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「１」 E. M. Burbidge, G. R. Burbidge, W. A. Fowler, and F. Hoyle, Rev. Mod. Phys. 29, 547 (1957) 「 2 」 A. G. W. Cameron, Chalk River Lab. Rep. CRL-41, A.E.C.L. No. 454, Ontario (1957) Periodic Table of the Elements

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R Rapid neutron-capture ( ,n) photodisintegration (n,γ)/(γ,n) equilibrium “waiting point” -decay T ~ 1-2 GK, n n ~ 10 20 -10 26 /cm 3 Density: 300 g/cm3 (~60% neutrons !) Neutron number Proton number Seed Rapid neutron capture n-capture timescale (τ n ): ~ 0.2 s τ n << τ β - The rapid n-capture process (r-process) is today understood to be responsible for the synthesis of about half of all the nuclei abundances present in Solar System matter in the mass region from approximately Zinc through the Actinides (e.g., Thorium, Uranium, and Plutonium), as well as the bulk of the heavy elements in the mass region A ≥ 60 in our Galactic and Cosmos matter. R-process still remains one of the most challenging open questions in modern nuclear astrophysics, since both the astrophysical scenarios where this process occurs and the needed nuclear physics input have not yet been unambiguously identified. Z+1 A X N-1 ZAXNZAXN A+1 Z X N+1

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chart of nuclides Estimated Neutron Drip Line FRDM (P. Möller et al. At. Data And Nucl. Data Tables 59 (1995) 185) n- captures must occur much faster than β − -decays far from stability the r-process “runs up” along the neutron drip line. ? R-process

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The r-process operating over the history of the Galaxy

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temperature (T 9 ) matter density neutron density (n n ) … radiation entropy (S rad ) r-process duration (τ r ) nuclear-masses (Q β, S n ) β-decay properties (T 1/2, P n ） n-capture rates fission properties neutrino interactions nuclear-structure-properties (J π …) for 1000’s of isotopes FAR-OFF β-stability r-abundances reproduction

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for the “main” r-process

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temperature (T 9 ) matter density neutron density (n n ) … radiation entropy (S rad ) r-process duration (τ r ) nuclear-masses (Q β, S n ) β-decay properties (T 1/2, P n ） n-capture rates fission properties neutrino interactions nuclear-structure-properties (J π …) for 1000’s of isotopes FAR-OFF β-stability r-abundances reproduction

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S n -values ⇒ r-process paths (i.e. S n ~ 3 MeV) T 1/2 of very neutron-rich nuclei T 1/2 (g.s., is.) ⇒ r-process progenitor abundances (N r,prog ) T 1/2 of waiting points ⇒ pre freeze-out isobaric abundances and regulate the speed of the process towards heavier elements. T 1/2 of heavy neutron-rich radionuclides ⇒ time scale for the matter flow from the r-process seeds to even heavier nuclei. Sum of T 1/2 ⇒ total r-process duration (τ r ) P n ⇒ smoothing N r,prog N r,final (N r, )

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Today, altogether 60 r-process nuclei are only known! Heaviest isotopes with measured T 1/2 new (MSU, 2009) “Waiting point” isotopes at: n n = 10 20 n n = 10 23 n n = 10 26 freeze-out networks. Today, altogether 60 r-process nuclei are only known! Heaviest isotopes with measured T 1/2 new (MSU, 2009) “Waiting point” isotopes at: n n = 10 20 n n = 10 23 n n = 10 26 freeze-out networks.

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GTGT2 SGT GT* Shell Model QRPA + ffGT FRDM + pnQRPA C-QRPAs R-QRPAs HFBSC + CQRPA ETFSI+CQRPA DF3+CQRPA R-QRPA+ff Theory-driven

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data-driven, stand-along statistical approaches

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Input Neurons Hidden Intermed. Layers Output Neuron Fully-connected Feed-forward Neural Network classification – function approximation Learning Machines

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Machine learning statistical framework comparison target (Log 10 T β,exp ) Output (Log 10 T β,calc ) input [Z,N,δ] Neural Network with C weights weights adjustment Levenberg-Marquardt BP update rule Learning Procedure Objective: minimization of cost function Back-propagation

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Input Scaling [-1, 1] Output Scaling [-1, 1] Max Fail Z[0, 230] Log 10 T 1/2 (ms) [0.18 - 8.98]300 epochs N[0, 230] Parity[-1, 1] Mode Training Algorithm Initialization Method BatchBayesian RegularizationNguyen-Widrow NetworkArchitecture Activation Functions Feed-forward Fully-connectedSize:3-5-5-5-5-1 tanh-tanh-tanh- tanh-satlins Weights: 116

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Database Half-life Range Decay Mode NuSet-B NuBase2003 * 0.15 χ 10 -2 s 35 Na 2.43 χ 10 23 s 113 Cd 100% β -Cutoff10 6 s Early Stopping To avoid overfitting effects Training Set Validation Set Test Set * A.H. Wapstra, G. Audi et al., Nucl Phys. A729 (2003) 337 NuSet-B. Uniform Nuclides Distribution over Half-lives All Nuclides Training Set (60%) Validation Set (20%) Test Set (20%) 843503167168

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Learning0.53 Validation0.60 Test0.65 Overall0.57 SetRMSE

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Recently measured* T β of eight heavier abuse to ff neutron-rich isotopes close to the neutron shell N = 126 around A = 195. *T. Kurtukian-Nieto et al.

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A = 70 − 80 mass region

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A = 120 − 130 mass region

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A = 195 − 205 mass region

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Exp. Data New Exp. FF-ANN FF-ANN pred. QRPA + ffGT GT*

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Exp. Data FF-ANN FF-ANN pred. QRPA + ffGT GT*

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32 RIBF Radioactive Ion Beam Facilities Timeline 2000 2005 2010 2015 2020 CARIBU@ATLAS NSCL HRIBF FRIB ISOLDE ISAC-II SPIRAL2 SIS FAIR RARF ISAC-I In Flight ISOL Fission+Gas Stopping Beam on target SPIRAL HIE-ISOLDE

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URL: http://www.pythaim.phys.uoa.grE-mail: pythaim@phys.uoa.gr *To be submitted to Phys. Rev. C

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NuBase03

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RMSE

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fact T 1/2 T 1/2Exp(s) Overall Mode Prediction Mode NBSC+pnQRPAm(%) K K σKσKσKσKm(%) σKσKσKσKm(%) σKσKσKσK <10 <10^690.52.461.7290.52.691.8576.73.00- <6096.52.211.5296.12.481.6487.22.81- <197.62.101.39982.241.3095.72.64- <5 <10^682.81.990.9579.22.100.97--- <6090.21.880.8487.32.050.91--- <193.71.880.8942.040.89--- <2<2<2<2<10^653.51.410.2749.41.480.2833.81.43- <6060.61.410.2753.91.480.2742.01.41- <161.91.410.26601.500.2750.71.43- Klapdor’s Metrics * must tends towards 1 whilemust tends towards 0. * H. Homma, M. Bender et al., Phys. Rev. C 54:6 (1996) 2972

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