Clusters of matter and antimatter

1
Clusters of matter and antimatter

• I.N. Mishustin1,2,3)

1) Kurchatov Institute, Moscow 2) Institute für
Theoretische Physik, J.W. Goethe Universität,
Frankfurt am Main 3) Niels Bohr Institute,
Copenhagen
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
(2002) 206
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The history of antimatter

• The history of antimatter has begun with
  Paul Dirac who suggested his famous
  equation in 1928
• This equation predicted existence of
  antiworld made of antimatter
• Since 1930 search for the possible
  constituents of antimatter, antiparticles,
  began

4
STAR detector at RHIC
Tracks of charged particles in central AuAu
collisions at
5
Antimatter production in laboratory
Significant amount of antimatter can be produced
in laboratory by colliding heavy nuclei with
highest energy RHIC (Brookhaven) AuAu at STAR
experiment ? invariant rapidity densities
(-0.3ltycmlt0.3)
(no 4He detected yet)
Almost baryon-symmetric matter!
BRAHMS experiment ? for and
(0ltycmlt3)
about 200 pairs are produced per event!
This is sufficient to make 208Pb but these
antibaryons are dispersed in the phase space
Light antimatter clusters are formed mainly via
coalescence of antinucleons
More exotic clusters like
can also be formed
6
Dirac picture of the vacuum

• Dirac Lagrangian for a fermion field
• Equation of motion for
• Plane wave solution
• Multiplying by one has for
• for particles with energy
  
• - for antiparticles with
  energy

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Dirac sea

• To ensure stability of matter, Dirac assumed that
  all negative energy states are filled (Dirac
  sea) and antiparticles are holes in this sea
• Now it is known that vacuum has a very
  complicated structure

8
The relativistic mean-field Lagrangian
Interaction terms
9
Parameters approximations

• Three RMF models were used TM1,NL3,NL-Z2
• 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

10
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
11
Wave functions for spherical nuclei
Effective Schrödinger equation
12
Equations for mean meson fields
G-parity
Source densities
Polarization of target matter due to presence of
antibaryons !
13
Infinite matter with antibaryons
-
TM1 calculation EOS of isospin-symmetric NN
matter at T0
Maximum binding energy
for net baryon-free matter
at
NJL model predicts similar results for qq matter
-
-
Binding energy of pO16
close to result for finite nucleus
14
Energy levels (NL-Z2)
Significant rearrangement of nuclear structure
due to the presence of an antiproton i.e. a
hole ( ) in the Dirac sea
15
Nucleon densities
NLZ
NL3
NL3
16
Nucleon densities (NL3)
g. s. deformation
17
Nucleon densities (NL-Z2)
superdense core normal halo
18
Density profiles in 16O and 16O

-
Cold compression of the nucleus induced by an
antibaryon
19
Effect of reduced couplings in 16O
-
p
20
Binding energies of 16O
-
p
Large effect remains even for reduced
couplings ( )
21
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
22
In-medium annihilation rate
From kinetic equation (W.Cassing, Nucl. Phys.
A700 (2002) 618)
? occupation probabilities of
? transition amplitude of
Invariant phase-space volume
23
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
24
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
25
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

26
Life times annihilation widths
-
partial widths of NN annihilation in MeV
Life time of
from numerical calculation
(NL-Z2)
(NL3)
27
Phase-space volume for NN?n
-
Phase-space suppression factors for
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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!
29
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
30
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
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Energy dependence of pp cross sections
-
10 GeV/c
data Particle Data Group
fit M.Bleicher et al., Phys. Lett. B485 (2000)
133
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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
( 0.01 for 10 GeV/c antiprotons)
- takes into account off-shell (binding) effects
( 0.1 is assumed)
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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
34
Cross section of pp??X
-
-
S. Banerjee et al., Nucl. Phys. B150 (1979) 119
3.6 GeV/c
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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

?
-
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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
37
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
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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,)
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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
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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 10 events/s with
  selection level 10-5
• 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)
-
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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

-