COMPETITION OF BREAKUP AND DISSIPATIVE PROCESSES

1. COMPETITION OF BREAKUP AND DISSIPATIVE PROCESSES IN 18O (35 MeV/n) + 9Be ( 181Ta ) REACTIONS AT FORWARD ANGLES Tatiana Mikhaylova, JINR, Dubna

2. B. Erdemchimeg 1,2,A.G. Artyukh1, M. Colonna3, M. di Toro3, G. Kaminski 1,4,Yu.M. Sereda1,5, H.H. Wolter6 1-Joint Institute for Nuclear Research, Dubna, Russia 2- Mongolian National University, Mongolia 3- LNS, INFN, Catania, Italy 4- Institute of Nuclear Physics PAN, Krakow, Poland 5 -Institute for Nuclear Research NAS, Kyiv, Ukraine 6 -University of Munich, Germany • Topics: • Motivation from experiment • Transport description • Evaporation • Velocity distributions. Residual Fragments • Break-up component • Results

3. New data in the region between the Coulomb Barrier and the Fermi Energy Motivation: Aprojectile loss of energy, friction exchange of mass impact parameter b Peripheral collisions at energies above the Coulomb barrier (A.G.Arthuk, et al., Nucl.Phys. A701(2002) 96c) Dissipation Atarget Afragment Peripheral reactions at Fermi Energy are expected to be the powerful tool to reach neutron reach isotopes ! G.A. Souliotis et al, Phys. Rev. Lett., v91 p022701-1(2003) Structure of primary fragments , investigation of reaction mechanism and production of primary fragments

4. Results of experiments at COMBAS spectrometer in FLNR LNR JINR Measured: isotope distributions velocity spectra Characteristicfeature: peakat beam velocity asymmetricshapewithtailtolowervelocities indicationoftwo-componentstructure Try to understand using transport theory!

5. s s 2 2 = = T T Fermi Fermi m m N N » » p p 265MeV/c 265MeV/c F F Û T=15MeV T=? Break-up (BU) component, comparison with Goldhaber: Statistical Model Of Fragmentation Processes Phys. Lett. V53B (1974) p306 the underlying picture: suppose nucleons chosen at random should go off together . What would be the mean square total momentum ? the underlying picture: suppose that the nucleus after excitation comes to equilibrium at temperature T : Then, the width of distribution is: P – projectile, F – fragment

6. Comparison with similar studies: Gelbke et al 1977, 16O+208Pb at 27 MeV/u : <<Fig. 1 Energy spectra of reaction products N, C, B, Be, Limeasured in the bombardment of 208Pb by 16Oions of 315MeV at the laboratory angle of 15 ° . The curves are calculatedfrom eq. (6) as explained in the text. The arrows denoted byVC, EF and EP correspond to the exit-channel Coulomb barrier,the energy predicted for a fragmentation of the projectileinto the observed fragment together with individual nucleonsand α-particles [ 10], and the energy of a product with theprojectile velocity.>> H. Fuchs and K. Moehring, Rep. Prog. Phys.,1994, v57, p 231

7. Lahmer et al, Transfer and fragmentation reactions of 14N at 60 MeV/u , Z. Phys. A - Atomic Nuclei 337, 425-437 (1990) M. Notani et.al. Fig. 9.Two-component fits to 13C spectra, measured for 60 MeV/u14Non various target nuclei High energy component also interpreted as direct break-up.

8. Test Particle (TP) representation (N number of TP per nucleon): Equations of motion of TP: 2-body collision term: Transport theory: one-body description, BNV approach time evolution of the one-body phase space density: f(r,p;t) Vlasov eq.: mean field:U(f) =Nuclear Mean Field + Coulomb + Surface + Symmetry terms Stochastic simulation of collision term: collision of test particles i, j F. Bertsch, S. Das Gupta , , Phys. Rep.,1988, v160, p 189 V. Baran, M. Colonna, M. Di Toro, Phys. Rep., v 410, 2005, p.335 U(f) = Nuclear Mean Field + Coulomb + Surface + Symmetry terms U(f) = Nuclear Mean Field + Coulomb + Surface + Symmetry terms U(f) = Nuclear Mean Field + Coulomb + Surface + Symmetry terms U(f) = Nuclear Mean Field + Coulomb + Surface + Symmetry terms

9. Residual fragments: Fragment recognition algorithm: cut-off density Deflection function (qualitative): Grazing angle, Coulomb rainbow Deflection angle Q Impact parameter b Nuclear rainbow Criterium for the definition of the boundaries of the fragment at freeze-out: density < 0.1 saturation density Density contour plots in the reaction 18O(35MeV/n)+181Ta. Six times (t=0,20,40,60,80,100 fm/c ) are shown attach Coulomb trajectories to obtain final angles and velocities

10. Definition of fragments: space integrals over region of density Number of particles Space position Velocity Phase space integrals

11. Isotope Distributions Normalized to unity for each isotope absolute Wilczynski-Plot: deflection angle – energy loss correlation More nuclear transfer More energy loss

12. Velocity Distributions, BNV approach 18O + 181Ta, 35 AMeV, O isotopes: Full solid angle Velocity Distributions, QMD approach (A.G. Artukh, et al., Acta Phys.Pol. 37 (2006) 1875 C Isotopes:

13. Comparison with the experiment, A.G. Artukh et al, FLNR, 2001 a Two components: Deep inelastic(DIC)+ Break-up(BU) b Characteristics of Break-up process (dark red curve in figure a): Velocity distribution peaked at V_projectile Gaussian distribution: c d The difference between total and break-up curves ,represents DIC (red curves in b,c,d) and agrees well with our calculations (blue curves).

14. To compare the results of the calculation with the experimental data we attach a statistical evaporation of the excited primary fragments. For this we use the Statistical Multifragmentation Model (SMM), by Botvina et al. (*). The crucial quantity in this process is the value of excitation energy. Here we use a rough estimate for the excitation energy, where the total excitation energy is given as where the potential energy is calculated from the Bethe and Weizsaecker mass formula], and the excitation energy is divided proportionally between target and projectile-like fragment. A more consistent evaluation of dissipated energy is under way, calculating the potential energy with BNV. The mass distribution, calculated with the the same angular restrictions as in experiment is too narrow. * Bondorf J.P.// Phys. Rep. 257 (1995) 133 To compare the results of the calculation with the experimental data we attach a statistical evaporation of the excited primary fragments. For this we use the Statistical Multifragmentation Model (SMM), by Botvina et al.[9]. The crucial quantity in this process is the value of excitation energy. Here we use a rough estimate for the excitation energy, where the total excitation energy is given as To compare the results of the calculation with the experimental data we attach a statistical evaporation of the excited primary fragments. For this we use the Statistical Multifragmentation Model (SMM), by Botvina et al.[9]. The crucial quantity in this process is the value of excitation energy. Here we use a rough estimate for the excitation energy, where the total excitation energy is given as To compare the results of the calculation with the experimental data we attach a statistical evaporation of the excited primary fragments. For this we use the Statistical Multifragmentation Model (SMM), by Botvina et al.[9]. The crucial quantity in this process is the value of excitation energy. Here we use a rough estimate for the excitation energy, where the total excitation energy is given as To compare the results of the calculation with the experimental data we attach a statistical evaporation of the excited primary fragments. For this we use the Statistical Multifragmentation Model (SMM), by Botvina et al.[9]. The crucial quantity in this process is the value of excitation energy. Here we use a rough estimate for the excitation energy, where the total excitation energy is given as To compare the results of the calculation with the experimental data we attach a statistical evaporation of the excited primary fragments. For this we use the Statistical Multifragmentation Model (SMM), by Botvina et al.[9]. The crucial quantity in this process is the value of excitation energy. Here we use a rough estimate for the excitation energy, where the total excitation energy is given as

15. BNV SMM we show the dependence of the centroidsof the dissipative velocity distribution XDICbefore(BNV) and after (SMM) evaporation for the calculations without and with angular restriction compared to the experiment. Several symbols for one mass correspond to different elements. Experiment - blue squares. Calculation without angular restriction- green circles. Calculation with angular restriction - red stars. For BNV the description is rather good, for SMM there are considerable deviations. These last values are preliminary and may be due to insufficient sampling of the reaction. Comparing the results of BNV and SMM calculations one can see that the fragments corresponding to the same mass number A has larger velocity in the SMM plot than in BNV one. This is due to the fact that they are produced by evaporation of the heavier fragment that had larger mass in BNV plot.

16. Experiment

17. Ratio of the yields in the dissipative and the direct components as a function of the mass of the fragment. Deflection functions: red lines indicate the angular restriction of the experiment The relative yield of the dissipative over the direct contributions is much smaller for the Ta target. This can be understood from the deflection function, which shows that for Ta only a small rangeof impact parameters contributes to the dissipative process.

18. Conclusions: 1. The study of heavy ion collisions in the Fermi energy regime gives the opportunity to learn about equilibration processes in low-energy heavy ion collisions and to provide estimates of yields of exotic nuclei. 2. We studied such reactions with a transport description, including secondary evaporation of the excited primary fragments. 3. We find, that the dissipative part of the observed yield is qualitatively described by the calculations: the velocity distributions are in reasonable agreement, while the isotope distributions are still too narrow with the present simple estimate of the excitation energy. 4. The direct components follows the behaviour of the Goldhaber model, but it would be desirable, to have a more microscopis theory for this. 5. The relative ratio of the two contribution can be understood qualitatively from the deflections functions

19. Thank you for attention

20. Incomplete fusion model: M. Veselsky, Nucl. Phys. A 705 (2002) 193 Application to 22Ne + 9B experiment: G.Kaminsky, et al. (NUFRA2007 conference, Antalya, Turkey, 2007) partly also shift to lower velocities

21. Theoretical Description of DIC: Classical trajectories with Friction (e.g. Gross and Kalinowski) radial and tangential friction, transport properties Diabatic Dissipative Dynamics (e.g. Nörenberg) two-center shell model and avoided Landau-Zener crossings here: Transport Theory : early work: M.F.Rivet et al, Phys Lett. B215(1988)55, reaction Ar +Ag, E/A = 27 MeV Experimental Description of DIC: В. В. Волков , Ядерные реакции глубоконеупругих передач, Москва, Энергоиздат, 1982 J.Wilczynski, Phys. Lett., 1973, B 47, p 484 U. Schroeder and J.R. Huizinga, Treatise on Heavy-Ion Science Vol 2, ed. A Bromley, Plenum, New York, p. 113-726 (1984)

22. Goldhaber dependance, results of G. Kaminski 18O + 181Ta, 35 Mev/nucl 18O + 9Be 35 Mev/nucl 22Ne + 9Be 40 Mev/nucl