Screened hydrogenic radial integrals.

G S Khandelwal; W M Pritchard; G Grubb; F Khan

Home/Archive/PubMed

PubMed · 11538868

Screened hydrogenic radial integrals.

G S Khandelwal·W M Pritchard·G Grubb·F Khan

View original source ↗Export metadata ↓

Abstract

The screened hydrogenic radial integral both for discrete-discrete and discrete-continuum transitions is expressed in forms suitable for obtaining closed-form expressions for specific transitions. Two effective charge parameters Zi and Zf, respectively, for the initial state and for the final state are retained in these formulas. As examples, explicit expressions for a few transitions are derived and a method for obtaining a series for a discrete-discrete radial integral, suitable for large final-state principal quantum numbers, is indicated.

Explore related subjects

Electrons Hydrogen Mathematics Models, Theoretical NASA Discipline Number 04-10 NASA Discipline Radiation Health NASA Program Biomedical Research Journal Article Research Support, U.S. Gov't, Non-P.H.S.Research Support, U.S. Gov't, P.H.S.

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

G S Khandelwal, W M Pritchard, G Grubb, F Khan. 1989-04-15. Screened hydrogenic radial integrals.. https://pubmed.ncbi.nlm.nih.gov/11538868/

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2026

Technical note: reconstructing dose distributions from manually planned electron boosts in breast radiotherapy.

PURPOSE: In breast radiotherapy, delivery of manually-calculated electron boosts limits retrospective dose-response analyses as dose distribution is unavailable. This work evaluates the feasibility of reconstructing dose distributions from manually planned electron boosts in breast-conserving radiotherapy. METHODS: Only 72 out of 198 breast cancer patients had complete stored dose distributions from sequential electron boosts in the REQUITE study. Arbitrary data from 70/72 patients were used to develop and validate dose reconstruction method. Twenty patients were used to determine optimal parameters for Monte-Carlo-based (MC) electron dose reconstruction on RayStation (v.11B-R), considering CT-calibration curve, MC-history number, andcalculation grid resolution. Remaining 50 patients were used to quantify dose reconstruction accuracy. The similarity between reconstructed and stored dose was evaluated using 3D-gamma index and dosimetric parameters extracted from breast and tumour bed contours. Dose difference location was evaluated using dose-location histogram. RESULTS: Calculation grid resolution significantly impacted electron dose distribution (p < 0.01), where the finest grid (0.15 cm) showed highest similarity to stored doses. CT-calibration curve and MC-history number had a negligible influence on dose reconstruction. Dosimetric difference between reconstructed and stored doses was < 1 Gy for breast and tumour bed. Reconstructed dose was achieved > 90% gamma passing rate in the validation set. However, around 2.5 Gy dose differences were observed at the skin and tissue interface regions. CONCLUSIONS: Retrospective electron boost dose reconstruction is feasible with acceptable accuracy, and could increase data completeness in large cohort studies. Caution is advised when assessing dose near tissue interface and further validation is needed outside the REQUITE dataset.

Electrons↗

PubMed2007

The effect of Glc6P uptake and its subsequent oxidation within pea root plastids on nitrite reduction and glutamate synthesis.

In roots, nitrate assimilation is dependent upon a supply of reductant that is initially generated by oxidative metabolism including the pentose phosphate pathway (OPPP). The uptake of nitrite into the plastids and its subsequent reduction by nitrite reductase (NiR) and glutamate synthase (GOGAT) are potentially important control points that may affect nitrate assimilation. To support the operation of the OPPP there is a need for glucose 6-phosphate (Glc6P) to be imported into the plastids by the glucose phosphate translocator (GPT). Competitive inhibitors of Glc6P uptake had little impact on the rate of Glc6P-dependent nitrite reduction. Nitrite uptake into plastids, using (13)N labelled nitrite, was shown to be by passive diffusion. Flux through the OPPP during nitrite reduction and glutamate synthesis in purified plastids was followed by monitoring the release of (14)CO(2) from [1-(14)C]-Glc6P. The results suggest that the flux through the OPPP is maximal when NiR operates at maximal capacity and could not respond further to the increased demand for reductant caused by the concurrent operation of NiR and GOGAT. Simultaneous nitrite reduction and glutamate synthesis resulted in decreased rates of both enzymatic reactions. The enzyme activity of glucose 6-phosphate dehydrogenase (G6PDH), the enzyme supporting the first step of the OPPP, was induced by external nitrate supply. The maximum catalytic activity of G6PDH was determined to be more than sufficient to support the reductant requirements of both NiR and GOGAT. These data are discussed in terms of competition between NiR and GOGAT for the provision of reductant generated by the OPPP.

Electrons↗

PubMed2007

Comparison between an event-by-event Monte Carlo code, NOREC, and ETRAN for electron scaled point kernels between 20 keV and 1 MeV.

An event-by-event Monte Carlo code called NOREC, a substantially improved version of the Oak Ridge electron transport code (OREC), was released in 2003, after a number of modifications to OREC. In spite of some earlier work, the characteristics of the code have not been clearly shown so far, especially for a wide range of electron energies. Therefore, NOREC was used in this study to generate one of the popular dosimetric quantities, the scaled point kernel, for a number of electron energies between 0.02 and 1.0 MeV. Calculated kernels were compared with the most well-known published kernels based on a condensed history Monte Carlo code, ETRAN, to show not only general agreement between the codes for the electron energy range considered but also possible differences between an event-by-event code and a condensed history code. There was general agreement between the kernels within about 5% up to 0.7 r/r (0) for 100 keV and 1 MeV electrons. Note that r/r (0) denotes the scaled distance, where r is the radial distance from the source to the dose point and r (0) is the continuous slowing down approximation (CSDA) range of a mono-energetic electron. For the same range of scaled distances, the discrepancies for 20 and 500 keV electrons were up to 6 and 12%, respectively. Especially, there was more pronounced disagreement for 500 keV electrons than for 20 keV electrons. The degree of disagreement for 500 keV electrons decreased when NOREC results were compared with published EGS4/PRESTA results, producing similar agreement to other electron energies.

Electrons↗