Strong interactions at low energies

The lectures review some of the basic concepts relevant for an understanding of the low energy properties of the strong interactions: chiral symmetry, spontaneous symmetry breakdown, Goldstone bosons, quark condensate. The effective field theory used to analyze the low energy structure is briefly sketched. As an illustration, I discuss the implications of the recent data on the decay K→ππeν for the magnitude of the quark condensate.     

Application of EFT at thermal energies

We have evaluated some observables of n-d systems by using pionless effective field theory (EFT( ${\not}\pi$ )) and insertion of the three-body force up to next-to-next to leading order (N²LO). The evaluated data has been compared with experiment and a three-nucleon calculation of the total cross section with modern realistic two- and three-nucleon force AV18/UrbIX potential models.     

Hydrogen-antihydrogen interactions at low energies

The main cause of loss of trapped AH is due to collisions with H₂ and He. As a first step towards treating these reactions we are studying the interaction of AH with H. We have carried out variational calculations to determine an upper bound to the smallest internuclear distance at which the light particles are still bound to the nuclei. We are currently in the process of taking into account the motion of the nuclei. This will enable us to calculate cross-sections for low energy H-AH scattering. This revised version was published online in August 2006 with corrections to the Cover Date.     

Inelastic interactions with deuterons at very high energies

Cross sections for inelastic reactions of hadrons, photons and leptons with deuterons are derived from the Coherent Tube Model for particle-nucleus collisions. Predictions are compared with recent experimental data. Good agreement between experiments and theory is demonstrated.     

Measurement of the antiproton-nucleus annihilation cross-section at very low energies

The ASACUSA collaboration at the Antiproton Decelerator at CERN is planning to measure the hyperfine splitting of the ground state of antihydrogen using an atomic beam line. This will be a measurement of the antiproton magnetic moment, and also a test of the CPT invariance. The planned experimental method and setup, including the radiofrequency resonance cavity, are described, and results of Monte Carlo simulations are shown. These simulations predict that the antihydrogen ground-state hyperfine splitting can be determined with a relative precision of ～10^???7.     

Lepton scattering off few-nucleon systems at medium and high energies

The interpretation of recent JLab experimental data on the exclusive process A(e,e′p)B off few-nucleon systems is analyzed in terms of realistic nuclear wave functions and the Glauber multiple scattering theory, both in its original form and within a generalized eikonal approximation. The relevance of the exclusive process ⁴He(e,e′p)³H for possible investigations of QCD effects is illustrated.     

On the pion-nucleus dynamics at low energies

Low-energy pion scattering (up to 50 MeV) on ¹²C and ¹⁶O is described quantitatively in the framework of the UST approach. It is shown that at T_π ∼ 50 MeV the differential cross sections arise as a result of a strong interference between the pure potential and absorption channels. The importance of nuclear structure effects in the pion-nucleus dynamics at low energies is discussed.     

Influence of magnetic fields on electron-Ion recombination at very low energies

Radiative recombination (inverse photoionization) is believed to be well understood since the beginning of quantum mechanics. Still, modern experiments consistently reveal excess recombination rates at very low electron-ion center-of-mass energies. In a detailed study on recombination of F6+ and C6+ ions with magnetically guided electrons we explored the yet unexplained rate enhancement, its dependence on the magnetic field B, the electron density n(e), and the beam temperatures T( perpendicular) and T( ||). The excess scales as T(-1/2)( perpendicular) and, surprisingly, as T(-1/2)( ||), increases strongly with B, and is insensitive to n(e). This puts strong constraints on explanations of the enhancement.     

Experimental determinations of electron stopping power at low energies

Abstract

An accurate knowledge of electron stopping power is important for calculations and simulations of electron beam interactions with solids especially in the low energy region (< 10 keV). This paper describes a simplified and rapid experimental procedure using based on electron energy loss spectroscopy which permits accurate stopping power determinations to be made from any material which can be observed in a transmission electron microscope. It is demonstrated that the stopping power and oscillator strength data so generated is in good agreement with other measurements and theoretical predictions. The technique is now being applied to a wide variety of materials of semiconductor interest.     

Measurement of the spectral flux density of negative muons at very low energies

The spectral flux density of negative muons has been measured down to 5 eV.     

On the mobility of very pure semiconductors at very low temperatures

The mobility μ of a very pure semiconductor at very low temperatures is investigated in terms of a model where electrons are scattered by charged impurities distributed uniformly in space, and the electron-electron interaction is taken into account by the Debye-Hueckel screening in the interaction potential. The equation for the current relaxation rate Γ, derived previously by the proper connected diagram expansion, incorporates the quasi-particle effect in a self-consistent manner. The solution of this equation at high carrier concentrations n yields the so-called Brooks-Herring formula. At lower concentrations, the solution deviates significantly from the latter. The solution is in general smaller than the standard expression for the rate based on the Boltzmann equation; and this is consistent with the existing conductivity data available. At the very low concentrations e.g. n = n₃ = 10¹³cm^?3 or lower for Ge, the mobility calculated is inversely proportional to the square-root of the impurity concentration n_s, and has a $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$-dependence (T: temperature).

$\text{μ = 0.3597\&z.xl;h}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{k(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{(ze)}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{m}{}^1{}^{\mathrm{<mtext>?3</mtext><mtext>4</mtext>}}$

, where k is the dielectric constant. The conductivity data directly comparable with this formula are not available at present. However, the quasi-particle effect which led to this peculiar concentration-dependence should also show itself in the cyclotron resonance width; there, experiment and theory both show the ${}_{\mathrm{n}}{}_{\mathrm{s}}$-dependence for very pure semiconductors.     

Recombination of electrons with highly charged heavy ions at very low energies

Recombination of highly charged ions with free electrons is studied in merged-beams experiments at the UNILAC accelerator in Darmstadt and at the heavy-ion storage ring TSR in Heidelberg. Unexpected high recombination rates are observed for a number of ions at very low energiesE _cm in the electron-ion center-of-mass frame. In particular, theoretical estimates for radiative recombination are dramatically exceeded by the experimental recombination rates of U²⁸⁺ ions nearE _cm=0 eV. The observations point to a general phenomenon in electron ion recombination depending onE _cm, on the ion charge state, and possibly also on electron density, electron beam temperature, and strength of external magnetic fields.     

Meson exchange interactions at low and intermediate energies: colour screening effects

We consider the colour screening effects of constituent quarks and the exchange of effective gluons in the interaction of hadrons. To this end we propose two different processes derived from fundamental properties of the underlying microscopic theory (QCD). Sum rules for diagrams providing colour screening are also given.     

The YN interactions and K− reactions on deuterium at low energies

The K^?d → π^?Λp reaction, as well as the other three-body K^? reactions on deuterium, are considered for s-wave kaons in the Faddeev formalism for charge-independent separable two-body coupled-channel interactions fitted to the available low-energy data. In particular we study the effect of a hypothetical $\text{I =}\text{1}\text{2}\text{, S = 1, Σ}\text{N}$ unstable bound state near the πΣN threshold on the shape of the calculated Λp invariant mass distribution near the ΣN threshold. This calculated distribution always exhibits a cusp behavior at the ΣN threshold, but considerable structure and broadening may be reached by varying the parameters of the YN interaction. Multiple scatterings in the initial K?NN and intermediate πΣN channels play a dominant role at low energy. The calculation compares favorably with the measurements at rest and at low energies. This comparison suggests that a ΣN bound state does not exist near the ΣN threshold.     

Stopping power of some elemental and complex SSNTD media at low energies

Stopping power calculations using Hubert et al. formulation have been extended beyond its recommended range of validity, i.e. 2.5–500 MeV/n. It has been established that, for elemental targets up to copper and for complex polymeric SSNTD materials, e.g. CR-39, LR-115, Mylar and Kapton, the formulation provides good agreement with experimental data for projectiles with Z≤29 down to energies as low as 0.5 MeV/n.     

Antiproton stopping at low energies: confirmation of velocity-proportional stopping power

The stopping power for antiprotons in various solid targets has been measured in the low-energy range of 1-100 keV. In agreement with most models, in particular free-electron gas models, the stopping power is found to be proportional to the projectile velocity below the stopping-power maximum. Although a stopping power proportional to velocity has also been observed for protons, the interpretation of such measurements is difficult due to the presence of charge exchange processes. Hence, the present measurements constitute the first unambiguous support for a velocity-proportional stopping power due to target excitations by a pointlike projectile.