Sufficient conditions for the existence of bound states in a central potential

We show how a large class of sufficient conditions for the existence of bound states, in non-positive central potentials, can be constructed. These sufficient conditions yield upper limits on the critical value, $g_{\rm{c}}^{(\ell)}$, of the coupling constant (strength), $g$, of the potential, $V(r)=-g v(r)$, for which a first $\ell$-wave bound state appears. These upper limits are significantly more stringent than hitherto known results.Comment: 7 page

Critical strength of attractive central potentials

We obtain several sequences of necessary and sufficient conditions for the existence of bound states applicable to attractive (purely negative) central potentials. These conditions yields several sequences of upper and lower limits on the critical value, $g_{\rm{c}}^{(\ell)}$, of the coupling constant (strength), $g$, of the potential, $V(r)=-g v(r)$, for which a first $\ell$-wave bound state appears, which converges to the exact critical value.Comment: 18 page

Experimental results on radiation-induced bulk damage effects in float-zone and epitaxial silicon detectors

A comparative study of the radiation hardness of silicon pad detectors, manufactured from Float-Zone and Epitaxial n-type monocrystals and irradiated with protons and neutrons up to a fluence of 3.5 1014 cm-2 is presented. The results are compared in terms of their reverse current, depletion voltage, and charge collection as a function of fluence during irradiation and as a function of time after irradiation

Study of charge collection and noise in non-irradiated and irradiated silicon detectors

The large collection and noise were studied in non-irradiated and irradiated silicon detectors as a function of temperature (T), shaping time (0) and fluence , up to about 1,2 x 10(14) protons per cm2 for minimum-ionizing electrons yielded by a 106 Ru source. The noise of irradiated detectors is found to be dominted for short shaping times (¾50ns) by a series noise compo- nent, while for longer shaping times (80ns) a parallel noise component (correlated with the reverse current) prevails. For non-irradiated detectors, where the reverse current is three orders of magnetude smaller compared with irradiated detectors, the series noises dominates over the whole range of shaping times investigated (20-150ns). A signal degradation is observed for irradiated detectors. However, the signal ca be distinguished from noise, even after a fluence of about 1.2 x10(14) protons per cm2, at a temperature of 6øC and with a shaping time tipical of rge LHC inter-bunch crossing time (20-30ns). The measurements of the signal as a function of voltage shows that irradiated detectors depleted at 50% of the full depletion voltage can still provide a measurable signal-to-noise ratio

Radiation Monitoring in Mixed Environments at CERN: from the IRRAD6 Facility to the LHC Experiments

RadFET and p-i-n diode semiconductor dosimeters from different manufacturers will be used for radiation monitoring at the Experiments of the CERN LHC accelerator. In this work these sensors were exposed over three months in the CERN-IRRAD6 facility that provides mixed high-energy particles at low rates. The aim was to validate the operation of such sensors in a radiation field where the conditions are close to the ones expected inside full working LHC particle detectors. The results of this long-term irradiation campaign are presented, discussed and compared with measurements by other dosimetric means as well as Monte Carlo simulations. Finally, the integration of several dosimetric devices in one sensor carrier is also presented

Necessary and sufficient conditions for existence of bound states in a central potential

We obtain, using the Birman-Schwinger method, a series of necessary conditions for the existence of at least one bound state applicable to arbitrary central potentials in the context of nonrelativistic quantum mechanics. These conditions yield a monotonic series of lower limits on the "critical" value of the strength of the potential (for which a first bound state appears) which converges to the exact critical strength. We also obtain a sufficient condition for the existence of bound states in a central monotonic potential which yield an upper limit on the critical strength of the potential.Comment: 7 page

The Random Discrete Action for 2-Dimensional Spacetime

A one-parameter family of random variables, called the Discrete Action, is defined for a 2-dimensional Lorentzian spacetime of finite volume. The single parameter is a discreteness scale. The expectation value of this Discrete Action is calculated for various regions of 2D Minkowski spacetime. When a causally convex region of 2D Minkowski spacetime is divided into subregions using null lines the mean of the Discrete Action is equal to the alternating sum of the numbers of vertices, edges and faces of the null tiling, up to corrections that tend to zero as the discreteness scale is taken to zero. This result is used to predict that the mean of the Discrete Action of the flat Lorentzian cylinder is zero up to corrections, which is verified. The ``topological'' character of the Discrete Action breaks down for causally convex regions of the flat trousers spacetime that contain the singularity and for non-causally convex rectangles.Comment: 20 pages, 10 figures, Typos correcte

Upper and lower limits on the number of bound states in a central potential

In a recent paper new upper and lower limits were given, in the context of the Schr\"{o}dinger or Klein-Gordon equations, for the number $N_{0}$ of S-wave bound states possessed by a monotonically nondecreasing central potential vanishing at infinity. In this paper these results are extended to the number $N_{\ell}$ of bound states for the $\ell$-th partial wave, and results are also obtained for potentials that are not monotonic and even somewhere positive. New results are also obtained for the case treated previously, including the remarkably neat \textit{lower} limit $N_{\ell}\geq \{\{[\sigma /(2\ell+1)+1]/2\}\}$ with $V(r)| ^{1/2}]$ (valid in the Schr\"{o}dinger case, for a class of potentials that includes the monotonically nondecreasing ones), entailing the following \textit{lower} limit for the total number $N$ of bound states possessed by a monotonically nondecreasing central potential vanishing at infinity: N\geq \{\{(\sigma+1)/2\}\} {(\sigma+3)/2\} \}/2 (here the double braces denote of course the integer part).Comment: 44 pages, 5 figure