Title: Clusters of matter and antimatter
1Clusters of matter and antimatter
1) Kurchatov Institute, Moscow 2) Institute für
Theoretische Physik, J.W. Goethe Universität,
Frankfurt am Main 3) Niels Bohr Institute,
Copenhagen
2Contents
 Introduction
 Strongly bound systems
  RMF formalism using parity
  infinite systems with and
  finite  nuclear systems
  antihypernuclei
  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
3The 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
4STAR detector at RHIC
Tracks of charged particles in central AuAu
collisions at
5Antimatter 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 baryonsymmetric 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
6Dirac 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
7Dirac 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
8The relativistic meanfield Lagrangian
Interaction terms
9Parameters approximations
 Three RMF models were used TM1,NL3,NLZ2
 The model parameters were adjusted to reproduce
properties of nuclei from to  Gparity 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
10Dirac equations for fermion fields
Scalar potential generating
effective mass
Vector potential
Gparity for (
)
Optical potentials
at normal density 0.15 fm3
where isospin,
Coulomb terms
11Wave functions for spherical nuclei
Effective Schrödinger equation
12Equations for mean meson fields
Gparity
Source densities
Polarization of target matter due to presence of
antibaryons !
13Infinite matter with antibaryons

TM1 calculation EOS of isospinsymmetric NN
matter at T0
Maximum binding energy
for net baryonfree matter
at
NJL model predicts similar results for qq matter


Binding energy of pO16
close to result for finite nucleus
14Energy levels (NLZ2)
Significant rearrangement of nuclear structure
due to the presence of an antiproton i.e. a
hole ( ) in the Dirac sea
15Nucleon densities
NLZ
NL3
NL3
16Nucleon densities (NL3)
g. s. deformation
17Nucleon densities (NLZ2)
superdense core normal halo
18Density profiles in 16O and 16O

Cold compression of the nucleus induced by an
antibaryon
19Effect of reduced couplings in 16O

p
20Binding energies of 16O

p
Large effect remains even for reduced
couplings ( )
21Antibaryon 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 4momenta)
Within semiclassical approximation
where inmedium effective mass
22Inmedium annihilation rate
From kinetic equation (W.Cassing, Nucl. Phys.
A700 (2002) 618)
? occupation probabilities of
? transition amplitude of
Invariant phasespace volume
23Rate 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
24Partial annihilation widths
Integration over target volume
Inmedium partial width
 vacuum partial width at rest (
),
normalized to
for
Phasespace suppression factor
Overlap integral
Reduced available energy in medium
25Characteristics 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
26Life times annihilation widths

partial widths of NN annihilation in MeV
Life time of
from numerical calculation
(NLZ2)
(NL3)
27Phasespace volume for NN?n

Phasespace suppression factors for
28Multinucleon annihilation
Pontecorvolike 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!
29Multinucleon 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
30Formation 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
31Energy dependence of pp cross sections

10 GeV/c
data Particle Data Group
fit M.Bleicher et al., Phys. Lett. B485 (2000)
133
32Probability 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 offshell (binding) effects
( 0.1 is assumed)
33Production rates of superbound nuclei
Rate of reaction
where luminosity of beam 21032
cm2 s1 (planned at GSI)
For 10 GeV/c central collisions and
For reduction factor due to
conversion
in reactions
34Cross section of pp??X


S. Banerjee et al., Nucl. Phys. B150 (1979) 119
3.6 GeV/c
35Observable signatures
 Supertransitions from Fermi to Dirac sea
 onebody 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
?

36Annihilation 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
37Multifragmentation 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 breakup of nuclear remnant with
strong radial flow
before
after
38Multiquarkantiquark 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
quarkgluon 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,)
39Energy 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
40Conclusions
 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 105  Possible signatures
 radial collective flow of secondary fragments
 emission of particles within a narrow energy
range (E 1 GeV)  production of exotic multiqq clusters

trigger particles
(assuming 100 detector efficiency)

41Outlook
 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
