1 Z.Q. Feng( 冯兆庆 ) 1 G.M. Jin( 靳根明 ) 2 F.S. Zhang ( 张丰收 ) 1 Institute of Modern Physics, CAS 2 Institute of Low Energy Nuclear Physics Beijing NormalUniversity A microscopic transport model for synthesis of superheavy nuclei 中日 NP2006, 上海

Outline 1. Introduction 2. Improved isospin dependent quantum molecular dynamics model 3. Coulomb barrier 4. Fusion/capture cross section 5. Conclusions and perspectives

1. Introduction

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/ 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 (Feng, Zhang, Jin, NPA750,232(2005)) ?

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: 2. Improved isospin dependent quantum molecular dynamics model molecular dynamics model

mean field (corresponds to interactions) U vol : density dependent potential U surf : surface potential U Coul : Coulomb energy U Sym : symmetry energy U MDI : momentum dependent interaction 2.1 From QMD model to IQMD model

two-body collisions, Pauli blocking initialization, Coalescence model

2.2 From IQMD model to ImIQMD model The parameters: C 1 =0, C 2 =0, C 3 =0, C 4 =-15, C 5 =6 Which ensure the continuities of E and its first derivative dE/dR R up =20-30 fm, R low =0 fm, respectively Surface energy

As we know that shell effect is the diversity of shell model (shell structure) and macroscopic model (bulk property). Thus, the shell correction energy can be obtained from the variance of shell levels and uniformed levels, which is written as the smooth level density is given by is Gaussian distribution width, is a correction function (3-order Laguerre polynomial) is the i-th level calculated by DTCSM Shell correction energy

From the nucleon number N, we can obtain the Fermi energy, which is expressed as 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)

Deformed Two-Center Shell Model (DTCSM) Gherhhescu, Greiner, Munzenberg, PRC68,054314(2003)

Shell correction energies for 40 Ca+ 238 U

3. Coulomb Barrier Static Fusion barrier for 40 Ca 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

Dynamical Coulomb barriers: incident energy dependence

N/Z in neck region for 40 Ca / 48 Ca + 40 Ca/ 48 Ca

4. Fusion/Capture cross sections 16 O+ 16 O 40 Ca+ 40 Ca, 40 Ca+ 48 Ca, 48 Ca+ 48 Ca 16 O U, 40 Ca+ 208 Pb

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

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)

Capture cross sections 16 O+ 208 Pb/ 238 U 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)

5. Conclusions and perspectives Theoretical Models phenomenological:  Dynamical liquid-drop model  Fluctuation-dissipation model  DNS model physical problem ! 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

a couplet        中日 NP2006, 上 海 谢谢！