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We derive a set of symmetry relations for the three-neutrino mixing angles, including the MSW matter effect. Though interesting in their own right, these relations are used to choose the physical region of the mixing angles such that oscillations are parameterized completely and uniquely. We propose that the preferred way of setting the bounds on the mixing angles should be $\theta_{12} \in [0,\pi/2]$, $\theta_{13} \in [-\pi/2,\pi/2]$, $\theta_{23}\in [0,\pi/2]$, and $\delta \in [0,\pi)$. No CP violation then results simply from setting $\delta=0$. In the presence of the MSW effect, this choice of bounds is a new result. Since the size of the asymmetry about $\theta_{13} = 0$ is dependent on the details of the data analysis and is a part of the results of the analysis, we argue that the negative values of $\theta_{13}$ should not be ignored.Comment: 4 page

Elastic scattering of pions from finite nuclei is investigated utilizing a contemporary, momentum-space first-order optical potential combined with microscopic estimates of second-order corrections. The calculation of the first-order potential includes: (1) full Fermi-averaging integration including both the delta propagation and the intrinsic nonlocalities in the π-N amplitude, (2) fully covariant kinematics, (3) use of invariant amplitudes which do not contain kinematic singularities, and (4) a finite-range off-shell pion-nucleon model which contains the nucleon pole term.The effect of the delta-nucleus interaction is included via the mean spectral-energy approximation. It is demonstrated that this produces a convergent perturbation theory in which the Pauli corrections (here treated as a second-order term) cancel remarkably against the pion true absorption terms. Parameter-free results, including the delta-nucleus shell-model potential, Pauli corrections, pion true absorption, and short-range correlations are presented.Pion-scattering measurements, in combination with phenomenological descriptions [1] of the propagation of the pion and the delta in the nuclear medium, have proved useful 1

In relativistic heavy-ion collisions, the strong Lorentz-contracted electromagnetic 6elds are capable of producing copious numbers of lepton pairs through the two-photon mechanism. Monte Carlo techniques have been developed that allow the exact calculation of production by this mechanism when a semiclassical approximation is made for the motion of the two ions. Here we develop a hybrid Monte Carlo technique that enables us to calculate the i.mpact-parameter dependence of the two-photon mechanism for lepton-pair production, and by using this result we obtain the probability distribution for multiple-pair production as a function of impact parameter. Computations are performed for S+Au and Pb+Pb systems at 200 and 160 A GeV, respectively. We also compare our results with the equivalent-photon approximation and elucidate the differences.PACS number(s): 12.20. Ds, 25.75.+r, 02.70.Lq