arXiv subjects

A. Schwenk

Publications and source records attributed to A. Schwenk.

195 records · Page 11Linked to original sources

arXiv2005

Is nuclear matter perturbative with low-momentum interactions?

The nonperturbative nature of inter-nucleon interactions is explored by varying the momentum cutoff of a two-nucleon potential. Conventional force models, which have large cutoffs, are nonperturbative because of strong short-range repulsion, the iterated tensor interaction, and the presence of bound or nearly-bound states. But for low-momentum interactions with cutoffs around 2 fm^{-1}, the softened potential combined with Pauli blocking leads to corrections in nuclear matter in the particle-particle channel that are well converged at second order in the potential, suggesting that perturbation theory can be used in place of Brueckner resummations. Calculations of nuclear matter using the low-momentum two-nucleon force V_{low k} with a corresponding leading-order three-nucleon (3N) force from chiral effective field theory (EFT) exhibit nuclear binding in the Hartree-Fock approximation, and become less cutoff dependent with the inclusion of the dominant second-order contributions. The role of the 3N force is essential to obtain saturation, and the contribution to the total potential energy is compatible with EFT power-counting estimates.

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arXiv2005

Resonant Fermi gases with a large effective range

We calculate the equation of state of a Fermi gas with resonant interactions when the effective range is appreciable. Using an effective field theory for large scattering length and large effective range, we show how calculations in this regime become tractable. Our results are model-independent, and as an application, we study the neutron matter equation of state at low densities of astrophysical interest 0.002 fm^{-3} < rho < 0.02 fm^{-3}, for which the interparticle separation is comparable to the effective range. We compare our simple results with those of conventional many-body calculations.

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arXiv2004

Towards Density Functional Calculations from Nuclear Forces

We propose a method for microscopic calculations of nuclear ground-state properties in the framework of density functional theory. We discuss how the density functional is equivalent to the effective action for the density, thereby establishing a constructive framework for density functional calculations from nuclear forces. The presented approach starts from non-interacting nucleons in a background potential (a simple approximation for the mean field). The nuclear forces are then gradually turned on, while the background potential is removed. The evolution equation yields the ground-state energy and density of a system of interacting nucleons, including exchange-correlations beyond the RPA approximation. The method can start from non-local low momentum (V_{low k}) or chiral interactions.

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arXiv2004

Neutrino Bremsstrahlung in Neutron Matter from Effective Nuclear Interactions

We revisit the emissivity from neutrino pair bremsstrahlung in neutron-neutron scattering, nn -> nn nu nubar, which was calculated from the one-pion exchange potential including correlation effects by Friman and Maxwell. Starting from the free-space low-momentum nucleon-nucleon interaction V_{low k}, we include tensor, spin-orbit and second-order medium-induced non-central contributions to the scattering amplitude in neutron matter. We find that the screening of the nucleon-nucleon interaction reduces the emissivity from neutrino bremsstrahlung for densities below nuclear matter density. We discuss the implications of medium modifications for the cooling of neutron stars via neutrino emission, taking into account recent results for the polarization effects on neutron superfluidity.

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arXiv2004

Polarization contributions to the spin-dependence of the effective interaction in neutron matter

We calculate the modification of the effective interaction of particles on the Fermi surface due to polarization contributions, with particular attention to spin-dependent forces. In addition to the standard spin-spin, tensor and spin-orbit forces, spin non-conserving effective interactions are induced by screening in the particle-hole channels. Furthermore, a novel long-wavelength tensor force is generated. We compute the polarization contributions to second order in the low-momentum interaction V_{low k} and find that the medium-induced spin-orbit interaction leads to a reduction of the 3P2 pairing gap for neutrons in the interior of neutron stars.

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arXiv2003

Instanton contribution to the pion and proton formfactors at Q^2 greater than 1 GeV^2

Studying the instanton-induced contributions to various hard exclusive reactions provides physical insight into the transition from the non-perturbative to the perturbative regime of QCD. To this end, we study the leading-instanton contribution to the electro-magnetic and transition formfactors, using an effective theory of the Instanton Liquid Model. We report predictions for the space-like electro-magnetic formfactor of the pion, as well as recent results for the Dirac formfactor of the proton.

hep-ph↗

arXiv2003

Towards a Model-Independent Low Momentum Nucleon-Nucleon Interaction

We provide evidence for a high precision model-independent low momentum nucleon-nucleon interaction. Performing a momentum-space renormalization group decimation, we find that the effective interactions constructed from various high precision nucleon-nucleon interaction models, such as the Paris, Bonn, Nijmegen, Argonne, CD Bonn and Idaho potentials, are identical. This model-independent low momentum interaction, called V_{low k}, reproduces the same phase shifts and deuteron pole as the input potential models, without ambiguous assumptions on the high momentum components, which are not constrained by low energy data and lead to model-dependent results in many-body applications. V_{low k} is energy-independent and does not necessitate the calculation of the Brueckner G matrix.

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arXiv2003

Model-independent low momentum nucleon interaction from phase shift equivalence

We present detailed results for the model-independent low momentum nucleon-nucleon interaction V_{low k}. By introducing a cutoff in momentum space, we separate the Hilbert space into a low momentum and a high momentum part. The renormalization group is used to construct the effective interaction V_{low k} in the low momentum space, starting from various high precision potential models commonly used in nuclear many-body calculations. With a cutoff in the range of $Λ~ 2.1 fm^{-1}$, the new potential V_{low k} is independent of the input model, and reproduces the experimental phase shift data for corresponding laboratory energies below $E_{lab} ~ 350 MeV$, as well as the deuteron binding energy with similar accuracy as the realistic input potentials. The model independence of V_{low k} demonstrates that the physics of nucleons interacting at low momenta does not depend on details of the high momentum dynamics assumed in conventional potential models. V_{low k} does not have momentum components larger than the cutoff, and as a consequence is considerably softer than the high precision potentials. Therefore, when V_{low k} is used as microscopic input in the many-body problem, the high momentum effects in the particle-particle channel do not have to be addressed by performing a Brueckner ladder resummation or short-range correlation methods. By varying the cutoff, we study how the model independence of V_{low k} is reached in different partial waves. This provides numerical evidence for the separation of scales in the nuclear problem, and physical insight into the nature of the low momentum interaction.

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arXiv2003

Renormalization Group Methods for the Nuclear Many-Body Problem

The application of renormalization group methods to microscopic nuclear many-body calculations is discussed. We present the solution of the renormalization group equations in the particle-hole channels for neutron matter and the application to S-wave pairing. Furthermore, we point out that the inclusion of tensor and spin-orbit forces leads to spin non-conserving effective interactions in nuclear matter.

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arXiv2002

Instanton Contribution to the Proton and Neutron Electric Form Factors

We study the instanton contribution to the proton and neutron electric form factors. Using the single instanton approximation, we perform the calculations in a mixed time-momentum representation in order to obtain the form factors directly in momentum space. We find good agreement with the experimentally measured electric form factor of the proton. For the neutron, our result falls short of the experimental data. We argue that this discrepancy is due to the fact that we neglect the contribution of the sea quarks. We compare to lattice calculations and a relativistic version of the quark-diquark model.

hep-ph↗

arXiv2002

Instanton Contribution to the Pion Electro-Magnetic Formfactor at Q^2 > 1 GeV^2

We study the effects of instantons on the charged pion electro-magnetic formfactor at intermediate momenta. In the Single Instanton Approximation (SIA), we predict the pion formfactor in the kinematic region Q^2=2-15 GeV^2. By developing the calculation in a mixed time-momentum representation, it is possible to maximally reduce the model dependence and to calculate the formfactor directly. We find the intriguing result that the SIA calculation coincides with the vector dominance monopole form, up to surprisingly high momentum transfer Q^2~10 GeV^2. This suggests that vector dominance for the pion holds beyond low energy nuclear physics.

hep-ph↗

arXiv2002

The nucleon interaction and neutron matter from the renormalization group

We show that the renormalization group decimation of modern nucleon potential models to low momenta results in a unique nucleon interaction V_{low k}. This interaction is free of short-ranged singularities and can be used directly in many-body calculations. The RG scaling properties follow directly from the invariance of the scattering phase shifts. We discuss the RG treatment of Fermi liquids. The RG equation for the scattering amplitude in the two particle-hole channels is given at zero temperature. The flow equations are simplified by retaining only the leading term in an expansion in small momentum transfers. The RG flow is illustrated by first studying a system of spin-polarized fermions in a simple model. Finally, results for neutron matter are presented by employing the unique low momentum interaction V_{low k} as initial condition of the flow. The RG approach yields the amplitude for non-forward scattering, which is of great interest for calculations of transport properties and superfluid gaps in neutron star interiors. The methods used can also be applied to condensed matter systems in the absence of long-ranged interactions.

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arXiv2002

Low Momentum Nucleon-Nucleon Interaction and Fermi Liquid Theory

We use the induced interaction of Babu and Brown to derive two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction V_low k in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. We derive the full renormalization group equations in the particle-hole channels from the induced interaction. The new constraints, together with the Pauli principle sum rules, define four combinations of Fermi liquid parameters that are invariant under the renormalization group flow. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints and the Pauli principle sum rules. The effects of tensor forces are discussed.

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arXiv2001

Renormalization Group Equation for Low Momentum Effective Nuclear Interactions

We consider two nonperturbative methods originally used to derive shell model effective interactions in nuclei. These methods have been applied to the two nucleon sector to obtain an energy independent effective interaction V_{low k}, which preserves the low momentum half-on-shell T matrix and the deuteron pole, with a sharp cutoff imposed on all intermediate state momenta. We show that V_{low k} scales with the cutoff precisely as one expects from renormalization group arguments. This result is a step towards reformulating traditional model space many-body calculations in the language of effective field theories and the renormalization group. The numerical scaling properties of V_{low k} are observed to be in excellent agreement with our exact renormalization group equation.

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arXiv2001

Effective Nucleon-Nucleon Interaction and Fermi Liquid Theory

We present two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. Moreover, the new constraints define two combinations of Fermi liquid parameters, which are invariant under the renormalization group flow in the particle-hole channels. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints as well as the Pauli principle sum rules.

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