We discuss charge symmetry and charge independence breaking in a chiral effective field theory approach for few-nucleon systems based on a modified Weinberg power counting. We construct a two-nucleon potential with bound and scattering states generated by means of a properly regularized Lippmann-Schwinger equation. We systematically introduce strong isospin-violating and electromagnetic operators in the theory. We use standard procedures to treat the Coulomb potential between two protons in momentum space. We present results for phase shifts in the protonproton, neutron-proton and the neutron-neutron systems. We discuss the various contributions to charge dependence and charge symmetry breaking observed in the nucleon-nucleon scattering lengths.
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We calculate elastic electron-deuteron scattering in a chiral effective field theory approach for few-nucleon systems based on a modified Weinberg power counting. We construct the current operators and the deuteron wave function at next-toleading (NLO) and next-to-next-to-leading (NNLO) order simultaneously within a projection formalism. The leading order comprises the impulse approximation of photons coupling to point-like nucleons with an anomalous magnetic moment. At NLO, we include renormalizations of the single nucleon operators. To this order, no unknown parameters enter. At NNLO, one four-nucleon-photon operator appears. Its strength can be determined from the deuteron magnetic moment. We obtain not only a satisfactory description of the deuteron structure functions and form factors measured in electron-deuteron scattering but also find a good convergence for these observables.
We consider several notions of setwise stability for many-to-many matching markets with contracts and provide an analysis of the relations between the resulting stable sets and pairwise stable sets for general, substitutable, and strongly substitutable preferences. Apart from obtaining "set inclusion results" on all three domains, we prove that for substitutable preferences the set of pairwise stable matchings is nonempty and coincides with the set of weakly setwise stable matchings. For strongly substitutable preferences the set of pairwise stable matchings coincides with the set of setwise stable matchings. We also show that Roth's (1984b) stability coincides with pairwise stability for substitutable preferences. JEL classification: C62, C78, D78, J41.
We show that for any roommate market the set of stochastically stable matchings coincides with the set of absorbing matchings. This implies that whenever the core is non-empty (e.g., for marriage markets), a matching is in the core if and only if it is stochastically stable, i.e., stochastic stability is a characteristic of the core. Several solution concepts have been proposed to extend the core to all roommate markets (including those with an empty core). An important implication of our results is that the set of absorbing matchings is the only solution concept that is core consistent and shares the stochastic stability characteristic with the core.JEL classification: C62, C71, C78.
There is a heated debate on whether markets erode social responsibility and moral behavior. However, it is a challenging task to identify and measure moral behavior in markets. Based on a theoretical model, we examine in an experiment the relation between trading volume, prices and moral behavior by setting up markets that either impose a negative externality on third parties or not. We find that moral behavior reveals itself in lower trading volume in markets with a negative externality, while prices mostly depend on the market structure. We further investigate individual characteristics that explain trading behavior in markets with negative externalities.
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