EURISOL workshop, ECT* Trento, 16-20 Jan. 2006 1

Two-component (neutron/proton)statistical description

of low-energy heavy-ion reactions

E. Běták & M. Veselský

Institute of Physics, Slovak Academy of Sciences

84511 Bratislava, Slovakia

EURISOL workshop, ECT* Trento, 16-20 Jan. 2006 2

• Introduction

• Deep-inelastic – effect of neutron/proton composition at periphery

• Time scales of the processes

• Possible playground for pre-equilibrium

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Experiments: 86Kr on 64Ni, 112,124Sn at 25 A MeV:

- observed excess of exp. yields of neutron-rich nuclei with Z=32-34 (sometimes in wider range)

- explainable within DIT, but better fit with scaled transfer probabilities

(for details: Veselský, Souliotis: Nucl. Phys. A765 (2006), 252)

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Standard DIT ( Tassan-Got & Stefan, NPA 524 (1991) )86Kr + 64Ni at 25 AMeV

Solid - GEMINI, dash-SMM

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Correlation of skin thickness to isovector chemical potential(V. Kolomietz et al, PRC 64(2001)024315, extended Thomas-Fermi calculation)

Rn-R

p determines the difference

of N/Z at (Rn+R

p)/2 ( surface ) from

the bulk N/Z, correlates to isovector chemical potential

DIT (T-G) : macroscopic formula for R

n-R

p used, values unrealistically

large, but bulk N/Z dynamics described well

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Modified DIT (Veselský & Souliotis: Nucl.Phys. A765 (2006)):phenomenological correction, effect of shell structure on nuclear periphery (assuming Rn-Rp vs.

n-

p correlation) and

thus on transfer probabilities estimated as:

where S... = S

...exp - S

...ld , is a free parameter ( = 0.53 determined

as optimal value), s > 0 fm (only non-overlapping configurations considered)

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Modified DIT (Veselský & Souliotis: Nucl. Phys. A765)86Kr + 64Ni at 25 AMeV

solid - GEMINI, dash -SMM

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DIT Conclusions - 86Kr + 64Ni, 112,124Sn at 25 AMeV

- a microscopic correction to macroscopic DIT describes the effect of isospin asymmetry at nuclear periphery

- inversion of the bulk isospin flow due to microscopic structure at nuclear periphery

- consistent parameters for all reactions

- SMM reproduces the yields of n-rich species well while overestimating the yields of -stable isotopes close to the projectile

- GEMINI typically overestimates the width of mass distributions

- for p-rich target 112Sn stronger Coulomb interaction supresses the effect of isospin asymmetry at nuclear periphery at s < 1 fm

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Time scale (example):

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Pre-equilibrium (exciton model – master eq.):

- initial excited zone should follow the Z/N composition of overlapping region – importance of surfaces

- initial number of excitons can be estimated from the overlap of nuclei in momentum space

at higher energies and

at lower energies (below 5 or 10 A MeV above Coulomb)

projCcm AVEnE /)(54.06.4/ 0

projCcmprojT

projTproj AVE

AA

AAAn /)()08.038.0(09.0/0

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Inclusion of spin - HIC:

)()(' lEElE rotcmcm

(Běták: Fizika B12 (2003), 11)

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Pre-equilibrium exciton model suitable instrument to describe the effect of the neutron/proton composition of the initial overlapping region.

Features:

- model estimates of n0

- spin- and energy- distributions of initial phase

- spin couplings as necessary

- includes also equilibrated (CN) emission

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Thank you

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EURISOL workshop, ECT* Trento, 16-20 Jan. 2006 18

Experiments at fragment separator MARS ( Cyclotron Lab, Texas A&M University ).

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86Kr + 124Sn at 25 AMeV Standard DIT ( Tassan-Got )

solid - GEMINI, dash -SMM

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86Kr + 124Sn at 25 AMeV Modified DIT (nucl-th/0507026):

solid - GEMINI, dash -SMM

EURISOL workshop, ECT* Trento, 16-20 Jan. 2006 21

86Kr + 112Sn at 25 AMeV Standard DIT ( Tassan-Got )

solid - GEMINI, dash -SMM

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86Kr + 112Sn at 25 AMeV Modified DIT (nucl-th/0507026):

solid - GEMINI, dash -SMM Dash-dotted - SMM, s > 0.8 fm

EURISOL workshop, ECT* Trento, 16-20 Jan. 2006 2386Kr + 64Ni at 25 AMeV, Exp. vs. Sim. vs Sim. ICF-only

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Isoscaling in nuclear processes

M.B. Tsang et al., PRL 86(2001)5023

G. Souliotis et al., PRC 68(2003)24605

M. Veselský et al., PRC 69(2004)44607