Search for hyperheavy toroidal nuclear structures formed in heavy ion collisions Anna Sochocka and...

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

1

This idea was introduced by Wilson (1946) and Wheeler ( 1950 ). Theyproposed nuclei with new exotic types of topology and investigated the stability of toroidal nuclei

Motivations:Motivations:

Stability of systems with exotic shapesStability 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. P.J. Siemens andSiemens and H. H. BetheBethe, , PhysPhys. . RevRev. . LettLett 18 18 (1967(1967) ) 704704--706 706

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. C.Y. WongWong, , PhysPhys. . RevRev. . LettLett 55 ( 1985 ) 55 ( 1985 ) 19731973--1975 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

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=450-3000K. 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 aboveconfigurations

The lightest semi bubbels are foreseen around mass A300, while the true bubble appear at A400, the lighter nuclei prefer ordinary solution

J. Decharge et all. Phys. Lett. B (1999) 275 - 282

Q 2 - quadrupole moment

RMSR – root mean square radius

d – tube radius

Torus is another topology which is investigated

M.Warda, Int. J. Mod. Phys. E 16, 2 (452-458), 2006

Minimum potential energy for the toroidal shape

RMSR

d

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 predictionsDynamical 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.L. G. Moretto et al.,, Phys. Rev. Lett. 78 ( 1997 Phys. Rev. Lett. 78 ( 1997 824824 - -827827))

Lien-Ven Chen et all. Phys. Rev. C 68 (2003 ) 014605

BUU calculations

zbeam

direction

x

y

x

Boltzmann – Uehling – Uhlenbeck model

The BUU transport equation for the nucleonic one-body density distribution function f = is given by: tprf ,,

212133

221212

1223

23

3

21111

2

1,,

ppppffffffff

d

ddpdpdtprfU

t prr

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

,1, ,00

asypnczz VVBAU

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

BUU calculations

y

y

xx

zbeamdirection

E=15MeV/nucleon

E=23MeV/nucleon

E=40MeV/nucleon

K=200MeV

y

z

x

Simulation results for central collisions of Au+Au

Ksym =-69MeV – blue line

Ksym =61 MeV – red line

K=200 MeV K=380 MeV

flat bubble

toroid

toroid

flat sphere

disc

toroid

Central density ( x=0, y=0, z=0 )

E=15 MeV/A

E=23MeV/A

E=40MeV/A

BUU calculations

y

x’

Simulation results for non-central Au+Au at 23 MeV/A

z

xy

x

y

zx’

z’

z’

beamdirection

K=200 MeV

x’

b=1.25 fm

b=3 fm

b=8 fm

Time = 200 fm/c

Results for central collisions of 124Sn+124Sn

y

x

z

x

E=35MeV/nucleon

E=50MeV/nucleon

E=25MeV/nucleon

K=200MeV

BUU calculations

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

Drawing of fragments:

•Gaussian distribution

Established : Zi , Ai ; i = 1,N ( N=5 )

All the fragments are placed in ball, bubble and toroidal configuration with additional condition: Rij > Ri + Rj + 2fm

ACN = AT + AP

ZCN = ZT + ZP

-minus preequilibrium nucleons Partition of the available energy:

Eava = ECM + Q –ECOULOMB

Acceleration in mutual Coulomb field

Detection of particles in the CHIMERA

detector

, detector number rand ,rand

Non - central collisions are taken into acount up to give impact parameter b

Ethr=1 MeV/A

Global characteristics of ETNA codesimulation 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

n

n

n n

nj

ni

jip

p

pp

F

,

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:

j j

ii t

tq

2

2

Then sphericity and coplanarity parameters are defined as:

312

3qS 122

3qqC

ETNA`s simulation results

ETNA`s simulation results

)()(,

lkjklij

i vvvv

planarityplanarity

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 nuclearequations of the state ( BUU predictions )

Preliminary predictions of ETNA code indicate that at 23 MeV/Athe 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 dlamiekkiego rownania stanu

Vlasov Boltzman Langevin

Characterizaton of the dynamical models

Vlasov model – paricles experience only the self – consistent effective field, leading to a singledynamical 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 outcomes to develop independently, leading to a continualtrajectory 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

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]

CHIMERA - ISOSPIN Collaboration

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

Beam direction

Main axis of events

Definition of sphericity and coplanarity

flow

n

n

n n

nj

ni

jip

p

pp

F

,

where p(n) i is the i-th Cartesian momentum component of

the n-th particle, and is the n-th fragment momentum vector.

From the cartesian components of fragment Z 5 momenta in the centre of mass may construct the tensor

Events selection for central collisions

events located in „3” are well measured events :

120 Ztot ( ZP+ZT =156)

0.8 Ptot II /Pproj 1.1

= 93mb

J.D Frankland et al., Nucl. Phys. A 689 (2001),905-939

II

Total reaction cross sectionR = 6500 mb

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 massenergy, 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

The average kinetic energyof the largest fragment is smaller than energy of theother fragments and show maximum for Z30-35

G.Tabacaru Nucl. Phys A 764 ( 2006 ) 371-386

simulationdate

Ftotal

Results

simulationdate

G.Tabacaru Nucl.Phys. A 764 ( 2006 ) 371-386

In the region Z=15-25 the heaviest fragment, Zmax, has always the lowest average kinetic energy

G.Tabacaru Nucl.Phys A 764 ( 2006 ) 371-386


i ) Zi,j5

ii ) 5 Zi,j 20

iii ) Zi Zmax

Black line – experimental dataRed symbols - dynamical simulation

The one body density evolution calculated in a Boltzmann-Nordheim-Vlasov approach (BNV) up to 40 fm/c (the instant of maximum compression) after Brownian One Body (BOB) dynamics

BOB simulation

35L [hbar]1500

L

2,6 mb

Sharp cut off approximation

Experimatal event selection

Here is the place for other event geometries

02

2209

symsym

eK

2

0

0

0

00 183

symsymsym

KLee

symeee 20,,

pn

Binding energy per nucleon e( , ) as a function of density and isospin asymmetry parameter :

Where:

N - density of neutron

P - density of proton

Experimental observables

)(1 redvR

),(

),(

21

212

ppY

ppYC

b

where:where:

),( 212 ppY

- two particle coincidence yieldtwo particle coincidence yield

),( 21 ppYb

- background yield obtained by event mixingbackground yield obtained by event mixing

jiij vvv

- relative velocityrelative velocity

v red =ji

ij

ZZ

v

- reducereducedd velocity velocity

--

Space distribution of fragments fordisc and torus configurations; ( = 0/3 )

x

y

beam direction

z

Au+Au at 15 MeV/nucleons

Invariant velocity plots

Common temperature

ztrtr dvdvv

d 2

Au+Au at 15 MeV/nucleons

General decay characteristics for Au + Au reaction at 15 MeV/nucleons

Granulation of the CHIMERA detector taken into account

Common temperature

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

Simulation predictions

)(1 redvR

),(

),(

21

212

ppY

ppYC

b

),( 212 ppY

),( 21 ppYb

jiij vvv

v red = ji

ij

ZZ

v

where:where:

- two particle coincidence yieldtwo particle coincidence yield

-background yield obtained by event mixingbackground yield obtained by event mixing

- - relative velocityrelative velocity

- reducereducedd velocity velocity

Definition of 1+R correlation function

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

E = E*

Energia wzbudzenia

Energia ruchu termicznegoE = ETh

Eavailable = E*Eth=0

Eavailable =Eth

E*= 0

Hachaj prescription

BUU predictions for central collisions of Mo + Mo at 75 MeV/nucleon

K = 200 MeV K = 540 MeV

20fm/c

60fm/c

120fm120fm/c/c

180fm/c

Common temperature of thermal motion and fragments excitation

Temperature T

kTEaTETETEE ThN

i

Thiiava 2

3,*;)()(* 2

1

Common temperature of thermal motion and fragments excitation

Hachaj prescription Gaussian distribution

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; 305m Si; =74o

58Ni + Au _100MeV

We observed energy spectrum for nickel in reaction 58Ni + Au at 100MeV



Elastic scattering

16O + Au _100MeV

We observed energy spectrum for oxygen in reaction 16O + Au at 100MeV

Elastic scattering




16O + Au at 60MeV

E160 el. scater. = 52.25MeV

E 160 el. scater. = 88.02MeV

16O + Au at 100MeV

58Ni + Au at 100MeV

E 58Ni el. scater. = 88.02MeV

Calculations

Alpha line

Desilpg 218.31 272.3 Time 2565.1 2599.5

Carbon line

Desilpg 218.31 272.3 Time 2565.1 2599.5

3H punch through

Desilpg 205.62 208.13Time 2605 2612.5


Au + C at 15MeV/A

Experimentaldata

Simulation results for central collisions Ar + Sc at 80 MeV/nucleon

10fm/c 50fm/c 100fm/c 150fm/c

x

y

zbeam direction

BUU calculations

D.O. Handzy et al. Phys. Rev. C 51, 2237 (1995)

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


Au + Au at 15MeV/A

Au fission

Desilpg 262.77 637.47Time 2339.3 2479

Alpha punch through

Ealpha = 24.7 Mev

Experimentaldata

Mass spectrum

Au + C at 15MeV/A

Yield vs mass

C

BUU equation is solved by test – particle method

Each nucleon is replaced by N test- particles

NA - number of nucleons A nucleusNB - number of nucleons B nucleus

NB * NNA * N

A B=+ ( NA +NB )*N

( r ) = N’/[N(NA + NB )]( r )3

N’ - number of test particles in small volume ( r )3 around the point

Test particles collide with a cross section nn/N

r

Multiplicity distribution of the heavy fragments

R=8 barn / R =3,5% for b=3fm

Search for hyperheavy toroidal nuclear structures formed in heavy ion collisions Anna Sochocka and...

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