arXiv subjects

N. Kaiser

Publications and source records attributed to N. Kaiser.

At least 181 records · Page 10Linked to original sources

arXiv2010

Nuclear energy density functional from chiral pion-nucleon dynamics: Isovector terms

We extend a recent calculation of the nuclear energy density functional in the framework of chiral perturbation theory by computing the isovector surface and spin-orbit terms: $(\vec \nabla ρ_p- \vec \nabla ρ_n)^2 G_d(ρ)+ (\vec \nabla ρ_p- \vec \nabla ρ_n)\cdot(\vec J_p-\vec J_n) G_{so(ρ)+(\vec J_p-\vec J_n)^2 G_J(ρ)$ pertaining to different proton and neutron densities. Our calculation treats systematically the effects from $1π$-exchange, iterated $1π$-exchange, and irreducible $2π$-exchange with intermediate $Δ$-isobar excitations, including Pauli-blocking corrections up to three-loop order. Using an improved density-matrix expansion, we obtain results for the strength functions $G_d(ρ)$, $G_{so}(ρ)$ and $G_J(ρ)$ which are considerably larger than those of phenomenological Skyrme forces. These (parameter-free) predictions for the strength of the isovector surface and spin-orbit terms as provided by the long-range pion-exchange dynamics in the nuclear medium should be examined in nuclear structure calculations at large neutron excess.

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arXiv2009

Nuclear energy density functional from chiral pion-nucleon dynamics revisited

We use a recently improved density-matrix expansion to calculate the nuclear energy density functional in the framework of in-medium chiral perturbation theory. Our calculation treats systematically the effects from $1π$-exchange, iterated $1π$-exchange, and irreducible $2π$-exchange with intermediate $Δ$-isobar excitations, including Pauli-blocking corrections up to three-loop order. We find that the effective nucleon mass $M^*(ρ)$ entering the energy density functional is identical to the one of Fermi-liquid theory when employing the improved density-matrix expansion. The strength $F_\nabla(ρ)$ of the $(\vec\nabla ρ)^2$ surface-term as provided by the pion-exchange dynamics is in good agreement with that of phenomenological Skyrme forces in the density region $ρ_0/2 <ρ<ρ_0$. The spin-orbit coupling strength $F_{so}(ρ)$ receives contributions from iterated $1π$-exchange (of the ``wrong sign'') and from three-nucleon interactions mediated by $2π$-exchange with virtual $Δ$-excitation (of the ``correct sign''). In the region around $ρ_0/2 \simeq 0.08 $fm$^{-3}$ where the spin-orbit interaction in nuclei gains most of its weight these two components tend to cancel, thus leaving all room for the short-range spin-orbit interaction. The strength function $F_J(ρ)$ multiplying the square of the spin-orbit density comes out much larger than in phenomenological Skyrme forces and it has a pronounced density dependence.

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arXiv2009

Density-dependent effective nucleon-nucleon interaction from chiral three-nucleon forces

We derive density-dependent corrections to the in-medium nucleon-nucleon interaction from the leading-order chiral three-nucleon force. To this order there are six distinct one-loop diagrams contributing to the in-medium nucleon-nucleon scattering T-matrix. Analytic expressions are presented for each of these in both isospin-symmetric nuclear matter as well as nuclear matter with a small isospin asymmetry. The results are combined with the low-momentum nucleon-nucleon potential V(low-k) to obtain an effective density-dependent interaction suitable for nuclear structure calculations. The in-medium interaction is decomposed into partial waves up to orbital angular momentum L = 2. Our results should be particularly useful in calculations where an exact treatment of the chiral three-nucleon force would otherwise be computationally prohibitive.

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arXiv2009

Hypernuclear single particle spectra based on in-medium chiral SU(3) dynamics

A previously derived relativistic energy density functional for nuclei, based on low-energy in-medium chiral dynamics, is generalized to implement constraints from chiral SU(3) effective field theory and applied to $Λ$ hypernuclei. Density-dependent central and spin-orbit mean fields are calculated for a $Λ$ hyperon using the SU(3) extension of in-medium chiral perturbation theory to two-loop order. Long range $ΛN$ interactions arise from kaon-exchange and from two-pion-exchange with a $Σ$ hyperon in the intermediate state. Short-distance dynamics is encoded in contact interactions. They include scalar and vector mean fields reflecting in-medium changes of quark condensates, constrained by QCD sum rules. The $Λ$ single particle orbitals are computed for a series of hypernuclei from $^{13}_Λ$C to $^{208}_Λ$Pb. The role of a surface (derivative) term is studied. Its strength is found to be compatible with a corresponding estimate from in-medium chiral perturbation theory. Very good agreement with hypernuclear spectroscopic data is achieved. The smallness of the $Λ$-nuclear spin-orbit interaction finds a natural explanation in terms of an almost complete cancellation between short-range scalar/vector contributions and longer range terms generated by two-pion exchange.

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arXiv2009

Chiral three-nucleon interaction and the carbon-14 dating beta decay

We present a shell model calculation for the beta decay of 14-C to the 14-N ground-state, treating the relevant nuclear states as two 0p-holes in an 16-O core. Employing the universal low-momentum nucleon-nucleon potential V(low-k) only, one finds that the Gamow-Teller matrix element is too large to describe the known (very long) lifetime of 14-C. As a novel approach to the problem, we invoke the chiral three-nucleon force (3NF) at leading order and derive from it a density-dependent in-medium NN interaction. Including this effective in-medium NN interaction, the Gamow-Teller matrix element vanishes for a nuclear density close to that of saturated nuclear matter. The genuine short-range part of the three-nucleon interaction plays a particularly important role in this context, since the medium modifications to the pion propagator and pion-nucleon vertex (due to the long-range 3NF) tend to cancel out in the relevant observable. We discuss also uncertainties related to the off-shell extrapolation of the in-medium NN interaction. Using the off-shell behavior of V(low-k) as a guide, we find that these uncertainties are rather small.

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arXiv2008

Radiative corrections to pion-nucleus bremsstrahlung

We calculate the one-photon loop radiative corrections to virtual pion Compton scattering $π^- γ^* \to π^- γ$, that subprocess which determines in the one-photon exchange approximation the pion-nucleus bremsstrahlung reaction $π^- Z\to π^- Z γ$. Ultraviolet and infrared divergencies of the loop integrals are both treated by dimensional regularization. Analytical expressions for the ${\cal O}(α)$ corrections to the virtual Compton scattering amplitudes, $A(s,u,Q)$ and $B(s,u,Q)$, are derived with their full dependence on the (small) photon virtuality $Q$ from 9 classes of contributing one-loop diagrams. Infrared finiteness of these virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $λ$. In the region of low $π^- γ$ center-of-mass energies, where the pion-nucleus bremsstrahlung process is used to extract the pion electric and magnetic polarizabilities, we find radiative corrections up to about -3% for $λ=5 $MeV. Furthermore, we extend our calculation of the radiative corrections to virtual pion Compton scattering $π^-γ^* \to π^- γ$ by including the leading pion structure effect in form of the polarizability difference $α_π- β_π$. Our analytical results are particularly relevant for analyzing the data of the COMPASS experiment at CERN which aims at measuring the pion electric and magnetic polarizabilities with high statistics using the Primakoff effect.

hep-ph↗

arXiv2008

Radiative corrections to pion Compton scattering

We calculate the one-photon loop radiative corrections to charged pion Compton scattering, $π^- γ\to π^- γ$. Ultraviolet and infrared divergencies are both treated in dimensional regularization. Analytical expressions for the ${\cal O}(α)$ corrections to the invariant Compton scattering amplitudes, $A(s,u)$ and $B(s,u)$, are presented for 11 classes of contributing one-loop diagrams. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy threshold $λ$, and its relation to the experimental detection threshold is discussed. We find that the radiative corrections are maximal in backward directions, reaching e.g. -2.4% for a center-of-mass energy of $\sqrt{s}=4m_π$ and $λ=5 $MeV. Furthermore, we extend our calculation of the radiative corrections by including the leading pion structure effect (at low energies) in form of its electric and magnetic polarizability difference, $α_π- β_π\simeq 6\cdot 10^{-4} $fm$^3$. We find that this structure effect does not change the relative size and angular dependence of the radiative corrections to pion Compton scattering. Our results are particularly relevant for analyzing the COMPASS experiment at CERN which aims at measuring the pion electric and magnetic polarizabilities with high statistics using the Primakoff effect.

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arXiv2008

Chiral condensate in neutron matter

A recent chiral perturbation theory calculation of the in-medium quark condensate $<\bar q q>$ is extended to the isospin-asymmetric case of pure neutron matter. In contrast to the behavior in isospin-symmetric nuclear matter we find only small deviations from the linear density approximation. This feature originates primarily from the reduced weight factors (e.g. 1/6 for the dominant contributions) of the $2π$-exchange mechanisms in pure neutron matter. Our result suggests therefore that the tendencies for chiral symmetry restoration are actually favored in systems with large neutron excess (e.g. neutron stars). We also analyze the behavior of the density-dependent quark condensate $<\bar q q>(ρ_n)$ in the chiral limit $m_π\to 0$.

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arXiv2008

Core-collapse supernovae in low-metallicity environments and future all-sky transient surveys

Aims: Massive stars in low-metallicity environments may produce exotic explosions such as long-duration gamma-ray bursts and pair-instability supernovae when they die as core-collapse supernovae (CCSNe). Here we determine the feasibility of searching for these CCSNe in metal-poor dwarf galaxies using various survey strategies. Methods: We determine oxygen abundances and star-formation rates for all spectroscopically typed star-forming galaxies in the Sloan Digital Sky Survey, Data Release 5, within z = 0.04. We then estimate the CCSN rates for sub-samples of galaxies with differing upper-metallicity limits. Using Monte-Carlo simulations we then predict the fraction of these CCSNe that we can expect to detect using different survey strategies. Results: Using a single 2m telescope (with a standard CCD camera) search we predict a detection rate of ~1.3 CCSNe/yr in galaxies with metallicities below 12 + log(O/H) < 8.2 which are within a volume that will allow detailed follow-up with 4m and 8m telescopes (z = 0.04). With a network of seven 2m telescopes we estimate ~9.3 CCSNe/yr could be found, although this would require more than 1,000 hrs of telescope time allocated to the network. Within the same radial distance, a volume-limited search in the future Pan-STARRS PS1 all-sky survey should uncover 12.5 CCSNe/yr in low-metallicity galaxies. Over a period of a few years this would allow a detailed comparison of their properties. We then extend our calculations to determine the total numbers of CCSNe that can potentially be found in magnitude-limited surveys with PS1 (24,000/yr, within z < 0.6), PS4 (69,000/yr, within z < 0.8) and LSST (160,000/yr, within z < 0.9) surveys.

astro-ph↗

arXiv2008

Cross sections for low-energy $π^-γ$ reactions

We review the cross sections for low-energy $π^- γ$ reactions in the framework of chiral perturbation theory. Charged pion Compton scattering, $π^- γ\to π^-γ$, is considered up to one-loop order where the pion's internal structure enters through the difference of the electric and magnetic pion polarizability, $α_π- β_π$. The ongoing COMPASS experiment aims at measuring this important structure constant with high statistics using the Primakoff effect. In the same way, the reaction $π^- γ\to π^- π^0$ serves as a test of the QCD chiral anomaly (via the $γ3π$-coupling constant $F_{\gamma3π}$). Furthermore, we calculate the total cross sections for neutral and charged pion-pair production, $π^- γ\to π^- π^0π^0$ and $π^- γ\to π^-π^+π^-$, which are governed by the chiral $ππ$-interaction. Finally, we investigate the radiative (correction) process $π^- γ\to π^- γγ$ and calculate the corresponding two-photon mass spectrum. This information will be useful for analyzing the $π^-$ Primakoff scattering events with photons in the final state.

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arXiv2008

Note on spin-orbit interactions in nuclei and hypernuclei

A detailed comparison is made between the spin-orbit interactions in $Λ$ hypernuclei and ordinary nuclei. We argue that there are three major contributions to the spin-orbit interaction: 1) a short-range component involving scalar and vector mean fields; 2) a ''wrong-sign'' spin-orbit term generated by the pion exchange tensor force in second order; and 3) a three-body term induced by two-pion exchange with excitation of virtual $Δ(1232)$-isobars (a la Fujita-Miyazawa). For nucleons in nuclei the long-range pieces related to the pion-exchange dynamics tend to cancel, leaving room dominantly for spin-orbit mechanisms of short-range origin (parametrized e.g. in terms of relativistic scalar and vector mean fields terms). In contrast, the absence of an analogous $2π$-exchange three-body contribution for $Λ$ hyperons in hypernuclei leads to an almost complete cancellation between the short-range (relativistic mean-field) component and the ''wrong-sign'' spin-orbit interaction generated by second order $π$-exchange with an intermediate $Σ$ hyperon. These different balancing mechanisms between short- and long-range components are able to explain simultaneously the very strong spin-orbit interaction in ordinary nuclei and the remarkably weak spin-orbit splitting in $Λ$ hypernuclei.

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arXiv2007

In-medium chiral SU(3) dynamics and hypernuclear structure

A previously introduced relativistic energy density functional, successfully applied to ordinary nuclei, is extended to hypernuclei. The density-dependent mean field and the spin-orbit potential are consistently calculated for a $Λ$ hyperon in the nucleus using the SU(3) extension of in-medium chiral perturbation theory. The leading long range $ΛN$ interaction arises from kaon-exchange and $2π$-exchange with $Σ$ hyperon in the intermediate state. Scalar and vector mean fields reflecting in-medium changes of the quark condensates are constrained by QCD sum rules. The model, applied to oxygen as a test case, describes spectroscopic data in good agreement with experiment. In particular, the smallness of the $Λ$ spin-orbit interaction finds a natural explanation in terms of an almost complete cancellation between scalar-vector background contributions and long-range terms generated by two-pion exchange.

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arXiv2007

In-medium chiral condensate beyond linear density approximation

In-medium chiral perturbation theory is used to calculate the density dependence of the quark condensate $<\bar qq>$. The corrections beyond the linear density approximation are obtained by differentiating the interaction contributions to the energy per particle of isospin-symmetric nuclear matter with respect to the pion mass. Our calculation treats systematically the effects from one-pion exchange (with $m_π$-dependent vertex corrections), iterated $1π$-exchange, and irreducible $2π$-exchange including intermediate $Δ(1232)$-isobar excitations, with Pauli-blocking corrections up to three-loop order. We find a strong and non-linear dependence of the ``dropping'' in-medium condensate on the actual value of the pion (or light quark) mass. In the chiral limit, $m_π=0$, chiral restoration appears to be reached already at about 1.5 times normal nuclear matter density. By contrast, for the physical pion mass, $m_π= 135 $MeV, the in-medium condensate stabilizes at about 60% of its vacuum value above that same density. Effects from $2π$-exchange with virtual $Δ(1232)$-isobar excitations turn out to be crucial in generating such pronounced deviations from the linear density approximation above $ρ_0$. The hindered tendency towards chiral symmetry restoration provides a justification for using pions and nucleons as effective low-energy degrees of freedom at least up to twice nuclear matter density.

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arXiv2007

Parity-violating two-pion exchange nucleon-nucleon interaction

We calculate in chiral perturbation theory the parity-violating two-pion exchange nucleon-nucleon potentials at leading one-loop order. At a distance of $r= m_π^{-1} \simeq 1.4 $fm they amount to about $\pm 16%$ of the parity-violating $1π$-exchange potential. We evaluate also the parity-violating effects arising from $2π$-exchange with excitation of virtual $Δ(1232)$-isobars. These come out to be relatively small in comparison to those from diagrams with only nucleon intermediate states. The reason for this opposite behavior to the parity-conserving case is the blocking of the dominant isoscalar central channel by CP-invariance. Furthermore, we calculate the T-matrix related to the iteration of the parity-violating $1π$-exchange with the parity-conserving one. The analytical results presented in this work can be easily implemented into calculations of parity-violating nuclear observables.

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arXiv2007

$Σ$-nuclear spin-orbit coupling from two-pion exchange

Using SU(3) chiral perturbation theory we calculate the density-dependent complex-valued spin-orbit coupling strength $U_{Σls}(k_f)+ i W_{Σls}(k_f)$ of a $Σ$ hyperon in the nuclear medium. The leading long-range $ΣN$ interaction arises from iterated one-pion exchange with a $Λ$ or a $Σ$ hyperon in the intermediate state. We find from this unique long-range dynamics a sizeable ``wrong-sign'' spin-orbit coupling strength of $U_{Σls}(k_{f0}) \simeq -20$ MeVfm$^2$ at normal nuclear matter density $ρ_0 = 0.16 $fm$^{-3}$. The strong $ΣN\to ΛN$ conversion process contributes at the same time an imaginary part of $W_{Σls}(k_{f0}) \simeq -12$ MeVfm$^2$. When combined with estimates of the short-range contribution the total $Σ$-nuclear spin-orbit coupling becomes rather weak.

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arXiv2007

Chiral pion-nucleon dynamics in finite nuclei: spin-isospin excitations

The nuclear density functional framework, based on chiral dynamics and the symmetry breaking pattern of low-energy QCD, is extended to the description of collective nuclear excitations. Starting from the relativistic point-coupling Lagrangian previously introduced [Nucl. Phys. A770 (2006) 1], the proton-neutron (quasiparticle) random phase approximation is formulated and applied to investigate the role of chiral pion-nucleon dynamics in excitation modes involving spin and isospin degrees of freedom, e.g. isobaric analog states and Gamow-Teller resonances.

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arXiv2006

Dominant $2πγ$-exchange nucleon-nucleon interaction: Spin-spin and tensor potentials

We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the two-pion exchange nucleon-nucleon interaction that is generated by the isovector spin-flip $ππNN$ contact-vertex proportional to the large low-energy constant $c_4\simeq 3.4 $GeV$^{-1}$. We find that the respective $2πγ$-exchange potentials contain sizeable isospin-breaking components which reach up to -4% of corresponding isovector $2π$-exchange potentials. The typical values of these novel charge-independence breaking spin-spin and tensor potentials are $-0.11 $MeV and $0.09 $MeV, at a nucleon distance of $r=m_π^{-1}=1.4 $fm. The charge-symmetry breaking spin-spin and tensor potentials come out a factor of 2.4 smaller. Our analytical results for these presumably dominant isospin-violating spin-spin and tensor NN-forces are in a form such that they can be easily implemented into phase-shift analyses and few-body calculations.

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arXiv2006

Scales in nuclear matter: Chiral dynamics with pion nucleon form factors

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 $\bar E(k_f)$. 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, $ρ_0 \simeq 0.16 $fm$^{-3}$, $\bar E_0\simeq -16 $MeV, is well reproduced with a monopole mass of $Λ\simeq 4πf_π\simeq 1.16 $GeV. As in the recent approach based on the universal low-momentum $NN$-potential $V_{\rm low-k}$, 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 $\bar E(k_f)$ 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 $<\bar q q >(ρ)$ beyond the linear density approximation. For $ρ\leq 1.5 ρ_0$ we find small corrections from the derivative $d \bar E(k_f)/d m_π$, which are stable against variations of the monopole regulator mass $Λ$.

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