Nucleon DIffusion in Heavy-Ion Collisions S. Saatci1, O. Yılmaz1, B. Yılmaz2, and Ş. Ayık3 1Physics Department, Middle East Technical University, Ankara, Turkey 2Physics Department, Ankara University, Ankara, Turkey 3Physics Department, Tennessee Techn University, Cookeville, USA NUFRA 2015, Fifth International Conference on Nuclear Fragmentation, Antalya, Kemer October 05, 2015

Outline Heavy-Ion Reactions Nucleon Exchange and Transport Coefficients Formalism for Nucleon Exchange Quantal Diffusion Coefficients Preliminary Results

Heavy-Ion Reactions Fusion Small impact parameters and energies above Coulomb barrier. Target and projectile can merge to produce one nuclei. Deep-Inelastic Collisions Close collisions, low energies near Coulomb barrier, Ecm ≈0.95Vc. Colliding projectile and target ions exchange a few nucleons through the window and seperate again.

Nucleon Exchange and Transport Coefficients Transport coefficients for nucleon exchange are related to macroscopic variables such as mass and charge transfer of target-like and projectile-like fragments. The nucleon number of the projectile-like fragments or its mass distribution can be deduced from transport coefficients. Fluctuations of collective variables play important role in processes such as deep inelastic heavy-ion collisions and heavy-ion fusion near Coulomb barrier energies. Standard mean-field theories Cannot describe the dynamics of fluctuations of collective motion. Provide a good description of the average evolution, however, the width of the fragment mass distribution appears smaller. Stochastic mean-field approximation an ensemble of single-particle density matrices is constructed by incorporating quantal and thermal fluctuations in the initial state. Not only the mean value of an observable, but the probability distribution of the observable is also found. Two mechanisms for fluctuations: collisional fluctuations generated by two-body collisions (at high energy nuclear collisions), one-body mechanism or mean-field fluctuations originating from quantal and thermal fluctuations in the initial state (at low energies).

Formalism for Nucleon Exchange A member of single-particle density matrix of each event, λ : Time-independent elements of density matrix determined by the initial condition, which are Gaussian random numbers with mean value Occupied (hole) and unoccupied (particle) states Spin-isospin quantum number The variance of the fluctuating part is given by : Non-zero initial fluctuations only between particle and hole states! ensemble average Mean values of the single-particle occupation factors that is zero or one at zero temperature, Fermi-Dirac distribution at finite temperature Time evolution of each wave function by its own mean-field of each event :

Quantal Diffusion Coefficients Nucleon density Continuity equation Current density Mass number of the projectile-like fragments: Step function Location of the window Nucleon Flux: Nucleon drift coefficient , its mean value is zero for symmetric systems Fluctuating part of nucleon flux (quantal effect)

Variance of the fragment mass distribution is calculated by Quantal and memory dependent diffusion coefficient for nucleon exchange is determined by the correlation function of the stochastic part of the nucleon flux Diffusion coefficient particle hole Variance of the fragment mass distribution is calculated by We extended Umar’s TDHF code to calculate the time-dependent unoccupied single-particle wave functions in addition to the occupied hole states.

Preliminary Results Quantal diffusion coefficient for nucleon exchange in the central collision of t=400 fm/c t=700 fm/c t=1000 fm/c The calculations exibit a smooth behavior as a function of time. As expected, neutron exchange becomes larger than proton for neutron rich system. Quantal variance of the fragment mass distributions is obtained in a stochastic approach.