arXiv subjects

N. Kaiser

Publications and source records attributed to N. Kaiser.

At least 235 records · Page 13Linked to original sources

arXiv2002

Chiral Dynamics of Deeply Bound Pionic Atoms

We present and discuss a systematic calculation, based on two-loop chiral perturbation theory, of the pion-nuclear s-wave optical potential. A proper treatment of the explicit energy dependence of the off-shell pion self-energy together with (electromagnetic) gauge invariance of the Klein-Gordon equation turns out to be crucial. Accurate data for the binding energies and widths of the 1s and 2p levels in pionic ^{205}Pb and ^{207}Pb are well reproduced, and the notorious "missing repulsion" in the pion-nuclear s-wave optical potential is accounted for. The connection with the in-medium change of the pion decay constant is clarified.

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arXiv2002

Chiral dynamics of nuclear matter at finite temperature

We extend a recent three-loop calculation of nuclear matter in the systematic framework of chiral perturbation theory to finite temperatures T. The contributions from one- and two-pion exchange diagrams which cause nuclear binding and saturation at T=0 are included for T>0 in the density and temperature dependent free energy per particle, $\bar F(rho,T)$. The so-called anomalous 2pi-exchange contribution $\bar A(rho,T)$ (with no counterpart in the ground state energy density at T=0) is consistently included. The calculated pressure isotherms display the familiar first-order liquid-gas phase transition of isospin symmetric nuclear matter with a critical point at T_c = 25.5 MeV and rho_c = 0.09 fm^{-3}. The too high value of the critical temperature originates from the strong momentum dependence of the underlying single-particle potential U(p,k_{f0}) near the Fermi-surface. We also consider pure neutron matter at T>0 in the same framework and find fair agreement with sophisticated many-body calculations for neutron densities rho_n < 0.2 fm^{-3}.

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arXiv2002

Single-particle potential in a chiral approach to nuclear matter including short range NN-terms

We extend a recent chiral approach to nuclear matter of Lutz et al. [Phys. Lett. B474 (2000) 7] by calculating the underlying (complex-valued) single-particle potential U(p,k_f) + i W(p,k_f). The potential for a nucleon at the bottom of the Fermi-sea, U(0,k_{f0})= - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi-surface. Also, the imaginary single-particle potential, W(0,k_{f0}) = 51.1 MeV, is too large. More realistic single-particle properties together with a good nuclear matter equation of state can be obtained if the short range contributions of non-pionic origin are treated in mean-field approximation (i.e. if they are not further iterated with 1pi-exchange). We also consider the equation of state of pure neutron matter $bar E_n(k_n)$ and the asymmetry energy A(k_f) in that approach. The downward bending of these quantities above nuclear matter saturation density seems to be a generic feature of perturbative chiral pion-nucleon dynamics.

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arXiv2002

Nuclear spin-orbit interaction from chiral pion-nucleon dynamics

Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent nuclear spin-orbit strength $U_{ls}(p,k_f)$. This quantity is derived from the spin-dependent part of the interaction energy $Σ_{spin} = {i\over 2} \vec σ\cdot (\vec q \times\vec p) U_{ls}(p,k_f)$ of a nucleon scattering off weakly inhomogeneous isospin symmetric nuclear matter. We find that iterated $1π$-exchange generates at saturation density, $k_{f0}=272.7 $MeV, a spin-orbit strength at $p=0$ of $U_{ls}(0,k_{f0})\simeq 35$ MeVfm$^2$ in perfect agreement with the empirical value used in the shell model. This novel spin-orbit strength is neither of relativistic nor of short range origin. The potential $V_{ls}$ underlying the empirical spin-orbit strength $\widetilde U_{ls}= V_{ls} r_{ls}^2$ becomes a rather weak one, $V_{ls}\simeq 17$ MeV, after the identification $r_{ls}= m_π^{-1}$ as suggested by the present calculation. We observe however a strong $p$-dependence of $U_{ls}(p,k_{f0})$ leading even to a sign change above $p=200 $MeV. This and other features of the emerging spin-orbit Hamiltonian which go beyond the usual shell model parametrization leave questions about the ultimate relevance of the spin-orbit interaction generated by $2π$-exchange for a finite nucleus. We also calculate the complex-valued isovector single-particle potential $U_I(p,k_f)+ i W_I(p,k_f)$ in isospin asymmetric nuclear matter proportional to $τ_3 (N-Z)/(N+Z)$. For the real part we find reasonable agreement with empirical values and the imaginary part vanishes at the Fermi-surface $p=k_f$.

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arXiv2002

Chiral corrections to the isovector double scattering term for the pion-deuteron scattering length

The empirical value of the real part of the pion-deuteron scattering length can be well understood in terms of the dominant isovector $πN$-double scattering contribution. We calculate in chiral perturbation theory all one-pion loop corrections to this double scattering term which in the case of $πN$-scattering close the gap between the current-algebra prediction and the empirical value of the isovector threshold T-matrix $T_{πN}^-$. In addition to closing this gap there is in the $πd$-system a loop-induced off-shell correction for the exchanged virtual pion. Its coordinate space representation reveals that it is equivalent to $2π$-exchange in the deuteron. We evaluate the chirally corrected double scattering term and the off-shell contribution with various realistic deuteron wave functions. We find that the off-shell correction contributes at most -8% and that the isovector double scattering term explains at least 90% of the empirical value of the real part of the $πd$-scattering length.

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arXiv2001

Chiral 2$π$-exchange NN-potentials: Relativistic $1/M^2$-Corrections

We calculate in baryon chiral perturbation theory the relativistic $1/M^2$-corrections to the leading order two-pion exchange diagrams. We give explicit expressions for the corresponding one-loop NN-amplitudes in momentum space. The resulting isovector central and isoscalar spin-spin and tensor NN-amplitudes involve non-static terms proportional to the squared nucleon center-of-mass momentum $p^2$. From the two-pion exchange box diagrams we obtain an isoscalar quadratic spin-orbit NN-amplitude. We give also analytical expressions for the corresponding NN-potentials in coordinate space. The diagrammatic results presented here make the chiral NN-potential complete at next-to-next-to-next-to-leading order.

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arXiv2001

Role of Chiral Symmetry in the Nuclear Many-Body Problem

The role of chiral (pion) dynamics in nuclear matter is reviewed. Contributions to the energy per particle from one- and two-pion exchange are calculated systematically, and it is demonstrated that already at order $k^4_f$ in the Fermi momentum, two-pion exchange produces realistic nuclear binding together with very reasonable values for the compressibility and the asymmetry energy. Further implications of these results are discussed.

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arXiv2001

Chiral $2π$-exchange NN-potentials: Two-loop contributions

We calculate in heavy baryon chiral perturbation theory the local NN-potentials generated by the two-pion exchange diagrams at two-loop order. We give explicit expressions for the mass-spectra (or imaginary parts) of the corresponding isoscalar and isovector central, spin-spin and tensor NN-amplitudes. We find from two-loop two-pion exchange a sizeable isoscalar central repulsion which amounts to $62.3 $MeV at $r=1.0 $fm. There is a similarly strong isovector central attraction which however originates mainly from the third order low energy constants $\bar d_j$ entering the chiral $πN$-scattering amplitude. We also evaluate the one-loop $2π$-exchange diagram with two second order chiral $ππNN$-vertices proportional to the low energy constants $c_{1,2,3,4}$ as well as the first relativistic 1/M-correction to the $2π$-exchange diagrams with one such vertex. The diagrammatic results presented here are relevant components of the chiral NN-potential at next-to-next-to-next-to-leading order.

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arXiv2001

Chiral Dynamics and Nuclear Matter

We calculate the equation of state of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The contributions to the energy per particle $\bar E(k_f)$ from one- and two-pion exchange diagrams are ordered in powers of the Fermi momentum $k_f$ (modulo functions of $k_f /m_π$). It is demonstrated that, already at order ${\cal O}(k_f^4)$, two-pion exchange produces realistic nuclear binding. The underlying saturation mechanism is surprisingly simple (in the chiral limit), namely the combination of an attractive $k_f^3$-term and a repulsive $k_f^4$-term. The empirical saturation point and the nuclear compressibility $K\simeq 250 $MeV are well reproduced at order ${\cal O}(k_f^5)$ with a momentum cut-off of $Λ\simeq 0.65$ GeV which parametrizes short-range dynamics. No further short-distance terms are required in our calculation of nuclear matter. In the same framework we calculate the density-dependent asymmetry energy and find $A_0\simeq 34 $MeV at the saturation point, in good agreement with the empirical value. The pure neutron matter equation of state is also in fair qualitative agreement with sophisticated many-body calculations and a resummation result of effective field theory, but only for low neutron densities $ρ_n <0.25 $fm$^{-3}$.

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arXiv2001

Isospin Breaking in Neutron $β$-decay and SU(3) Violation in Semi-leptonic Hyperon Decays

Present precision measurements of the neutron life time lead to a CKM matrix element $|V_{ud}|$ which is three standard deviations off the value inferred from heavy quark decays etc. We investigate the possibility whether isospin-breaking effects in the neutron-to-proton vector current transition matrix element $< p|V^+_0|n >=1+δg_V$ could eventually close this gap. For that we calculate in chiral perturbation theory the effect of pion and kaon loops on the matrix element $< p|V^+_0|n >$ taking into account the mass differences of the charged and neutral mesons. We find a negligibly small isospin-breaking effect of $δg_V \simeq -4 \cdot 10^{-5}$. The crucial quantity in the analysis of neutron beta-decay precision measurements is thus the radiative correction term $Δ_R$. Furthermore, we calculate in heavy baryon chiral perturbation theory the SU(3) breaking effects on the vector transition charges of weak semi-leptonic hyperon decays. We find for these quantities channel-dependent relative deviations from the SU(3) limit which range from -10% to $+1%$.

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arXiv2001

Systematic calculation of s-wave pion and kaon self-energies in asymmetric nuclear matter

We calculate the pion self-energies in asymmetric nuclear matter in the two-loop approximation of chiral perturbation theory. We find three types of corrections beyond the well-known linear density approximation. The resulting s-wave potential (or equivalent mass-shift) of a $π^-$ in the center of a heavy nucleus like Pb turns out to be $U_{π^-}=Δm_{π^-} \simeq 14$ MeV, about half of what is needed to form the deeply bound and narrow pionic atom-states recently observed at GSI. The potential for a $π^+$ under the same conditions is $U_{π^+}=Δm_{π^+} \simeq -1$ MeV. In the same way we calculate the mass-shifts of $K^+$-mesons in symmetric nuclear matter and neutron matter and find an increase of the $K^+$-mass by 9% and 5%, respectively. As a further application we give an analytical result for the third order term in the scattering length expansion of the in-medium self-energy of an interacting light-boson/heavy-fermion system.

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arXiv2001

Further comment on pion electroproduction and the axial form factor

We show that a recent claim (H.Haberzettl, Phys. Rev. Lett. 85 (2000) 3576) that one cannot extract the nucleon weak axial form factor G_A (t) from charged pion threshold electroproduction is incorrect. Thus previous calculations remain valid and threshold charged pion electroproduction experiments can indeed be used to determine G_A (t), and they should certainly be pursued.

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arXiv2000

Weak Lensing by High-Redshift Clusters of Galaxies - I: Cluster Mass Reconstruction

We present the results of a weak lensing survey of six high-redshift (z > 0.5), X-ray selected clusters of galaxies. We have obtained ultra-deep R-band images of each cluster with the Keck Telescope, and have measured a weak lensing signal from each cluster. From the background galaxy ellipticities we create two-dimensional maps of the surface mass density of each cluster. We find that the substructure seen in the mass reconstructions typically agree well with substructure in both the cluster galaxy distributions and X-ray images of the clusters. We also measure the one-dimensional radial profiles of the lensing signals and fit these with both isothermal spheres and "universal" CDM profiles. We find that the more massive clusters are less compact and not as well fit by isothermal spheres as the less massive clusters, possibly indicating that they are still in the process of collapse.

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arXiv1999

Chiral SU(3) Dynamics with Coupled Channels: Inclusion of P-Wave Multipoles

We extend our recent non-perturbative chiral SU(3) coupled channel approach to pion- and photon-induced $η$- and $K$-meson production off protons by including all strong and electromagnetic p-wave multipoles. We identify the p-wave amplitudes of the next-to-leading order SU(3) chiral meson-baryon Lagrangian with a coupled channel potential which is iterated to infinite orders in a separable Lippmann-Schwinger equation. Our approach to $η$- and $K$-photoproduction introduces no additional free parameters. By adjusting a few finite range parameters and the unknown parameters in the Lagrangian, we are able to simultaneously describe a very large amount of low-energy data. These include the total and differential cross sections of the $π$-induced reactions $π^- p \to ηn, K^0 Λ, K^0 Σ^0, K^+ Σ^-$ and $π^+ p \to K^+ Σ^+$ as well as those of photoproduction $γp \to ηp, K^+Λ, K^+ Σ^0, K^0 Σ^+$. The polarization observables measured in $η$- and $K$-photoproduction are particularly sensitive to interference terms between the s- and p-wave multipoles. The total cross section data are remarkably well reproduced in all channels. There remain, however, some open questions concerning details of angular distributions and polarization observables.

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arXiv1999

Chiral $π$-exchange NN-potentials: Results for diagrams proportional to g_A^4 and g_A^6

We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by the three-pion exchange diagrams proportional to g_A^4 and g_A^6. Surprisingly, we find that the total isoscalar central $3π$-exchange potential vanishes identically. The individually largest $3π$-exchange potentials are of isoscalar spin-spin, isovector central and isoscalar tensor type. For these potentials simple analytical expressions can be given. The strength of these dominant $3π$-exchange potentials at r=1.0 fm is 4.6 MeV, 2.9 MeV and 1.4 MeV, respectively. Furthermore, we observe that the spin-spin and tensor potentials due to the diagrams proportional to g_A^6 do not exist in the infinite nucleon mass limit.

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arXiv1999

A New Strategy for Deep Wide-Field High Resolution Optical Imaging

We propose a new strategy for obtaining enhanced resolution (FWHM = 0.12 arcsec) deep optical images over a wide field of view. As is well known, this type of image quality can be obtained in principle simply by fast guiding on a small (D = 1.5m) telescope at a good site, but only for target objects which lie within a limited angular distance of a suitably bright guide star. For high altitude turbulence this 'isokinetic angle' is approximately 1 arcminute. With a 1 degree field say one would need to track and correct the motions of thousands of isokinetic patches, yet there are typically too few sufficiently bright guide stars to provide the necessary guiding information. Our proposed solution to these problems has two novel features. The first is to use orthogonal transfer charge-coupled device (OTCCD) technology to effectively implement a wide field 'rubber focal plane' detector composed of an array of cells which can be guided independently. The second is to combine measured motions of a set of guide stars made with an array of telescopes to provide the extra information needed to fully determine the deflection field. We discuss the performance, feasibility and design constraints on a system which would provide the collecting area equivalent to a single 9m telescope, a 1 degree square field and 0.12 arcsec FWHM image quality.

astro-ph↗

arXiv1999

Weak Lensing Observations of High-Redshift Clusters of Galaxies

We present results of a weak gravitational lensing survey of six X-ray selected high-redshift clusters of galaxies. We find that the masses of the clusters derived from weak lensing are comparable to those derived from the X-ray observations. We show that many of the clusters have significant substructure not observed in the X-ray observations and that for the more massive clusters a singular isothermal sphere does not provide a good fit to the radial mass profile.

astro-ph↗

arXiv1999

Chiral $3π$-exchange NN-potentials: results for representation invariant classes of diagrams

We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by certain classes of three-pion exchange diagrams. We stress that the chiral $3πNN$-contact vertex depends on the particular choice of the interpolating pion-field and therefore one has to consider representation invariant classes of diagrams by supplementing graphs involving the chiral $4π$-vertex. We find that the resulting isovector spin-spin and tensor NN-potentials are negligibly small for $r\geq 0.8$ fm. One can conclude that the effects of uncorrelated chiral $3π$-exchange in the NN-interaction are very small and therefore of no practical relevance.

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