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PRE-EQUILIBRIUM (EXCITON) MODEL AND THE HEAVY-ION REACTIONS WITH CLUSTER EMISSION

PRE-EQUILIBRIUM (EXCITON) MODEL AND THE HEAVY-ION REACTIONS WITH CLUSTER EMISSION. E. B ěták Inst. of Physics, Slovak Acad. Sci., Bratislava, Slovakia ( betak@savba.sk ) J. Cseh ATOMKI, Debrecen, Hungary. Motivation Consistency of the exciton model – master eq. approach

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PRE-EQUILIBRIUM (EXCITON) MODEL AND THE HEAVY-ION REACTIONS WITH CLUSTER EMISSION

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  1. PRE-EQUILIBRIUM (EXCITON) MODELAND THE HEAVY-ION REACTIONSWITH CLUSTER EMISSION E. Běták Inst. of Physics, Slovak Acad. Sci., Bratislava, Slovakia (betak@savba.sk) J. Cseh ATOMKI, Debrecen, Hungary 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  2. Motivation • Consistency of the exciton model – master eq. approach • Coalescence and Iwamoto-Harada model for cluster emission in its density formulation • Extensions of the Iwamoto-Harada model • Cluster emission with angular momentum variables • Cluster emission from heavy-ion collisions 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  3. MOTIVATION Candidates for hyperdefomed nuclei are expected to be formed (relatively easily) in (light) heavy-ion reactions at not too high energy (say, incident energy of few tens or as a maximum few hundreds of MeV). Some combinations of colliding ions have been suggested. The question is, which energies seem to be favourable for their creation. We aim to get some hints for this process, and illustrate it on the 20Ne + 20Ne -> 36 Ar (plus something: α, 2n+2p, n+p+d, …) The production cross section serves as the main indiucator. Therefore we applied statistical pre-equilibrium model with additions suitable to this aim. 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  4. CONSISTENCY OF THE EXCITON MODEL - MASTER EQUATIONS APPROACH Master equations are capable to describe the whole process in time from the very creation of the composite system through its equilibration up to the decay of compound nucleus within a single formalism, not mixing various approaches. Using the density-dependent formulation of the so-called Iwamoto-Harada model (Dobes and Betak, 5 years before I+H) for cluster emission, pick-up as well as knock-out can be included. Obviously, one pays for the single approach with the lost of majority details, like details of the structures in spectra, but the cross sections describe the average trends rather satisfactorilly. A technical handicap remains: the set of master equations is huge, but we have a suitable algorithm to solve it. 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  5. COALESCENCE MODEL FOR CLUSTER EMISSION Kalbach (Cline, Kalbach-Cline, Kalbach-Walker), Ribanský & Obložinský Emision rate (nucleons): Coalescence clusters: 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 201 5

  6. COALESCENCE (IWAMOTO-HARADA) MODEL FOR CLUSTER EMISSION IN ITS DENSITY FORMULATION coalescence IH model IHB model knock-out 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  7. Generalized (coalescence + pickup) Iwamoto & Harada, Dobeš & Běták, Bisplinghoff EMISSION RATE PROPORTIONAL to the CLUSTER FORMATION PROBABILITY SINGLE-CLUSTER DENSITY INVERSELY PROPORTIONAL to theCLUSTER FORMATION PROBABILITY THEREFORE theresultisPARAMETERLESS !

  8. Bisplinghoff Pickup limited by the binding energy of nucleons in the cluster (i.e. about 28 MeV for alphas and 2 MeV for deuterons) • Now Limitation due to binding energy for all clusters Only low-exciton configurations with pickup (CN limit!) Thermal “blurring” considered Admixture allowed for all potential well (Heisenberg uncertainty relation) Possibility of knockout (initial stage only) for alphas 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  9. Calculations without spin (old) a) deuterons 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  10. Bb) alphas 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  11. c) α-knockout admixtures from the fit to the data 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  12. Cluster emission with angularmomentum variables 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  13. Spinvariables: Couplingofnucleons to form a coalescence or pickup clustermaybe – in a veryroughapproximation –consideredincluded in theformationprobability. Therefore, no additionalcouplingsappear in theemissionrates and theonlyplaceaffected by theangularmomentum are differenttransitioncoefficients and viacompetitions to other (nucleon,γ) channels. Exception: knock-out – α-particleisnotformedduringreaction, butitisalreadypresent in thetargetnucleus. 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  14. 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  15. Primary nucleon, deuteron, alpha and gamma energy spectra (gammas with cascades) from 197Au+p at 62 MeV 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  16. 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  17. HEAVY IONS – INITIAL CONFIGURATION(without spin variables today) Cindro et al.: for lower energies, where 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  18. HEAVY IONS – CLUSTER BREAKUP Kalbach Walker, www-nds.iaea.org/fendl3/docs/dBreakupRCM2.pdf where the normalizatoion factor is only weakly sensitive to the projectile. We use this as very rough initial approximation. 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  19. 20 Ne + 20 Ne P r e l i m i n a r y 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  20. CONCLUSIONS • Clusterization itself parameterless • Effective only at initial stages, what enables proper equilibrium (compound nucleus) limit • Thermal blurring of nucleons allowed • Pickup (IHB) generalized to all types of clusters • For strongly bound ejectiles knockout possible: • Includedangularmomentum, butthecouplings of nucleons to form a cluster are hidden in cluster formationprobability • Introductionofspinvariablesenhancesthe cluster emissioncompared to spin-independentcase. (Itplayssimilar role asdeformationaccording to Blann & Komoto) • Allcalculationspresentedhere are just with default parameters (leveldensities, inverse c.s., transition matrix element). • Possibility to indicate various contributing mechanisms leading to the same (nearly equilibrated) composite system, and to select the most suitable conditions for structure studies, like existence of hyperdeformednucli. • Further effort: heavy ions, cluster emission, pre-equilibrium with some elements of direct reactions and spin variables tgogether within one formalism 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

  21. Thank you 14th Internat. Conf. Nucl. Reaction Mechanisms, Varenna, 19th June 2015

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