Realistic Interactions and Configuration Mixing in Fermionic Molecular Dynamics

In Fermionic Molecular Dynamics the occurrence of multifragmentation depends strongly on the intrinsic structure of the many-body state. Slater determinants with narrow single-particle states and a cluster substructure show multifragmentation in heavy-ion collisions while those with broad wave functions, which resemble more a shell-model picture, deexcite by particle emission. Which of the two type of states occurs as the ground state minimum or as a local minimum in the energy depends on the effective interaction. Both may equally well reproduce binding energy and radii of nuclei. This ambiguity led us to reinvestigate the derivation of the effective interaction from realistic nucleon-nucleon potentials by means of a unitary correlation operator which is much more suited for dynamical calculations than the G-matrix or the Jastrow method. First results of mixing many Slater determinants are also presented. 1 Fermionic Molecular Dynamics Fermionic Molecular Dynamics (FMD) [2, 3, 5] is a model to describe ground states of atomic nuclei and heavy-ion reactions in the low to medium energy regime below the threshold for particle production. The FMD trial state ∣∣ Q̂〉 takes care of the Pauli principle explicitly by using a Slater determinant of gaussian single-particle states ∣∣qi 〉. ∣∣ Q̂〉 = C∼A∼ (∣∣q1 〉⊗·· ·⊗ ∣∣qA 〉) (1) A∼ is the antisymmetrization operator and C∼ is an optional unitary correlation operator which will be discussed later. The single-particle states ∣∣qi 〉 are gaussians with mean position and mean momentum parametrized by 3 complex parameters~b and a dynamical complex width a. Spin ∣∣χ 〉 and isospin ∣∣ξ 〉 are usually parametrized as two-spinors 〈 ~x ∣∣q〉 = 〈~x ∣∣a,~b,χ ,ξ 〉 = exp{−(~x−~b) 2a }∣∣χ 〉⊗ ∣∣ξ 〉 . (2) The description with gaussian single-particle states is the closest analogue to a classical phase-space trajectory and therefore allows for a descriptive interpretation of the FMD time evolution. The gaussians form an overcomplete set and allow to represent shell-model states as well as intrinsically deformed states. The dynamical equations are derived from the time-dependent variational principle δ Z dt 〈 Q̂ ∣∣ i d dt −H∼ ∣∣ Q̂〉 〈 Q̂ ∣∣ Q̂〉 = 0 . (3) The variation with respect to the parameters qν which are contained in the trial state ∣∣ Q̂〉 leads to the Euler-Lagrange equations of motion i∑ ν Cμν q̇ν = ∂H ∂qμ (4) with generalized forces given by the gradient of the Hamilton function H and the matrix C which describes the geometrical structure of the fermion phase-space. Cμν = ∂ ∂qμ ∂ ∂qν ln 〈 Q̂ ∣∣ Q̂〉 , H = 〈 Q̂ ∣H∼ ∣∣ Q̂〉 〈 Q̂ ∣∣ Q̂〉 (5) The initial state of a reaction, which is evolved in time according to eq. (4), is the antisymmetrized product of boosted ground states. 2 Multifragmentation The results of FMD calculations for multifragmentation reactions show a strong dependence on the intrinsic structure of the nuclear states which is determined by the effective interaction. All nucleon-nucleon interactions which we use are adjusted to describe well binding energies and radii of ground states. They differ mainly in their momentum dependent parts which are poorly determined by the ground state properties but can lead to very different behavior in the dynamics of a heavy-ion reaction. This effect is demonstrated in fig. 1 where we display density contour plots of 40Ca+40Ca reactions at energy Elab = 35 AMeV and impact parameter b = 2.75 fm. Figure 1: Density plots of 40Ca+40Ca at Elab = 35 AMeV and b = 2.75 fm. Crosses indicate centroids of gaussians. Crosses without surrounding contours are from wave packets which have spread so much that their density is below the lowest contour (evaporated nucleon). The used phenomenological interaction has an FMD ground state with an α cluster structure. Only 1 MeV above is a stationary FMD state (local minimum) which shows no clustering in coordinate space but looks more like a closed spherical sd-shell nucleus. These two energetically almost degenerate states behave completely different in heavy ion reactions. The clustered states lead to multifragmentation where the spatial correlations in the initial state survive to a large extend the collision. Reactions with the spherical states show no multifragmentation. Here we observe binary inelastic collisions followed by deexcitation through evaporation of single nucleons. Collisions between the two different types of FMD states result in a somewhat mixed situation. It also happens that a smooth nucleus sometimes jumps during a collision into a cluster configuration and vice-versa. The effect of initial correlations is further studied in the decay of excited 56Fe nuclei where the initial excitation energy was created in different ways. In the upper rows of fig. 2 we can see the effect of random excitations which destroy the spatial ra nd om d is pl ac em en ts