Energy Functionals from Low-Momentum Potentials

The nonperturbative nature of conventional inter-nucleon interactions is strongly scale or resolution dependent, and can be radically modified by using the renormalization group to lower the momentum cutoff of the two-nucleon potential. Recent calculations demonstrate that using low-momentum potentials (``$V_{{\rm low\ }k}$'') with consistent three-body forces leads to saturating nuclear matter at the Hartree-Fock level, with rapidly converging perturbative corrections in the particle-particle channel $^a$. With these interactions, the density matrix expansion (DME) becomes a natural tool for the microscopic construction of a universal energy functional for nuclei $^b$. By varying the cutoff, the resolution dependence of the functional can be studied. The use of sharp momentum cutoffs in $V_{{\rm low\ }k}$ complicates the application of the DME in coordinate space. This problem is resolved with the recent generalization of $V_{{\rm low\ }k}$ to smooth cutoff regulators. \newline \newline $^a$S.~K.~Bogner, A.~Schwenk, R.~J.~Furnstahl and A.~Nogga, Nucl.\ Phys.\ A {\bf 763}, 59 (2005). \\ $^b$J. W. Negele and D. Vautherin, Phys.\ Rev.\ C {\bf 5}, 1472 (1972).