Bargaining over perfect complements owned separately: with experimental test

This paper considers the situation in which two perfect complements belong to different owners. We calculate the Bayesian–Nash equilibrium in the mechanism of k + 1 − price bargaining with private value, and did experiment to test the theory

Pygmy Dipol Resonances as a Manifestation of the Structure of the Neutron-Rich Nuclei

Dipole excitations in neutron-rich nuclei below the neutron threshold are investigated. The method is based on Hartree-Fock-Bogoliubov (HFB) and Quasiparticle-Phonon Model (QPM) theory. Of our special interest are the properties of the low-lying 1- Pygmy Resonance and the two-phonon quadrupole-octupole 1- states in Sn-isotopes including exploratory investigations for the experimentally unknown mass regions. In particular we investigate the evolution of the dipole strength function with the neutron excess. The use of HFB mean-field potentials and s.p. energies is found to provide a reliable extrapolation into the region off stability.Comment: 8 pages, 3 figures, Proceedings of the International Conference on Collective Motion in Nuclei Under Extreme Conditions (COMEX1), Paris, France, 10-13 June 200

Orbital M1 versus E2 strength in deformed nuclei: A new energy weighted sum rule

Within the unified model of Bohr and Mottelson we derive the following linear energy weighted sum rule for low energy orbital 1$^+$ excitations in even-even deformed nuclei S_{\rm LE}^{\rm lew} (M_1^{\rm orb}) \cong (6/5) \epsilon (B(E2; 0^+_1 \rightarrow 2_1^+ K=0)/Z e^2^2) \mu^2_N with B(E2) the E2 strength for the transition from the ground state to the first excited state in the ground state rotational band, $$ the charge r.m.s. radius squared and $\epsilon$ the binding energy per nucleon in the nuclear ground state. It is shown that this energy weighted sum rule is in good agreement with available experimental data. The sum rule is derived using a simple ansatz for the intrinsic ground state wave function that predicts also high energy 1$^+$ strength at 2$\hbar \omega$ carrying 50\% of the total $m_1$ moment of the orbital M1 operator.Comment: REVTEX (3.0), 9 pages, RU924

Transition Rates between Mixed Symmetry States: First Measurement in 94Mo

The nucleus 94Mo was investigated using a powerful combination of gamma-singles photon scattering experiments and gamma-gamma-coincidence studies following the beta-decay of 94mTc. The data survey short-lived J^pi=1+,2+ states and include branching ratios, E2/M1 mixing ratios, lifetimes, and transition strengths. The mixed-symmetry (MS) 1+ scissors mode and the 2+ MS state are identified from M1 strengths. A gamma transition between MS states was observed and its rate was measured. Nine M1 and E2 strengths involving MS states agree with the O(6) limit of the interacting boson model-2 using the proton boson E2 charge as the only free parameter.Comment: 9 pages, 3 PostScript figures included, ReVTeX, accepted for publication in Physical Review Letters, tentatively scheduled for August 9, 199

Competing electric and magnetic excitations in backward electron scattering from heavy deformed nuclei

Important $E2$ contributions to the $(e,e^{\prime})$ cross sections of low-lying orbital $M1$ excitations are found in heavy deformed nuclei, arising from the small energy separation between the two excitations with $I^{\pi}K = 2^+1$ and 1$^+1$, respectively. They are studied microscopically in QRPA using DWBA. The accompanying $E2$ response is negligible at small momentum transfer $q$ but contributes substantially to the cross sections measured at $\theta = 165 ^{\circ}$ for $0.6 < q_{\rm eff} < 0.9$ fm$^{-1}$ ($40 \le E_i \le 70$ MeV) and leads to a very good agreement with experiment. The electric response is of longitudinal $C2$ type for $\theta \le 175 ^{\circ}$ but becomes almost purely transverse $E2$ for larger backward angles. The transverse $E2$ response remains comparable with the $M1$ response for $q_{\rm eff} > 1.2$ fm$^{-1}$ ($E_i > 100$ MeV) and even dominant for $E_i > 200$ MeV. This happens even at large backward angles $\theta > 175 ^{\circ}$, where the $M1$ dominance is limited to the lower $q$ region.Comment: RevTeX, 19 pages, 8 figures included Accepted for publication in Phys Rev

Strong fragmentation of low-energy electromagnetic excitation strength in 117^{117}Sn

Results of nuclear resonance fluorescence experiments on $^{117}$Sn are reported. More than 50 $\gamma$ transitions with $E_{\gamma} < 4$ MeV were detected indicating a strong fragmentation of the electromagnetic excitation strength. For the first time microscopic calculations making use of a complete configuration space for low-lying states are performed in heavy odd-mass spherical nuclei. The theoretical predictions are in good agreement with the data. It is concluded that although the E1 transitions are the strongest ones also M1 and E2 decays contribute substantially to the observed spectra. In contrast to the neighboring even $^{116-124}$Sn, in $^{117}$Sn the $1^-$ component of the two-phonon $[2^+_1 \otimes 3^-_1]$ quintuplet built on top of the 1/2$^+$ ground state is proved to be strongly fragmented.Comment: 4 pages, 3 figure

Charged pion form factor between Q^2=0.60 and 2.45 GeV^2. II. Determination of, and results for, the pion form factor

The charged pion form factor, Fpi(Q^2), is an important quantity which can be used to advance our knowledge of hadronic structure. However, the extraction of Fpi from data requires a model of the 1H(e,e'pi+)n reaction, and thus is inherently model dependent. Therefore, a detailed description of the extraction of the charged pion form factor from electroproduction data obtained recently at Jefferson Lab is presented, with particular focus given to the dominant uncertainties in this procedure. Results for Fpi are presented for Q^2=0.60-2.45 GeV^2. Above Q^2=1.5 GeV^2, the Fpi values are systematically below the monopole parameterization that describes the low Q^2 data used to determine the pion charge radius. The pion form factor can be calculated in a wide variety of theoretical approaches, and the experimental results are compared to a number of calculations. This comparison is helpful in understanding the role of soft versus hard contributions to hadronic structure in the intermediate Q^2 regime.Comment: 18 pages, 11 figure