P. B. Siegel

Chiral dynamics and the low-energy kaon-nucleon interaction

Abstract We examine the meson-baryon interaction in the strangeness S = −1 sector using an effective chiral Lagrangian. Potentials are derived from this Lagrangian and used in a coupled-channel calculation of the low-energy observables. The potentials are constructed such that in the Born approximation the s-wave scattering length is the same as that given by the effective chiral Lagrangian, up to order q2. A comparison is made with the available low-energy hadronic data of the coupled K−p, Σπ, Λπ system, which includes the Λ(1405) resonance, K−p elastic and inelastic scattering, and the threshold branching ratios of the K−p decay. Good fits to the experimental data and estimates of previously unknown Lagrangian parameters are obtained.

Chiral dynamics and the S11 (1535) nucleon resonance

Abstract The SU(3) chiral effective lagrangian at next-to-leading order is applied to the S-wave meson-baryon interaction in the energy range around the ηN threshold. A potential is derived from this lagrangian and used in a coupled channel calculation of the πN, ηN, KΛ, KΣ system in the isospin - 1 2 , l = 0 partial wave. Using the same parameters as obtained previously from a fit to the low energy K N data it is found that a quasi-bound KΣ-KΛ-state is formed, with properties remarkably similar to the S11(1535) nucleon resonance. In particular, we find a large partial decay width into ηN consistent with the empirical data.

Σ− hypernuclear spectra from (K−, π+) inclusive reactions

Abstract We report on DWIA calculations of the pion inclusive spectra related to Σ-formation in (K−, π+) reactions on nuclei. Realistic distorted waves are used to describe the incoming kaon and outgoing pion. The Σ wave function is calculated in a real Woods-Saxon potential, the depth of which provides information about the underlying Σ N effective interaction. The absorptive effect due to the Σ-Λ conversion process in the nuclear medium is taken into account by effective two-channel coupled equations. Comparisons are made with the available data on 12C and 16O. Using a weak Σ-nucleus potential the overall agreement is satisfactory for the spectrum derived from kaon-in-flight experiments. Concerning the three peaks reported in a stopped kaon experiment on 12C, the lowest peak structure can be generated by increasing the depth of the Σ potential in 12C. However, the remaining two narrow structures cannot be reproduced as Σ-particle-proton-hole states in our continuum treatment of the Σ spectrum. The difficulties in extracting the strength of the Σ-nucleus spin-orbit potential are also discussed.

Initial State Interactions for K -Proton Radiative Capture

The effects of the initial state interactions on the K − p radiative capture branching ratios are examined and found to be quite sizable. A general coupled-channel formalism for both strong and electromagnetic channels using a particle basis is presented, and applied to all the low energy K − p data with the exception of the 1s atomic level shift. Satisfactory fits are obtained using vertex coupling constants for the electromagnetic channels that are close to their expected SU(3) values.

Putting your heart into physics

We describe techniques for measuring the time interval between successive heartbeats. This time series data can be used in undergraduate physics classes for instruction in resonance phenomena, scaling, and other methods of analysis including Fourier analysis and Poincare plots. Using methods from physics on data from human physiology are of particular interest to life science students.

Period-speed analysis of a pendulum

We analyze a simple pendulum by measuring the period and the maximum speed of the bob. Both quantities are measured to high precision using a laser diode and an infrared photodetector located at the bottom of the pendulum. Expressing the period in terms of the maximum speed enables students to examine the large angle dependence of the period, and provides a method to calibrate the speed and do a detailed analysis of the effect of air friction on a sphere. We find that the force due to air friction is well described by a linear and quadratic term in the speed. We investigate the dependence of each term on the sphere’s diameter for Reynolds numbers from 250 to 104.

Going bananas in the radiation laboratory

A simple setup for measuring the amount of potassium in foods is described. A 3-in. NaI detector is used to measure samples that are 3000 cm3 in size. With moderate shielding, the potassium content can be measured down to a detection limit of a few parts per 10 000.

Data analysis in the undergraduate nuclear laboratory

Experiments for introducing data analysis techniques in the undergraduate nuclear laboratory are presented. In particular, data from gamma spectroscopy using NaI detectors are ideal for teaching curve fitting and chi‐square analysis. An experiment well suited for error analysis is the measurement of the half‐life of a radioisotope, since the uncertainties are primarily statistical and can be determined by a well‐defined procedure. All software used in our experiments was written by students as special projects.

Coupled channel calculation of Σ-hypernuclear spectra from 12C, 16O and 6Li targets☆

Abstract We present coupled channels calculations of Σ -hypernuclear spectra produced in (K − , π + ) reactions at p K −⋍710 MeV /c . This is an extension of previous work which concentrated on recoilless production and stopped kaon kinematics. The emphasis here is on a proper treatment of Σ continuum states. Satisfactory results are obtained for 12 C and 16 O targets; no narrow structures are seen in these spectra. The 6 Li case is also discussed.

Dead time correction via the time series

We present a method that allows us to correct for dead time and check for the proper operation of a radiation detector while recording data. The method is based on the exponential probability density of the time interval between successive detector pulses, and involves examining the ratio of the moments of the time series with a delay time.