Transcript Egzotyczne kształty materii jądrowej dla reakcji Au + Au

Search for hyperheavy toroidal nuclear
structures formed in heavy ion collisions
Anna Sochocka and Roman Płaneta,
M. Smoluchowski Institute of Physics,
Jagellonian University, Cracow, Poland
Motivations:
This idea was introduced by Wilson (1946) and Wheeler ( 1950 ). They
proposed nuclei with new exotic types of topology and investigated the stability
of toroidal nuclei
Stability of systems with exotic shapes:
Siemens and Bethe showed that some bubble nuclei with sufficiently large charge can
be stable against breathing deformation ( monopole oscilations) P.J. Siemens and H.
Bethe, Phys. Rev. Lett 18 (1967) 704-706
 Wong showed that as nuclear temperature increases, the surface tension coefficient
decreases and the Coulomb repulsion is pushing nuclear matter outward leading to the
formation of exotic nuclei
C.Y. Wong,
Wong, Phys.
Phys. Rev.
Rev. Lett 55 ( 1985 ) 19731973-1975
 For heaviest nuclear systems (A > 300)
a pocket of the potential energy even at zero
angular momentum appears for toroidal shape
C. Fauchard, G. Royer, Nucl. Phys. A 598 ( 1996 ) 125 - 138
1
The theoretical analysis of properties of super-heavy
nuclei do not predict any long living nuclei with
compact shapes beyond the island of stability (N ~ 184,
Z ~ 114).
Liquid drop model with shell corrections and Hartree –
Fock – Bogoliubov theory with the Gogny D1S force
calculations have shown that metastable islands of
nuclear bubbles can exist for nucleon numbers in the
range A=450-3000
K. Dietrich, K.Pomorski Phys. Rev. Lett. 80, 37 (1998)
J. Decharge et al. Nucl. Phys.A 716, 55 (2003 )
Predictions of the HFB model with the Gogny D1S force
bubbles
semi - bubbels
ordinary nuclei
typical density profiles
corresponding to the above
configurations
J. Decharge et all. Phys. Lett. B (1999) 275 - 282
The lightest semi bubbels are foreseen around mass A300, while the
true bubble appear at A400, the lighter nuclei prefer ordinary solution
Torus is another topology which is investigated
M.Warda, Int. J. Mod. Phys. E 16, 2 (452-458), 2006
Q 2 - quadrupole moment
RMSR – root mean square radius
d – tube radius
d
Minimum potential
energy for the
toroidal shape
RMSR
Prediction for the toroidal shapes
 The energy of the toroidal minimum decrease relatively to the potential
energy of the spherical configuration with increase of the mass of the
system
 For Z>140 , the global minimum of potential energy corresponds to the
toroidal shape
M. Warda, poster on XIII Nuclear Physics Workshop in Kazimierz 2006
Dynamical model predictions:

BUU transport calculations showed that exotic nuclear shapes
may be created in central heavy ion collisions at intermediate energies
L. G. Moretto et al., Phys. Rev. Lett. 78 ( 1997 824 -827)
y
x
z
x
beam
direction
BUU calculations
Lien-Ven Chen et all. Phys. Rev. C 68 (2003 ) 014605
Boltzmann – Uehling – Uhlenbeck model
The BUU transport equation for the nucleonic one-body density
 
distribution function f = f r , p, t  is given by:
1
d
 
  
3
3
 t    r   r U  p  f r , p, t    2 3  d p2 d p2 d d 12



3 3 
f f 2  1  f1 1  f 2   f1 f 2 1  f 1  f 2 2    p1  p2  p1  p2 

d /d - nucleon-nucleon cross section
v12 - relative velocity for the colliding nucleons,
U - mean-field potential consisting of the Coulomb potential and a nuclear
potential with isoscalar and symmetry terms.

The potential field is approximated by

  
  
U  , z   A    B     1   z Vc  Vnasy
, p  ,  
 0 
 0 
0 - normal nuclear matter density,
, n , p - nucleon, neutron, and proton densities,
z - equals 1 or -1 for neutrons or protons, respectively.
 = (n - p) /( n+ p) – asymmetry parameter
EOS
A[MeV] B[MeV] 
K[MeV]
STIFF
-124.69
74.24
2
380
SOFT
-356
306.1
7/6
200
Simulation results for central collisions of Au+Au
K=200MeV
E=15MeV/nucleon
E=23MeV/nucleon
y
z
E=40MeV/nucleon
y
y
x
x
BUU calculations
z
beam
direction
x
Simulation results for central collisions of Au+Au
K=380 MeV
K=200 MeV
flat sphere
flat bubble
Ksym =61 MeV – red line
E=15 MeV/A
toroid
disc
E=23MeV/A
Central density
 ( x=0, y=0, z=0 )
toroid
toroid
E=40MeV/A
BUU calculations
Ksym =-69MeV – blue line
Simulation results for non-central Au+Au at 23 MeV/A
b=1.25 fm
y
z’
z
y
x

b=3 fm
beam
direction
z
x’
x’
b=8 fm
Time = 200 fm/c
z’
x’
x
y
K=200 MeV
Results for central collisions of 124Sn+124Sn
K=200MeV
E=25MeV/nucleon
E=35MeV/nucleon
z
y
E=50MeV/nucleon
x
BUU calculations
x
Decay characteristics for non compact nuclear
objects (dynamical model predictions)
 more of intermediate mass fragments ( Z > 3 )
should be generated than would be expected for
the decay of a compact object at the same
temperature
 enhanced similarity in the charges of fragments
ETNA – Expecting Toroidal Nuclear
Agglomeration
Flow diagram
ACN = AT + AP
ZCN = ZT + ZP
preequilibrium
nucleons
Non - central collisions are taken into
acount up to give impact parameter b
-minus
Drawing of fragments:
•Gaussian distribution
Partition of the available energy:
Eava = ECM + Q –ECOULOMB
Acceleration in mutual Coulomb field
Established : Zi , Ai ; i = 1,N ( N=5 )
Detection of particles in the CHIMERA
All the fragments are placed in ball,
bubble and toroidal configuration with
additional condition: Rij > Ri + Rj + 2fm
detector
,   detector number  rand ,rand
Ethr=1 MeV/A
Global characteristics of ETNA code
simulation for Au+Au
Definition of sphericity and coplanarity
From the Cartesian components of fragment (Z 5) momenta in the centre
of mass one may construct the tensor
Fi ,
j
pi n  p jn 
 n 
n p

 n 
p
n
where p(n) i is the i-th Cartesian momentum component of the n-th
particle, and is the n-th fragment momentum vector. For eigenvalues
t1 < t2 < t3 of the tensor F one dehines the reduced quantities:
qi 
ti2
2
t
j j
Then sphericity and coplanarity parameters are defined as:
3
S  1  q3 
2
C
3
q2  q1 
2
ETNA`s simulation results
ETNA`s simulation results

ij , kl
 


(vi  v j )  (vk  vl )
planarity
Conclusions
 Microscopic models of the nuclear system predict that
for Z>130 the exotic shapes ( bubbles, toroids ) corresponds
to the stable configuration of very heavy nuclear matter
The threshold energy for toroidal shapes formation decrease with
increasing mass of the system ( BUU predictions )
This threshold energy depends on the stiffness of the nuclear
equations of the state ( BUU predictions )
 Preliminary predictions of ETNA code indicate that at 23 MeV/A
the proposed signitures able to distinguish between different
freeze-out configurations
 Comparison with other dynamical models in progress
Conclusions
Przewidywania modeli mikroskopowych wskazuja na egzotyczne
ksztalty dla systemow o duzych masach
bedacych w rownowadze
Energia progowa na formowanie sie toroidalnych ksztaltow maleje wraz
z rosnaca masa zderzajacych sie jader
Dla rownania stanu ksztalty toroidalne tworza sie przy wyzszych
energiach w porownaniu dla przewidywan dla
miekkiego rownania stanu
Characterizaton of the dynamical models
Vlasov model – paricles experience only the
self – consistent effective field, leading to a single
dynamical trajectory
Boltzman model – various possible outcomes
of the residual collisions are being averaged at each step,
leading to a different but still single dynamical trajectory
Langevin model – various stochastic collisions
Vlasov
Boltzman
Langevin
outcomes to develop independently, leading to a continual
trajectory branching, corresponding ensemble of histories
A.Sochockag*, C.Agodia, R.Albaa, F.Amorinia, A.Anzalonea, L.Auditored, V.Barane, I.Berceanue, J.Blicharskaf, J.Brzychczykg, B.Borderieh, R.Bougaulti, M.Brunoj,
G.Cardellab, S.Cavallaroa, R.Coniglionea, M.B.Chatterjeek, A.Chbihil, J.Ciborm, M.Colonnaa, M.D’Agostinoj, E.DeFilippob, R. Dayraso, A.DelZoppoa, M.DiToroa,
J.Franklandl, E.Galicheth, W. Gawlikowiczg, E.Geracij, F.Giustolisia, A.Grzeszczukf, P.Guazzonip, D.Guinetq, P.Hachaju, M.Iacono-Mannoa, S.Kowalskif, E. La Guidaraa,
G.Lanzanòb, G.Lanzalonea, C.Maiolinoa, N.LeNeindreh, N.G.Nicolist , Z.Majkag, A.Paganob, M.Papab, M.Petrovicie, E.Piaseckir, S.Pirroneb, R.Płanetag, G.Politib, A.Pope,
F.Portoa, M.F.Riveth, E.Rosatos, F.Rizzoa, S.Russop, P.Russottol, D.Santonocitoa, M.Sassip, K.Schmidtf, K.Siwek-Wilczyńskar, I.Skwirar, M.L.Sperdutob, L.Świderskir,
A.Trifiròd, M.Trimarchid, G.Vanninij, G.Verdeb, M.Vigilantes, J.P.Wieleczkol, J.Wilczyńskic, L.Zettap, and W.Zipperf
CHIMERA - ISOSPIN Collaboration
a) INFN, Laboratori Nazionali del Sud and Dipartimento di Fisica e Astronomia, Università di Catania, Italy
b) INFN, Sezione di Catania and Dipartamento di Fisica e Astronomia, Università di Catania, Italy
c) A. Sołtan Institute for Nuclear Studies, Swierk/Warsaw, Poland
d) INFN, Gruppo Collegato di Messina and Dipartamento di Fisica, Università di Messina, Italy
e) Institute for Physics and Nuclear Engineering, Bucharest, Romania
f) Institute of Physics, University of Silesia, Katowice, Poland
g) M. Smoluchowski Institute of Physics, Jagellonian University, Cracow, Poland
h) Institute de Physique Nuclèaire, IN2P3-CNRS, Orsay, France
i) LPC, ENSI Caen and Universitè de Caen, France
j) INFN, Sezione di Bologna and Dipartimento di Fisica, Università di Bologna, Italy
k) Saha Institute of Nuclear Physics, Kolkata, India
l) GANIL, CEA, IN2P3 – CNRS, Caen, France
m) H. Niewodniczanski Institute of Nuclear Physics, Cracow, Poland
o) DAPNIA / SPhN, CEA – Saclay, France
p) INFN, Sezione di Milano and Dipartimento di Fisica, Università di Milano, Italy
q) IPN, IN2P3 – CNRS and Universitè Claude Bernard, Lyon, France
r) Institute for Experimental Physics, Warsaw University, Warsaw, Poland
s) INFN, Sezione Napoli and Dipartamento di Fisica, Università di Napoli, Italy
t) Department of Physics, University of Ioannina, Ioannina, Greece
u) Cracow University of Technology, Cracow, Poland
* Corresponding author, e-mail: [email protected]
Outlook
Incorporation of angular momentum into the ETNA code
Additional calculation with BUU code
Introduction of novel signatures of exotic shapes
Test of signatures for systems with different masses:
Au+Au @ 40 MeV/nucleons; INDRA, GSI
U+U @ 24 MeV/nucleons; INDRA, GANIL
Sn + Sn @ 35 MeV/nucleon, CHIMERA, INFN-LNS
Definition of sphericity and coplanarity
From the cartesian components of fragment Z 5 momenta in
the centre of mass may construct the tensor
Fi ,
j
pi n  p jn 
 n 
n p

 n 
n p
where p(n) i is the i-th Cartesian momentum component of
the n-th particle, and is the n-th fragment momentum
vector.
Main axis of events
flow
Beam direction
Events selection for central collisions
Total reaction cross section
R = 6500 mb
events located in „3”
are well measured
events :
120 Ztot  ( ZP+ZT =156)
0.8  Ptot II /Pproj  1.1
 = 93mb
II
J.D Frankland et al., Nucl. Phys. A 689 (2001),905-939
Definition of TKE
TKE – total mesured c.m kinetic energy of detected
charged products
TKE = EC.M + Q -  Eneutron -  E
Where EC.M , Q,  Eneutron,  E are the available centre of mass
energy, the mass balance of the reaction and total neutron and gamma ray
kinetic energies, respectively
Events selection
flow  700
 = 2,6 mb
G.Tabacaru Nucl. Phys. A 764 ( 2006 ) 371-386
Results
The average kinetic energy
of the largest fragment is
smaller than energy of the
other fragments and show
maximum for Z30-35
simulation
date
G.Tabacaru Nucl. Phys A 764 ( 2006 ) 371-386
Ftotal
In the region Z=15-25 the
heaviest fragment, Zmax,
has always the lowest
average kinetic energy
simulation
date
G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386
G.Tabacaru Nucl.Phys A 764 ( 2006 ) 371-386
BOB simulation
The one body density evolution calculated in a Boltzmann-NordheimVlasov approach (BNV) up to 40 fm/c (the instant of maximum
compression) after Brownian One Body (BOB) dynamics
i ) Zi,j5
ii ) 5  Zi,j 20
iii ) Zi  Zmax
Black line – experimental data
Red symbols - dynamical simulation
G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386
Here is the place for other event
geometries
L
2,6 mb
35
Sharp cut off approximation
Experimatal event selection
1500
L [hbar]
Binding energy per nucleon e( ,  ) as a function of
density  and isospin asymmetry parameter  :
e,    e, 0   2esym  
Where:
n   p


N - density of neutron
 P - density of proton
L     0  K sym
 
esym    esym  0   
3   0  18
2

esym
2
K sym  9 0

2
  0
2
   0 

  
 0 
Experimental observables
1  R (vred ) 

Y
(
p

2
1,
C

Y
(
p
 b 1,

p2 )

p2 )
where:
 
Y2 ( p1, p2 )
- two particle coincidence yield
 
Yb ( p1, p2 )
- background yield obtained by event mixing
 
vij  vi  v j
v red =
- relative velocity
vij
Zi  Z
- reduced velocity
j
-
Space distribution of fragments for
disc and torus configurations; (  = 0/3 )
Au+Au at 15 MeV/nucleons
y
z
x
beam
direction
Invariant velocity plots
Au+Au at 15 MeV/nucleons
d 
vtr dvtr dvz
2
Common temperature
General decay characteristics for
Au + Au reaction at 15 MeV/nucleons
Common
temperature
Granulation of the CHIMERA detector taken into account
Simulation predictions
Planarity is able to
disantangle between ball,
disc and toroidal shapes
for the heavy Au + Au
system and unable for the
lighter system
Simulation predictions
Noticeable differences in
1+R function are observed
for the heavier system, for
the lighter system are less
visible
Definition of 1+R correlation function
1  R (vred ) 

Y
(
p

2
1,
C

 Yb ( p1 ,

p2 )

p2 )
where:
 
Y2 ( p1, p2 )
 
Yb ( p1, p2 )
 
vij  vi  v j
- two particle coincidence yield
-background yield obtained by event mixing
- relative velocity
vij
v red =
Zi  Z
- reduced velocity
j
G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386
G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386
Summary and conclusions:
 preliminary simulations with ETNA code were performed
 observables discriminating different exotic shapes were
found ( 1+R, planarity) for heavy Au + Au system, for lighter
Sn + Sn system discrimation is less obvious
 it is necessery to performed additional simulations for
more realistic mass distribution ( experimental data )
 simulations with dynamical models are necessery in order
to rushed more light at the dynamics of exotic systems
formation
Angular momentum
Eavailable=E *( T ) + Eth( T )
Invariant velocity plots
Eavailable = E*
Eth=0
Energia wzbudzenia
E = E*
Hachaj prescription
Eavailable
=Etermicznego
th
Energia
ruchu
E*=
E =0ETh
BUU predictions for central collisions
of Mo + Mo at 75 MeV/nucleon
K = 200 MeV
K = 540 MeV
20fm/c
60fm/c
120fm/c
180fm/c
Temperature T
Common temperature of thermal motion and fragments excitation
Hachaj prescription
Gaussian distribution
Common temperature of thermal
motion and fragments excitation
N


Eava   Ei * ( T )  EiTh ( T ) ; E *  aT 2 , E Th 
i 1
3
kT
2
Detector 850; 305m Si;  =74o
16O + Au _60MeV
We observed energy
spectrum for oxygen in
reaction 16O + Au at
60MeV
Elastic scattering
Elab_p vs yield abs(theta_p-74o ).lt. 4o
Detector 850; 305m Si;  =74o
58Ni + Au _100MeV
We observed energy spectrum
for nickel in reaction
58Ni + Au at 100MeV
Elastic scattering
Elab_p vs yield abs(theta_p-74o ).lt. 4o
Detector 850; 305m Si;  =74o
16O + Au _100MeV
We observed energy spectrum for
oxygen in reaction 16O + Au at
100MeV
Elastic scattering
Elab_p vs yield abs(theta_p-74o ).lt. 4o
Detector 850; 305m Si;  =74o
16O + Au at 60MeV
E160 el. scater. = 52.25MeV
16O + Au at 100MeV
E 160 el. scater. = 88.02MeV
58Ni + Au at 100MeV
E 58Ni el. scater. = 88.02MeV
Calculations
Detector 850; 305m Si;  =74o
Au + C at 15MeV/A
Alpha line
Desilpg
Time
218.31
2565.1
272.3
2599.5
Experimental
data
Carbon line
Desilpg
Time
218.31
2565.1
272.3
2599.5
3H punch through
Desilpg
205.62
Time
2605
208.13
2612.5
Simulation results for central
collisions Ar + Sc at
80 MeV/nucleon
10fm/c
50fm/c
100fm/c
150fm/c
Decay characteristics for non
compact nuclear objects
( model predictions)
 more of intermediate mass fragments
( Z > 3 ) should be generated than would
be expected for the decay of a compact
object at the same temperature
 enhanced similarity in the charges of
fragments
 suppressed sphericity in the emission
of fragments
y
BUU calculations
D.O. Handzy et al. Phys. Rev. C 51, 2237 (1995)
x
z
beam
direction
Detector 850; 305m Si;  =74o
Au + Au at 15MeV/A
Au fission
Desilpg
Time
262.77
2339.3
Alpha punch through
Ealpha = 24.7 Mev
637.47
2479
Experimental
data
Mass spectrum
Au + C at 15MeV/A

C
Yield vs mass
BUU equation is solved by test – particle method
Each nucleon is replaced by N test- particles
NA - number of nucleons A nucleus
NB - number of nucleons B nucleus
A
B
NA *
N
+
NB *
N
=
( NA +NB )*N
 ( r ) = N’/[N(NA + NB )]( r )3
N’ - number of test particles in small volume ( r
Test particles collide with a cross section nn/N
)3 around
the point

r
Multiplicity distribution of the heavy fragments
R=8 barn
 / R =3,5% for b=3fm