Electromagnetic corrections to π−\pi ^-p scattering length from pionic hydrogen

We derive a closed, model space independent, expression for the electromagnetic correction factor $\delta$ to the scattering length $a$ extracted from a hydrogenic atom with an extended charge to order $\alpha ^2$ and $a^3$ in the limit of a short ranged hadronic interaction.Comment: 4 pages; PANIC02, XVIth Conference on Particles and Nuclei, Osaka, to appear in Nuclear Physics

Precision determination of the pi-N scattering lengths and the charged pi-NN coupling constant

We critically evaluate the isovector GMO sumrule for the charged $\pi N N$ coupling constant using recent precision data from $\pi ^-$p and $\pi^-$d atoms and with careful attention to systematic errors. From the $\pi ^-$d scattering length we deduce the pion-proton scattering lengths ${1/2}(a_{\pi ^-p}+a_{\pi ^-n})=(-20\pm 6$(statistic)$\pm 10$ (systematic))~$\cdot 10^{-4}m_{\pi_c}^{-1}$ and ${1/2}(a_{\pi ^-p}-a_{\pi ^-n})=(903 \pm 14)\cdot 10^{-4}m_{\pi_c}^{-1}$. From this a direct evaluation gives $g^2_c(GMO)/4\pi =14.20\pm 0.07$(statistic)$\pm 0.13$(systematic) or $f^2_c/4\pi= 0.0786\pm 0.0008$.Comment: 4 pages, 1 figure, latex and postscript; invited talk at PANIC99; to appear in Nucl. Phys. A; changed notation: g^2 and f^2 replaced by conventional g^2/4\pi and f^2/4\p

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.Comment: preprint ECT*-02-16, 4 pages, 3 figure

The Pion-Nucleon coupling constant from np charge exchange scattering

A novel extrapolation method has been used to deduce the charged Pion-Nucleon coupling constant from backward $np$ differential scattering cross sections. We applied it to new measurements performed at 162 MeV at the The Svedberg Laboratory in Uppsala. In the angular range $150^\circ-180^\circ$, the carefully normalized data are steeper than those of most previous measurements. The extracted value, $g^2_{\pi^\pm} = 14.52 \pm 0.26$, in good agreement with the classical value, is higher than those determined in recent nucleon-nucleon partial-wave analyses.Comment: 6 pages, 3 encapsulated figures, epsfig, menu97.cls (included

St. Patrick Inspires a Shamrock Luncheon

The March hostess who is looking for something different may well · take advantage of the possibilities offered by St. Patrick\u27s Day. A green and white color scheme, besides commemorating the venerable Irishman, is very dainty and suggestive of the spring season

Videoconferencing via satellite. Opening Congress to the people: Technical report

The feasibility of using satellite videoconferencing as a mechanism for informed dialogue between Congressmen and constituents to strengthen the legislative process was evaluated. Satellite videoconferencing was defined as a two-way interactive television with the TV signals transmitted by satellite. With videoconferencing, one or more Congressmen in Washington, D. C. can see, hear and talk with groups of citizens at distant locations around the country. Simultaneously, the citizens can see, hear and talk with the Congressmen

Unusual statistics of interference effects in neutron scattering from compound nuclei

We consider interference effects between p-wave resonance scattering amplitude and background s-wave amplitude in low-energy neutron scattering from a heavy nucleus which goes through the compound nucleus stage. The first effect is in the difference between the forward and backward scattering cross sections. Because of the chaotic nature of the compound states, this effect is a random variable with zero mean. However, a statistical consideration shows that the probability distribution of this effect does not obey the standard central limit theorem. That is, the probability density for the effect averaged over n resonances does not become a Gaussian distribution with the variance decreasing as 1/sqrt(n) (``violation'' of the theorem!). We derive the probability distribution of the effect and the limit distribution of the average. It is found that the width of this distribution does not decrease with the increase of n, i.e., fluctuations are not suppressed by averaging. Furthermore, we consider the correlation between the neutron spin and the scattering plane and find that this effect, although much smaller, shows fluctuations which actually increase upon averaging over many measurements. Limits of the effects due to finite resonance widths are also considered. In the appendix we present a simple derivation of the limit theorem for the average of random variables with infinite variances.Comment: 15 pages, RevTeX, submitted to Phys. Rev.

Correlation Widths in Quantum--Chaotic Scattering

An important parameter to characterize the scattering matrix S for quantum-chaotic scattering is the width Gamma_{corr} of the S-matrix autocorrelation function. We show that the "Weisskopf estimate" d/(2pi) sum_c T_c (where d is the mean resonance spacing, T_c with 0 <= T_c <= 1 the "transmission coefficient" in channel c and where the sum runs over all channels) provides a very good approximation to Gamma_{corr} even when the number of channels is small. That same conclusion applies also to the cross-section correlation function

A Perturbative Calculation of the Electromagnetic Form Factors of the Deuteron

Making use of the effective field theory expansion recently developed by the authors, we compute the electromagnetic form factors of the deuteron analytically to next-to-leading order (NLO). The computation is rather simple, and involves calculating several Feynman diagrams, using dimensional regularization. The results agree well with data and indicate that the expansion is converging. They do not suffer from any ambiguities arising from off-shell versus on-shell amplitudes.Comment: 22 pages, 8 figures. Discussion of effective range theory added, typos correcte

Spherical codes, maximal local packing density, and the golden ratio

The densest local packing (DLP) problem in d-dimensional Euclidean space Rd involves the placement of N nonoverlapping spheres of unit diameter near an additional fixed unit-diameter sphere such that the greatest distance from the center of the fixed sphere to the centers of any of the N surrounding spheres is minimized. Solutions to the DLP problem are relevant to the realizability of pair correlation functions for packings of nonoverlapping spheres and might prove useful in improving upon the best known upper bounds on the maximum packing fraction of sphere packings in dimensions greater than three. The optimal spherical code problem in Rd involves the placement of the centers of N nonoverlapping spheres of unit diameter onto the surface of a sphere of radius R such that R is minimized. It is proved that in any dimension, all solutions between unity and the golden ratio to the optimal spherical code problem for N spheres are also solutions to the corresponding DLP problem. It follows that for any packing of nonoverlapping spheres of unit diameter, a spherical region of radius less than or equal to the golden ratio centered on an arbitrary sphere center cannot enclose a number of sphere centers greater than one more than the number that can be placed on the region's surface.Comment: 12 pages, 1 figure. Accepted for publication in the Journal of Mathematical Physic