Teoretyczny opis de-ekscytacji j ader gor acych

Teoretyczny opis de-ekscytacji j ader gor acych K. Mazurek, M. Ciema la, M. Kmiecik, A. Maj, D. Lacroix The Niewodniczanski Institute of Nuclear Physics - PAN, Kraków, Poland IPNO, CNRS/INP, Université Paris-Sud, Université Paris-Saclay, F-946 Orsay, France April 9, 8 (The Niewodniczanski GDR+HIPSE Institute of Nuclear Physics April 9, 8 - PAN, Kraków /

Outline Tworzenie j adra z lożonego i przedrównowagowa emisja cz astek (HIPSE) Metoda termicznych fluktuacji kszta ltu i Gigantyczne Rezonanse Dipolowe Statystyczna deekscytacja j adra z lożonego (GEMINI++) Równania Langevina i dynamika rozszczepienia (The Niewodniczanski GDR+HIPSE Institute of Nuclear Physics April 9, 8 - PAN, Kraków /

Experimental Results - 48 Ti+ 4 Ca 88 Mo M. Ciema la et al. Phys. Rev. C 9, 54 (5) (The Niewodniczanski GDR+HIPSE Institute of Nuclear Physics April 9, 8 - PAN, Kraków /

Sequential Fission Procedure Dynamical evolution of compound nucleus and later each primary fission fragment. Fusion CN I fission II fission Xe+Sn central collision from 8 to 5 MeV/A measured with INDRA (The Niewodniczanski GDR+HIPSE Institute of Nuclear Physics April 9, 8 - PAN, 4 Kraków /

Sequential Fission Procedure: II step II. Dynamical evolution of each primary fission fragment. (The Niewodniczanski GDR+HIPSE Institute of Nuclear Physics April 9, 8 - PAN, 5 Kraków /

-fragments -fragments Final fragment charge distribution Xe + Sn Rf Yield (in arb. units) theo exp E * =MeV (a) 4 6 8 Fragment charge (Z) Yield (in arb. units) 4 E * =47MeV (b) 4 6 8 Fragment charge (Z) Yield (in arb. units) 4 E * =656MeV (c) 4 6 8 Fragment charge (Z) Yield (in arb. units) (d) Yield (in arb. units) (e) Yield (in arb. units) (f) 4 6 8 Fragment charge (Z) 4 4 6 8 Fragment charge (Z) 4 6 8 Fragment charge (Z) E lab =8 AMeV E lab = AMeV E lab =5 AMeV (The Niewodniczanski GDR+HIPSE Institute of Nuclear Physics April 9, 8 - PAN, 6 Kraków /

Reaction scenarios - HIPSE (The Niewodniczanski GDR+HIPSE Institute of Nuclear Physics April 9, 8 - PAN, 7 Kraków /

HIPSE dynamical model (The Niewodniczanski GDR+HIPSE Institute of Nuclear Physics April 9, 8 - PAN, 8 Kraków /

HIPSE dynamical model (The Niewodniczanski GDR+HIPSE Institute of Nuclear Physics April 9, 8 - PAN, 9 Kraków /

HIPSE - Results (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /

HIPSE (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /

Entrance channel effect - 48 Ti+4 Ca 88 Mo Mass distribution Outcome from the HIPSE code Elab= MeV 6 MeV Yield [a.u.] Quasi-projectile Pre-equilibrium A [mass units].. 4 5 6 7 8 9 Mass 9 85 HIPSE CN 8 75 7 65 A 6 HIPSE pre-equilibrium 9 55 85 5 8 75 45 7 65 6 55 5 45 4 5 6 4 5 6 7 8 L [h] Compound nuclei created by HIPSE code. The Lcut =64 ~ marks the spin at which the fission barrier vanishes. K.M. et al Acta Phys. Pol. B Proc. Supp., 9 (8) B The correlation of the prefragment mass with the impact parameter in 48 Ti(6 MeV)+4 Ca. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN,Krako w /

Entrance channel effect - 48 Ti+ 4 Ca 88 Mo Distance between colliding nuclei and compound mass MeV 6MeV B 7 B 7 6 6 5 5 4 4 4 5 6 7 8 9 A Excitation energy of composed nuclei 4 5 6 7 8 9 A Ex [MeV] 5 5 Ex 4 5 4 5 8 5 6 4 5 5 4 5 6 7 8 9 A 4 5 6 7 8 9 A (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /

Giant Dipole Resonance - GDR (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 4 Kraków /

Thermal Shape Fluctuation Model - GDR β sin(γ+ ) βsin(γ+ ) 9 9 7 5 9 9 Critical Spin and the Jacobi Instability.5 I=. E=. I=. E=6. I=. E=.7..7. -. -.5.5 I=6. E=6.5 I=. E=46.8 I=4. E=56.4 5..7. -. -.5..6..8..6..8..6..8 46 β Ti cos(γ+ ) β cos(γ+ ) β cos(γ+ ) 4 7 5 5 9 7 9 9 9 5 9 5 5 9 7 7 9 5 9 5 7 5 9 9 9 5 5 9 7 5 7 9 E [MeV] 47. 45. 4. 4. 9. 7. 5... 9. 7. 5... 9. 7. 5... 9. 7. 5... Minimized over multips 4, 6 and 8 K. Mazurek, J. Dudek Experiment: A. Maj et al., Nucl. Phys. A 7, 9 (4). (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 5 Kraków /

Thermal Shape Fluctuation Model - GDR [ K. Pomorski, J. Dudek, Phys. Rev. C 67,446() ]. (A=Z+N; t=(n-z)/a) The macroscopic energy: Lublin - Strasbourg Drop E LSD (Z, N; def ) = b vol ( κ vol t )A +b surf ( κ surf t )A / B surf (def ) +b curv ( + κ curv t )A / B curv (def ) + Z 5 e r ch B Z A/ Coul (def ) C 4 A exp ( 4. t ) Free energy F (T ) = E LSD + I (I + ) J (def ) TS(def, I, T ) The GDR probability { } p(def ; I ; T ) = exp F (T ) kt (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 6 Kraków /

Thermal Shape Fluctuation Model - GDR σ(e γ, T, I ) = (x,y) p((def ); I ; T ) 5 f k (E γ, (def )) k= σ k Γ k E K. M., M. Kmiecik, A. Maj, J. Dudek, γ f k (E γ, (def )) = (Eγ E GDR,k ) + Eγ Γ N. Schunck, Acta Phys. Pol. B 8, 455 (7) k Katarzyna Mazurek, IFJ -( PAN ).9 (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 7 Kraków /

Entrance channel effect - 48 Ti+ 4 Ca 88 Mo Angular momentum and temperature distribution Yield (a.u.).5..5..5..5.8.6 HIPSE CN HIPSE pre-equilibrium 4 5 6 7 8 9 HIPSE CN HIPSE pre-equilibrium Angular Momentum (/h) (a) (b) HIPSE + TSFM Yield [a.u.].4...8.6.4. <L<64 5 5 5 E γ [MeV] CN, T= 4.6 MeV HIPSE, A>6 HIPSE pre-equilibrium HIPSE CN Yield (a.u.).4 <L<64 The strength functions of the GDR built in compound nucleus 88 Mo (CN). 4 5 6 Temperature (MeV) Blue line shows the values of the spin/ temperature taken usually for hot compound nucleus 88 Mo. For ensemble of nuclei generated in the HIPSE code: compound nucleus (HIPSE CN), the nuclei produced with pre-equilibrium emission (HIPSE pre-equilibrium) and integrated over the prefragment mass distribution (HIPSE A>6). All calculations were done for -64 range of angular momentum. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 8 Kraków /

Entrance channel effect - 48 Ti+ 4 Ca 88 Mo HIPSE + TSFM Yield [a.u.].4...8.6.4. <L<64 5 5 5 E γ [MeV] CN, T= 4.6 MeV HIPSE, A>6 HIPSE pre-equilibrium HIPSE CN Yield [a.u.].4...8.6.4. 48 Ti()+ 4 Ca 5 5 5 E γ [MeV] CN, T=. MeV HIPSE, CN pre pre+cn The strength functions of the GDR built in compound nucleus 88 Mo (CN) For ensemble of nuclei generated in the HIPSE code: compound nucleus (HIPSE CN), the nuclei produced with pre-equilibrium emission (HIPSE pre-equilibrium) and integrated over the prefragment mass distribution (HIPSE A>6). All calculations were done for -64 range of angular momentum. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 9 Kraków /

Fission of the Nucleus as a Stochastic Process Stochastic process or often random process, is a collection of random variables representing the evolution of some system of random values over time. This is the probabilistic counterpart to a deterministic process (or deterministic system). Instead of describing a process which can only evolve in one way (as in the case, for example, of solutions of an ordinary differential equation), in a stochastic, or random process, there is some indeterminacy: even if the initial condition (or starting point) is known, there are several (often infinitely many) directions in which the process may evolve.( http://pl.wikipedia.org) Binary fission (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /

Statistical model of compound nucleus decay GEMIN++ statistical model (R.j. Charity, Phys. Rev. C8,46 ()) is widely used statistical model code adopts a default set of parameters obtained by fitting data from several previous experiemnts parameters are tuned for heavy nuclei (A>5) there aren t many experimental data to fix parametrs for medium-light nuclei tunning parameters of GEMINI++ are: level density Coulomb barrier distribution yrast energy parametrization etc.... M. Ciema la: In the present studies, the statistical code GEMINI++ with an option allowing to treat explicitly the GDR emission [Ciemala et al. Acta Phys. Pol B44, 6 ()] was employed for the first time for such an analysis. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /

Mass/charge distribution of initial set of nuclei done with HIPSE MeV 6MeV Z 5 Z 5 45 4 45 4 4 4 5 5 5 5 5 5 5 5 4 5 6 7 8 9 4 5 6 7 8 9 A A Mass/charge distribution after de-excitation with GEMINI++ Z res. 5 4 Z res. 5 4 45 45 4 4 5 5 5 5 5 5 5 5 4 5 6 7 8 9 A res. 4 5 6 7 8 9 A res. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /

Entrance channel effect - 48 Ti+ 4 Ca 88 Mo Angular momentum of initial set of nuclei MeV 6MeV L CN [h] 9 L CN [h] 9 5 8 8 7 7 5 6 6 5 5 4 4 5 5 4 5 6 7 8 9 4 5 6 7 8 9 A A Angular momentum after de-excitation with GEMINI++ L CN [h] 9 L CN [h] 9 8 8 7 7 6 6 5 5 4 4 4 5 6 7 8 9 4 5 6 7 8 9 A res. A res. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /

Entrance channel effect - 48 Ti+ 4 Ca 88 Mo Number of products of de-excitation Nb. products 8 6 4 4 Nb. products 8 6 4 8 8 6 6 4 4 4 5 6 7 8 9 4 5 6 7 8 9 A res. A res. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 4 Kraków /

Stochastic approach Dynamical effect path from equilibrium to scission slowed-down by the nuclear viscosity description of the time evolution of the collective variables like the evolution of Brownian particle that interacts stochastically with a heat bath. excess of prescission particles all the parameters of the two dimensional fission fragment distribution and their dependence on various parameters of compound nucleus Brownian motion (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 5 Kraków /

Stochastic Approach Observables Pre- and post-scission particle multiplicity and energy spectra Mass, charge, angular distributions of the fragments Total Kinetic Energy distribution Isotopic distribution, N/Z... Binary fission Limitations Wide domain in compound nucleus mass (from 5 to 5) Excitation energy E (from to 5MeV) Angular momentum L (from to ) Fission-fragment distributions within dynamical approach K. M., P. N. Nadtochy, E. G. Ryabov, G. D. Adeev, Eur. Phys. J. A, 5 (7) 79E (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 6 Kraków /

Stochastic Approach Langevin Equations are stochastic differential equations describing the time evolution of a subset of the degrees of freedom. These degrees of freedom typically are collective (macroscopic) variables changing only slowly in comparison to the other (microscopic) variables of the system. The fast (microscopic) variables are responsible for the stochastic nature of the Langevin equation. dq i dt = j [M ( q)] ij p j dp i dt = j,k d[m ( q)] jk df( q, K) p j p k dq i dq i γ ij ( q)[m ( q)] jk p k + j,k j g ij ( q)γ j (t) Ingredients Inertia ([M ( q)] ij ) Friction (γ i (t)) and fluctuation ( g ik ) Macroscopic potential (V ( q, K) F ( q, K) = V ( q, K) a( q)t ) Coupling to the evaporation Pre and post- scission emission of neutrons, protons, α and γ. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 7 Kraków /

Model Ingredients Collective coordinates (4D) Description of the nuclear shape by elongation, neck and asymmetry parameters. K spin about the fission (symmetry) axis Tilting coordinates - K δk = γ K I V K δt + γ KIψ Tδt where ψ - random number, γ K - friction parameter (coupling K with heat bath) J.P.Leastone,S.G.McCalla,PRC79,446 Fission-fragment distributions within dynamical approach K. M., P. N. Nadtochy, E. G. Ryabov, G. D. Adeev, Eur. Phys. J. A, 5 (7) 79E (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 8 Kraków /

Model Ingredients Energies Potential energy in deformation space e.g: FRLDM + Wigner or LSD + Congruence E lsd (q) = b vol { κ vol T } A + b surf { κ surf T } A / B surf (q) + b curv{ κ curvt } A / B curv(q) + 5 e Z T = (N Z)/A Rotational energy: E rot (q, I, K) = I (I +) J (q) + K J eff (q) where J eff = J J - the rigid-body moments of inertia. r ch A/ B Coul(q) (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, 9 Kraków /

Model Ingredients P.N.Nadtochy, et al., PRC 89,466 Dissipation of the driving forces The wall and window formula reduced by chaos-weighted viscosity parameter k s ( q). J. B locki, J.-J. Shi, W.J.Świ atecki, Nucl. Phys. A554, 87; G. Chaudhuri, Santanu Pal, Phys.Rev C6, 646 η cwwf = µη wf ; µ - measure of the chaos in the single particle motion and depends on the instantaneus shape of the nucleus The friction parameter controlling coupling between K coordinate and the heat bath. T. Dosing, J. Randrup, Nucl. Phys. A 4,5; J. Randrup, Nucl.Phys. A 8, 468 γ K = R N R cm π n J J eff J R J where R N - neck radius, R cm- distance between the center of the nascent fragments, n =.6 MeV zs fm 4 - the bulk flux in standard nuclear mass and J R = M Rcm /4 for reflection symmetric shape. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /

Isotopic Distributions: U + C Cf (E lab =6. AMeV) The charge variance is necessary to reproduce the isotopic distribution. a) 4.5 Yield [%].5.5.5 d) 4.5 Yield [%].5.5.5 5 Cf, ks =, Z FF = 8 exp σ Z =..8 8 85 9 95 5 g) 4.5 Yield [%] Z FF = 46 5 5 5.5.5.5 Z FF = 54 b) 4.5.5.5.5 e) 4.5.5.5.5 Z FF = 4 85 9 95 5 5 h) 4.5 Z FF = 49 5 5 5 5.5.5.5 Z FF = 56 c) 4.5.5.5.5 f) 4.5.5.5.5 Z FF = 44 95 5 5 5 i) 4.5.5.5.5 Z FF = 5 5 5 5 4 45 Z FF = 6 Yield [%] 4 8 6 4 5 Cf 5 4 45 5 55 6 65 Z FF k s (q ) k s =. exp A finite charge dispersion is necessary to reproduce the isotopic distribution. ZFFi UCD = A FFiZ fiss A fiss ZFFi NUCD = ZFFi UCD ± ; ±... 5 5 4 45 5 A FF 5 5 4 45 5 55 A FF K.M., C. Schmitt, P. Nadtochy PRC 9, 46(R) (5), M. Caamano et al. PRC 88, 465 (4) 5 4 45 5 55 6 65 A FF A.V. Karpov, G.D. Adeev Phys.At.Nucl. 65,596 (); Eur.Phys.J. A 4,69 () (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /

Entrance channel effect - 48 Ti+ 4 Ca 88 Mo CN + 4DLangevin HIPSE + 4DLangevin E= MeV, ER FF E=6 MeV, ER FF 48 Ti+ 4 Ca E= MeV, ER+FF, CN QPT E=6 MeV, ER+FF, CN QPT 48 Ti+ 4 Ca Yield [a.u.] Yield [a.u.].. 4 5 6 7 8 9 4 5 6 7 8 9 Mass Mass GDR+HIPSE April 9, 8 / (The Niewodniczanski Institute of Nuclear Physics - PAN, Kraków

Summary The study of the pre-equilibrium particle emission is crucial for discussion of de-excitation of hot nuclei. The preliminary estimation of the influence of the pre-equilibrium emission on the shape of the GDR strength function has been done with the Thermal Shape Fluctuation Model. The difference between GDR emitted from HIPSE CN and standard CN is due to higher spin influence in the later. The pre-equilibrium emission causes the lowering of the spin and temperature of prefragments thus the low-energy component in GDR spectrum is suppressed. Fission, evaporation observables by coupling HIPSE prefragments with statistical (GENIMI++) and dynamical (4DLangevin) de-excitation codes. Plans: applying the experiemntal filters and compare with the data. (The Niewodniczanski GDR+HIPSE Institute of Nuclear April Physics 9, 8 - PAN, Kraków /