Pion-mass dependence of three-nucleon observables

We use an effective field theory (EFT) which contains only short-range interactions to study the dependence of a variety of three-nucleon observables on the pion mass. The pion-mass dependence of input quantities in our “pionless” EFT is obtained from a recent chiral EFT calculation. To the order we work at, these quantities are the ¹ S ₀ scattering length and effective range, the deuteron binding energy, the ³ S ₁ effective range, and the binding energy of one three-nucleon bound state. The chiral EFT input we use has the inverse ³ S ₁ and ¹ S ₀ scattering lengths vanishing at m _π ^crit = 197.8577 MeV. At this “critical” pion mass, the triton has infinitely many excited states with an accumulation point at the three-nucleon threshold. We compute the binding energies of these states up to next-to-next-to-leading order in the pionless EFT and study the convergence pattern of the EFT in the vicinity of the critical pion mass. Furthermore, we use the pionless EFT to predict how doublet and quartet nd scattering lengths depend on m _π in the region between the physical pion mass and m _π = m _π ^crit .     

Polarization observables in π-d scattering

Exact calculations of vector and tensor polarizations are presented for the reaction $\text{π +}\text{d}\text{→ π +}\text{d}$ at T_π = 142 MeV. They are aimed at meeting the apparent demand raised by upcoming pertinent experiments. The effects of (i) deuteron D state, (ii) participating π-N partial waves and (iii) coupling of different π-d orbital angular momenta are found to be very important.     

Axial observables in d-->p--> breakup and the three-nucleon force

We have measured three axial polarization observables in d-->p--> breakup with a polarized 270 MeV deuteron beam on a polarized proton target. Axial observables are zero by parity conservation in elastic scattering but can be easily observed in the breakup channel at the present energy. Based on a symmetry argument, the sensitivity of these observables to the three-nucleon force might be enhanced. Calculations without three-nucleon force are in fair agreement with our measurement, indicating that the expected sensitivity of axial observables to the three-nucleon force is not confirmed. Including a three-nucleon force in the calculation does not improve the agreement with the data.     

Polarization observables in the reaction pn↦dφ

The reaction pn↦dφ is studied within a covariant boson exchange model. The behavior of polarization observables being accessible in forthcoming experiments near threshold is predicted. Received: 13 February 2001 / Accepted: 25 March 2002     

Correlated hyperspherical-harmonic expansion for three-nucleon systems

The hyperspherical-harmonic-expansion method is applied to solve the Schrödinger equation for a three-particle system interacting via central spin-dependent potentials. The convergence of the expansion has been improved by multiplying the hyperspherical basis by an appropriate correlation factor, chosen as a product of one-dimensional functions fixed by means of a two-body Schrödinger equation. The results obtained for three nucleons interacting via the Malfliet-Tjon potential are in close agreement with those given by the most accurate methods.     

Three-nucleon forces and the three-nucleon systems

The basic principles and philosophy which have guided the area of few-nucleon physics are motivated and discussed. Recent advances have made it possible to solve accurately the Schrödinger (or Faddeev) equation for many of the configurations of the few-nucleon systems, A brief review is given of some of the results of these calculations, which also Indicate that one-pion exchange plays roughly the same role in binding these systems that it plays in electromagnetic meson-exchange currents. Finally, a qualitative discussion of chiral perturbation theory is presented, which highlights the role that chiral symmetry plays in the nuclear force. Three-body forces from different areas of physics are discussed, as well as the significance of three-nucleon forces in few-nucleon systems.Lectures held at the Indian Summer School on Electromagnetic and Weak Interactions of Particles with Nuclei, Sázava, Czechoslovakia, 6–11 September 1992The work of J. L. F. was performed under the auspices of the U. S. Department of Energy. The support of the Alexander von Humboldt-Stiftung is gratefully acknowledged. The author gratefully acknowledges discussions with B. Holstein, whose superb lectures on this topic introduced him to chiral perturbation theory.     

Relativistic calculations for two- and three-nucleon systems

The relativistic theory for few-nucleon systems developed by Glöckle and Müller is evaluated numerically for a model of scalar particles exchanging scalar mesons to lowest order in the coupling constant. 2-nucleon binding energies and scattering phases and 3-nucleon binding energies are compared with the usual non-relativistic calculation for different choices of the potential. The relativistic treatment gives a weaker binding. The mechanism of this is studied in more detail. We compare our results with the relativistic correction in the 1/c² expansion of Foldy and Krajcik.     

Two-pion exchange three-nucleon potential and D-waves in trinucleon systems

Equipotential plots are employed in the qualitative study of the coupling between S- and D-waves in trinucleon systems. Two forms of a two-pion exchange three-nucleon potential based on chiral symmetry are considered, namely that produced by the Tucson-Melbourne collaboration and a redefined version that excludes contact interactions. In both cases the contributions of the three-nucleon potential are comparable to those of two-nucleon interactions, showing that the usual treatment of the former by means of perturbation theory is not justified.     

Polarization observables in high-energy deuteron photo-disintegration within the Quark-Gluon Strings Model

Deuteron two-body photodisintegration is analysed within the framework of the Quark-Gluon Strings Model. The model describes fairly well the recent experimental data from TJNAF in the few GeV region. Angular distributions at different -energies are presented and the effect of a forward-backward asymmetry is discussed. New results from the QGSM for polarization observables from 1.5-6 GeV are presented and compared with the available data.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.40.-f Electromagnetic processes and properties - 25.20.-x Photonuclear reactions     

Polarization observables in the 3πν decay mode of the τ

A method is described to measure τ polarization in its 3πν decay mode.     

Polarization observables in elastic electron deuteron scattering including parity- and time-reversal-violating contributions

The general formalism for polarization observables in elastic electron deuteron scattering is extended to incorporate parity- and time-reversal-violating contributions. Parity-violating effects arise from the interference of γ and Z exchange as well as from the hadronic sector via a small parity-violating component in the deuteron. In addition we have allowed for time-reversal-invariance-violating contributions in the hadronic sector. Formal expressions for the additional structure functions are derived, and their decomposition into the various multipole contributions are given explicitly. Received: 19 December 2000 / Accepted: 14 February 2001     

Extreme value laws in dynamical systems under physical observables

Extreme value theory for chaotic deterministic dynamical systems is a rapidly expanding area of research. Given a system and a real function (observable) defined on its phase space, extreme value theory studies the limit probabilistic laws obeyed by large values attained by the observable along orbits of the system. Based on this theory, the so-called block maximum method is often used in applications for statistical prediction of large value occurrences. In this method, one performs statistical inference for the parameters of the Generalised Extreme Value (GEV) distribution, using maxima over blocks of regularly sampled observable values along an orbit of the system. The observables studied so far in the theory are expressed as functions of the distance with respect to a point, which is assumed to be a density point of the system’s invariant measure. However, at least with respect to the ambient (usually Euclidean) metric, this is not the structure of the observables typically encountered in physical applications, such as windspeed or vorticity in atmospheric models. In this paper we consider extreme value limit laws for observables which are not expressed as functions of the distance (in the ambient metric) from a density point of the dynamical system. In such cases, the limit laws are no longer determined by the functional form of the observable and the dimension of the invariant measure: they also depend on the specific geometry of the underlying attractor and of the observable’s level sets. We present a collection of analytical and numerical results, starting with a toral hyperbolic automorphism as a simple template to illustrate the main ideas. We then formulate our main results for a uniformly hyperbolic system, the solenoid map. We also discuss non-uniformly hyperbolic examples of maps (Hénon and Lozi maps) and of flows (the Lorenz63 and Lorenz84 models). Our purpose is to outline the main ideas and to highlight several serious problems found in the numerical estimation of the limit laws.     

Partial and complete observables for Hamiltonian constrained systems

We will pick up the concepts of partial and complete observables introduced by Rovelli in Conceptional Problems in Quantum Gravity, Birkhäuser, Boston (1991); Class Quant Grav, 8:1895 (1991); Phys Rev, D65:124013 (2002); Quantum Gravity, Cambridge University Press, Cambridge (2007) in order to construct Dirac observables in gauge systems. We will generalize these ideas to an arbitrary number of gauge degrees of freedom. Different methods to calculate such Dirac observables are developed. For background independent field theories we will show that partial and complete observables can be related to Kucha?’s Bubble-Time Formalism (J Math Phys, 13:768, 1972). Moreover one can define a non-trivial gauge action on the space of complete observables and also state the Poisson brackets of these functions. Additionally we will investigate, whether it is possible to calculate Dirac observables starting with partially invariant partial observables, for instance functions, which are invariant under the spatial diffeomorphism group.     

Dissipative time evolution of observables in non-equilibrium statistical quantum systems

We discuss differential– versus integral–equation based methods describing out–of thermal equilibrium systems and emphasize the importance of a well defined reduction to statistical observables. Applying the projection operator approach, we investigate on the time evolution of expectation values of linear and quadratic polynomials in position and momentum for a statistical anharmonic oscillator with quartic potential. Based on the exact integro-differential equations of motion, we study the first and naive second order approximation which breaks down at secular time-scales. A method is proposed to improve the expansion by a non–perturbative resummation of all quadratic operator correlators consistent with energy conservation for all times. Motion cannot be described by an effective Hamiltonian local in time reflecting non-unitarity of the dissipative entropy generating evolution. We numerically integrate the consistently improved equations of motion for large times. We relate entropy to the uncertainty product, both being expressible in terms of the observables under consideration. Received: 21 July 1998 / Revised version: 28 September 1998 / Published online: 2 November 1998