Feldmeier, H.

Neff, T.

Weber, D.

GSI Repository

Short-range correlations studied with unitarily transformed operators∗T. Neff1, H. Feldmeier1, and D. Weber1,21GSI, Darmstadt, Germany; 2ExtreMe Matter Institute EMMI, GSI, Darmstadt, GermanyIntroductionShort-range correlations in nuclei are of great interest forthe theoretical understanding of nuclear matter at high den-sities. Experimental investigations for example in (e, e′pp)and (e, e′pn) reactions at large momentum transfer [1]illustrate that the momentum distributions for momentalarger than the Fermi momentum are dominated by tensorcorrelations. In a previous study [2] we investigated short-range correlations and momentum distributions in A =2, 3, 4 nuclei using exact few-body wave functions. Forheavier nuclei this is no longer feasible and one has to useother many-body approaches like the no-core shell model.It is however not possible to obtain converged results withbare interactions. One therefore employs unitary transfor-mations to soften the Hamiltonian. Typical approaches arethe unitary correlation operator method (UCOM) [3] or thesimilarity renormalization group (SRG).Similarity Renormalization GroupIn the SRG approach one solves the flow equationdHˆαdα= (2μ)2[[Tˆint, Hˆα], Hˆα](1)with Hˆα=0 = Hˆ to obtain an effective Hamiltonian Hˆα.With increasing flow parameter α the effective interactionbecomes softer and the eigenstates |Ψα〉 of the evolvedHamiltonianHˆα |Ψα〉 = Eα |Ψα〉 (2)contain less and less high-momentum components thanthe eigenstates |Ψ〉 of the bare Hamiltonian. To recoverthe high-momentum components one has to use effectivedensity operators that are obtained using the same unitarytransformation as for the Hamiltonian. For computationalreasons the flow equation (1) is solved in two-body approx-imation which induces a dependence on the flow parameterfor observables like the energiesEα and also the two-bodydensities. This dependence on α can be used to study theimportance of the omitted higher body contributions.ResultsIn Fig. 1 we show the two-body densities of the 4He nu-cleus in momentum space obtained in no-core shell modelcalculations using SRG transformedHamiltonians and baredensity operators (top) and SRG transformed density oper-ators (bottom). With the bare interaction the two-body den-sities contain high-momentum components caused by the∗ supported by Helmholtz Alliance EMMIS0,T1bareΑ0.01Α0.04Α0.20104103102101100101102nrel kfm3 S1,T0bareΑ0.01Α0.04Α0.20S0,T1bareΑ0.01Α0.04Α0.200 1 2 3 4104103102101100101102k fm1nrel kfm3 S1,T0bareΑ0.01Α0.04Α0.200 1 2 3 4k fm1Figure 1: Two-body densities in momentum space for theS=0, T=1 and S=1, T=0 channels calculated with theeigenstates of SRG transformed AV8’ Hamiltonians forflow parameters α of 0.01 fm4, 0.04 fm4 and 0.20 fm4 us-ing bare density operators (top) and effective density oper-ators (bottom).short-range repulsion in the Argonne interaction. The sig-nificantly larger high momentum components in the S=1,T=0 channel are caused by the tensor force. With increas-ing α the high-momentum components in the wave func-tion get smaller. By using the transformed density oper-ators the high-momentum components can be recovered.Comparing the two channels we observe a striking differ-ence in the momentum region between 1.5 and 3.0 fm−1.Whereas the two-body densities in the S=1, T=0 channelare almost independent from α, the two-body densities inthe S=0, T=1 channel show a significant α-dependence.This reflects many-body correlations in the wave functioninduced by the tensor force.References[1] R. Subedi et al., Science 320, 1476 (2008).[2] H. Feldmeier, W. Horiuchi, T. Neff, Y. Suzuki, Phys. Rev. C84, 054003 (2011).[3] R. Roth, T. Neff, H. Feldmeier, Prog. Part. Nucl. Phys. 65, 50(2010).[4] T. Neff, H. Feldmeier, D. Weber, in preparationGSI SCIENTIFIC REPORT 2012 PHN-ENNA-THEORY-01215

Short-range correlations studied with unitarily transformed operators

http://repository.gsi.de/record/52114/files/PHN-ENNA-THEORY-01.pdf

Short-range correlations studied with unitarily transformed operators

Abstract

Similar works

Full text

Available Versions

GSI Repository