Formation of Super-Heavy Elements

Transcription

1 Formation of Super-Heavy Elements Uncertainties in theoretical modeling Hongliang LÜ GANIL, CEA/DSM-CNRS/IN2P3, Bd Henri Becquerel, Caen, France Normandie Université, France Supervisor and Co-supervisor: Abdelouahad CHBIHI and David BOILLEY. December 16, 2014

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3 Where is the Island of Stability? How to get there?

4 How to synthesize SHE? Theoretical viewpoint Schematic of fusion-evaporation reaction Fusion-evaporation reaction: a p n Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

5 How to synthesize SHE? Theoretical viewpoint Schematic of fusion-evaporation reaction Fusion-evaporation reaction: Nuclear fission is the dominant decay channel of SHE formed in fusion-evaporation reactions. Typically, one has B f < S n. a p n Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

6 How to synthesize SHE? Theoretical viewpoint Schematic of fusion-evaporation reaction Fusion-evaporation reaction: Nuclear fission is the dominant decay channel of SHE formed in fusion-evaporation reactions. Typically, one has B f < S n. p n a... Re-separation (or quasifission) process only occurs in heavy binary systems. This phenomenon is usually called the Fusion hindrance. Key open question for the synthesis of SHE! Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

7 How to synthesize SHE? Theoretical viewpoint Evaporation-residue (ER) cross-setion of SHE σ res = σ cap P form W sur Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

8 How to synthesize SHE? Theoretical viewpoint Evaporation-residue (ER) cross-setion of SHE σ res = σ cap P form W sur For light systems, P form = 1; For heavy systems (Z t Z p ), P form < 1. Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

9 How to synthesize SHE? Modeling of statistical decay of SHE W sur? KEWPIE2 code... For guiding experiments KEWPIE2 Level density Gamma decay Particle evaporation Nuclear fission Nuclear mass table... Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

10 How to synthesize SHE? Modeling of statistical decay of SHE W sur? KEWPIE2 code... For guiding experiments KEWPIE2 Level density Gamma decay Particle evaporation Nuclear fission Basic features: Not a Monte-Carlo cascade code, due to low survival probabilities. Based on the discretization of the energy spectrum. More efficient! Nuclear mass table... Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

11 How to synthesize SHE? Modeling of statistical decay of SHE W sur? KEWPIE2 code... For guiding experiments KEWPIE2 Level density Gamma decay Particle evaporation Nuclear fission Basic features: Not a Monte-Carlo cascade code, due to low survival probabilities. Based on the discretization of the energy spectrum. More efficient! Nuclear mass table... A. Marchix, PhD thesis (2007); H. LÜ et al., in preparation for submission to CPC. Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

12 How to synthesize SHE? Modeling of fusion hindrance Fusion hindrance...?! An example Xe Sn Fusion cross-section [mb] 10 3 B Coulomb σ cap σ fus =σ cap P form (J=0) Exp. data from INDRA Fusion without hindrance Fusion with hindrance E cm [MeV] Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

13 Current status of research on synthesis of SHE Theoretical issue Large discrepancies among fusion models... Naik, Loveland et al, Phys. Rev. C 76, Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

14 Current status of research on synthesis of SHE Theoretical issue But, predictions highly consistent with measurements! Naik, Loveland et al, Phys. Rev. C 76, Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

15 Current status of research on synthesis of SHE Theoretical issue What can we learn from this delicate situation? Questions: All fusion-evaporation models reproduce well the experimental data, however large discrepancies among formation probabilities, why? Can we constrain formation probabilities by examining the decay step (better understood)? Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

16 Current status of research on synthesis of SHE Theoretical issue What can we learn from this delicate situation? Questions: All fusion-evaporation models reproduce well the experimental data, however large discrepancies among formation probabilities, why? Can we constrain formation probabilities by examining the decay step (better understood)? Solutions: Estimating the survival probability W sur by code; Uncertainty analysis of P form via σ1n res(experimental) σ cap W sur (theoretical). KEWPIE2 + Uncertainty propagation (MCM, proposed in GUM-S1) Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

17 Current status of research on synthesis of SHE Theoretical issue Propagation of Uncertainty (MCM) The MCM determines numerically a probability density function (PDF) which encodes the knowledge about the quantity of interest. An estimate and its associated uncertainty are then determined as the expectation and standard deviation of this PDF. Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

18 In the present work Uncertainty analysis Modeling with uncertainties Uncertainty sources: Parameters and Models Parameters: Experimental data (Gaussian distribution); Reduced friction coefficient β zs 1 (flat distribution); Damping-shell factor E d MeV (flat distribution). Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

19 In the present work Uncertainty analysis Modeling with uncertainties Parameters: Models: Uncertainty sources: Parameters and Models Experimental data (Gaussian distribution); Reduced friction coefficient β zs 1 (flat distribution); Damping-shell factor E d MeV (flat distribution). Kramers factor for fission-decay width; Collective enhancement factor for state density; Fission barriers taken from different models differ by 1 2 MeV (B f B LDM E sh or multidimensional calculation). Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

20 In the present work Uncertainty analysis Modeling with uncertainties Parameters: Models: Uncertainty sources: Parameters and Models Experimental data (Gaussian distribution); Reduced friction coefficient β zs 1 (flat distribution); Damping-shell factor E d MeV (flat distribution). Kramers factor for fission-decay width; Collective enhancement factor for state density; Fission barriers taken from different models differ by 1 2 MeV (B f B LDM E sh or multidimensional calculation). What will we get? Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

21 Parameters Uncertainty analysis Results Pb( 50 Ti,1n) 257 Rf PCN 10 1 Experiment Damping energy 10 2 Reduced friction Total uncertainty Pb( 58 Fe,1n) 265 Hs PCN Damping energy Experiment Reduced friction Total uncertainty 10 6 Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

22 Models Uncertainty analysis Results Pb( 58 Fe,1n) 265 Hs PCN Without Kramers Without both factors With both factors Without Coll. Enh PCN Myers Ivanyuk Moller Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

23 Summary Uncertainty analysis Results Rf Sg Adamian Feng Loveland Swiatecki Siwek-Wilczynska KEWPIE2+Moller KEWPIE2+Ivanyuk 266 Hs Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

24 Conclusion Uncertainty analysis Conclusion The uncertainty contribution from the decay step has the same order of magnitude as the fusion step... How to access different fusion models? Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

25 Conclusion Uncertainty analysis Conclusion The uncertainty contribution from the decay step has the same order of magnitude as the fusion step... How to access different fusion models? Entrance chanel 1 (with hindrance) Compound nucleus Same exit chanel Entrance chanel 2 (without hindrance) Hopefully, one can constrain P form directly from experimental measurements. Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

26 Perspectives Bayesian inference How to infer B f from experimental data? Bayes rule: P (Parameters Data) = P (Data Parameters) P (Parameters) P (Data) For light systems without fusion hindrance, the ER cross-section is given by σ thr 1n = σ cap Γ n Γ n + Γ f, The posterior distribution P (Parameters Data) is thus proportional to [ exp 1 ] 2 (y exp y thr ) T X 1 (y exp y thr ) P (Parameters), where y = {σ 1n } and X the variance matrix. Prior distribution P (Parameters) is non-informative. P (Data) evaluated by Gauss quadrature or MC integration. Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

27 Perspectives Bayesian inference How to infer B f from experimental data? Bayes rule: P (Parameters Data) = P (Data Parameters) P (Parameters) P (Data) For light systems without fusion hindrance, the ER cross-section is given by σ thr 1n = σ cap Γ n Γ n + Γ f, The posterior distribution P (Parameters Data) is thus proportional to [ exp 1 ] 2 (y exp y thr ) T X 1 (y exp y thr ) P (Parameters), where y = {σ 1n } and X the variance matrix. Prior distribution P (Parameters) is non-informative. P (Data) evaluated by Gauss quadrature or MC integration. From the posterior distribution, one can determine P (B f ) by marginalization and thus the conditional expectation value and its uncertainty. Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20

28 Perspectives Bayesian inference Thanks for your attention! Hongliang LÜ (GANIL, Caen Univ.) Formation of Super-Heavy Elements December 16, / 20