Helium- and Lithium-like ionic sequences: Critical charges

In non-relativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without any visible irregularities. Thus, for both systems the physical integer charges $Z=1,2,...$ do not play a distinguished role as would be associated with charge quantization. By definition, a critical charge $Z_{cr}$ is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For both systems the critical charges are found, $Z_{cr,2e}=0.91085$ and $Z_{cr,3e}=2.009$, respectively. Based on numerical analysis, the Puiseux expansion in fractional powers of $(Z-Z_{cr})$ is constructed for both systems. Our results indicate the existence of a square-root branch point singularity at $Z_{cr}$ with exponent 3/2. A connection between the critical charge and the radius of convergence of 1/Z-expansion is briefly discussed.Comment: 10 pages, LaTeX, typos corrected, Fig.1 added, a Note Added with calculated critical charge for $2^1S$ state for $(Z,e,e)$ system, $Z_{cr,2e}^{(2^1S)}\ =\ 1.02

The development of a model to describe the influence of temperature and relative humidity on respiration rate of prickly pear cactus stems in reduced O2 conditions

Respiration rate (RO2) of prickly pear cactus stems (Opuntia spp.) was measured as a function of 4 temperature (T) and 6 relative humidity (RH) combinations for O2 partial pressures between 15 and 0.8 kPa, which were considered to support aerobic respiration. The rate of respiration (RO2) was determined based on O2 depletion of the atmosphere in sealed containers containing 1 kg of stems. The O2 partial pressure declined linearly over time and the slopes of the fitted lines were used to calculate the rate of O2 uptake. The rate of O2 uptake increased with increasing temperature and decreased with increasing RH. The respiratory rate at 25°C was approximately 30 to 40 times higher than at 5°C. The respiratory rate at 65% RH was between 30 and 90% greater than at 90% RH, depending on the temperature. Data for ln(RO2) for each RH level were regressed against the inverse of the T (K-1) to determine Arrhenius constants and calculate the apparent Ea of respiration for the six RH conditions. The Ea was similar for each RH level, varying between a low of 113 to a high of 131 kJ•mol-1. An equation having an R2 of 0.95 was developed describing respiration as a function of RH and T (°C) using only four constant