Completeness of scattering states of the Dirac Hamiltonian with a step potential

The completeness, together with the orthonormality, of the eigenfunctions of the Dirac Hamiltonian with a step potential is shown explicitly. These eigenfunctions describe the scattering process of a relativistic fermion off the step potential and the resolution of the identity in terms of them (completeness) is shown by explicitly summing them up, where appropriate treatments of the momentum integrations are crucial. The result would bring about a basis on which a field theoretical treatment for such a system can be developed.Comment: 16 pages, 1 figure

Acceptance Corrections and Extreme-Independent Models in Relativistic Heavy Ion Collisions

Kopeliovich's suggestion [nucl-th/0306044] to perform nuclear geometry (Glauber) calculations using different cross sections according to the experimental configuration is quite different from the standard practice of the last 20 years and leads to a different nuclear geometry definition for each experiment. The standard procedure for experimentalists is to perform the nuclear geometry calculation using the total inelastic N-N cross section, which results in a common nuclear geometry definition for all experiments. The incomplete acceptance of individual experiments is taken into account by correcting the detector response for the probability of measuring zero for an inelastic collision, which can often be determined experimentally. This clearly separates experimental issues such as different acceptances from theoretical issues which should apply in general to all experiments. Extreme-Independent models are used to illustrate the conditions for which the two methods give consistent or inconsistent results.Comment: 4 pages, 1 figure, published in Physical Review

Pressure Tuning of an Ionic Insulator into a Heavy Electron Metal: An Infrared Study of YbS

Optical conductivity [$\sigma(\omega)$] of YbS has been measured under pressure up to 20 GPa. Below 8 GPa, $\sigma(\omega)$ is low since YbS is an insulator with an energy gap between fully occupied 4$f$ state and unoccupied conduction ($c$) band. Above 8 GPa, however, $\sigma(\omega)$ increases dramatically, developing a Drude component due to heavy carriers and characteristic infrared peaks. It is shown that increasing pressure has caused an energy overlap and hybridization between the $c$ band and 4$f$ state, thus driving the initially ionic and insulating YbS into a correlated metal with heavy carriers

Kondo effect in CeXc_{c} (Xc_{c}=S, Se, Te) studied by electrical resistivity under high pressure

We have measured the electrical resistivity of cerium monochalcogenices, CeS, CeSe, and CeTe, under high pressures up to 8 GPa. Pressure dependences of the antiferromagnetic ordering temperature $T_{N}$, crystal field splitting, and the $\ln T$ anomaly of the Kondo effect have been studied to cover the whole region from the magnetic ordering regime at low pressure to the Fermi liquid regime at high pressure. $T_{N}$ initially increases with increasing pressure, and starts to decrease at high pressure as expected from the Doniach's diagram. Simultaneously, the $\ln T$ behavior in the resistivity is enhanced, indicating the enhancement of the Kondo effect by pressure. It is also characteristic in CeX$_{c}$ that the crystal field splitting rapidly decreases at a common rate of $-12.2$ K/GPa. This leads to the increase in the degeneracy of the $f$ state and further enhancement of the Kondo effect. It is shown that the pressure dependent degeneracy of the $f$ state is a key factor to understand the pressure dependence of $T_{N}$, Kondo effect, magnetoresistance, and the peak structure in the temperature dependence of resistivity.Comment: 9 pages, 5 figures, accepted for publication in J. Phys. Soc. Jp