Relationship of Bohr Orbital Quantum Condition to Planck Oscillator Energy Levels

1964 ◽  
Vol 32 (8) ◽  
pp. 643-644
Author(s):  
A. D. Crowell

The mechanism of the 12 C(γ, 3α) reaction, for γ-ray energies, E γ , up to about 40 MeV, has been determined from a study of over 2500 stars in nuclear emulsions. The study includes investigation of the angular distributions and correlations of the α-particles. The reaction is initiated mainly by electric-dipole and electric-quadrupole γ-ray interaction, the former being unexpectedly strong when E γ < 20 MeV. For E γ < 25 MeV the reaction proceeds mainly by transitions to the ground-state of 8 Be (spin J = 0), and to 2⋅95 ± 0⋅10 MeV ( J = 2) and 4⋅0 ± 0⋅1 MeV ( J = 2 or 4) levels of 8 Be. Transitions to levels near 6, 10 and 15 MeV (all J = 0, 2 or 4) become predominant when 25 MeV ≤ E γ <26 MeV. For E γ ≥ 26 MeV, most transitions lead to 16⋅8 ± 0⋅2 MeV ( J = 2) and 17⋅6 ± 0⋅2 MeV ( J = 2, possibly 0) levels, and possibly to a further 16⋅4 ± 0⋅2 MeV ( J = 0 or 2) level, levels which have not been detected in other reactions. The reaction mechanism is interpreted in terms of competing modes of decay of a compound nucleus, demonstrating the strong influence of the isotopic spins ( T ) of the levels of 12 C and 8 Be involved. For example, the 2 + levels of 12 C involved when 16 MeV ≤ E γ <20 MeV are (unexpectedly) found to have T = 1, and the 16⋅8 and 17⋅6 MeV levels of 8 Be are also found to have T = 1. The relationship of the 12 C (γ, 3α) reaction to other 12 C photodisintegration reactions (including some new reactions established during the present experiments) is discussed.


2012 ◽  
Vol 560-561 ◽  
pp. 651-654
Author(s):  
Yi Huang ◽  
Feng Miao

Considering the crystal field parameter Dq and average covalent factor N, the energy levels of NaMg3Al(MoO4)5: Cr3+ crystal at 295 K are calculated by diagonalizing the energy matrix of 3d3. At low temperature 9 K the bond length of Mg-O is calculated by adjusting the value to fit the spectra of Mg site. The value of Mg-O bond length is 2.0528 Å. The equation relationship of Mg-O between bond length and temperature is achieved.The calculated values are consistent with the experimental spectra.


2014 ◽  
Vol 1 (1) ◽  
pp. 21-26
Author(s):  
Frank Znidarsic P.E.

Charles-Augustin de Coulomb introduced his equations over two centuries ago. These equations quantified the force and the energy of interacting electrical charges. The electrical permittivity of free space was factored into Coulomb’s equations. A century later James Clear Maxwell showed that the velocity of light emerged as a consequence this permittivity. These constructs were a crowning achievement of classical physics. In spite of these accomplishments, the philosophy of classical Newtonian physics offered no causative explanation for the quantum condition. Planck’s empirical constant was interjected, ad-hoc, into a description of atomic scale phenomena. Coulomb’s equation was re-factored into the terms of an elastic constant and a wave number. Like Coulomb’s formulation, the new formulation quantified the force and the energy produced by the interaction of electrical charges. The Compton frequency of the electron, the energy levels of the atoms, the energy of the photon, the speed of the atomic electrons, and Planck’s constant, spontaneously emerged from the reformulation. The emergence of these quantities, from a classical analysis, extended the realm of classical physics into a domain that was considered to be exclusively that of the quantum.


2021 ◽  
Vol 8 (2) ◽  
pp. 326-339
Author(s):  
Koshun Suto

Einstein’s energy-momentum relationship is not applicable to the electron in a hydrogen atom. Therefore, the author has previously derived an energy-momentum relationship applicable to the electron inside the hydrogen atom where potential energy exists. However, the initially-derived relationship did not incorporate the discontinuities in energy which are characteristic of quantum mechanics. Therefore, the author derived a new quantum condition to take the place of Bohr’s quantum condition, i.e., , and that was used to incorporate discontinuity into the relationship derived by the author. When that relationship is solved, it is evident that, in addition to the existing energy levels, there are also ultra-low energy levels where the electron mass becomes negative. A previously unknown state of the hydrogen atom exists, formed from an electron with negative mass and a proton with positive mass. The electron with negative mass exists near the proton. The author predicts that this unknown matter is the true nature of dark matter, an unknown source of gravity whose true nature is currently unknown.


1995 ◽  
Vol 378 ◽  
Author(s):  
William C. McColgin ◽  
J. P. Lavine ◽  
C. V. Stancampiano

AbstractWe have investigated the role of heavy metals in causing visible pixel defects in Charge Coupled Device (CCD) image sensors. Using a technique we call dark current spectroscopy, we can probe for deep-level traps in the active areas of completed image sensors with a sensitivity of 1 × 109 traps/cm3 or better. Analysis of histograms of dark current images from these sensors shows that the presence of traps causes quantization in the dark current. Different metal traps have characteristic dark current generation rates that can identify the contaminant trap. By examining the temperature dependence of the dark current generation, we have calculated the energy levels and generation cross sections for gold, iron, nickel, and cobalt. Our results show the relationship of these traps to the “white spot” defects reported for image sensors.


2004 ◽  
Vol 59 (12) ◽  
pp. 947-951 ◽  
Author(s):  
Shao-Yi Wu ◽  
Hui-Ning Dong

The gyromagnetic factors for Nd3+ in scheelite-type ABO4 compounds (A = Cd, Ca, Pb, Ba;B = Mo, W) are theoretically studied by the perturbation formulas of the anisotropic g factors g∥ and g⊥ for a 4f3 ion in tetragonal symmetry. In these formulas, the contributions to the g factorsdue to the second-order perturbation terms and the admixtures of various energy levels are takeninto account. The relevant crystal-field parameters are determined by the superposition model andthe local geometrical relationship of the A2+ sites occupied by the impurity Nd3+. The obtained gfactors agree reasonably with the observed values. The discrepancies between theory and experimentare discussed.


2000 ◽  
Vol 622 ◽  
Author(s):  
M. Kato ◽  
M. Ichimura ◽  
E. Arai ◽  
Y. Masuda ◽  
Y. Chen ◽  
...  

ABSTRACTn-type 3C-SiC was heteroepitaxially grown on n-type Si(100) substrates using HMDS (hexamethyldisilane) and characterized by DLTS (deep level transient spectroscopy) measurements. In order to investigate relationship of defect density with epilayer thickness, epilayers with various thicknesses were grown. Relatively thin (<1.0μm thick) epilayers were found to contain defects with energy levels distributed in a wide energy range, while relatively thick (>2.2μm thick) epilayers contain a defect with an activation energy of 0.25eV. This defect level is slightly shallower than that in 3C-SiC grown by SiH4 and C3H8 (∼0.3eV).


2020 ◽  
Vol 62 (7) ◽  
pp. 1074
Author(s):  
В.П. Смагин ◽  
Л.В. Затонская ◽  
Е.Г. Ильина ◽  
Е.П. Харнутова

Luminescent nanoscale particles (quantum dots) (Zn,Cu,Ag)S:Eu3+ were synthesized during decomposition of thioacetamide complexes of metals in a methylmethacrylate medium during block polymerization under heating. The formation of quantum dots is confirmed by the corresponding band in the optical absorption spectrum of polymer compositions. Photoluminescence of PMMA/(Zn,Cu,Ag)S:Eu3+ compositions is manifested as a complex band associated with defects in the crystal structure formed when ZnS was doped with copper and silver ions, and a set of narrow bands of luminescence of Eu3+ ions. Luminescence excitation occurs as a result of inter-zone transitions and electron transitions from the valence band to the ZnS defect levels, and self-absorption of energy by Eu3+ ions. The relationship of ions Eu3+ particles of ZnS is confirmed by the dependence of the intensity of the broadband luminescence of ZnS with increasing concentration of ions Eu3+ and an increase in intensity narrow-band luminescence of ions Eu3+ as a result of energy transfer from levels of doped ZnS crystals on the energy levels of the ions Eu3+.


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