Short-range correlations in nuclei with similarity renormalization group transformations

Abstract

$\mathbf{Background}:$ Realistic nucleon-nucleon interactions induce short-range correlations in nuclei. To solve the many-body problem unitary transformations like the similarity renormalization group (SRG) are often used to soften the interactions. $\mathbf{Purpose}:$ Two-body densities can be used to illustrate how the SRG eliminates short-range correlations in the wave function. The short-range information can however be recovered by transforming the density operators. $\mathbf{Method}:$ The many-body problem is solved for ${}^4$He in the no core shell model (NCSM) with SRG transformed AV8' and chiral N3LO interactions. The NCSM wave functions are used to calculate two-body densities with bare and SRG transformed density operators in two-body approximation. $\mathbf{Results}:$ The two-body momentum distributions for AV8' and N3LO have similar high-momentum components up to relative momenta of about $2.5{\mathrm{fm}}^{-1}$, dominated by tensor correlations, but differ in their behavior at higher relative momenta. The contributions of many-body correlations are small for pairs with vanishing pair momentum but not negligible for the momentum distributions integrated over all pair momenta. Many-body correlations are induced by the strong tensor force and lead to a reshuffling of pairs between different spin-isospin channels. $\mathbf{Conclusions}:$ When using the SRG it is essential to use transformed operators for observables sensitive to short-range physics. Back-to-back pairs with vanishing pair momentum are the best tool to study short-range correlations.

13 pages, 9 figures, submitted to Phys. Rev. C

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