Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyrme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in arXiv:0910.4979 by Gebremariam et al. to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N²LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a coupling constant arising from zero-range contact interactions and a coupling function of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A link to a downloadable Mathematica notebook containing the novel density-dependent couplings is provided.     

Antikaon production in nucleon- nucleon reactions near threshold

The antikaon production cross section from nucleon-nucleon reactions near threshold is studied in a meson exchange model. We include both pion and kaon exchange, but neglect the interference between the amplitudes. In case of pion exchange the antikaon production cross section can be expressed in terms of the antikaon production cross section from a pion-nucleon interaction, which we take from the experimental data if available. Otherwise, a K* -resonance exchange model is introduced to relate the different reaction cross sections. In case of kaon exchange the antikaon production cross section is related to the elastic KN and K?N cross sections, which are again taken from experimental measurements. We find that the one-meson exchange model gives a satisfactory fit to the available data for the NN → NN KK? cross section at high energies. We compare our predictions for the cross section near threshold with an earlier empirical parameterization and that from phase space models.     

The weak pion-nucleon vertex revisited

We evaluate the parity-violating weak pion-nucleon vertex in the framework of a chiral soliton model including pions and the vector mesons ρ and ω. The weak πN coupling constant >G_π is enhanced by a factor of 13.3 for the standard electro-weak model as compared to the Cabbibo model, with its absolute value given by G_π ≈ 2.7 · 10⁻⁸. We compare our results to available data and other theoretical determinations. In particular, we predict the γ-asymmetry in ¹⁸F to be |P(¹⁸F)|= 1.2 · 10⁻⁴. We also discuss calculational differences to standard quark model estimates.     

A computation of Adler's β sum rule II

We improve our previous calculation of Adler's β sum rule by including the Born contributions to the πN states. The result is that the sum rule is only balanced if the weak axial nucleon form factor g_A(q²) and the strong pion-nucleon form factor have roughly the same q² dependance.     

A study of the nuclear response function

We examine the excitation properties of spherical nuclei in the Random Phase Approximation using the Green's function method. The calculations are done with interactions of the Skyrme type for nuclei from ¹⁶O to ²⁰⁸Pb. Different Skyrme interactions can have the same predictions for ground state Hartree-Fock properties, but give quite different predictions for the dynamic response. Our calculations favor a mild velocity-dependence in the interaction, such as given by Skyrme I. The level of agreement with empirical properties is as follows: energies of low-lying states, ≈25%; positions of giant resonances, ≈10%; transition rates of low states, factor of 2 typical. Inelastic scattering of electrons is reasonably accounted for by the model, but nucleon inelastic scattering has difficulties with the noncollective strength.     

η Production in proton-nucleus reactions

The production ofη-mesons in proton-nucleus reactions is analysed with respect to primary nucleon-nucleon (NN→NNη) and secondary pion-nucleon (πN→ηN) production processes on the basis of Hartree-Fock groundstate momentum distributions and free on-shell production processes. The folding model adopted compares well for meson production with more involved simulations based on VUU transport equations. Similar to K⁺ production in proton-nucleus reactions theη-mesons are primarily produced by theπN →ηN channel. However,η-mesons are absorbed in nuclei via excitation of the N^* (1535) resonance which leads to strong distortions of the primordial spectra. On the other hand, the experimental mass dependence of the differential cross sections might yield information about the in-medium properties of this resonance.     

Vertex form factors of the rho-meson nucleon interaction at low momentum transfer

We calculated the one pion loop contributions to the form factors of the rho-nucleon interaction within a field theoretical model using effective Lagrangians. The results show that the tensor interaction is likely to be described well within such an approach. We obtain a magnetic coupling in the range of 3.5–7.1 atQ ²=0, depending on the choice of pion-nucleon form factor and a dipole form for theQ ² dependence tensor form factor with a scale of roughly 900 MeV for space-like momentum transfer. The results agree with the findings of the recent analysis of thep-N interaction and support a small scale parameter (0.5 GeV) for the pion-nucleon form factor.This work is supported by BMFT (06BO7027) and COSY-KFA Jülich (41140512)     

Helicity flip in exclusive deep-inelastic ϱ0 production

The European Muon Collaboration reports that in exclusive ϱ⁰ production in deep-inelastic muon scattering from hydrogen and nitrogen targets, the ϱ⁰ is found predominately in a longitudinally polarised state. The t-dependence is typical of a hard scattering process. The ϱ⁰'s are claimed to be mainly produced by transverse photons. The cross section decreases as (Q²)⁻². While the latter is expected in a vector dominance model, the dominance of helicity flip is inconsistent with such a model. We show that it is possible to reconcile these experimental results in a simple hard scattering model. However, we must suppose the photons mainly longitudinal, in agreement with Donnachie and Landshoff.     

Effective Interactions in the Delta-Shells Potential

We determine two-body Skyrme force parameters from a nucleon–nucleon interaction as a function of the maximal momentum fitting NN scattering data. We find general agreement with V _{low k} interactions based on high quality potentials.     

Threshold electroproduction experiments and the axial vector form factor

Data from three coincidence experiments which measure the cross section for π⁺ electroproduction around threshold are compared. Application of the PCAC motivated pseudovector Born approximation model yields corresponding values of the nucleon axial vector form factor for spacelike momentum transfer up to 0.6 GeV². Attention is paid to possible theoretical uncertainties and to the influence of the first pion-nucleon resonance. (Recent single arm SLAC results are also included.)     

ωNN vertex function and the γπππ anomaly

We show that the empirical ωNN form factor (cut-off 1400–C1500 MeV) can be understood as arising from a combination of a quark model form factor (typical cut-off 700–C800 MeV) and an anomalous form factor ～ q ² arising from the 3π-intermediate state. The anomaly contributes to the Dirac form factor F ₁(q ²) with F ₁(0) = 0, (and sizable), and to the Pauli form factor F ₂(q ²) with F ₂(0) ≠ 0. The resulting tensor coupling F2(0) is sensitive to the cut-off of the pion momenta in the two-loop integrals and turns out to be small for values around 1 GeV. The quark model ωNN tensor coupling F ²(0) vanishes for point-like quarks. The anomaly, however, contributes a non-vanishing tensor coupling which can be seen to effectively enhance the vector coupling in NN models which do not include a tensor coupling.     

Effective chiral meson lagrangian with Weinberg and KSFR relations from microscopic four-quark interactions

An effective chiral meson lagrangian is derived from a microscopic quark lagrangian. It contains a partial Higgs mechanism for ϱ-A₁ mass splitting reproducing Weinberg and KSFR relations, and includes quartic derivative “Skyrme” terms and the gauges Wess-Zumino term. The connection to previous approaches deriving the effective lagrangian exclusively from the chiral anomaly including “normal-parity” terms is established.     

Electric monopole transitions from low energy excitations in nuclei

Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ϱ²(E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also pay attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between ϱ²(E0) and isotopic shifts.     

Form factors in the projected linear chiral sigma model

Several nucleon form factors are computed within the framework of the linear chiral soliton model. To this end variational means and projection techniques applied to generalized hedgehog quark-boson Fock states are used. In this procedure the Goldberger-Treiman relation and a virial theorem for the pion-nucleon form factor are well fulfilled demonstrating the consistency of the treatment. Both proton and neutron charge form factors are correctly reproduced, as well as the proton magnetic one. The shapes of the neutron magnetic and of the axial form factors are good but their absolute values at the origin are too large. The slopes of all the form factors at zero momentum transfer are in good agreement with the experimental data. The pion-nucleon form factor exhibits to great extent a monopole shape with a cut-off mass ofΛ=690 MeV. Electromagnetic form factors for the vertexγNΔ and the nucleon spin distribution are also evaluated and discussed.     

Model independent determination of GEn from the d(e′n)p reaction

Electrodisintegration of vector polarized deuterium by longitudinally polarized electrons offers a possibility for measuring the neutron electric form factor G_En. In principle, the electron asymmetry is essentially proportional to G_En when quasi-free kinematics are employed. We investigate the model dependence of this result by employing several NN force models both with and without meson-exchange and isobar corrections. We find the asymmetry to be remarkably model independent near the neutron quasi-elastic peak.     

The Skyrme-TQRPA calculations of electron capture on hot nuclei in pre-supernova environment

We combine the thermal QRPA approach with the Skyrme energy density functional theory (Skyrme–TQRPA) for modelling the process of electron capture on nuclei in supernova environment. For a sample nucleus, ⁵⁶Fe, the Skyrme–TQRPA approach is applied to analyze thermal effects on the strength function of GT₊ transitions which dominate electron capture at E _e ≤ 30 MeV. Several Skyrme interactions are used in order to verify the sensitivity of the obtained results to the Skyrme force parameters. Finite-temperature cross sections are calculated and the results are comparedwith those of the other model calculations.     

Core polarization effects on transition densities in medium-heavy nuclei

We propose a microscopic model to study the core-polarization effects of giant resonances on the transition densities of open-shell nuclei. We use the Hartree-Fock-RPA method for the calculation of the single-particle wave functions and the response function of the giant resonances. Particle-vibration coupling is applied to take into account the core polarization effect on the valence many-body wave functions. We apply our model to the quadrupole transitions in the several medium-heavy nuclei. Valence many-body wave functions are calculated with the generalized seniority scheme and with the shell model. Results for the proton and neutron effective charges and the Coulomb form factors for the N = 82 isotones and for ¹¹⁶Sn and ¹¹⁰Pd are presented and discussed. The effective coupling hamiltonian is determined by the Skyrme interaction SGII which is used also in the HF and RPA calculations. The calculated core polarization charges show some state dependences. The average theoretical values are δe_p = 0.4–0.5 and δe_n = 0.6–0.7 compared to typical empirical values of δe_p = 0.6 and δe_n = 1.2.     

Fermi sea effects on pion and kaon properties in the Nambu-Jona-Lasinio model

We study modifications of hadronic properties in dense nuclear and neutron matter, in the context of a generalized three-flavor Nambu-Jona-Lasinio model, focussing mainly on Fermi sea effects. In symmetric nuclear matter, we observe the splitting between K^± and the occurrence of a low-lying K⁻ branch at baryonic densities around 0.4 times normal nuclear matter density ϱ₀. This branch is not significantly affected by the inclusion of strange matter in the medium while the flavor asymmetry is preserved. A similar π⁺ branch is found in neutron matter at neutron densities around 0.3ϱ₀. These low-lying modes are particle-hole excitations of the Fermi sea and decrease smoothly with density. In any case, the vacuum does not exhibit signs of instability associated with boson condensation.