Unitary Correlation Operator Method

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y [fm] y [fm] 6 4 2 0 -2 -4 -6 1.0 1.5 0.5 0.1 0.01 4 He y [fm] 6 4 2 0 -2 -4 -6 Afnan-Tang S3M Potential Groundstate Densities ρ(r) [ρ [ρ0] 0] 10 -1 10 -1 10 -2 10 -2 0.1 0.5 0.01 1 1.0 10 -3 10 -3 10 -4 10 -4 0.01 total neutron proton y [fm] 7 Li 6 4 2 0 -2 -4 -6 ρ(r) [ρ [ρ0] 0] 4 He 6 -6 -4 -2 0 2 4 6 -6 -4 -2 0 0 1 2 2 4 3 6 -6 4 -4 5 -2 0 0 1 2 2 4 3 6 -6 4 -4 5 -2 0 0 1 2 2 4 3 6 4 5 0 20 24 20 28 24 40 28 x [fm] Ne 1 x [fm] r Mg [fm] Ne 1 x [fm] r [fm] Si Mg 1 x [fm] r [fm] Ca Si 1 4 4 4 4 2 0 -2 -4 -6 1.0 0.01 0.01 0.5 0.1 0.1 y [fm] -2 -4 -6 -6 -4 -2 0 x [fm] 2 4 6 2 0 ρ(r) [ρ [ρ0] 0] 0.1 0.01 0.01 10 -1 10 -1 10 -2 10 -2 1.0 0.5 10 -3 10 -3 10 -4 10 -4 • one gaussian per nucleon, fixed spin 0.1 0.5 total neutron proton y [fm] 2 0 -2 -4 -6 ρ(r) [ρ [ρ0] 0] 0.1 0.01 10 -1 10 -1 1.0 1 10 -2 10 -2 10 -3 10 -3 0.5 0.1 0.01 10 -4 10 -4 10 -1 10 -1 10 -2 10 -2 1.0 0.5 10 -3 10 -3 10 -4 10 -4 0.01 1.0 0.01 0.1 1.0 total neutron proton 0.1 total neutron proton 12 C y [fm] 6 4 2 0 -2 -4 -6 ρ(r) [ρ [ρ0] 0] 7 Li 1 10 -1 10 -1 10 -2 10 -2 1.0 0.5 10 -3 10 -3 0.1 0.01 10 -4 10 -4 0.01 0.1 total neutron proton -6 -4 -2 0 0 1 2 2 4 3 6 -6 4 -4 5 -2 0 0 1 2 2 4 3 6 -6 4 -4 5 -2 0 0 1 2 2 4 3 6 4 5 x [fm] r [fm] x [fm] r [fm] x [fm] r [fm] y [fm] 2 0 -2 -4 -6 ρ(r) [ρ [ρ0] 0] 0.01 10 -1 10 -1 10 -2 10 -2 0.5 1.0 10 -3 10 -3 0.1 0.01 10 -4 10 -4 0.1 1.5 0.5 total neutron proton 16 O 0.01 R. Roth ρ(r) [ρ [ρ0] 0] ρ(r) [ρ [ρ0] 0] 12 C 1 10 -1 10 -1 10 -2 10 -2 10 -3 10 -3 10 -4 10 -4 10 -1 10 -1 10 -2 10 -2 10 -3 10 -3 10 -4 10 -4 0
Outlook Summary UCOM & FMD Summary & Outlook • Unitary Correlation Operator Method describes short-range correlations by a distance-dependent transformation in the relative two-body coordinate • correlated Hamiltonian / effective interaction in two-body approximation is given in closed form; higher cluster orders are negligible in case of finite nuclei • variational model based on a Slater determinant of Gaussian trial states (Fermionic Molecular Dynamics) to describe groundstate structure of light and intermediate mass nuclei • for central potentials (MTV/ATS3M) the results are comparable with quasi-exact and expensive many-body techniques • need realistic NN-interaction, e.g. Bonn or Argonne potential, including a proper treatment of tensor correlations • ready for systematic and nearly ab initio nuclear structure studies • can be used for the description of low-energy nucleus-nucleus collisions right away R. Roth
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Unitary Correlation Operator Method

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