Calculation Of Transition Probabilities Research Articles

The third spectrum of rhenium (Re III): Analysis of the (5d5 + 5d46s)–(5d46p + 5d36s6p) transition array

The spectrum of rhenium was observed in the (1017–2074) Å wavelength region. The (5d5 + 5d46s)–(5d46p + 5d36s6p) transition array of two times ionized rhenium, Re III, has been investigated and 1305 spectral lines have been classified in the region. The analysis has led to the determination of the 5d5, 5d46s, 5d46p and 5d36s6p configurations. Seventy levels of the 5d5 and 5d46s configurations in the even system and 161 levels of the 5d46p and 5d36s6p configurations in the odd system have been established. The orthogonal operators technique was used to calculate the level structure and transition probabilities. The energy parameters have been determined by the least squares fit to the observed levels. Calculated transition probability and energy values, as well as LS-compositions obtained from the fitted parameters are presented.

Parametric multistate survival models: Flexible modelling allowing transition-specific distributions with application to estimating clinically useful measures of effect differences.

Multistate models are increasingly being used to model complex disease profiles. By modelling transitions between disease states, accounting for competing events at each transition, we can gain a much richer understanding of patient trajectories and how risk factors impact over the entire disease pathway. In this article, we concentrate on parametric multistate models, both Markov and semi-Markov, and develop a flexible framework where each transition can be specified by a variety of parametric models including exponential, Weibull, Gompertz, Royston-Parmar proportional hazards models or log-logistic, log-normal, generalised gamma accelerated failure time models, possibly sharing parameters across transitions. We also extend the framework to allow time-dependent effects. We then use an efficient and generalisable simulation method to calculate transition probabilities from any fitted multistate model, and show how it facilitates the simple calculation of clinically useful measures, such as expected length of stay in each state, and differences and ratios of proportion within each state as a function of time, for specific covariate patterns. We illustrate our methods using a dataset of patients with primary breast cancer. User-friendly Stata software is provided.

Current recommendations on the estimation of transition probabilities in Markov cohort models for use in health care decision-making: a targeted literature review.

ObjectiveAlthough Markov cohort models represent one of the most common forms of decision-analytic models used in health care decision-making, correct implementation of such models requires reliable estimation of transition probabilities. This study sought to identify consensus statements or guidelines that detail how such transition probability matrices should be estimated.MethodsA literature review was performed to identify relevant publications in the following databases: Medline, Embase, the Cochrane Library, and PubMed. Electronic searches were supplemented by manual-searches of health technology assessment (HTA) websites in Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and the UK. One reviewer assessed studies for eligibility.ResultsOf the 1,931 citations identified in the electronic searches, no studies met the inclusion criteria for full-text review, and no guidelines on transition probabilities in Markov models were identified. Manual-searching of the websites of HTA agencies identified ten guidelines on economic evaluations (Australia, Belgium, Canada, France, Germany, Ireland, Norway, Portugal, Sweden, and UK). All identified guidelines provided general guidance on how to develop economic models, but none provided guidance on the calculation of transition probabilities. One relevant publication was identified following review of the reference lists of HTA agency guidelines: the International Society for Pharmacoeconomics and Outcomes Research taskforce guidance. This provided limited guidance on the use of rates and probabilities.ConclusionsThere is limited formal guidance available on the estimation of transition probabilities for use in decision-analytic models. Given the increasing importance of cost-effectiveness analysis in the decision-making processes of HTA bodies and other medical decision-makers, there is a need for additional guidance to inform a more consistent approach to decision-analytic modeling. Further research should be done to develop more detailed guidelines on the estimation of transition probabilities.

New scheme for calculating the kinetic coefficients in CdTe based on first-principle wave function

The main innovative issue of this paper is the calculation of kinetic coefficients using ab initio DFT wave functions. In the framework of short-range scattering models the calculations of transition probabilities presented without fitting parameters for electron interaction with polar and nonpolar optical phonons, piezoelectric, acoustic phonons and ionized impurities. Transition matrix elements have been evaluated by the numerical eigenfunctions obtained within the ab initio density functional theory (DFT). It is used here in the generalized gradient approximation (GGA) suggested by Perdew, Burke and Ernzerhof. For the first time temperature dependences of calculated CdTe electron mobility and Hall factor in the range of 10–1210K are well compared with experiment. For the first time seven scattering mechanisms are treated without fitting parameters. It is shown that short-range scattering models describe qualitatively and quantitatively the experiment in comparison with long-range scattering models.

The fourth spectrum of rhenium (Re IV): Determination of the 5d4, 5d36s and 5d36p configurations

The spectrum of rhenium was observed in the (500–2100) Å wavelength region. The (5d4 + 5d36s) − 5d36p transition array of three times ionized rhenium, Re IV, has been investigated and 975 spectral lines have been classified in the region of (786–2063) Å. The analysis has led to the determination of the 5d4, 5d36s and 5d36p configurations. Thirty two of 34 theoretically possible 5d4 levels, 33 of 38 possible 5d36s levels and 95 of 110 possible 5d36p levels have been established. The orthogonal operators technique was used to calculate the level structure and transition probabilities. The energy parameters have been determined by the least squares fit to the observed levels. Calculated transition probability and energy values, as well as LS-compositions obtained from the fitted parameters are presented.

Transition probabilities for explaining the origin of L-emission satellite

The X-ray satellites are caused by transitions in atoms which are doubly ionized or multiply ionized. To explain the origin of X-ray satellites, the relative intensities of the various possible transitions between the doubly ionized initial and final states of an atom, have to be calculated. The intensity can be calculated from the probability of creation of the double vacancy states. These probabilities are due to Coster-Kronig and Auger transitions and can be calculated using the tables of McGuire. These tables are based on non-relativistic calculations. The latter calculations of transition probabilities are of Chen et al., who have done relativistic calculations in elements with 18 ≤ Z ≤ 96. The aim of the present work is to study the variation with atomic number (Z) of the transition probabilities for the different Coster-Kronig transitions as given in McGuire’s tables and Chen et al’s tables and to discuss the difference between the two calculations. The present study shows that for calculation of the intensity of a satellite, the tables of Chen et al. should be preferred over the tables of McGuire while investigating the origin of L-emission satellites.

Relativistic calculations of one-photon transition probabilities in hydrogen-like ions

The one-photon transition probabilities in hydrogen-like ions are calculated for nuclear charge numbers in the range 1 ≤ Z ≤ 100. The calculations are performed in the framework of the relativistic Dirac’s theory for the states with the principal quantum numbers n = 2,3, 4. The finite nuclear size effect is taken into account. The role of the quantum electrodynamics (QED) and nuclear recoil corrections is also considered.

The Cu II Spectrum

New wavelength measurements in the vacuum ultraviolet (VUV), ultraviolet and visible spectral regions have been combined with available literature data to refine and extend the description of the spectrum of singly ionized copper (Cu II). In the VUV region, we measured 401 lines using a concave grating spectrograph and photographic plates. In the UV and visible regions, we measured 276 lines using a Fourier-transform spectrometer. These new measurements were combined with previously unpublished data from the thesis of Ross, with accurate VUV grating measurements of Kaufman and Ward, and with less accurate older measurements of Shenstone to construct a comprehensive list of ≈2440 observed lines, from which we derived a revised set of 379 optimized energy levels, complemented with 89 additional levels obtained using series formulas. Among the 379 experimental levels, 29 are new. Intensities of all lines observed in different experiments have been reduced to the same uniform scale by using newly calculated transition probabilities (A-values). We combined our calculations with published measured and calculated A-values to provide a set of 555 critically evaluated transition probabilities with estimated uncertainties, 162 of which are less than 20%.

Revised analysis of the fifth spectrum of rhenium (Re V)

The spectrum of rhenium was observed in the (500–2100) Å wavelength region. A 6.65 m normal incidence VUV spectrograph has been used to record the spectrum. The (5d3+5d26s)–5d26p transition array of four times ionized rhenium, Re V, has been investigated. The configurations 5d3, 5d26s and 5d26p had been previously studied, and all but one levels of these configurations (19, 15 and 45 levels, respectively) had been established. The previous analysis was based on 382 classified spectral lines. In the current analysis we have rejected 74 previously identified spectral lines and added 90 newly classified lines. New list of identified lines contains 398 entries. Comparing with the previous analysis, the current study is based on new spectrograms and significantly more accurate wavelength measurements. We have detected a large (up to 35 mÅ) systematic shift in wavelength measurements used in the previous analysis. In the current study, the standard deviations (by regions) of the undisturbed isolated lines from their Ritz positions are three to five times smaller and the largest deviation of strong isolated lines from their Ritz positions is about seven times smaller than in the previous work. We have confirmed identification of all but three previously found levels. One level has been rejected and two levels have been determined at new positions. One previously unidentified 5d26s level has been added. Based on the new wavelength measurements, we have corrected positions of all previously known 5d3, 5d26s and 5d26p energy levels (except for the ground level, rejected and newly determined levels) by up to 8.31cm−1. From all 80 theoretically possible levels of the configurations 5d3, 5d26s and 5d26p, only the level 5d26s (1S)2S1/2 is still not determined. The orthogonal operators technique was used to calculate the level structure and transition probabilities. The energy parameters have been determined by the least squares fit to the observed levels. Calculated transition probabilities, energy values, as well as LS-compositions obtained from the fitted parameters are presented.

Configuration interactions of class 11: An error in Cowan’s atomic structure theory

For about 35 years since its creation, the suite of atomic structure codes created by R.D. Cowan remains the working horse of atomic spectroscopists and is cited in more than 4000 publications. This note concerns one aspect of those codes: calculation of configuration interaction (CI) parameters. It was found that the last of the eleven classes of CI described in Cowan’s book and implemented in his codes erroneously sets some of the CI parameters in Rydberg series of interacting configurations to zero. This leads to inaccurate description of eigenstates and sizeable errors in calculated transition probabilities.

Duality-based calculations for transition probabilities in stochastic chemical reactions.

An idea for evaluating transition probabilities in chemical reaction systems is proposed, which is efficient for repeated calculations with various rate constants. The idea is based on duality relations; instead of direct time evolutions of the original reaction system, the dual process is dealt with. Usually, if one changes rate constants of the original reaction system, the direct time evolutions should be performed again, using the new rate constants. On the other hands, only one solution of an extended dual process can be reused to calculate the transition probabilities for various rate constant cases. The idea is demonstrated in a parameter estimation problem for the Lotka-Volterra system.

Evaluation of the probability of hydrogen atoms photoionization in a strong ultrashort laser field using the trajectory method

A method for calculating transition probabilities based on an earlier developed trajectory approach is tested by the example of evaluating the probability of photoionization of the hydrogen atom exposed an ultrashort optical pulse.

The sixth spectrum of platinum (Pt VI)

The spectrum of platinum was observed in the (300–2100) Å wavelength region. The (5d5+5d46s)–5d46p transition array of five times ionized platinum, Pt VI, has been investigated and 1390 spectral lines have been classified in the region of (399–1564) Å. The analysis has led to the determination of the 5d5, 5d46s and 5d46p configurations. All 37 theoretically possible 5d5 levels, 46 of 63 possible 5d46s levels and 167 of 180 possible 5d46p levels have been established. The orthogonal operators technique was used to calculate the level structure and transition probabilities. The energy parameters have been determined by the least squares fit to the observed levels. Calculated transition probability and energy values, as well as LS-compositions obtained from the fitted parameters are presented. The uncertainties of the established energy levels and calculated (Ritz) wavenumbers are included.

PRM89 - Recommendations for the Calculation of Transition Probabilities in Markov Cohort Models: A Targeted Literature Review

PRM89 - Recommendations for the Calculation of Transition Probabilities in Markov Cohort Models: A Targeted Literature Review

Revised and extended analysis of the eighth spectrum of platinum (Pt VIII)

The spectrum of platinum was observed in the 300–2100 Å wavelength region. Grazing and normal incidence VUV spectrographs have been used to record the spectrum. The (5d3+5d26s)−5d26p transition array of seven times ionized platinum, Pt VIII, has been investigated. The configurations 5d3 and 5d26p had been previously studied, and all levels of these configurations (19 and 45 levels, respectively) had been established. The previous analysis was based on 178 classified spectral lines. In the current analysis we have confirmed identification of all previously found levels and all but 10 previously assigned spectral lines, although we have detected a large (up to 35 mÅ) systematic shift in wavelength measurements used in the previous analysis. Based on new wavelength measurements, we have corrected the 5d3 and 5d26p energy level values (by up to 55 cm−1) and established for the first time 14 out of 16 theoretically possible 5d26s levels in Pt VIII. The total list of identified lines (including 180 new lines) contains 349 entries. The orthogonal operators technique was used to calculate the level structure and transition probabilities. The energy parameters have been determined by the least squares fit to the observed levels. Calculated transition probability and energy values, as well as LS-compositions obtained from the fitted parameters are presented.

The seventh spectrum of platinum (Pt VII): Analysis of the [formula omitted]–[formula omitted] transition array

The spectrum of platinum was observed in the (300–2100) Å wavelength region. The (5d4+5d36s)–5d36p transition array of six times ionized platinum, Pt VII, has been investigated and 759 spectral lines have been classified in the region of (337–1273) Å. The analysis has led to the determination of the 5d4, 5d36s and 5d36p configurations. All 34 theoretically possible 5d4 levels, 35 of 38 possible 5d36s levels and 108 of 110 possible 5d36p levels have been established. The orthogonal operators technique was used to calculate the level structure and transition probabilities. The energy parameters have been determined by the least squares fit to the observed levels. Calculated transition probability and energy values, as well as LS-compositions obtained from the fitted parameters are presented.

Fierz relations for Volkov spinors and the simplification of Furry picture traces

Transition probability calculations of strong field particle processes in the Furry picture, typically use fermion Volkov solutions. These solutions have a relatively complicated spinor due to the interaction of the electron spin with a strong external field, which in turn leads to unwieldy trace calculations. The simplification of these calculations would aid theoretical studies of strong field phenomena such as the predicted resonance behaviour of higher order Furry picture processes. Here, Fierz transformations of Volkov spinors are developed and applied to a 1st order and a 2nd order Furry picture process. Combined with symmetry properties, the techniques presented here are generally applicable and lead to considerable simplification of Furry picture analytic calculations.

Calculation of Coster-Kronig energies and transition probabilities by linear interpolation method

The X-ray emission spectrum consists of two types of spectral lines heaving different origins. The diagram lines originate because of transitions in singly ionized atom, while the nondiagram lines or satellites originate due to transitions in doubly or multiply ionized atom. The X- ray satellite energy is the difference between the energies of initial and final states which are both doubly or multiply ionized. Thus, the satellite has a different energy than the energy of the X-ray diagram line. Once the singly ionized state has been created, it is the probability of a particular subsequent process that will lead to the formation of two-hole state. The single hole may get converted through a Coster-Kronig transition to a double hole state. The probability of formation of double hole state via this process is written as σ.σ', where σ is the probability of creation of single hole state and σ' is the probability of the Coster-Kronig transition. The value of σ' can be taken from the tables of Chen et al. [1], who have presented the calculated values of σ' for almost all possible Coster-Kronig transitions in some elements. The energies of the satellites can be calculated by using the tables of Parente et al. [2]. Both of these tables do not give values for all the elements. The aim of the present work is to show that the values for other elements, for which values are not listed by Chen et al. and Parente et al., can be calculated by linear interpolation method.

Nuclear alternating parity bands and transition rates in a model of coherent quadrupole–octupole motion in neutron-rich barium isotopes

Deformed even–even nuclei Barium isotopes with quadrupole–octupole deformations are investigated on the basis of a collective model. The model describes energy levels of the yrast band with alternating parity in the neutron-rich \(^{140,142,144,146,148}\)Ba. The structure of the alternating parity bands is examined by odd–even \((\Delta I =1)\) staggering diagrams. An analytical method of the collective model is proposed for the calculation of E2 transition probabilities in alternating spectra of the nuclei \({}^{140,142,144,146}\)Ba.

Continuous affine processes: transformations, Markov chains and life insurance

Abstract Affine processes possess the property that expectations of exponential affine transformations are given by a set of Riccati differential equations, which is the main feature of this popular class of processes. In this paper we generalise these results for expectations of more general transformations. This is of interest in, e.g. doubly stochastic Markov models, in particular in life insurance. When using affine processes for modelling the transition rates and interest rate, the results presented allow for easy calculation of transition probabilities and expected present values.