Three-body spin-orbit forces from chiral two-pion exchange

Using chiral perturbation theory, we calculate the density-dependent spin-orbit coupling generated by the two-pion exchange three-nucleon interaction involving virtual $\Delta$-isobar excitation. From the corresponding three-loop Hartree and Fock diagrams we obtain an isoscalar spin-orbit strength $F_{\rm so}(k_f)$ which amounts at nuclear matter saturation density to about half of the empirical value of $90$MeVfm$^5$. The associated isovector spin-orbit strength $G_{\rm so}(k_f)$ comes out about a factor of 20 smaller. Interestingly, this three-body spin-orbit coupling is not a relativistic effect but independent of the nucleon mass $M$. Furthermore, we calculate the three-body spin-orbit coupling generated by two-pion exchange on the basis of the most general chiral $\pi\pi NN$-contact interaction. We find similar (numerical) results for the isoscalar and isovector spin-orbit strengths $F_{\rm so}(k_f)$ and $G_{\rm so}(k_f)$ with a strong dominance of the p-wave part of the $\pi\pi NN$-contact interaction and the Hartree contribution.Comment: 8 pages, 4figure, published in : Physical Review C68, 054001 (2003

Bethe-Salpeter Approach for the P33P_{33} Elastic Pion-Nucleon Scattering in Heavy Baryon Chiral Perturbation Theory

Heavy Baryon Chiral Perturbation Theory (HBChPT) to leading order provides a kernel to solve the Bethe-Salpeter equation for the $P_{33}$ ($\Delta(1232)$-channel) $\pi-N$ system, in the infinite nucleon mass limit. Crossed Born terms include, when iterated within the Bethe-Salpeter equation, both {\it all} one- and {\it some} two-pion intermediate states, hence preserving elastic unitarity below the two-pion production threshold. This suggests searching for a solution with the help of dispersion relations and suitable subtraction constants, when all in-elasticities are explicitly neglected. The solution allows for a successful description of the experimental phase shift from threshold up to $\sqrt{s}=1500$ MeV in terms of four subtraction constants. Next-to-leading order HBChPT calculations are also used to estimate the unknown subtraction constants which appear in the solution. Large discrepancies are encountered which can be traced to the slow convergence rate of HBChPT.Comment: 11 pages, 3 figure

Tripartite entanglement in parametric down-conversion with spatially-structured pump

Most investigations of multipartite entanglement have been concerned with temporal modes of the electromagnetic field, and have neglected its spatial structure. We present a simple model which allows to generate tripartite entanglement between spatial modes by parametric down-conversion with two symmetrically-tilted plane waves serving as a pump. The characteristics of this entanglement are investigated. We also discuss the generalization of our scheme to 2N+1-partite entanglement using 2N symmetrically-tilted plane pump waves. Another interesting feature is the possibility of entanglement localization in just two spatial modes.Comment: 6 pages, 2 figure

Chiral 3π\pi-exchange NN-potentials: Results for dominant next-to-leading order contributions

We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by the three-pion exchange diagrams with one insertion from the second order chiral effective pion-nucleon Lagrangian proportional to the low-energy constants $c_{1,2,3,4}$. The resulting isoscalar central potential vanishes identically. In most cases these $3\pi$-exchange potentials are larger than the ones generated by the diagrams involving only leading order vertices due to the large values of $c_{3,4}$ (which mainly represent virtual $\Delta$-excitation). A similar feature has been observed for the chiral $2\pi$-exchange. We also give suitable (double-integral) representations for the spin-spin and tensor potentials generated by the leading-order diagrams proportional to $g_A^6$ involving four nucleon propagators. In these cases the Cutkosky rule cannot be used to calculate the spectral-functions in the infinite nucleon mass limit since the corresponding mass-spectra start with a non-vanishing value at the $3\pi$-threshold. Altogether, one finds that chiral $3\pi$-exchange leads to small corrections in the region $r\geq 1.4$ fm where $1\pi$- and chiral $2\pi$-exchange alone provide a very good strong NN-force as shown in a recent analysis of the low-energy pp-scattering data-base.Comment: 11 pages, 7 figures, to be published in The Physical Review

Unitarized pion-nucleon scattering within Heavy Baryon Chiral Perturbation Theory

By means of the Inverse Amplitude Method we unitarize the elastic pion-nucleon scattering amplitudes obtained from Heavy Baryon Chiral Perturbation Theory to O(q^3). Within this approach we can enlarge their applicability range and generate the Delta(1232) resonance. We can find a reasonable description of the pion nucleon phase shifts with (q^2) parameters in agreement with the resonance saturation hypothesis. However, the uncertainties in the analysis of the low energy data as well as the large number of chiral parameters, which can have strong correlations, allow us to obtain very good fits with rather different sets of chiral constants.Comment: Shortened version to appear in Phys. Rev. D. Brief Report

LEASE VERSUS PURCHASE OF A CENTER-PIVOT IRRIGATION SYSTEM: A GEORGIA EXAMPLE

Farm Management,

Nucleon Polarizibilities for Virtual Photons

We generalize the sum rules for the nucleon electric plus magnetic polarizability $\Sigma=\alpha+\beta$ and for the nucleon spin-polarizability $\gamma$, to virtual photons with $Q^2>0$. The dominant low energy cross sections are represented in our calculation by one-pion-loop graphs of relativistic baryon chiral perturbation theory and the $\Delta(1232)$-resonance excitation. For the proton we find good agreement of the calculated $\Sigma_p(Q^2)$ with empirical values obtained from integrating up electroproduction data for $Q^2<0.4 GeV^2$. The proton spin-polarizability $\gamma_p(Q^2)$ switches sign around $Q^2= 0.4 GeV^2$ and it joins smoothly the "partonic" curve, extracted from polarized deep-inelastic scattering, around $Q^2=0.7 GeV^2$. For the neutron our predictions of $\Sigma_n(Q^2)$ and $\gamma_n(Q^2)$ agree reasonably well at $Q^2=0$ with existing determinations. Upcoming (polarized) electroproduction experiments will be able to test the generalized polarizability sum rules investigated here.Comment: 12 pages, 5 figures, submittes to Nuclear Physics

QCD Accurately Predicts the Induced Pseudoscalar Coupling Constant

Using chiral Ward identities of QCD, we derive a relation for the induced pseudoscalar coupling constant which is accurate within a few percent, $g_P = 8.44 \pm 0.16$.Comment: 5pp, LaTeX, CRN-94/1

Topics in Chiral Perturbation Theory

I consider some selected topics in chiral perturbation theory (CHPT). For the meson sector, emphasis is put on processes involving pions in the isospin zero S-wave which require multi-loop calculations. The advantages and shortcomings of heavy baryon CHPT are discussed. Some recent results on the structure of the baryons are also presented.Comment: 30 pp, TeX, Review talk, Third Workshop on High Energy Particle Physics (WHEPP III), Madras, India, January 1994. 7 figures available upon request. CRN--94/0

Study and optimization of ion-irradiated High-Tc Josephson nanoJunctions by Monte Carlo simulations

High Tc Josephson nanoJunctions (HTc JnJ) made by ion irradiation have remarkable properties for technological applications. However, the spread in their electrical characteristics increases with the ion dose. We present a simple model to explain the JnJ inhomogeneities, which accounts quantitatively for experimental data. The spread in the slit's width of the irradiation mask is the limiting factor.Monte Carlo simulations have been performed using different irradiation conditions to study their influence on the spread of the JnJ charcateristics. A "universal" behavior has been evidenced, which allows to propose new strategies to optimize JnJ reproducibility.Comment: 14 pages, 6 Figures. accepted in Journal of Applied Physic