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Hyperon atom : Σ atom , Ξ, analysis of atomic data
Level width : Determination of the coupling constants
Σatom : Ξatom :
Level Shift : Determination of the optical potential depth
Hyperon Atom and Y-N Interaction
ストレンジネスとエキゾティクス・理論の課題 2007/3/1--3 三重・鳥羽
Akihiro Haga RCNP and Yataro Horikawa J.U.
Hyperon 原子
強い相互作用による Level shifts と level widths の微細構造に対する影響
Anomalous moment
R. J. Powers et al., Phys. Rev .C 47, 1263(1993)
R.J. Powers et al. Phys. Rev. C47, 1263 (1993)
Energies of the 10l to 9k transitions in Pb and W
l
Experience in muonic atom
• Nuclear size effect• Vacuum polarization of e--e+ field
⇒ Solve the Dirac equation with the Coulomb field.
• Nuclear polarization• Self-energy effect (Bethe log. + Anomalous moment)• Vacuum polarization of μ--μ+ field• Relativistic recoil effect• Electron screening effect
+ +
(a) (b) (c)
ミュオン
核分極テンソル
N
光子
原子核 原子核 原子核ミュオンミュオン ミュオン
ミュオン
電子・陽電子の真空偏極
原子核
真空偏極と結合した核分極補正ダイアグラム(単独でゲージ不変)
=ゲージ不変
核分極補正ダイアグラム
最低次の核分極補正
• Hydrogenlike atom ー QED の高精度検証 ー muon
Theoretical value :
Pure Coulomb energy of circular orbits (MeV)
κ E(C) E(point) ΔE
-1 -20.456929 -238.04010 217.583478
1 -17.060348 -61.067249 44.0069011
-2 -17.060348 -54.851392 37.7982685
7 -3.3568652..
-3.3570843 0.00021917
-8 -3.3541835 -3.3543925 0.00020903
8 -2.6510666 -2.6510719 5.3129E-06
-9 -2.6495983 -2.6496034 5.0486E-06
9 -2.1465824 -2.1465825 8.83E-8
-10 -2.1457267 -2.1457268 8.37E-8
Hyperon atom and Relativistic EFT
))(( 23
cM
Spectra of Σ- Pb atom
-35
-30
-25
-20
-15
-10
-5
0-10 -8 -6 -4 -2 0 2 4 6 8 10
Bin
din
g en
ergy
(M
eV)
Quantum number κ of angular momentum
Parameter set NLSH + Mares
-35
-30
-25
-20
-15
-10
-5
0-10 -8 -6 -4 -2 0 2 4 6 8 10
-35
-30
-25
-20
-15
-10
-5
0-10 -8 -6 -4 -2 0 2 4 6 8 10
-35
-30
-25
-20
-15
-10
-5
0-10 -8 -6 -4 -2 0 2 4 6 8 10
-35
-30
-25
-20
-15
-10
-5
0-10 -8 -6 -4 -2 0 2 4 6 8 10
NLSH
TM1
RHAT
Binding due to the strong interaction
becomes w
eak
J. Mares and B. K. Jennings, Phys. Rev. C49, 2472 (1994)
using NLSH for nucleon sector
Transition energy of 10l to 9k in 208Pb; 505.321(48) keV
One can reproduce this data by adjusting a parameter of σ-Σ coupling constant.
Parameter set g σ gσΣ
NLSH 10.4444 6.258(59.9%)
TM1 10.0289 5.959(59.4%)
RHAT 6.0350 3.270(54.2%)
A l most same ratio !Level shifts of 10l and 9k in 208Pb ; less than 1keV !!
repulsive unbound potential
Potential necessary to reproduce energy shifts
width の計算
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