Microscopic DC-TDHF study of heavy-ion potentials and fusion cross sections, V. E. Oberacker, Vanderbilt University, USA − The calculation of heavy-ion interaction potentials is of fundamental importance for the study of fusion reactions between stable and neutron-rich nuclei, and for the study of superheavy element production.

We have developed a new microscopic method to extract ion-ion potentials directly from the TDHF time-evolution of the nuclear system.  The only input is the effective NN interaction (Skyrme), there are no adjustable parameters.

In the DC-TDHF approach [1] the TDHF time-evolution takes place with no restrictions.  At certain times during the evolution the instantaneous density is used to perform a static Hartree-Fock minimization while holding the neutron and proton densities constrained to be the corresponding instantaneous TDHF densities. There is no need to introduce constraining operators which assume that the collective motion is confined to the constrained phase space.  Rather, we have a self-organizing system which selects its path following the microscopic dynamics.

Some of the effects included in DC-TDHF are: neck formation, mass exchange, internal excitations, deformation effects to all order, and nuclear alignment for deformed systems.

From the calculations, carried out on a 3-D lattice, we obtain heavy-ion interaction potentials, fusion/capture cross sections, dynamic excitation energies E*(t) during the collision, and pre-equilibrium photon emission due to giant resonances excitation in fusion reactions. The theory has been applied to the reactions ⁶⁴Ni+¹³²Sn [2], ⁶⁴Ni+⁶⁴Ni [3], ¹⁶O+²⁰⁸Pb [4], ⁷⁰Zn+²⁰⁸Pb and ⁴⁸Ca+²³⁸U [5], and ^132,124Sn+⁹⁶Zr [6]. Very recent calculations for ^40,48Ca+^124,132Sn fusion rections (measured at HRIBF) will be presented.

We have also developed a new method [7] to calculate the ion-ion potential in terms of building blocks which we refer to as ”single-particle interaction potentials''.  The breakdown of the ion-ion potential to the single-particle level shows which states are driving the system towards fusion (bonding states) and which states resist fusion (anti-bonding states).

[1] A. S. Umar and V. E. Oberacker, Phys. Rev. C 74, 021601(R) (2006).

[2] A. S. Umar and V. E. Oberacker, Phys. Rev. C 76, 014614 (2007).

[3] A. S. Umar and V. E. Oberacker, Phys. Rev. C 77, 064605 (2008).

[4] A. S. Umar and V. E. Oberacker, Eur. Phys. J. A 39, 243 (2009).

[5] A. S. Umar, V. E. Oberacker, J. A. Maruhn and P.-G.  Reinhard, Phys. Rev. C 81, 064607 (2010).

[6] V. E. Oberacker, A. S. Umar, J. A. Maruhn and P.-G. Reinhard, Phys. Rev. C 82, 034603 (2010).