Introduction
Model
Results
Conclusions
Antibaryon nuclear bound states
Jaroslava Hrtánková and Jiří Mareš
Nuclear Physics Institute, Řež, Czech Republic
NUFRA 2013, Kemer, Sept 29 - 6 Oct 2013
1
Introduction
Model
Results
Conclusions
Introduction
study of p̄, Λ̄, Σ̄, Ξ̄ bound states in selected nuclei:
behavior of B̄ in the nuclear medium
changes of the nuclear binding energy, single particle energies and
density distributions
testing models of (anti)hadron–hadron interactions
knowledge of B̄–nucleus interaction for future experiments
(PANDA@FAIR)
2
Introduction
Model
Results
Conclusions
RMF approach
standard RMF models TM1(2); density dependent RMF model TW99
Dirac equation for nucleons and antibaryon
~ + β(mj + Sj ) + Vj ]ψjα = αj ψjα ,
[−i α
~∇
j = N, B̄ ,
1 + τ3
A0 + Σ R ,
2
∂gρN
∂gωN
∂gσN
ΣR =
ρVN ω0 +
ρIN ρ0 −
ρSN σ .
∂ρVN
∂ρVN
∂ρVN
Klein-Gordon equations for meson fields
Sj = gσj σ,
Vj = gωj ω0 + gρj ρ0 τ3 + ej
(−4 + mσ2 )σ = −gσN (ρVN )ρS −gσB̄ (ρVN )ρS B̄
(−4 + mω2 )ω0 = gωN (ρVN )ρV +gωB̄ (ρVN )ρV B̄
(−4 + mρ2 )ρ0 = gρN (ρVN )ρI +gρB̄ (ρVN )ρI B̄
−4A0 = eρp +eB̄ ρB̄ .
3
Introduction
Model
Results
Conclusions
Antibaryon potential
-400
0.6
ξ=1
-600
0.5
TM
-800
-20
TM
16
-40
16
16
-60
16
0
1
2
3 4
r [fm]
16
Op
16
OΛ
16
OΣ0
16
OΞ0
5
0
1
2
3 4
r [fm]
Op
-1000
OΛ
-1200
OΣ0
-1400
OΞ0
5
-3
S+V [MeV]
0
0.8
ξ=0.25
ξ=0.5
ξ=0.75
ξ=1
208
0.4
208
208
Pbp TM1
Pb
Pbp TW99
0.7
0.6
0.5
0.4
0.3
0.3
0.2
0.2
0.1
-3
0.7
ρcore [fm ]
0.8
-200
ρcore [fm ]
0
20
0.1
-1600
6
Fig.1: The B–nucleus (left) and
B̄–nucleus (right) potentials in
16 O (ξ = 1).
0
1
2
3 4
r [fm]
5
60
1
2
3 4
r [fm]
5
6
Fig.2: The core density
distribution 208 Pbp̄ , calculated for
different values of the parameter
ξ in the TM1 and TW99 models.
Introduction
Model
Results
Conclusions
Density dependent model
0.1
Pbp TW99
Pbp TM1
0.08
18
-0.01
16
0.06
-0.02
14
0.04
-0.03
12
0.02
0
-0.02
0
-0.04
ξ=0.25
ξ=0.5
ξ=0.75
ξ=1
-0.05
-0.06
Pb
2
3
r [fm]
4
0
1
2
3
r [fm]
4
10
8
208
6
Gσ
Gω
Gρ
Pbp TW99 ξ=1
4
208
1
G [-]
-3
ρp - ρn [fm ]
20
0
208
208
5
Fig.3:The isovector density in
208 Pb , calculated within the
p̄
TM1 and TW99 model.
2
0
1
2
3
4
r [fm]
5
6
7
8
Fig.4:Coupling constants as a
function of radial coordinate r
in 208 Pbp̄ for corresponding
meson fields.
Introduction
Model
Results
Conclusions
The issue of the p̄ self-interaction
KG equations for a meson
field acting on nucleons:
1.2
2
(−4 + mM
)ΦN =gMN ρMN
0.8
acting on p̄:
2
)Φp̄ =gMN ρMN
(−4 + mM
X XX
+gM
p̄ ρX
MX
p̄
1
-3
ρp [fm ]
+ gM p̄ ρM p̄
ξ=0.25
ξ=0.5
ξ=0.75
ξ=1
208
208
Pbp TM1
1.2
1
0.8
Pbp TM1
0.6
no self-interaction 0.6
0.4
0.4
0.2
0.2
0
0.5
1
r [fm]
1.5
0
0.5
1
r [fm]
1.5
2
Fig.5: The p̄ density in 208 Pbp̄ ,
calculated with and without the p̄
self-interaction.
6
Introduction
Model
Results
Conclusions
The p̄ absorption
1.2
p̄–nucleus optical
potential:
1.0
0.8
fs [-]
2π
ReVp̄ =ξVRMF ,
X
ImVp̄ =
fs Br Imb0 ρRMF ,
πω
0.6
ηω
πρ
ρω
2ω
0.4
3π
0.2
4π
5π
ξ = 0.2, Imb0 = 1.9 fm
6π
0
0.5
s
1/2
1
[GeV]
1.5
7π
2
Fig.6: The phase space suppression
factor fs as a function of the
√
center-of-mass energy s.
Introduction
Model
Results
Conclusions
The p̄ absorption
Table 1: The 1s single particle energies Ep̄ and widths Γp̄
(in MeV) in 16 Op̄ , calculated dynamically (Dyn) and
statically (Stat) with the real, complex and complex with fs
potentials (TM2 model), consistent with p̄–atom data.
Ep̄
Γp̄
Real
Dyn
Stat
193.7 137.1
-
Complex
Dyn
Stat
175.6 134.6
552.3 293.3
Complex + fs
Dyn
Stat
192.3 136.6
145.4 116.8
8
Introduction
Model
Results
Conclusions
Conclusions
p̄, Λ̄, Σ̄, Ξ̄ are strongly bound in atomic nuclei
large polarization effects of the nuclear core due to B̄
p̄ absorption in a nucleus – p̄ widths are suppressed due to the phase
space reduction, but still remain large for potentials consistent with
p̄–atom data
9