Counter terms for low momentum nucleon–nucleon interactions

Holt, J. D.; Kuo, T.T.S.; Brown, G. E.; Bogner, S. K.

doi:10.1016/j.nuclphysa.2003.12.004

Cited by 18 publications

(26 citation statements)

References 40 publications

(64 reference statements)

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“…This is consistent with the modification taking the form of a regulated delta function in coordinate space, which is primarily a uniform shift in momentum space below the cutoff scale. Such a shift has been previously identified for the SRG [27,28] and for the V low k RG [29]. We see a rapid and dramatic dissolution of the repulsive core and a relatively weak modification at longer ranges (r > 2 fm) once we have evolved below about 2 fm −1 .…”

Section: Visualizationsupporting

confidence: 82%

Local projections of low-momentum potentials

2012

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Nuclear interactions evolved via renormalization group methods to lower resolution become increasingly non-local (off-diagonal in coordinate space) as they are softened. This inhibits both the development of intuition about the interactions and their use with some methods for solving the quantum many-body problem. By applying "local projections", a softened interaction can be reduced to a local effective interaction plus a non-local residual interaction. At the two-body level, a local projection after similarity renormalization group (SRG) evolution manifests the elimination of short-range repulsive cores and the flow toward universal low-momentum interactions. The SRG residual interaction is found to be relatively weak at low energy, which motivates a perturbative treatment.

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Section: Visualizationsupporting

confidence: 82%

Local projections of low-momentum potentials

2012

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“…In a recent work it has been made clear that the momentum-space V lowk approach [24] displays a remarkable symmetry pattern which in the case of Wigner SU (4) spin-isospin symmetry with nucleons in the fundamental representation may be related unambiguously to large N c dynamical features of QCD [29] as analyzed in detail in Refs. [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Symmetries of the similarity renormalization group for nuclear forces

2012

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We analyze the role played by Long Distance Symmetries within the context of the Similarity Renormalization Group (SRG) approach, which is based on phase-shift preserving continuous unitary transformations that evolve hamiltonians with a cutoff on energy differences. We find that there is a SRG cutoff for which almost perfect fulfillment of Wigner symmetry is found. We discuss the possible consequences of such finding.

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“…V low−k , on the other hand, is energy independent so no such difficulties are encountered. Since detailed treatments of V low−k have been given elsewhere [12,13,14,15,16,17,18], here we provide only a brief description. We define V low−k through the T -matrix equivalence equations…”

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Low momentum shell model effective interactions with all-order core polarizations

Holt

Kuo

et al. 2005

Phys. Rev. C

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An all-order summation of core polarization diagrams using the low-momentum nucleon-nucleon interaction V low−k is presented. The summation is based on the Kirson-Babu-Brown (KBB) induced interaction approach in which the vertex functions are obtained self consistently by solving a set of non-linear coupled equations. It is found that the solution of these equations is simplified by using V low−k , which is energy independent, and by employing Green functions in the particle-particle and particle-hole channels. We have applied this approach to the sd-shell effective interactions and find that the results calculated to all orders using the KBB summation technique are remarkably similar to those of second-order perturbation theory, average differences being less than 10%. . In microscopic calculations of effective interactions, core polarization has played an essential role, as illustrated by the familiar situation in 18 O. There the spectrum calculated with the bare G-matrix was too compressed compared with experiment, while the inclusion of core polarization had the desirable effect of both lowering the 0 + ground state and raising the 4 + state, leading to a much improved agreement with experiment [1, 2]. As pointed out by Zuker [4], the Kuo-Brown matrix elements, although developed quite some time ago, continue to be a highly useful shell model effective interaction. It should be noted that the core polarization (CP) diagrams associated with the above interactions were all calculated to second order (in the G-matrix) in perturbation theory. But what are the effects of core polarization beyond second order, and how can they be calculated? In this Letter we would like to address these questions and present an all-order summation of CP diagrams for the sd-shell interactions.

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Counter terms for low momentum nucleon–nucleon interactions

Cited by 18 publications

References 40 publications

Local projections of low-momentum potentials

Local projections of low-momentum potentials

Symmetries of the similarity renormalization group for nuclear forces

Low momentum shell model effective interactions with all-order core polarizations

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