Low momentum nucleon-nucleon potentials with half-on-shell T-matrix equivalence

We show that realistic nucleon-nucleon (NN) potentials VNN can be reduced, in a physically equivalent way, to an effective low-momentum potential Veff whose momentum-space matrix elements Veff (k , k) are non-vanishing only within a cut-off momentum kcut. Our effective potential is obtained using the folded-diagram method of Kuo, Lee and Ratcliff, and this effective potential is shown to preserve the half-on-shell T-matrix. Applications have been performed for the Bonn-A and Paris NN potentials, using various choices for kcut such as 2 fm. The deuteron binding energy given by VNN is reproduced by Veff , and so are the low-energy phase shifts up to Elab = 2k 2 cuth̄ /M . In addition, the low-momentum half-on-shell T-matrices given by VNN and Veff are identical, namely 〈k | T (ω = εk) | k〉 = 〈k ′ | Teff (ω = εk) | k〉; k , k ≤ kcut. For kcut ≈ 2 fm , our derived low-momentum Veff is generally smooth and may be used directly for nuclear many-body calculations, without first calculating the Brueckner G matrix. 13.75.cs;21.30.+y;21.60.Cs;27.20.+n Typeset using REVTEX