ROTATIONAL WINGS OF RAMAN BANDS AND FREE ROTATION IN LIQUID OXYGEN, NITROGEN, AND METHANE

1952 ◽  
Vol 30 (2) ◽  
pp. 81-98 ◽  
Author(s):  
M. F. Crawford ◽  
H. L. Welsh ◽  
J. H. Harrold
Keyword(s):  
Raman Spectrum ◽  
Transition Probability ◽  
Energy Levels ◽  
Anisotropic Scattering ◽  
Rotational Energy ◽  
Rate Of Change ◽  
Liquid Oxygen ◽  
Discrete Structure ◽  
Anisotropic Part ◽  
Liquid Methane

Rotation-vibrational Raman bands have been observed in liquid oxygen, nitrogen, and methane, and in solid methane. In every case the Q branches associated with isotropic Raman scattering are sharp lines; but the Q branches and rotational wings associated with anisotropic scattering form broad continuous bands, with extent and intensity distribution consistent with free molecular rotation. The lack of discrete structure in the broad bands is attributed to a removal of the m degeneracy of the rotational energy levels in the intermolecular force fields. Removal of the m degeneracy broadens those transitions for which the transition probability depends on the anisotropic part of the rate of change of the polarizability, but not those for which J and m are unchanged and for which the transition probability depends only on the isotropic part. The Raman spectrum of liquid oxygen yields no evidence for O4 aggregates. The Raman spectrum of liquid methane displays all fundamental vibrations of the molecule and two overtones, with Raman shifts (in cm.−1): 1300, band (ν4); 1535, band (ν2); 2570, line, and 2600, band (2ν4); 2906, line (ν1); 3020, band (ν3); 3053, line (2ν2).

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

Adiabatic Markov Decision Process: Convergence of Value Iteration Algorithm

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Thai Duong ◽  
Duong Nguyen-Huu ◽  
Thinh Nguyen
Keyword(s):  
Markov Decision Process ◽  
Decision Process ◽  
Transition Probability ◽  
Transition Probability Matrix ◽  
Rate Of Change ◽  
Optimal Decision ◽  
Iteration Algorithm ◽  
Value Iteration ◽  
Markov Decision ◽  
Value Iteration Algorithm

Markov decision process (MDP) is a well-known framework for devising the optimal decision-making strategies under uncertainty. Typically, the decision maker assumes a stationary environment which is characterized by a time-invariant transition probability matrix. However, in many real-world scenarios, this assumption is not justified, thus the optimal strategy might not provide the expected performance. In this paper, we study the performance of the classic value iteration algorithm for solving an MDP problem under nonstationary environments. Specifically, the nonstationary environment is modeled as a sequence of time-variant transition probability matrices governed by an adiabatic evolution inspired from quantum mechanics. We characterize the performance of the value iteration algorithm subject to the rate of change of the underlying environment. The performance is measured in terms of the convergence rate to the optimal average reward. We show two examples of queuing systems that make use of our analysis framework.

scholarly journals Large Scale Shell Model Calculations of the Negative-Parity States Structure in 24Mg Nucleus

2021 ◽  
Vol 66 (4) ◽  
pp. 293
Author(s):  
A.A. Al-Sammarraie ◽  
F.A. Ahmed ◽  
A.A. Okhunov
Keyword(s):  
Shell Model ◽  
Large Scale ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Energy Levels ◽  
Form Factors ◽  
Model Space ◽  
Negative Parity ◽  
Matrix Elements ◽  
Model Calculations

The negative-parity states of 24Mg nucleus are investigated within the shell model. We are based on the calculations of energy levels, total squared form factors, and transition probability using the p-sd-pf (PSDPF) Hamiltonian in a large model space (0 + 1) hW. The comparison between the experimental and theoretical states showed a good agreement within a truncated model space. The PSDPF-based calculations successfully reproduced the data on the total squared form factors and transition probabilities of the negative-parity states in 24Mg nucleus. These quantities depend on the one-body density matrix elements that are obtained from the PSDPF Hamiltonian. The wave functions of radial one-particle matrix elements calculated with the harmonic-oscillator potential are suitable to predict experimental data by changing the center-of-mass corrections.

scholarly journals The Temperature Dependence of Fundamental Photophysical Properties of [Eu(MeOH-d4)9]3+ Solvates and [Eu.DOTA(MeOH-d4)]- Complexes

2021 ◽  
Author(s):  
Nicolaj Kofod ◽  
Lea Gundorff Nielsen ◽  
Thomas Just Sørensen
Keyword(s):  
Transition Probabilities ◽  
Photophysical Properties ◽  
Transition Probability ◽  
Energy Levels ◽  
Emission Spectra ◽  
Lanthanide Ions ◽  
Quantum Yields ◽  
Luminescence Spectra ◽  
Absorption Cross ◽  
Apparent Lack

The trivalent lanthanide ions show optical transitions between energy levels within the 4f shell. All these transitions are formally forbidden according to the quantum mechanical selection rules used in molecular photophysics. Nevertheless, highly luminescent complexes can be achieved, and terbium(iii) and europium(iii) ions are particularly efficient emitters. This report started when an apparent lack of data in the literature led us to revisit the fundamental photophysics of europium(iii). The photophysical properties of two complexes – [Eu.DOTA(MeOH-d4)]- and [Eu(MeOH-d4)9]3+ – were investigated in deuterated methanol at five different temperatures. Absorption spectra showed decreased absorption cross sections as the temperature was increased. Luminescence spectra and time-resolved emission decay profiles showed a decrease in intensity and lifetime as a temperature was increased. Having corrected the emission spectra for the actual number of absorbed photons and differences in non-radiative pathways, the relative emission probability was revealed. These were found to increase with increasing temperature. The transition probability for luminescence was shown to increase with temperature, while the transition probability for light absorption decreased. The changes in transition probabilities were correlated to a change in the symmetry of the absorber or emitter, with an average increase in symmetry lowering absorption cross section and access to more asymmetric structures increasing the emission rate constant. Determining luminescence quantum yields and the Einstein coefficient for spontaneous emission allowed us to conclude that lowering symmetry increases both. Further, it was found that collisional self-quenching is an issue for lanthanide luminescence, when high concentrations are used. Finally, detailed analysis revealed results that show the so-called ‘Werts’ method’ for calculating radiative lifetimes and intrinsic quantum yields are based on assumption that does not hold for the two systems investigated here. We conclude that we are lacking a good theoretical description of the intraconfigurational f-f transition, and that there are still aspects of fundamental lanthanide photophysics to be explored.<br>

Sign in / Sign up

Export Citation Format

Share Document