Isovector part of nuclear energy density functional from chiral two- and three-nucleon forces

A recent calculation of the nuclear energy density functional from chiral two- and three-nucleon forces is extended to the isovector terms pertaining to different proton and neutron densities. An improved density-matrix expansion is adapted to the situation of small isospin asymmetries and used to calculate in the Hartree-Fock approximation the density-dependent strength functions associated with the isovector terms. The two-body interaction comprises of long-range multi-pion exchange contributions and a set of contact terms contributing up to fourth power in momenta. In addition, the leading-order chiral three-nucleon interaction is employed with its parameters fixed in computations of nuclear few-body systems. With this input one finds for the asymmetry energy of nuclear matter the value A(?? ₀) ? 26.5 MeV, compatible with existing semi-empirical determinations. The strength functions of the isovector surface and spin-orbit coupling terms come out much smaller than those of the analogous isoscalar coupling terms and in the relevant density range one finds agreement with phenomenological Skyrme forces. The specific isospin and density dependences arising from the chiral two- and three-nucleon interactions can be explored and tested in neutron-rich systems.     

Exact calculation of three-body contact interaction to second order

For a system of fermions with a three-body contact interaction the second-order contributions to the energy per particle [`(E)](k<sub>f</sub>)\ensuremath \bar E(k_f) are calculated exactly. The three-particle scattering amplitude in the medium is derived in closed analytical form from the corresponding two-loop rescattering diagram. We compare the (genuine) second-order three-body contribution to [`(E)](k_f) ~ k_f¹⁰\ensuremath \bar E(k_f)\sim k_f^{10} with the second-order term due to the density-dependent effective two-body interaction, and find that the latter term dominates. The results of the present study are of interest for nuclear many-body calculations where chiral three-nucleon forces are treated beyond leading order via a density-dependent effective two-body interaction.     

Triton photodisintegration in three-dimensional approach

Two- and three-particles photodisintegration of the triton is investigated in a three-dimensional (3D) Faddeev approach. For this purpose the Jacobi momentum vectors for three-particles system and spin-isospin quantum numbers of the individual nucleons are considered. Based on this picture the three-nucleon Faddeev integral equations with the two-nucleon interaction are formulated without employing the partial-wave decomposition. The single-nucleon current as well as π- and ρ-like exchange currents are used in an appropriate form to be employed in the 3D approach. The exchange currents are derived from AV18 NN force. The two-body t-matrix, deuteron and triton wave functions are calculated in the 3D approach by using the AV18 potential. Benchmarks are presented to compare the total cross-section for the two- and three-particles photodisintegration in the range of E _γ < 30 MeV. The 3D Faddeev approach shows promising results.     

On the influence of a square-root van Hove singularity on the critical temperature of high-T c superconductors

It is shown that the square-root van Hove singularity appearing in the density of states ν (E _F )∼(E _F −E ₀)^−1/2 as a result of extended saddle-point singularities in the electron spectrum of high-T _c superconductors based on hole-type cuprate metal-oxide compounds gives a nonmonotonic dependence of the critical temperature T _c on the position of the Fermi level E _F relative to the bottom E ₀ of the saddle. Because the divergence of ν(E _F ) is canceled in the electron-electron interaction constant renormalized by strong-coupling effects, T _c approaches zero as E _F →E ₀, in contrast to the weak-coupling approximation, where in this limit T _c approaches a finite (close to maximum) value. The dependence obtained for T _c as a function of the doped hole density in the strong-coupling approximation agrees qualitatively with the experimental data for overdoped cuprate metal oxides. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 473–477 (10 April 1998)     

Self-consistent treatment of the quark condensate and hadrons in nuclear matter

We calculate the contribution of pions to the $\bar qq$-expectation value κ(ρ) =<M|ˉq q|M> in symmetric nuclear matter. We employ exact pion propagator renormalized by nucleon-hole and isobar-hole excitations. Conventional straightforward calculation leads to the “pion condensation” at unrealistically small values of densities, causing even earlier restoration of chiral symmetry. This requires a self-consistent approach, consisting in using the models, which include direct dependence of in-medium mass values on κ(ρ), e.g. the Nambu–Jona-Lasinio–model. We show, that in the self-consistent approach the ρ-dependence of the condensate is described by a smooth curve. The “pion condensate” point is removed to much higher values of density. The chiral restoration does not take place at least while ρ < 2.8ρ₀ with ρ₀ being the saturation value. Validity of our approach is limited by possible accumulation of heavier baryons (delta isobars) in the ground state of nuclear matter. For the value of effective nucleon mass at the saturation density we found m ^*(ρ₀) = 0.6m, consistent with nowadays results of other authors. Received: 8 October 1998     

Constructing Entanglement Witnesses for States in?Infinite-Dimensional Bipartite Quantum Systems

In this paper, two approaches of constructing entanglement witnesses for finite- or infinite-dimensional bipartite quantum systems are presented. Let H _A and H _B be complex Hilbert spaces and {E _k } and {F _k } be sequences of self-adjoint Hilbert-Schmidt operators on H _A and H _B , respectively, such that Tr(E^f_kE_l)=Tr(F^f_kF_l)=d_kl\mathrm{Tr}(E^{\dag}_{k}E_{l})=\mathrm{Tr}(F^{\dag}_{k}F_{l})=\delta_{kl}. Then W=I−∑ _k E _k ⊗F _k is an entanglement witness on H _A ⊗H _B if W\not 3 0W\not\geq 0. If ρ is an entangled state and τ ₀ is the nearest separable state to ρ under the Hilbert-Schmidt norm, then W=c ₀ I+τ ₀−ρ with c ₀=Tr[τ ₀(ρ−τ ₀)] is an entanglement witness.     

On parity-violating three-nucleon interactions and the predictive power of few-nucleon EFT at very low energies

We address the typical strengths of hadronic parity-violating three-nucleon interactions in “pion-less” Effective Field Theory (EFT) in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we conclude that no such interactions are needed at leading order, O(eQ^-1)\ensuremath {O}(\epsilon Q^{-1}) . The only two distinct parity-violating three-nucleon structures with one derivative mix ²S_\frac12\ensuremath ^2S_{\frac{1}{2}} and ²P_\frac12\ensuremath ^2P_{\frac{1}{2}} waves with iso-spin transitions D \Delta I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order, O(eQ⁰)\ensuremath {O}(\epsilon Q^0) . This observation is based on the approximate realisation of Wigner’s combined SU(4) spin-isospin symmetry in the two-nucleon system, even when effective-range corrections are included. Parity-violating three-nucleon interactions thus only appear beyond next-to-leading order. This guarantees renormalisability of the theory to that order without introducing new, unknown coupling constants and allows the direct extraction of parity-violating two-nucleon interactions from three-nucleon experiments.     

Scales in nuclear matter: Chiral dynamics with pion nucleon form factors<Superscript>⋆</Superscript>

A systematic calculation of nuclear matter is performed which includes the long-range correlations between nucleons arising from one- and two-pion exchange. Three-body effects from 2π exchange with excitations of virtual Δ(1232)-isobars are also taken into account in our diagrammatic calculation of the energy per particle ˉ(k _f). In order to eliminate possible high-momentum components from the interactions we introduce at each pion-baryon vertex a form factor of monopole type. The empirical nuclear matter saturation point, ρ₀ ≃ 0.16fm^-3, ˉ₀ ≃ - 16MeV, is well reproduced with a monopole mass of Λ ≃ 4πf _π ≃ 1.16GeV. As in the recent approach based on the universal low-momentum NN potential V _low-k, the inclusion of three-body effects is crucial in order to achieve saturation of nuclear matter. We demonstrate that the dependence of the pion exchange contributions to ˉ(k _f) on the “resolution” scale Λ can be compensated over a wide range of Λ by counterterms with two “running” contact couplings. As a further application we study the in-medium chiral condensate 〈ˉq〉(ρ) beyond the linear density approximation. For ρ ⩽ 1.5ρ₀ we find small corrections from the derivative dˉ(k _f)/dm _π, which are stable against variations of the monopole regulator mass Λ.     

Triplet superfluidity in neutron matter with Skyrme forces at subnuclear and supranuclear densities in a strong magnetic field

Within a generalized non-relativistic Fermi-liquid approach we have found general analytical formulae for phase-transition temperatures T _c,1(n, H) and T _c,2(n, H) (which are nonlinear functions of density, n, and linear of magnetic field, H) for phase transitions in spatially uniform, dense, pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases ³He - A₁ and ³He - A₂) in steady and homogeneous sufficiently strong magnetic field (but |μ _n |H ≪ E _c < ɛ _F (n), where μ _n is the magnetic dipole moment of a neutron, E _c is the cutoff energy and ɛ _F (n)is the Fermi energy in neutron matter). General formulae for T _c,1,2(n,H) are valid for arbitrary parameterization of the effective Skyrme forces in neutron matter. We have used for definiteness the so-called SLy2, Gs and RATP parameterizations of the Skyrme forces with different exponents in their power dependence on density n (at sub- and supranuclear densities) from the interval 0.7 n ₀ ≲ n < n _c (Skyrme)< 2 n ₀, where n ₀ =0.17 fm⁻³ is the nuclear density and n _c (Skyrme)is the the critical density of the ferromagnetic instability in superfluid neutron matter. These phase transitions might exist in the liquid outer core of magnetized neutron stars.     

Quantum Monte Carlo calculations of light nuclei

Quantum Monte Carlo calculations using realistic two- and three-nucleon interactions are presented for nuclei with up to ten nucleons. Our Green's function Monte Carlo calculations are accurate to ∼1-2% for the binding energy. We have constructed Hamiltonians using the Argonne v₁₈ NN interaction and reasonable three-nucleon interactions that reproduce the energies of these nuclear states with only ∼500 keV rms error. Other predictions, such as form factors, decay rates, and spectroscopic factors also agree well with data. Some of these results are presented to show that ab initio calculations of light nuclei are now well in hand. Received: 1 May 2001 / Accepted: 4 December 2001     

Renormalization and Asymptotic Expansion of Dirac’s Polarized Vacuum

We perform rigorously the charge renormalization of the so-called reduced Bogoliubov-Dirac-Fock (rBDF) model. This nonlinear theory, based on the Dirac operator, describes atoms and molecules while taking into account vacuum polarization effects. We consider the total physical density ρ _ph including both the external density of a nucleus and the self-consistent polarization of the Dirac sea, but no ‘real’ electron. We show that ρ _ph admits an asymptotic expansion to any order in powers of the physical coupling constant α _ph, provided that the ultraviolet cut-off behaves as L ~ e^{3p(1-Z₃)/2a_ph} >> 1{\Lambda\sim e^{3\pi(1-Z_3)/2\alpha_{\rm ph}} \gg 1}. The renormalization parameter 0 < Z ₃ < 1 is defined by Z ₃ = α _ph/α, where α is the bare coupling constant. The coefficients of the expansion of ρ _ph are independent of Z ₃, as expected. The first order term gives rise to the well-known Uehling potential, whereas the higher order terms satisfy an explicit recursion relation.     

η(1475) and <Emphasis Type="Italic">f</Emphasis><Subscript>1</Subscript>(1420) resonances in the decay processes <Emphasis Type="Italic">J</Emphasis>/ψ → γ(ρρ, γρ<Superscript>0</Superscript>, γϕ) and in γγ* collisions

A scenario that removes the contradiction between the suppression of the η(1475) → γγ decay width and the strong coupling of η(1475) to the ρρ, ωω, and γρ⁰ channels and which leads to a nontrivial prediction for the manifestation of η(1475) in γγ*(Q ²) collisions is considered. Data on the dependence of the cross section for the reaction γγ*(Q ²) → K[`(K)]pK\bar K\pi on the photon virtuality in the energy range 1.35–1.55 GeV are explained here by the production of an η(1475) resonance in contrast to their standard interpretation in terms of the f <sub>1</sub>(1420) resonance. Experimental verification of the present explanation requires determining the spin-parity of resonance contributions, R, in the reactions γγ*(Q <sup>2</sup>) R → R → K[`(K)]pK\bar K\pi and J/ψ → γR → γ(γρ⁰, γϕ).     

Nuclear mean fields through self-consistent semiclassical calculations

Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density τ( r) and the spin-orbit density J( r) as functions of the local density ρ( r) are used to determine the central nuclear potentials V _n( r) and V _p( r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of the resulting semiclassical expansions for these potentials is fast and that they reproduce quite accurately the corresponding Hartree-Fock average fields. Received: 12 February 2000 / Accepted: 14 March 2002     

Free Energies of Dilute Bose Gases: Upper Bound

We derive an upper bound on the free energy of a Bose gas at density ϱ and temperature T. In combination with the lower bound derived previously by Seiringer (Commun. Math. Phys. 279(3): 595–636, 2008), our result proves that in the low density limit, i.e., when a ³ ϱ≪1, where a denotes the scattering length of the pair-interaction potential, the leading term of Δf, the free energy difference per volume between interacting and ideal Bose gases, is equal to 4pa(2r²-[r-r_c]²₊)4\pi a(2\varrho^{2}-[\varrho-\varrho_{c}]^{2}_{+}). Here, ϱ _c (T) denotes the critical density for Bose–Einstein condensation (for the ideal Bose gas), and [⋅]₊=max {⋅,0} denotes the positive part.     

A role of the axial-vector mesons on the photon production in heavy-ion collisions and their relevant decays

A role of the axial-vector mesons, such as K₁ and a₁, on the emitted-photon spectrum in hot hadronic matter is studied through the channels πρ→a ₁→πγ and Kρ→K ₁→Kγ. Both channels could be dominant over the region lower than E _γ∼ 0.5 GeV, while the role of the K₁ meson is diminished in the higher E _γ region. This study is carried out with an SU _L(3) ⊗SU _R(3) effective chiral Lagrangian which includes vector and axial-vector mesons systematically and explains well their hadronic and radiative decays simultaneously. Received: 8 August 2001 / Accepted: 4 February 2002     

A study of the nuclear-medium influence on <Emphasis Type="Italic">ρ</Emphasis><Superscript>0</Superscript> neutrinoproduction

The nuclear effects in ρ ⁰-meson neutrino production are investigated using the data obtained with the SKAT bubble chamber. The nuclear-medium influence on the ρ ⁰ total yield and inclusive distributions on z = E _ρ /v and Feynman x _F variable is found to be approximately the same as for pions. It is shown that these distributions with increasing A tend to shift toward smaller values of z and x _F, thus indicating an increasing role of secondary intranuclear interactions. The predictions of a simple model incorporating the latter are found to be in qualitative agreement with experimental data. The text was submitted by the authors in English.     

Possible manifestation of spin fluctuations in the temperature behavior of the resistivity of Sm<Subscript>1.85</Subscript>Ce<Subscript>0.15</Subscript>CuO<Subscript>4</Subscript> thin films

A pronounced step-like (kink) behavior in the temperature dependence of resistivity ρ(T) is observed in the optimally doped Sm_1.85Ce_0.15CuO₄ thin films around T _sf = 87 K and attributed to the manifestation of strong-spin fluctuations induced by Sm³⁺ moments with the energy ħω_sf = k _B T _sf ≃ 7 meV. The experimental data are found to be well fitted by the residual (zero-temperature) ρ_res, electron-phonon ρ_e-ph(T) = AT, and electron-electron ρ_e-e(T) = BT ² contributions in addition to the fluctuation-induced contribution ρ_sf(T) due to thermal broadening effects (of the width ω_sf). According to the best fit, the plasmon frequency, impurity scattering rate, electron-phonon coupling constant, and Fermi energy are estimated as ω_p = 2.1 meV, τ ₀ ⁻¹ = 9.5 × 10⁻¹⁴ s⁻¹, λ = 1.2, and E _F = 0.2 eV, respectively. The text was submitted by the authors in English.     

Analytic solution of the BCS gap equation inD dimensions (D=1, 2, 3), at finite temperatures

The Bardeen-Cooper-Schrieffer (BCS) gap equation is solved analytically in one, two and three dimensions, for temperatures close to zero andT _c. We work in the weak coupling limit, but allow the interaction widthν≡ħω _m/E _F to lie in the interval (0, ∞) Here,ħω _m is the maximum energy of a force-mediating boson, andE _F denotes the Fermi energy. We obtain expressions forT _c and ΔC, the jump in the electronic specific heat acrossT=T _c, in the limitsν≪1 (the usual phonon pairing) andν>1 (non-phononic pairing). This enables us to see howT _c scales with the mediating boson cut off. Our results predict a larger jump in the specific heat for the caseν>1, compared toν≪1. We also briefly touch upon the role of a van Hove singularity in the density of states.