Self-adjoint extensions for confined electrons: From a particle in a spherical cavity to the hydrogen atom in a sphere and on a cone

In a recent study of the self-adjoint extensions of the Hamiltonian of a particle confined to a finite region of space, in which we generalized the Heisenberg uncertainty relation to a finite volume, we encountered bound states localized at the wall of the cavity. In this paper, we study this situation in detail both for a free particle and for a hydrogen atom centered in a spherical cavity. For appropriate values of the self-adjoint extension parameter, the bound states localized at the wall resonate with the standard hydrogen bound states. We also examine the accidental symmetry generated by the Runge–Lenz vector, which is explicitly broken in a spherical cavity with general Robin boundary conditions. However, for specific radii of the confining sphere, a remnant of the accidental symmetry persists. The same is true for an electron moving on the surface of a finite circular cone, bound to its tip by a 1/r1/r potential.

The ArgoNeuT detector in the NuMI low-energy beam line at Fermilab

The ArgoNeuT liquid argon time projection chamber has collected thousands of neutrino and anti-neutrino events during an extended run period in the NuMI beam-line at Fermilab. This paper focuses on the main aspects of the detector layout and related technical features, including the cryogenic equipment, time projection chamber, read-out electronics, and off-line data treatment. The detector commissioning phase, physics run, and first neutrino event displays are also reported. The characterization of the main working parameters of the detector during data-taking, the ionization electron drift velocity and lifetime in liquid argon, as obtained from through-going muon data complete the present report.

Quantitative analysis of OCT characteristics in patients with achromatopsia and blue-cone monochromatism

PURPOSE: To quantify optical coherence tomography (OCT) images of the central retina in patients with blue-cone monochromatism (BCM) and achromatopsia (ACH) compared with healthy control individuals. METHODS: The study included 15 patients with ACH, 6 with BCM, and 20 control subjects. Diagnosis of BCM and ACH was established by visual acuity testing, morphologic examination, color vision testing, and Ganzfeld ERG recording. OCT images were acquired with the Stratus OCT 3 (Carl Zeiss Meditec AG, Oberkochen, Germany). Foveal OCT images were analyzed by calculating longitudinal reflectivity profiles (LRPs) from scan lines. Profiles were analyzed quantitatively to determine foveal thickness and distances between reflectivity layers. RESULTS: Patients with ACH and BCM had a mean visual acuity of 20/200 and 20/60, respectively. Color vision testing results were characteristic of the diseases. The LRPs of control subjects yielded four peaks (P1-P4), presumably representing the RPE (P1), the ovoid region of the photoreceptors (P2), the external limiting membrane (ELM) (P3), and the internal limiting membrane (P4). In patients with ACH, P2 was absent, but foveal thickness (P1-P4) did not differ significantly from that in the control subjects (187 +/- 20 vs. 192 +/- 14 microm, respectively). The distance from P1 to P3 did not differ significantly (78 +/- 10 vs. 82 +/- 5 microm) between ACH and controls subjects. In patients with BCM, P3 was lacking, and P2 advanced toward P1 compared with the control subjects (32 +/- 6 vs. 48 +/- 4 microm). Foveal thickness (153 +/- 16 microm) was significantly reduced compared with that in control subjects and patients with ACH. CONCLUSIONS: Quantitative OCT image analysis reveals distinct patterns for controls subjects and patients with ACH and BCM, respectively. Quantitative analysis of OCT imaging can be useful in differentiating retinal diseases affecting photoreceptors. Foveal thickness is similar in both normal subjects and patients with ACH but is decreased in patients with BCM.