Feng-Shou Zhang ( 张丰收 ) College of Nuclear Science and Technology Beijing Normal University, Beijing, China Tel: ， Fax: Shell correction energy and the entrance channel effect on the formation of heavy and superheavy nuclei IWND2009 ， Shanghai, Aug ， 2009

2. Maria Goeppert-Mayer and Hans Jensen For their discoveries concerning nuclear shell structure 1.Eugene Paul Wigner For contributions to fundamental symmetry principles in both nuclear and particle physics The Nobel Prize in Physics By the end of 1940, Mayer and Jensen put up their model by a strong spin-orbit coupling of nuclear force, which can explains why nuclei with so-called magic numbers of protons and neutrons are particular stable.

What are the limits of atoms and nuclei?

What will be doing in China?

Theoretical Models 1/ Phenomenological model Dynamical liquid-drop model (Blocki, Feldmeier, Swiatecki, NPA459,145(1986)) Fluctuation-dissipation model (Aritomo, Wada, Ohta, Abe, PRC59,2634(1999)) Di-nucelar system(DNS) model (Adamain, Antonenko, Scheid, PRC68,034601(2003)) 2/ Macroscopic-Microscopic model (transport theory) Macroscopic-Microscopic model (Ichikawa, Iwamoto, Moller, PRC79,014305(2009)) 3/ Microscopic model (transport theory) ImQMD (Wang, Li, Wu, PRC67,024604(2004)) Main problem: lose or did not take shell effect in a proper way ! ImIQMD (Bian, Feng, Jin, Zhang, NPA750,232(2005), NPA802,91(2008),PLB665,314(2008)314)

Quantum molecular dynamics model (QMD) The QMD model represents the many body state of the system and thus contains correlation effects to all orders. In QMD, nucleon i is represented by a Gaussian form of wave function. After performing Wigner transformations, the density distribution of nucleon i is: Improved isospin dependent quantum Improved isospin dependent quantum molecular dynamics model molecular dynamics model

From QMD model to IQMD model lmean field (corresponds to interactions)  two-body collisions  pauli blocking  initialization  coalescence model U loc : density dependent potential U Yuk : Yukawa (surface) potential U Coul : Coulomb energy U Sym : symmetry energy U MD : momentum dependent interaction

Nuclear dynamics at intermediate and high energies by IQMD and IBL Photographs of the reaction?? Projectile Target ? What happened? Size? Lifetime? Shape ?   T~ K Detectors Dense and hot nuclear matter Equation of State Of Nuclear Matter E( ,T,p)=? Phase transition?

Nuclear Multifragmentation ， F. S. Zhang and L. X. Ge, Science Press, Beijing, 1998 《原子核多重碎裂》，张丰收，葛凌霄， 科学出版社

From compound nuclei (    0, T  1-2 MeV,) hot nuclei(    0,T>5 MeV), highly excited nuclei (   3  0,T>5 MeV) asymmetrical highly excited nuclei (   3  0,T>5 MeV,  >0) Physical indications IEOS   0, T > 0,  >0 E( , T,  ) = ?

Chapter 10: “ Isospin-Dependent Quantum Molecular Dynamics Model and Its Applications in Heavy Ion Collisions, ”

MSU,  112,124 Sn(40MeV/nucl.)+ 112,124 Sn isospin effects in multifragmentation  58 Fe( MeV/nucl.)+ 58 Fe, 58 Ni( MeV/nucl.)+ 58 Ni, disappearance of isospin effects in multifragmentation  Physical indications and challenges   0, T > 0,  >0 E( , T,  ) = ? Important to production of RIB &Neutron Stars !!!

Averaged number of IMF as a function of N C, NLC, and N N (4  analyzing)

Averaged number of IMF as a function of N C, N LC,and N N (4   pre equilibrium emissions)

Average n multiplicity, as a function of charged-particle multiplicity N C

Averaged number of IMF as a function of Z bound

Fusion/capture

Key problems for synthesis of superheavy nuclei 1.Stability: Friction force method 2. Surface energy: Switch function 3. Structure (Shell, pair, …) : Shell model, 2-center Shell model, Deformed 2-center shell model From IQMD model to ImIQMD model

The parameters: C 0 =0, C 1 =0, C 2 =0, C 3 =10, C 4 =-15, C 5 =6 Which ensure the continuities of E and its first derivative dE/dR R up =R T +R P, R low =0 fm, respectively Surface energy

As an approximative treatment, we can write the shell correction energy in the model as Derivating the equation, we can easily obtain the force derived from the shell correction energy as The ordering of filling of nucleons in the levels is taken according to angular momentum size ( ) as well as single nucleon energy (for the same angular momentum)

DTCSM (PRC68,2003, Gherghescu,Greiner, Munzenberg)

Shell corrections for Magic numbers Moller, Nix, Myers, Swiatecki Nucl. Data Tables 59(1995)185 E p shell (82)=-5.5 MeV, E n shell (126)=-6.8 MeV E p,n shell (50)=-5.1 MeV E p,n shell (28)=-1.24 MeV E p,n shell (20)=-3.6 MeV E p,n shell (8)=-2.2 MeV

DTCSM for cold fusion reaction

Coulomb Barrier Static fusion barrier for 40 Ca / 48 Ca + 40 Ca/ 48 Ca

Static Coulomb barriers of different systems to various isotopes of 110, 112, 114, 116 as a function of neutron number of Proj

Dynamic fusion barrier for 40 Ca / 48 Ca + 40 Ca/ 48 Ca

Dynamical Coulomb barriers: incident energy dependence

Dynamic barrier distribution for 36 S + 90 Zr at 80, 85 MeV

Fusion/Capture cross sections 16 O+ 16 O 40 Ca+ 40 Ca, 40 Ca+ 48 Ca, 48 Ca+ 48 Ca 48 Ca+ 154 Sm, 16 O W 16 O Pb, 16 O U 48 Ca+ 208 Pb, 48 Ca+ 238 U

Fusion cross section for 16 O+ 16 O  32 S exp: Saint-Laurent et al NPA327, 517 (1979) Maruyama et al. PRC53, 297(1996)

Z.Q. Feng, F.S. Zhang, G. M. Jin, X.Huang, NPA750(2005)

Fusion cross sections for 40 Ca+ 40 Ca, 40 Ca+ 48 Ca, and 48 Ca+ 48 Ca exp:Trotta et al, PRC65, R011601(2001), Aljuwair et al., PRC301223, (1984)

B.A. Bian, F.S. Zhang, H. Y. Zhou, PLB665(2008)

Capture cross sections 48 Ca+ 154 Sm / 16 O+ 186 W － > 202 Pb exp:Trotta et al., NPA734, 245(2004) Leigh et al., PRC52, 3151(1995) B. A. Biao, F.S. Zheng, H.Y. Zhou, entrance channel effect

Z.Q. Feng, G. M. Jin, F.S. Zhang, NPA802(2008)91-106

Capture cross sections 16 O+ 208 Pb/ 238 U  224 Th, 254 Fm exp:Shen et al., PRC36, 115(1987) Prokhorova et al., nucl-exp/

Capture cross sections 48 Ca+ 208 Pb/ 238 U  , exp: Dasgupta et al., NPA734, 148(2004) Nishio et al., PRL93, (2004)

Capture cross sections 48 Ca+ 244 Pu  , 48 Ca+ 248 U  exp: M.G. Itkis et al., NPA734, 136(2004)

,, and. The comparison between the calculated capture excitation functions and the available experimental data for the reactions below.,, and.

Conclusions and perspectives Theoretical Models phenomenological:  Dynamical liquid-drop model  Fluctuation-dissipation model  DNS model physical problem ! Macroscopic-Microscopic model microscopic:  Improved Isospin dependent quantum molecular dynamics model  Boltzmann-like model, such as IBL  Some others (AMD, FMD, etc.) large computer resource !

Experimental aspect  Reaction system (P-T composition)  Incident energy energy, etc. to do that, we need large computer resource ! Next development of the model  Quantum effects (tunnel effect) must be checked  Transport theory must developed from more fundamental point of view  To study nuclear reaction induced by drip-line nuclei Thank you for your attention Collaborators: Sai-Sai Du, Min Liu, Bao-An Biao, Zhao-Qing Feng, Gen-Min Jin,Hong-Yu Zhou (CNST-BNU, IMP-CAS)

共聚在师大 “ 京师 ” 广场 Workshop picture in Jing-Shi Square