Heavy-ion interaction potential deduced from density-constrained time-dependent Hartree-Fock calculation

Abstract

We present a new method for calculating the heavy-ion interaction potential from a densityconstrained time-dependent Hartree-Fock calculation.PACS numbers: 21.60.Jz,25.60.Pj, The study of internuclear potentials for heavy-ion collisions is of fundamental importance for the formation of superheavy elements and nuclei far from stability. While asymptotically such potentials are determined from Coulomb and centrifugal interactions, the short distance behavior strongly depends on the nuclear surface properties and the readjustments of the combined nuclear system, resulting in potential pockets, which determine the characteristics of the compound nuclear system.Among the various approaches for calculating ion-ion potentials are: 1) Phenomenological models such as the Bass model [1,2], the proximity potential [3,4,5,6], and potentials obtained via the double-folding method [7,8,9,10]. Some of these potentials have been fitted to experimental fusion barrier heights and have been remarkably successful in describing scattering data. 2) Semi-microscopic and full microscopic calculations such as the macroscopic-microscopic method [11,12,13], the asymmetric two-center shell-model [14], constrained Hartree-Fock (CHF) with a constraint on the quadrupole moment or some other definition of the internuclear distance [15,16], and other mean-field based calculations [17,18,19].One common physical assumption used in many of the semi-microscopic calculations is the use of the frozen density or the sudden approximation. As the name suggests, in this approximation the nuclear densities are unchanged during the computation of the ion-ion potential as a function of the internuclear distance. On the other hand, the microscopic calculations follow a minimum energy path and allow for the rearrangement of the nuclear densities as the relevant collective parameter changes. As it was pointed out in Ref. [12], CHF calculations seldom produce the correct saddle-point since the system can follow any one of the minimum potential valleys in the multidimensional potential energy surface. In this paper, we shall call this the static adiabatic approximation since a real adiabatic calculation would involve a fully dynamical calculation, thus also including the effects of dynamical rearrangements.One conclusion that may be reached from the discussion above is that ultimately we would like to have an approach for calculating internuclear potentials which is time-dependent and is unrestricted in the choice of collective variables. In this paper we provide such an approach in which time-dependent Hartree-Fock (TDHF) is used for the nuclear dynamics and the potential energy is calculated by constraining the time-dependent density.The density constraint is a novel numerical method that was developed in the mid 1980's [20,21] and was used to provide a microscopic description of the formation of shape resonances in light systems [21]. In this approach the TDHF time-evolution takes place with no restrictions. At certain times during the evolution the instantan...

Shape evolution and collective dynamics of quasifission in the time-dependent Hartree-Fock approach

“…In addition, the quality of effective interactions has been substantially improved [94][95][96][97]. In order to overcome the lack of quantum tunneling preventing direct studies of sub-barrier fu-sion, the DC-TDHF method was developed to compute heavy-ion potentials [35] and excitation energies [98] directly from TDHF time-evolution. For instance, this method was applied to calculate capture cross-sections for hot and cold fusion reactions leading to superheavy element Z = 112 [65].…”

“…Dynamical microscopic approaches are a standard tool to extract macroscopic properties in heavy-ion collisions [35][36][37][38][39]. In particular, the time-dependent Hartree-Fock theory [40], has been recognized for its realistic description of several low-energy nuclear reaction mechanisms [41,42].…”

“…As a dynamical microscopic theory, TDHF provides us with the complete shape evolution of the nuclear densities which can be used to compute the time evolution of deformation and inertia parameters. Using an extension to TDHF, the so-called density constraint TDHF (DC-TDHF) approach [35], it is also possible to compute the excitation energy in the fragments.…”

Microscopic study ofCa40+Ni58,64fusion reactions

“…Microscopic potentials can be calculated directly from TDHF dynamics [12,55]. Alternatively, one can start with the bare potential computed from a frozen Hartree-Fock approach [12,21] and use a CC code to incorporate the dynamical couplings to collective modes following the approach proposed in Ref.…”

Theoretical study of fusion reactions 32S + 94,96Zr and 40Ca + 94,96Zr and quadrupole deformation of 94Zr

“…In the quantum coupled channel (QCC) model [48], the coupling to PQNT channels is treated approximately by using a macroscopic form factor. Within the microscopic dynamics models, such as the quantum molecular dynamic model [49][50][51][52][53][54] and the time-dependent HartreeFock method [55][56][57][58][59][60][61], the effects of surface excitations as well as nucleon transfer can be automatically included. Up to now, although many experiments and theoretical efforts have been devoted to study the mechanism of the coupling to PQNT channels, the underlying mechanism is still far from a clear understanding.…”