Michela D'Agostino Bologna

University INFN-Bologna (Italy)

Eurisol and the nuclear EOS: experimental Eurisol and the nuclear EOS: experimental challengeschallenges

Eurisol and the nuclear EOS: experimental Eurisol and the nuclear EOS: experimental challengeschallenges

Keyword from the 2003 Eurisol report: Keyword from the 2003 Eurisol report: IsospinIsospin

Level density parameter dependence on Level density parameter dependence on (N,Z)(N,Z)

Liquid gas phase transition Liquid gas phase transition Isospin effects and symmetry term of the Isospin effects and symmetry term of the

EOSEOS

Isospin effects in semi-peripheral Heavy-Ion Isospin effects in semi-peripheral Heavy-Ion reactions: symmetry term of the EOSreactions: symmetry term of the EOS

Keyword from the 2003 Eurisol report: Keyword from the 2003 Eurisol report: IsospinIsospin

Level density parameter dependence on Level density parameter dependence on (N,Z)(N,Z)

Liquid gas phase transition Liquid gas phase transition Isospin effects and symmetry term of the Isospin effects and symmetry term of the

EOSEOS

Isospin effects in semi-peripheral Heavy-Ion Isospin effects in semi-peripheral Heavy-Ion reactions: symmetry term of the EOSreactions: symmetry term of the EOS

Thermodynamics Thermodynamics of a single sourceof a single source

Dynamics of Dynamics of many-sources many-sources

1. Are we ready to do this?2. What do we need to improve?

It depends on the approximation wecan accept

Heavy Ion collisionsHeavy Ion collisionsHeavy Ion collisionsHeavy Ion collisions

~100 fm/c

DDEETTEECCTTOORR

~20 fm/c(10-22 sec)

~100÷1000 fm/c

~1014 fm/c

Vacuum (10-6 mb)

Expansion

γ emission

Freeze-outconfiguration

124Sn+ 124Sn, E/A = 50 MeV/A b = 6 fm

Freeze-outconfiguration

80 fm/c(2.4x10-22 sec)

180 fm/c(5.4x10-22 sec)

DDEETTEECCTTOORR

Secondary decays

~÷1000 fm/c ~1014 fm/c

In event by event measurements statistical, multidimensional analyses

allow a centrality sorting

H.I. collisions: 1-st generation 4π devices

•The decaying system can be identified and its calorimetric excitation energy results from the energy balance:

nnni

M

ii kmMkmmE

)(*1

0

•Zi, ki, θi, φi are measured for almost all charged products, event by event, with high energy resolution (few %) and low energy thresholds (gas detectors)

•Statistical multidimensional analyses performed on global (event) observables allow to sort the events in classes of centrality.

•Fragments and particles are detected at ~1014 fm/c, as they were at 103 fm/c, since the propagation in vacuum does not allow further interactions with matter.

•mi are measured only for light products•neutrons and γ are not detected

Sorting the events: multidimensional Sorting the events: multidimensional analysisanalysis

Central collisions: one source

),(i,j wppT kM

k

k

j

k

iij31

1

)()()(

Central collisionsAu+C Au+Cu Au+Cu Au+Au*=1.5 *=3 *=4.5 *=7 A.MeV

Nucl.Phys.A 724 (2003) 455

25 AMeV 35 AMeVCentral collisions

Au+C Au+Cu Au+Cu Au+Au*=1.5 *=3 *=4.5 *=7 A.MeV

Nucl.Phys.A 724 (2003) 455

Central collisionsAu+C Au+Cu Au+Cu Au+Au*=1.5 *=3 *=4.5 *=7 A.MeV

Nucl.Phys.A 724 (2003) 455

25 AMeV 35 AMeV

Multics-NPA724 (2003) 329

Filtered CMD model

E. Geraci et al.,NPA732(2004)173,NPA734 (2004)524

Z>8 open circles >18 full points >28 open squares >38 full squares >48 open triangles >58 full triangles >68 open crosses

MulticsNPA734(2004)487

Vbeam

A Z

Z,A for

light Ions

124Sn+64Ni 35MeV/APeripheral

collisions: many sources

Chimeradata

1-st generation 4π devices & stable beams (V.Viola, R.Bougault-WCI-2005 TexasA&M)

• For all multifragmentation experiments,  the region in which there is a dramatic change in reaction observables corresponds to  E*/A =  5 +/-1 A.MeVWithin a phase-transition scenario, this value represents the transition energy.

Multics-NPA724 (2003) 329

Central collisions

• The current state of nuclear calorimetry permits determination of the E*/A of the fragmenting source to an accuracy of about 20%.Nearly all experiments can be made self-consistent within this range

Multics: Central from Z0=85 to Z0=100 (lines)Multics: Au peripheral Z0=79 (symbols)

Isis: π+Au 8 GeV/c NPA734(2004)487

Fasa: p,α+Au 4-14 GeV NPA709(2002)392

Z-2.1

J. Pochodzalla et al, PRL 75, 1040 (1995)

For the caloric curve one needs to measure:

• Heavy residue (or QP)

• Slopes of 1-st chance l.c.p. energy spectra

• Isotopes (for double ratios)

Temperature and caloric curveTemperature and caloric curve

R. Wada et al., PRC 39, 497 (1989)

N.Le Neindre et al , NIM A490 (2002) 251

Sequential feeding?

T from double ratios: Y(He3)/Y(He4) Y(Li6)/Y(Li7)

TB

p

n1 e)Z,N(Y

)Z,Y(N

: nuclei)mirror(forratioIsobaric

22

1

V1=V2

Isotope analysis

Symmetry energy and free nucleon densities

E. Geraci, et al., Nucl. Phys. A 732 (2004) 173, Nucl .Phys. A734 (2004) 524

ZN

NiSn

NiSn e)Z,N(Y

)Z,N(Y)Z,N(R

:ratioIsotopic

58112

64124

21

2

2

2

1

AZ

AZ

TCsym

TB

p

n1 e)Z,N(Y

)Z,Y(N

: nuclei)mirror(forratioIsobaric

22

1

= 0.44 ± 0.01

Symmetry Energy~18-20 MeV

112,124Sn+58,64Ni 35 AMeV central collisionsCHIMERA-REVERSE Experiment

Δ(Z/A)²

D.Shetty et al., P. R.C 70 (2004) 011601

E.Geraci et al.,NPA732(2004)A.Botvina et al., PRC65(2002):

Extraction of symmetry energy

Asy-softAsy-stiff

Sequential feeding?

Experiments with n-rich/poor systemsExperiments with n-rich/poor systems 3232S+S+58,6458,64Ni 14.5 AMeVNi 14.5 AMeV 3-IMF events3-IMF eventsExperiments with n-rich/poor systemsExperiments with n-rich/poor systems 3232S+S+58,6458,64Ni 14.5 AMeVNi 14.5 AMeV 3-IMF events3-IMF events

Before drawing conclusions on temperature, densities:Isotope emission time scales have to be checked through correlation functions

nucl-ex collaboration&garfield@LNLnucl-ex collaboration&garfield@LNL

Observed 35 resonances, from He4 (d+d) to Ne20 (a+O16) A rough calculation of “feeding correction” through correlation functions suggests an increase of T by 0.5 MeV for few % of decrease in the He4 yield

J.B. Natowitz et al., PRC 65, 034618 (2002)

N=Z

J.Besprosvany and S.Levit - PLB 217 (1989) 1

Al-Quraishi PRC63,065803(2001)

114,145Xe + 40,48Ca Ebeam=20-100 A.MeV ε*= 3-7 A.MeV

Level density (N,Z)Level density (N,Z)Level density (N,Z)Level density (N,Z)

Position-se

nsitive h

odoscope

Pochodzalla et al., PRC35 (1987)1695

t-α correlation function (Li7*)

m=multiplicity, N=number of detectors•ε (m) = ε(1)m •P(double)=(m-1)/(2N)

A reasonable compromise is P(double)<5%For m=3 N=10

Resonance spectroscopyResonance spectroscopyResonance spectroscopyResonance spectroscopy

Why many-bodyWhy many-bodycorrelations?correlations?

R.J. Charity et al., PRC63 024611 60Ni+100Mo 11 A.MeV

α-particles

α-α

Δθ≈ 0.6o high granularitybut in a limited angular coverage & not HR full identification

Neck emission in semi-peripheral collisions

58Ni + 112Sn at 35AMeV CHIMERA

MC with only statistical evaporation

QT QPfiltered

-Midvelocity LCP and fragments seem to be compatible with two sources, one “prompt”, the other like a “surface component”. This can be the evolution of the fast oriented fission for the most asymmetric splits

See: Di Toro et al. Prog.Part.Nucl.Phys 53(2004),81 -- A.Chernomoretz et al. PRC 65(2002)054613

Midvelocity Emissions: which origin?S.Piantelli et al. Phys.Rev.Lett.88(2002),052701

A.Mangiarotti et al. Phys.Rev.Lett93(2004)232701

Isospin effects: strange ‘chemical’ behaviour for midvelocity particles

Statistical Evaporation

-N/Z for hydrogen is in good agreement with statistical codes

Only protons N/Z=0

Only deuterons N/Z=1

Sn+Sn @ 38AMeV Preliminary

S.Piantelli et al.

(in preparation)

TKEL

N/ZFor Midvel emission we have a large neutron enrichment. Multifragmentation? Isospin Distillation?

THE HYDROGEN CASE

Neck emission in semi-peripheral collisions

Thermodynamics of finite systems:Thermodynamics of finite systems:phase transitionphase transition

We can back-trace from data

•the average volume of the system (Coulomb trajectories)

E*= Econfig + Ekin

E*= Ecoul(V)+Qv+ Eint(T)+Etr(T)

Events sorted as a function of E* (calorimetry)

•the temperature T

under the constraint of energy conservationMultics-Nucl.Phys.A699(2002)795

nnni

M

ii kmMkmmE

)(*1

0

<Ekin>=(3/2) <m-1>T+<aAIMF>T2

Microcanonical heat capacity from Microcanonical heat capacity from fluctuationsfluctuations

Ph.Chomaz , F.Gulminelli, NPA 647(1999) 153

The system being thermodynamically characterized:

Multics-PLB473 (2000) 219;NPA699 (2002) 795;NPA734 (2004) 512; NPA749(2005) 55

Microcanonical fluctuations

larger than the canonical expectation? Then

1-st order phase transition

Ckin/C = 1-2kin/2

can

where:

2can=T2Ckin=T2d<Ekin>/dT

Heat capacity from fluctuations Heat capacity from fluctuations

Grey area: peripheral collisions

Points: central collisions:

Indra: NPA699(2002)795

Au+C Au+Cu Au+Au

Multics:PLB473 (2000) 219NPA699 (2002) 795NPA734 (2004) 512NPA749(2005) 55

E*/A0(AMeV)

+ new analyses by Indra@GSI

Average values and variances

If we only use average and uncorrelated information on:•freeze-out multiplicity of neutrons, Z=1,2 and IMFs•sequential feeding•excitation energy of primary fragments•N/Z of final products

We see that one half of the game is played by missing correlations!!!!!!

Nucl.Phys.A699(2002)795

SMM events

3-d Spinodal 3-d Spinodal regionregion

3-d Spinodal 3-d Spinodal regionregion

M.Colonna et al. PRL 88(2002) 122701

Instability growth time 100 fm/c (dashed/orange) 50 fm/c (dotted/red)

More asymmetric systems are less unstable

Do we need to improve the detection for the Do we need to improve the detection for the “isospin” physics?“isospin” physics?

For all the measured reactions (high geometrical coverage, high energy resolution), event by event :•Z,A,E,θ,φ of the Heavy residue (QP&QT(?) for peripheral

collisions)•Z,A,E,θ,φ for fragments(*) and l.c.p. (high ε*)•correlations among charged products(*) is it enough mass for Z<=20?

At least on the average, for each reaction (sequential experiments)

•Neutron multiplicity & energy•(Gammas??)

Mass distribution of Ge (Z=32) isotopes

86Kr (25 MeV/u) + 64Ni @MARS Recoil separator Texas A&M

G.A. Souliotis NN2003(Moscow)

Heavy fragment mass&charge identification

1. Z, A, and E (low energy thresholds)

2. Granularity (for resonance spectroscopy)

3. Neutron detection (En, Mn), at least on the average

4. Cheap, flexible electronics

5. Easy transportability

6. Improvement of detector calibration (neural networks?)

Future detector needs Chimera: Pulse shape gives Z identification with ~ 4 MeV/A energy threshold for particles stopped in Si detector

Nuclex: Reverse mounting of the Si detector & Digital Pulse Shape give Z identification with ~ 2.5 MeV/A energy threshold for particles stopped in Si detector

FAZIA: Four π A-Z Indentification Array

• ~6000 telescopes: Si-ntd/Si-ntd/CsI• possibility of coupling with other detectors like spectrometer, gas chamber, neutron detectors• ~1000 hits/s• maximum multiplicity ~150/event• complete Z identification and A up to ~30• digital electronics for pulse-shape discrimination

half forward part

FAZIA: Four π A-Z Indentification Array