ANTIBARYONS BOUND IN NUCLEI

1
ANTIBARYONS BOUND IN NUCLEI

• I.N. Mishustin1,2)

1) Frankfurt Institute for Advanced Studies,
J.W. Goethe Universität, Frankfurt am Main 2)
Kurchatov Institute, Russian Research Center,
Moscow
2
Contents

• Introduction
• Strongly bound systems
• - RMF formalism using parity
• - infinite systems with and
• - finite - nuclear systems
• - anti-hypernuclei
• - reduced antibaryon couplings
• Estimates of life time
• Formation in reactions
• Observable signatures
• Conclusions

Recent results Th. Burvenich, I.N. Mishustin,
L.M. Satarov, J.A. Maruhn,
H. Stocker, and W. Greiner, Phys. Lett.
B542, 206 (2002)
I.N. Mishustin, L.M. Satarov, Th. Burvenich, H.
Stocker,
and W. Greiner, Phys. Rev. C 71, 035201
(2005)
3
The relativistic mean-field Lagrangian
Interaction terms
4
Parameters approximations

• Three RMF models were used TM1,NL3,NLZ2
• The model parameters were adjusted to reproduce
  properties of nuclei from to
• G-parity transformation for
• SU(3) for hyperons
• No dynamical effects static nuclei
• No sea approximation
• Dirac sea states are renormalized out
• real antibaryons ( ) are
  considered as independent degrees of freedom

5
Equations for mean meson fields
G-parity
Source densities
Modification of target nucleus due to presence of
antibaryon !
6
Dirac equations for fermion fields
Scalar potential generating
effective mass
Vector potential
G-parity for (
)
Optical potentials
at normal density 0.15 fm-3
where isospin,
Coulomb terms
7
Energy levels (NLZ2)
Significant rearrangement of nuclear structure
due to the presence of an antiproton i.e. a
hole ( ) in the Dirac sea
8
Nucleon densities
NLZ
NL3
NL3
9
Nucleon densities (NL3)
g. s. deformation
10
Nucleon densities (NLZ2)
superdense core normal halo
11
Nucleon densities (NL3)
12
Density profiles in 16O and 16O

-
Cold compression of the nucleus induced by an
antibaryon
13
Effect of reduced couplings in 16O
-
p
14
Binding energies of 16O
-
p
Large effect remains even for reduced
couplings
( follows from recent analysis by A.
Gal et al., nucl-th/0504030)
15
Antibaryon annihilation in nuclei
Annihilation channels with mesons
in a final state
? internal quantum numbers
? cm energy squared
transition amplitude
(assumed to be smooth
function of 4-momenta)
Within semiclassical approximation
where in-medium effective mass
16
In-medium annihilation rate
From kinetic equation (W.Cassing, Nucl. Phys.
A700 (2002) 618)
? occupation probabilities of
? transition amplitude of
Invariant phase-space volume
17
Rate of reaction BN?M1Mn
-
does not depend sensitively on
are evaluated at some average
isotopic effects are small
Approximations
where
exclusive annihilation cross section in vacuum
In the low density limit
18
Partial annihilation widths
Integration over target volume
In-medium partial width

- vacuum partial width at rest (
),
normalized to
for
Phase-space suppression factor
Overlap integral
Reduced available energy in medium
19
Characteristics of N annihilation
-

• Exp. data on exclusive channels
• where with
  mesonic
• resonances
  as well as direct pions were included in the
  analysis
• In the case of infinite matter, assuming
• Typical values in RMF models

20
Life times annihilation widths
-
partial widths of NN annihilation in MeV
Life time of
from numerical calculation
(NLZ2)
(NL3)
21
Phase-space volume for NN?n
-
Phase-space suppression factors
22
Probabilities of NN?n
-
23
Multinucleon annihilation
Pontecorvo-like reactions (in target nuclei with
A2)
-
Experimental data on p4He at rest (OBELIX
Collab., Nucl. Phys. A700 (2002) 159)
relatively small contribution
More exclusive data on multinucleon annihilation
are needed!
24
Multinucleon correlations probabilities
- average number of
nucleons in a strong interaction volume
surrounding antinucleon in a target nucleus
- typical density around antinucleon
- radius of annihilation volume
Assuming the Poisson distribution in number of
nucleons
Relative probability of multinucleon channels
25
Formation probability in pA collisions
-
High energy antiproton beam is needed to avoid
annihilation on the nuclear surface
Probability to form a superbound - nuclear
state
- fraction of central events (
is assumed)

• probability for to reach nuclear center

without annihilation
- probability to loose initial momentum in a
single
inelastic collision with capture of
into a bound state
26
Energy dependence of pp cross sections
-
10 GeV/c
data Particle Data Group
fit M.Bleicher et al., Phys. Lett. B485 (2000)
133
27
Probability of stopping capture

• Assumptions
• antiproton looses its longitudinal momentum
• in a single inelastic collision
• its final momentum is small

- probability of a single inelastic
collision
- probability of the momentum loss
( 10-3 for 10 GeV/c antiprotons)
- takes into account off-shell (binding) effects
( 0.1 is assumed)
28
Production rates of superbound nuclei
Rate of reaction
where luminosity of beam 21032
cm-2 s-1 (planned at GSI)
For 10 GeV/c central collisions and
For reduction factor due to
conversion
in reactions
29
Cross section of pp??X
-
-
S. Banerjee et al., Nucl. Phys. B150 (1979) 119
3.6 GeV/c
30
Shift of energy levels due to absorption

• Large effects are expected for shallow
• atomic states (effective repulsion)

C.J. Batty, E. Friedman, A. Gal, Nucl. Phys. A689
(2001) 721

• For antinucleon nuclear bound states
• solve equivalent Schrödinger equation
• in square well complex potential

Typical energy scale
for
31
Trajectories of 1s bound states
for deeply bound antinucleon states
relative shift
32
Observable signatures

• Super-transitions from Fermi to Dirac sea
• one-body annihilation (not possible
  in vacuum)
• sharp lines in spectra at
• Transitions between levels of each sea
• photon lines with
• Explosion of compressed nucleus after antibaryon
  annihilation
• strong radial flow of fragments
• Deconfinement transition
• formation of cold deconfined core and multi -
  qq clusters

?
-
33
Annihilation from supertransition
Antibaryons in superbound nuclei can
annihilate due to transition from upper to lower
energy well
sharp ( ) lines
in spectra at
for
This is analogue of Pontecorvo processes, but for
bound antibaryons
34
Multifragmentation of compressed nucleus
Initial stage inertial compression of a nucleus
due to inward motion of nucleons induced by a
trapped antibaryon Attractive forces compressing
a superbound nucleus disappear after antibaryon
annihilation break-up of nuclear remnant with
strong radial flow
before
after
35
Multi-quark-antiquark clusters
An antibaryon acts as a strong
attractor for surrounding nucleons forcing them
move towards the center
High density cloud containing and few
nucleons is in fact a relatively cold peace of
quark-gluon plasma
E.g. the whole 4He nucleus could be transformed
into deconfined phase by a deeply bound
p
n
-
-
-
p
p 4He
12q 3q
p
n
Heavy flavors ( ) can be also produced
(pentaquark, heptaquark,)
36
Energy per particle in cold qq matter
-
NJL calculations multi clusters may have
lower energy per particle than pure quark matter
I.N. Mishustin, L.M. Satarov et al., Phys. Rev.
C59 (1999) 3343 C62 (2000) 034901
in GeV
mesoballs with
and binding energy
per pair
pure quark matter at baryon density
37
Conclusions

• New types of nuclear systems containing
  antibaryons are predicted
• strong extra binding
• compressed core (2 - 3)
• reasonable life time
• similar results with reduced N couplings (by
  factor 3)
• Detection in pA reactions at GSI seems feasible
• most promising reactions
• estimated detection rate 1 events/s with
  selection level 10-8
• Possible signatures
• radial collective flow of secondary fragments
• emission of particles within a narrow energy
  range (E 1 GeV)
• production of exotic multi-qq clusters

-
trigger particles
(assuming 100 detector efficiency)
-
38
Outlook

• Nuclear rearrangement dynamics after capture of
  antibaryon
• (inward flow of target nucleons and its
  dissipation into heat)
• Experimental and theoretical studies of
  annihilation in nuclear environment
• Implementing finite widths and imaginary
  potentials into the RMF calculations
• Study of pA reactions within a transport approach
  
• Multifragmentation of nuclear remnant after
  annihilation of antibaryon
• Formation of hybrid nuclei with quark central
  core

-
39
Comparison of LA and KA systems
-
-

• Additional binding energy in should be at
  least

two times larger than in
(two instead of one )

• Life times are determined by the same matrix
• elements, but in different crossing channels

• Absorption rates are proportional to available
  phase

space should be of the same order