Systematic study of fusion reactions leading to superheavy

I. Capture cross sections with the Skyrme energy-density functional Density distributions of the reaction

1. Determination of density distributions according to Hohenberg-Kohn theorem Woods-Saxon form for densities Search

2. Entrance-channel fusion barrier E 2 E 1 R Sudden approximation for density V.

3. Fusion (capture) cross section D(B) considers the coupling between the relative motion and

for reactions with nuclei near the beta-stability line but the neutron-shell is not closed

The fusion excitation functions for a series of reactions with 16 O bombarding on

Deviations from exp. data for 120 reactions N. Wang et al. , J. Phys.

II. Survival probability Wsur with HIVAP The sensitive parameters: 1. fission barriers (Liquid-drop barriers,

Fusion-fission：EDF＋HIVAP Wang, Zhao, Scheid, Wu, PRC 77 (2008) 014603

Deviations of calculated evaporation (and fission) cross sections from exp. data for 51 fusion-fission

3). Masses of super-heavy nuclei WS* A reliable nuclear mass formula is crucial for

Alpha decay energies of super-heavy nuclei have been predicted rms ~ 248 ke. V

N=162 N=178 WS* Zhang, et al. , Phys. Rev. C 85, 014325 (2012)

III. Fusion probability 1) quasi-fission barrier Yu. Oganessian Wang, Tian, Scheid, PRC 84, 061601(R)

2) Evaporation residual cross sections Mean barrier height PRC 84, 061601(R) (2011)

Uncertainty at E>Bm : 1. 18 (capture) x 1. 85 (Wsur) x 2 (PCN)

Opt. Zagrebaev PRC(2008) 50 Ti+249 Bk 50 Ti+249 Cf ~ 50 fb ~ 40

Conclusion and discussion n Methods for calculations of capture cross sections, survival probability of

China Institute of Atomic energy： Zhu-Xia Li、Xi-Zhen Wu、Kai Zhao （李祝霞）（吴锡真）（赵凯） Institute of

Thanks for your attention Codes and data are available at：www. Im. QMD. com

Skyrme energy-density functional Skyrme force Sk. M* Kinetic Nuclear Coulomb M. Brack, C. Guet,

# Coulomb Barrier n I. Capture (Skyrme EDF) # Barrier Distribution # Deformation &

1). Fission barrier Nuclei Cohen-Swiatecki Sierk Dahlinger MWS 244 Pu 5. 17 1. 44

2). Level density parameters In the standard HIVAP code: Ed=18. 5 Me. V, ra=1.

Large-angle quasi-elastic scattering Tail of the barrier distribution influences the large-angle quasi-elastic cross sections

Tail of barrier distribution influences the large-angle quasi-elastic cross sections S. G. Zhou

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Systematic study of fusion reactions leading to super-heavy nuclei Ning Wang Guangxi Normal University www. Im. QMD. com/wangning/ 1. Introduction 2. capture cross sections 3. Survival probablity Wsur 4. Fusion probabilty PCN 5. Conclusion BLTP/JINR-KLFTP/CAS Joint Workshop on Nuclear Physics, Aug. 2 -6, 2012, Dubna

I. Capture cross sections with the Skyrme energy-density functional Density distributions of the reaction partners Skyrme energy-density functional Entrance-channel fusion barrier Fusion cross sections Barrier penetration & empirical fusion barrier distribution D(B) M. Liu, N. Wang, Z. Li, X. Wu and E. Zhao, Nucl. Phys. A 768 (2006) 80 Ning Wang, et al. , Phys. Rev. C 74 (2006) 044604

1. Determination of density distributions according to Hohenberg-Kohn theorem Woods-Saxon form for densities Search for the minimum of energy by varying densities (R 0 p, R 0 n, ap, an)

2. Entrance-channel fusion barrier E 2 E 1 R Sudden approximation for density V. Yu. Denisov and W. Noerenberg, Eur. Phys. J. A 15, 375 (2002).

3. Fusion (capture) cross section D(B) considers the coupling between the relative motion and other degrees of freedom such as dyn. deform. etc. with 16 O+208 Pb, E=80 Me. V, Im. QMD

for reactions with nuclei near the beta-stability line but the neutron-shell is not closed

The fusion excitation functions for a series of reactions with 16 O bombarding on medium mass targets. Wang et al. Sci China G 52, 1554 (2009)

Deviations from exp. data for 120 reactions N. Wang et al. , J. Phys. G: 34 (2007) 1935 rms deviation for (E>B) About 70% systems are less than 0. 005, which gives the system error 18%.

II. Survival probability Wsur with HIVAP The sensitive parameters: 1. fission barriers (Liquid-drop barriers, Sierk’s barriers…) 2. level density parameters (Fermi gas model, angular-momentum and shape-dependent) 3. masses shell corrections and particle separation energies In the standard HIVAP code: ra=1. 153 fm

Fusion-fission：EDF＋HIVAP Wang, Zhao, Scheid, Wu, PRC 77 (2008) 014603

Deviations of calculated evaporation (and fission) cross sections from exp. data for 51 fusion-fission reactions For 68% reactions, the deviations are smaller than 0. 0714, Estimated systematic errors of the HIVAP code: 1. 85 Wsur and Wsur /1. 85

3). Masses of super-heavy nuclei WS* A reliable nuclear mass formula is crucial for a description of the properties and production cross sections of super-heavy nuclei WS : PRC 81 (2010) 044322 WS*: PRC 82 (2010) 044304 WS 3: PRC 84 (2011) 014333

Alpha decay energies of super-heavy nuclei have been predicted rms ~ 248 ke. V to 46 Qa of SHN

N=162 N=178 WS* Zhang, et al. , Phys. Rev. C 85, 014325 (2012)

III. Fusion probability 1) quasi-fission barrier Yu. Oganessian Wang, Tian, Scheid, PRC 84, 061601(R)

Fusion probability

2) Evaporation residual cross sections Mean barrier height PRC 84, 061601(R) (2011)

Uncertainty at E>Bm : 1. 18 (capture) x 1. 85 (Wsur) x 2 (PCN) = 4. 4

Opt. Zagrebaev PRC(2008) 50 Ti+249 Bk 50 Ti+249 Cf ~ 50 fb ~ 40 fb 54 Cr+248 Cm ~ 20 fb Liu-Bao ~ 600 fb PRC(2011) ~ 100 fb Nasirov PRC(2011) ~ 100 fb ~ 70 fb 58 Fe+244 Pu ~ 5 fb Ning Wang PRC(2011) ~ 35 fb ~ 20 fb ~ 5 fb ~ 3 fb Nan Wang PRC(2012) ~ 110 fb ~ 50 fb ~ 6 fb ~ 4 fb Siwek. Wilczynska PRC(2012) ~ 30 fb ~ 6 fb ~ 1 fb ~ 0. 1 fb

Conclusion and discussion n Methods for calculations of capture cross sections, survival probability of compound nucleus and the fusion probability in fusion reactions leading to super-heavy nuclei have been established and checked step by step. n Coulomb barrier, fission barrier and quasi-fission barrier play important roles for the calculations of three parts. n More precise calculations for masses, fission barriers, fission fragment yields and the study of fusion dynamics are still required.

China Institute of Atomic energy： Zhu-Xia Li、Xi-Zhen Wu、Kai Zhao （李祝霞）（吴锡真）（赵凯） Institute of Theoretical Physics (CAS)： En-Guang Zhao （赵恩广） Justus-Liebig-Univ. Giessen： Werner Scheid Guangxi Normal Univ. Min Liu （刘敏） Anyang Normal Univ. Jun-Long Tian （田俊龙）

Thanks for your attention Codes and data are available at：www. Im. QMD. com

Skyrme energy-density functional Skyrme force Sk. M* Kinetic Nuclear Coulomb M. Brack, C. Guet, H. -B. Hakanson, Phys. Rep. 123, 275 (1985).

# Coulomb Barrier n I. Capture (Skyrme EDF) # Barrier Distribution # Deformation & Dynamics … (Im. QMD) # Fission Barrier n n II. Decay III. Formation # Masses & Shell corrections (mass formula) # Fission Fragment Yields … (DNS) # Quasi-fission barrier # Potential energy surface # Dynamics …

1). Fission barrier Nuclei Cohen-Swiatecki Sierk Dahlinger MWS 244 Pu 5. 17 1. 44 3. 95 1. 02 4. 13 1. 19 256 No 4. 16 1. 74

2). Level density parameters In the standard HIVAP code: Ed=18. 5 Me. V, ra=1. 153 fm

Large-angle quasi-elastic scattering Tail of the barrier distribution influences the large-angle quasi-elastic cross sections PRC 78, 014607 (2008)

Tail of barrier distribution influences the large-angle quasi-elastic cross sections S. G. Zhou