Bohr Formula Research Articles

SAMAY S24: a novel wireless 'online' device for real-time monitoring and analysis of volumetric capnography.

Volumetric capnography (VCap) provides information about CO2 exhaled per breath (VCO2br) and physiologic dead space (VDphys). A novel wireless device with a high response time CO2 mainstream sensor coupled with a digital flowmeter was designed to monitor all VCap parameters online in rabbits (SAMAY S24).Ten New Zealand rabbits were anesthetized and mechanically ventilated. VCO2br corresponds to the area under the VCap curve. We used the modified Langley method to assess the airway VD (VDaw) and the alveolar CO2 pressure. VDphys was estimated using Bohr's formula, and the alveolar VD was calculated by subtracting VDaw from VDphys. We compared (Bland-Altman) the critical VCap parameters obtained by SAMAY S24 (Langley) with the Functional Approximation based on the Levenberg-Marquardt Algorithm (FA-LMA) approach during closed and opened chest conditions.SAMAY S24 could assess dead space volumes and VCap shape in real time with similar accuracy and precision compared to the 'offline' FA-LMA approach. The opened chest condition impaired CO2 kinetics, decreasing the phase II slope, which was correlated with the volume of CO2 exhaled per minute.

Construction and Analysis of Public Management System Indicators Based on AHP (Analytic Hierarchy Process)

In the era of intelligent network, my country’s public management services are in a transition period, and many problems have gradually occurred, which have a certain impact on public management. In the previous management mode, the latest management requirements could not be met, and there were many problems in the actual management process. With the rapid development of social economy, public management is the key to promote social development. Only by constructing a reasonable index system of public management can public management play its due role in the era of rapid development. Therefore, this paper uses Bohr formula, Shannon formula, and entropy weight method to construct the public management system index based on AHP. The research results of this paper are in the stage of model checking, and the accuracy of this method is the highest in different data sets. The accuracy of big data analysis method and the original method decreases with the increase of data sets, which reflects the obvious advantages of this method. The response time of big data analysis methods increases gradually due to the increase of data sets, but the method in this paper grows slowly. All indicators show that the constructed public management index system has high reliability and validity.

Study the Nuclear Structure of Some Even-Even Ca Isotopes Using the Microscopic Theory

The root-mean square-radius of proton, neutron, matter and charge radii, energy level, inelastic longitudinal form factors, reduced transition probability from the ground state to first-excited 2+ state of even-even isotopes, quadrupole moments, quadrupole deformation parameter, and the occupation numbers for some calcium isotopes for A=42,44,46,48,50 are computed using fp-model space and FPBM interaction. 40Ca nucleus is regarded as the inert core for all isotopes under this model space with valence nucleons are moving throughout the fp-shell model space involving 1f7/2, 2p3/2, 1f5/2, and 2p1/2 orbits. Model space is used to present calculations using FPBM interaction, and with the effects of core-polarization are obtained by the first order core polarization through a microscopic theory is called modified surface delta interaction which allows all higher orbits are excited by particle-hole excitation from the core and model space orbits. Also, each isotope's effective charge is determined by using the collective model by Bohr and Mottelson formula. The current result corresponds to the experimental data by taking into account core polarization effects.

Bohr's stopping-power formula derived for a classical free-electron gas

Bohr's centenary stopping-power formula is rederived for a free electron gas (FEG) system within the framework of nonrelativistic classical mechanics. A simple and more concise expression for the stopping power of charged particles in FEG is demonstrated on classical grounds. Using semiclassical arguments and the Euler-Maclaurin well-known mathematical formula, Bloch's correction that links Bethe's quantum theory to Bohr's classical model is also recovered. The proposed semiclassical stopping-power formula contains the main physical ingredients for a general stopping formula applicable for different systems and energies and facilitates computational calculations.

An observation on the Balmer–Bohr formula

Hydrogen transition wavelengths computed with the familiar Balmer–Bohr formula are different than those reported in standard reference sources. The origin of this discrepancy, which is likely not well-known to instructors and students, is explained.

Prediction of moment of inertia of rotating nuclei * * Supported by the MOHE, Fundamental Research Grant Scheme FRGS19-039-0647 and also OT–F2–2017/2020 by the Committee for the Coordination of the Development of Science and Technology under the Cabinet of Ministers of the Republic of Uzbekistan

In this study, the mathematical expression formulated by Bohr for the moment of inertia of even-even nuclei based on the hydrodynamical model is modified. The modification pertains to the kinetic energy of the surface oscillations, including the second and third terms of the R-expansion as well as the first term, which had already been modified by Bohr. Therefore, this work can be considered a continuation and support of Bohr's hydrodynamic model. The procedure yields a Bohr formula to be multiplied by a factor that depends on the deformation parameter. Bohr's (modified) formula is examined by applying it on axially symmetric even-even nuclei with atomic masses ranging between 150 and 190 as well as on some triaxial symmetry nuclei. In this paper, the modification of Bohr's formula is discussed, including information about the stability of this modification and the second and third terms of the R-expansion in Bohr's formula. The results of the calculation are compared with the experimental data and Bohr's results recorded earlier. The results obtained are in good agreement with experimental data, with a ratio of approximately 0.7, and are better than those of the unmodified ones.

Quasiclassical approach to the interpretation of the Barkas effect

A correction to the Bohr formula making it possible to explain the difference between the stopping powers of positively and negatively charged particles (the Barkas effect) is obtained in the quasiclassical approximation taking into account the difference between electron motion in a hydrogen atom as a function of the charge sign of the moving particle. The influence on the atomic electron of the moving particle leads to a change in the contribution of the adiabatic interaction, in the case of which the energy is not transferred in the majority of collisions, which is the reason for a decrease in the energy losses of slow particles compared with Bohr theory. The results of calculations show that the energy losses per path length unit can be represented in the form of the product of two functions, namely, the energy loss function (in accordance with Bohr theory) and the dynamic function taking into account corrections related to correction of the electron position in the target atom during the collision. Calculations carried out within the framework of classical dynamics make it possible to qualitatively estimate differences between the interaction of protons and antiprotons with target material atoms.

Volume capnography: A narrative review

Volume capnography is the graph of expired carbon dioxide concentration against the expired volume. It often requires special and bulky equipment to be recorded. It can be used to estimate the dead space with fair amount of precision. Various formulae and equations have been described to estimate the dead space. While the Bohr formula is likely the most accurate for measurement of dead space, the Enghoff's equation is likely the most popular and convenient to use. Volume capnography has found uses in both the operating room (OR) and the Intensive Care Unit setting. It can be used to identify the optimal level of positive end-expiratory pressure in patients suffering from the acute respiratory distress syndrome as well as to identify its effect on the ventilation. In the OR, it can be invaluable to monitor ventilation and alveolar recruitment in the obese population. It is also a useful diagnostic adjunct in medical emergencies like pulmonary embolism. In the pediatric population, it finds uses in the monitoring of infants suffering from bronchiolitis. In spite of its multiple and diverse uses, it remains an underutilized technology; the main reasons for this being lack of experience of the providers with volume capnography and the expensive and bulky equipment that is often required. However, volume capnography has a great deal of potential and with further advances in technology, is likely to gain popularity.

Model of the Pulsing Atom

In this work, we reanalyzed the movement of an electron in the electrostatic field of nucleus. The trajectory of the electron’s motion is an ellipse with a minor semiaxis, tending towards zero. From a mathematical point of view the movement of an electron in such an orbit will be equivalent to the oscillation of an electron. The action produced by electrons in movement between stationary points is discrete and proportional to a Planck constant. This condition sets the allowable values of the electron energy and the radius of their orbit. Electrons on the same shell perform symmetric synchronous oscillations. Their frequency is of the order of 1016 Hz. Most of the time the electrons are located on the periphery of the atom, periodically they simultaneously rush to the nucleus, the atom rapidly compresses and immediately decompresses, i.e. pulsates. The model gives Bohr formula for the energy of single-electron atom and suitable values of ionization potentials of the atoms of the second period of the Periodic Table.

Stopping powers and energy loss straggling for (0.9–3.4) MeV protons in a kapton polyimide thin film

The energy loss and energy loss straggling widths have been measured in transmission for Ep≈(0.9–3.4) MeV protons traversing a thin kapton polyimide foil. In a prior step, the thickness and non-uniformity of the target foil were carefully investigated. The overall relative uncertainties in the stopping power and energy loss straggling variance data amount, respectively, to less than 2% and 8%. The S(E) experimental data show to be in excellent agreement with available previous ones and with those compiled in the ICRU-49 report. They are fully consistent with the predictions of Sigmund-Schinner’s binary collision theory of electronic stopping over the whole proton energy range explored. An average deviation of ∼2.5% relative to values calculated by the SRIM-2008 code, likely due to effects of valence electrons involving the CH, CC and CO bonds, is however observed at low proton velocities. The measured energy loss straggling data, which are unique to our knowledge, are found to be in good agreement with values derived by the classical Bohr formula for Ep≳1300keV but they significantly exceed Bohr’s collisional energy loss straggling at lower proton velocities where target electrons can no longer be considered as free. They also show to be consistent with the predictions of the Bethe-Livingston and Sigmund-Schinner theories over the low proton velocity region (Ep<1300keV). However, they are significantly overestimated by these theories over the intermediate and high proton velocity regions, which may be due to bunching effect by inner shell electrons of the polymer target. Besides, our energy loss straggling data are in better overall consistency with the Yang, O’Connor and Wang empirical formula for Ep>1300keV, while deviations above the latter amounting up to ∼18% are observed at lower proton velocities.

Spectral dimension and Bohr's formula for Schrödinger operators on unbounded fractal spaces

We establish an asymptotic formula for the eigenvalue counting function of the Schrödinger operator for some unbounded potentials V on several types of unbounded fractal spaces. We give sufficient conditions for Bohr’s formula to hold on metric measure spaces which admit a cellular decomposition, and then verify these conditions for fractafolds and fractal fields based on nested fractals. In particular, we partially answer a question of Fan, Khandker, and Strichartz regarding the spectral asymptotics of the harmonic oscillator potential on the infinite blow-up of a Sierpinski gasket.

Energy loss of charged particles colliding with an oscillator

Energy loss of fast charged particles colliding with an oscillator is considered in the dipole approximation. In this approximation, the problem is solved exactly and the energy loss of the oscillator from the initial state |m〉 = |0〉 is found in the form of the sum of single integrals. It is shown that passing to the limit, the Bethe theory for an atom with small perturbations can be obtained, and in the case of strong fields, the correction to the Bethe theory, analogous to the Bloch correction, can be calculated; in addition, a classical limit coinciding with the Bohr formula is possible.

Corrections of Enghoff's dead space formula for shunt effects still overestimate Bohr's dead space

Dead space ratio is determined using Enghoff's modification (VdB-E/Vt) of Bohr's formula (VdBohr/Vt) in which arterial is used as a surrogate of alveolar PCO2. In presence of intrapulmonary shunt Enghoff's approach overestimates dead space. In 40 lung-lavaged pigs we evaluated the Kuwabara's and Niklason's algorithms to correct for shunt effects and hypothesized that corrected VdB-E/Vt should provide similar values as VdBohr/Vt.We analyzed 396 volumetric capnograms and arterial and mixed-venous blood samples to calculate VdBohr/Vt and VdB-E/Vt. Thereafter, we corrected the latter for shunt effects using Kuwabara's (K) VdB-E/Vt and Niklason's (N) VdB-E/Vt algorithms. Uncorrected VdB-E/Vt (mean±SD of 0.70±0.10) overestimated VdBohr/Vt (0.59±0.12) (p<0.05), over the entire range of shunts. Mean (K) VdB-E/Vt was significantly higher than VdBohr/Vt (0.67±0.08, bias −0.085, limits of agreement −0.232 to 0.085; p<0.05) whereas (N)VdB-E/Vt showed a better correction for shunt effects (0.64±0.09, bias 0.048, limits of agreement −0.168 to 0.072; p<0.05).Neither Kuwabara's nor Niklason's algorithms were able to correct Enghoff's dead space formula for shunt effects.

Rationale of Dead Space Measurement by Volumetric Capnography

Dead space is the portion of a tidal volume that does not participate in gas exchange because it does not get in contact with blood flowing through the pulmonary capillaries. It is commonly calculated using volumetric capnography, the plot of expired carbon dioxide (CO(2)) versus tidal volume, which is an easy bedside assessment of the inefficiency of a particular ventilatory setting. Today, Bohr's original dead space can be calculated in an entirely noninvasive and breath-by-breath manner as the mean alveolar partial pressure of CO(2) (Paco(2)) which can now be determined directly from the capnogram. The value derived from Enghoff's modification of Bohr's formula (using Paco(2) instead of PACO(2)) is a global index of the inefficiency of gas exchange rather than a true "dead space" because it is influenced by all causes of ventilation/perfusion mismatching, from real dead space to shunt. Therefore, the results obtained by Bohr's and Enghoff's formulas have different physiological meanings and clinicians must be conscious of such differences when interpreting patient data. In this article, we describe the rationale of dead space measurements by volumetric capnography and discuss its main clinical implications and the misconceptions surrounding it.

Relativistic Theory of One- and Two Electron Systems: Valley of Stability in the Helium-Like Ions

A semi-relativistic total energy of the hydrogen-like ions is presented. The es- tablished expression taking only into account the dependence of the mass electron on the speed could be considered as a first correction of the Bohr's semi-classical formula. Com- parison with relativistic total energy expression obtained from the Dirac's relativistic wave equation is made. In addition, the present relativistic theory of the hydrogen- like ions is extended to the helium isoelectronic series. It is shown that, for the ground state of two electron systems, the relativistic screening constantσ rel decreases when increasing the nu- clear charge up to Z=5. Beyond,σ rel increases when increasing Z and, the plotσ rel = f (Z) is like a valley of stability where the bottom is occupied by the B 3+ -helium-like ion. As a result, only He, Li + , Be 2+ and B 3+ exist in the natural matter in low temperature. All the other helium-like positive-ions, such as C 4+ , N 5+ , O 6+ , F 7+ , Ne 8+ ,��� , can only exist in hot

Stopping Power and Energy Straggling of Channeled He-Ions in GaN

GaN epitaxial layers are usually grown on sapphire substrates. To avoid disastrous effect of the large lattice mismatch a thin polycrystalline nucleation layer is grown at 500 ◦C followed by the deposition of thick GaN template at much higher temperature. Remnants of the nucleation layer were visualized by transmission electron microscopy as defect agglomeration at the GaN/sapphire interface and provide a very useful depth marker for the measurement of channeled ions stopping power. Random and aligned spectra of He ions incident at energies ranging from 1.7 to 3.7 MeV have been measured and evaluated using the Monte Carlo simulation code McChasy. Impact parameter dependent stopping power has been calculated for channeling direction and its parameters have been adjusted according to experimental data. For virgin, i.e. as grown, samples, the ratio of channeled to random stopping power is constant and amounts to 0.7 in the energy range studied. Defects produced by ion implantation largely influence the stopping power. For channeled ions the variety of possible trajectories leads to different energy loss at a given depth, thus resulting in much larger energy straggling than that for the random path. Beam energy distributions at different depths have been calculated using the McChasy code. They are significantly broader than those predicted by the Bohr formula for random direction.

Experimental determination of electronic stopping for ions in silicon dioxide

The electronic energy loss for He4, Li7, Be9, C12, O16, F19, and Si28 ions in self-supporting silicon dioxide foils has been measured over a continuous range of energies. The measured He stopping powers are in good agreement with the SRIM-2003 (Stopping and Range of Ions in Matter) prediction. In the case of Li and C ions, the measured stopping powers exhibit some deviation from the SRIM-2003 predictions only around the Bragg peak; however, for Be, O, F, and Si ions, the measure stopping powers exhibit up to 10% deviation from the SRIM-2003 predictions over the entire energy range. The results indicate that the modified Bohr formula is suitable for scaling the stopping number for C and heavier ions in the classical interaction regime.

On the Bohr formula for the one-dimensional Schrödinger operator with increasing potential

This article contains the justification of the quasi-classical asymptotic formula (usually attributed to N. Bohr) for the counting function N(λ) of the 1-D Schrödinger operator with potential V increasing at infinity. Results were known under strong regularity conditions on V. Using direct methods based on the phase formalism, we give much wider sufficient conditions on V for the applicability of the Bohr formula. Several counterexamples show that these conditions cannot be significantly improved.

Charge exchange processes for semi-relativistic helium ions (β = 0.51) in solid gold

Interactions of 150MeV/amu 3He++ projectiles with solid gold targets have been studied at the isochronous cyclotron of the RCNP in Osaka. The 3He+ ions resulting from capture of the target electrons to the projectile were observed with the use of large magnetic spectrograph, Grand Raiden, set at θ=0° with respect to the beam. The yield ratio of singly to doubly ionized helium ions emerging from thin gold foils, He+/He++, has been measured as a function of the foil thickness. Extrapolating the results to zero Au target thickness permits to determine the cross section values for electron stripping from 3He+ ions, σSTRIP=1.05×10−17cm2, and for electron capture to 3He++ ions, σCAP=1.12×10−25cm2. The results obtained extend significantly the existing systematics for both processes to high (semi-relativistic) velocities. The collision strength deduced from the stripping cross sections deviates strongly from the theoretical predictions of Gillespie in absolute values as well as in the velocity dependence. It can, however, be well approximated by the simple Bohr formula for mid Z atoms. Also the capture data indicate the need to improve the theoretical approximations. A more detailed treatment of electrons captured from different shells in a high Z target is presumably needed. The astrophysical interest in the data of this kind for very light ions (hydrogen, helium) is indicated.

Angular distributions, relative orbital angular momenta, and spins of fragments originating from the binary fission of polarized nuclei

The angular distributions of fragments originating from the binary fission of odd and odd-odd nuclei capable of undergoing spontaneous fission that are polarized by a strong magnetic field at ultralow temperatures and from the low-energy photofission of even-even nuclei that is induced by dipole and quadrupole photons are investigated. It is shown that the deviations of these angular distributions from those that are obtained on the basis of the A. Bohr formula make it possible to estimate the maximum relative orbital angular momentum of fission fragments, this estimate providing important information about the relative orientation of the fragment spins. The angular distributions of fragments originating from subthreshold fission are analyzed for the case of the 238U nucleus. A comparison of the resulting angular distributions with their experimental counterparts leads to the conclusion that the maximum relative orbital angular momentum of binary-fission fragments exceeds 20, the fragment spins having predominantly a parallel orientation. The possibility is considered for performing an experiment aimed at measuring the angular distributions of fragments of the spontaneous fission of polarized nuclei in order to determine both the spins of such nuclei and the maximum values of the relative orbital angular momenta of fission fragments.