Effective-range function methods for charged particle collisions

Different versions of the effective-range function method for charged particle collisions are studied and compared. In addition, a novel derivation of the standard effective-range function is presented from the analysis of Coulomb wave functions in the complex plane of the energy. The recently proposed effective-range function denoted as $\Delta_\ell$ [Phys. Rev. C 96, 034601 (2017)] and an earlier variant [Hamilton et al., Nucl. Phys. B 60, 443 (1973)] are related to the standard function. The potential interest of $\Delta_\ell$ for the study of low-energy cross sections and weakly bound states is discussed in the framework of the proton-proton ${}^1S_0$ collision. The resonant state of the proton-proton collision is successfully computed from the extrapolation of $\Delta_\ell$ instead of the standard function. It is shown that interpolating $\Delta_\ell$ can lead to useful extrapolation to negative energies, provided scattering data are known below one nuclear Rydberg energy (12.5 keV for the proton-proton system). This property is due to the connection between $\Delta_\ell$ and the effective-range function by Hamilton et al. that is discussed in detail. Nevertheless, such extrapolations to negative energies should be used with caution because $\Delta_\ell$ is not analytic at zero energy. The expected analytic properties of the main functions are verified in the complex energy plane by graphical color-based representations.Comment: 17 pages, 11 figures, 46 references; typos fixe

On the practical interest of one-body overlap functions

Two types of one-body functions extracted from microscpic models of the 8B ground state are compared with one another and with a potential-model wave function. The one-body overlap function seems to have the strongest physical meaning.Comment: 2 pages, 1 figure, proceedings of the International Symposium "A New Era of Nuclear Structure Physics", Kurokawa (Japan), November 19-22, 200

Decoherence and determinism in a one-dimensional cloud-chamber model

The hypothesis by Sparenberg et al. (2013) that the particular linear tracks appearing in the measurement of a spherically-emitting radioactive source in a cloud chamber are determined by the (random) positions of atoms or molecules inside the chamber is further explored in the framework of a recently established one-dimensional model by Carlone et al. (2015). In this model, meshes of localized spins 1/2 play the role of the cloud-chamber atoms and the spherical wave is replaced by a linear superposition of two wave packets moving from the origin to the left and to the right, evolving deterministically according to the Schr\"odinger equation. We first revisit these results using a time-dependent approach, where the wave packets impinge on a symmetric two-sided detector. We discuss the evolution of the wave function in the configuration space and stress the interest of a non-symmetric detector in a quantum-measurement perspective. Next we use a time-independent approach to study the scattering of a plane wave on a single-sided detector. Preliminary results are obtained, analytically for the single-spin case and numerically for up to 8 spins. They show that the spin-excitation probabilities are sometimes very sensitive to the parameters of the model, which corroborates the idea that the measurement result could be determined by the atom positions. The possible origin of decoherence and entropy increase in future models is finally discussed.Comment: Published version in Foundations of Physics. Text modified according to referees' comment

On the phase-shift parameterization and ANC extraction from elastic-scattering data

We develop a method to parameterize elastic-scattering phase-shifts for charged nuclei, based on Pad\'e expansions of a simplified effective-range function. The method is potential independent and the input is reduced to experimental phase shifts and bound-state energies. It allows a simple calculation of resonance properties and of asymptotic normalization constants (ANCs) of subthreshold bound states. We analyze the $1^-$ and $2^+$ phase shifts of the $^{12}$C$+\alpha$ system and extract the ANCs of the corresponding bound states. For the $1^-$ state, a factor-3 improvement with respect to the best value available today is obtained, with a factor-10 improvement in reach. For the $2^+$ state, no improvement is obtained due to relatively larger error bars on the experimental phase shifts.Comment: 6 pages, 5 figures; v2: 4 references added, 2 figures modified, better comparison made with existing method

\u3ci\u3eThe Seduction of Yahu-El Betshintav\u3c/i\u3e

Recently an angel of heaven descended to earth. She was not one of the fiery seraphim. Nor was she an androgynous angel, an ofan