion
  effect
• Phase shift
• S-matrix (33 or 22 matrix) is parametrized in
  terms of the
• eigenphase shifts and mixing
  parameters.
• J-averaged central phase shift
• ????????????? ???? J ? eigenphase shift
  ??????

SC
7

• 3. Results
• 3.1 The J-averaged nd central phase shift

AV18 (UR 3N) A. Kievsky et al. NPA 607 ,402
(1996).
??????? AV18Urbana 3N potential ????? 2S fss2
???? AV18UR 3N potential ???????? AV18 ????? 4S
?? higher partial wave fss2, AV18, AV18UR 3N
??????????? Fss2 ?2?????? AV18UR 3N ???????????
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• 3.2 Effective range parameter
• Larger triton binding energy Smaller nd
  doublet scattering length
• 
  A. C. Phillips, Rep. Prog.
  Phys. 40, 905 (1977)
• ??????????????3N force ???????????
• ??????????????????????????
• Effective range expansion
• ????????????
• 2S ????????????? pole ??????????(4S??????)
• Parameter ????????????pole ???????????
• ????????????????????(??????????????)

correlation
L.M. Delves, PR 118, 1318 (1960)
L. Schlessinger, Phys. Rev. 167 (1968), 1411.
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• Quartet S-channel
  Doublet S-channel

6.30 fm (exp. 6.350.02 fm)
1.84 fm
Pole position
0.66 fm (exp. 0.650.04 fm)
-148 fm
W. Dilg et al. PL 36B, 208 (1971)
??? ??? Pauli ????????????? ??????? cross
section ?? 4S ? dominant?
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• nd scattering lengths Comparison with other
  calculations
• Doublet scattering length
• ?????? 0.91.2 fm
• ?????? TM 99 3N 0.6 fm
• Quark ?? (fss2) 0.66 fm
  (without CIB)
• 3???????????????????????????????????
• triton binding energy ?????????????? 0.760.8 fm
• ???????????????? 3 ??? ???????????
• (triton binding energy, nd phase shift
  ????consistent)
• NN ??????????????deuteron distortion effect ???

Ref. H. Witala et al. PRC68 ,034002 (2003).
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• 3.3 Coulomb correction to the differential cross
  sections
• ???????? error bar ???? pd ???????????????
• ???????? Coulomb effect ????
• ????
• AGS??????? Coulomb ????????????????
• ???????
• (????????) nd ??????? Rutherford ???????
• ?????J-averaged central phase shift ???????

P. Doleschall et al. NPA 380, 72 (1982).
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• The differential cross sections

Dash-dotted line Central phase shift solid
curve (exact ? nd ??) ????? Dotted curve
Coulomb ?? (phase shift ?????) Dashed curve 2S,
4S, 4P ?nuclear phase shift ?????????
(AV18?pd nuclear phase shift ? nd nuclear phase
shift ??)
Rutherford ??????????overestimation ????? ????pd
? nd ? nuclear phase shift ????(4S ??????
main) ??? 3 ??????? Coulomb ??????????
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• 4. Summary
• 1.??????????????? fss2 ? nd ??????????nd ????
• ?????????????? ??????????????
• 2 ???????????????????
• 2. fss2 ? 2S1 channel channel ?????????????
• (3H ????????, eigenphase shift ?? )
• 3. ?????????? J-averaged central phase shift
  ???????????
• pd ?????????????? Coulomb effect ???????? ?
• ????????????
• 1.fss2 ???Ay puzzle ???????????????????
• ? 15 ??????????
• 2. ?????????? Doleschall ???? Coulomb correction
  ?????
• ?????????????????