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Q: How to treat short-range correlations in-duced by the strong repulsive core of the2body interaction within a many-bodysystem?

A: Unitary Correlation Operator Method!

...some keywords

★ elements: correlation operator/function,correlated states, correlated opera-tors/Hamiltonian, equation of state,correlated density matrix

★ approximations: 2body approximation,3body contributions, effective higher or-der contributions

★ application I: homework problem forneutron matter, equation of state, 2bodydensity & occupation numbers

★ application II: phenomenological GCT-potential for nuclear matter, equation ofstate

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3body correlations

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Summary & Outlook#20

what was shown here...

✔ UCOM is a new and promising approach totame short-range correlations in the context ofquantum many-body problems

✔ unitary coordinate transformation of states oroperators to introduce correlations

✔ in 2body approximations the correlated inter-action has a simple analytic form

✔ higher order contributions can be calculatedexplicitly or included effectively

✔ convincing results for the homework problemand nuclear matter with the GCT potential

coming up next...

★ application to the zoo of atomic many-bodysystem: liquid � He, liquid

�He and droplets,

trapped Bose-Einstein condensates...

★ nuclear many-body systems with realistic in-teractions: tensor correlations!!!

★ use of the correlated realistic interactions as in-put for simulation of dynamics: nuclear colli-sions (FMD) and BEC dynamics.