Ridge regression energy levels calculation of neutral ytterbium(Z=70)

In view of the difficulty in calculating the atomic structure parameters of high-Z elements,the Hartree–Fock with relativistic corrections(HFR)theory in combination with the ridge regression(RR)algorithm rather than the Cowan code’s least squares fitting(LSF)method is proposed and applied.By analyzing the energy level structure parameters of the HFR theory and using the fitting experimental energy level extrapolation method,some excited state energy levels of the Yb I(Z=70)atom including the 4f open shell are calculated.The advantages of the ridge regression algorithm are demonstrated by comparing it with Cowan code’s LSF results.In addition,the results obtained by the new method are compared with the experimental results and other theoretical results to demonstrate the reliability and accuracy of our approach.

Distribution of Vibrational Energy Levels of Protein Molecular Chains

The distributions of the quantum vibrational energy levels of the protein molecular chain are found by the discretely nonlinear Schr?dinger equation appropriate to protein obtained from the Davydov theory. The results calculated by this method are basically consistent with the experimental values. Furthermore, the energy spectra at high excited states have also been obtained for the molecular chain which is helpful in researching the properties of infrared absorption and Raman scattering of the protein molecules.

The Quantum Condition That Should Have Been Assumed by Bohr When Deriving the Energy Levels of a Hydrogen Atom

Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr’s quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr’s quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr’s quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity v of an electron including the principal quantum number n is given by αc/n. This paper elucidates the fact that this formula is built into Bohr’s quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr’s quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.

Variation of the Observed Widths of La I Lines with the Energy of the Upper Excited Levels, Demonstrated on Previously Unknown Energy Levels

We performed systematic laser spectroscopic investigations of La I spectral lines, using optogalvanic detection. Sixteen previously unknown even parity levels, having energies between 40,300 and 44,300 cm-1, are reported. These levels classify altogether 67 lines, not listed in spectral tables. The new levels were found due to the observation of the depopulation of the lower levels of the excited transitions. We found a remarkable variation of the observed widths of single hyperfine structure components dependent on the energy of the upper excited levels. Some levels having energies higher than 43,000 cm-1 appear to have a very high ionization probability.

Energy Levels of Coupled Plasmonic Cavities

We demonstrate the hybridization of the plasmonic modes in directly coupled whispering gallery cavities fabricated on silver films and present the mode patterns and energy levels using cathodoluminescence spectroscopy. Although the energy of the most antisymmetrically coupled modes is higher than that of the corresponding symmetrically coupled ones, the contrary cases happen for small quantum number modes. We attribute the phenomenon to the different surface plasmon polariton paths between the symmetrically and antisymmetrically coupled modes; These results provide an understanding of the resonant properties in coupled plasmonic cavities, which have potential applications in nanophotonic devices.

Energy levels and transition data of 3p^(6)3d^(8)and 3p^(5)3d^(9)configurations in Fe-like ions(Z=57,60,62,64,65)

Atomic data of highly charged ions(HCIs)offer an attractive means for plasma diagnostic and stars identification,and the investigations on atomic data are highly desirable.Herein,based on the fully relativistic multi-configuration Dirac–Hartree–Fock(MCDHF)method,we have performed calculations of the fine-structure energy levels,wavelengths,transition rates,oscillator strengths,and line strengths for the lowest 21 states of 3p^(6)3d^(8)–3p^(5)3d^(9)electric dipole(E1)transitions configurations in Fe-like ions(Z=57,60,62,64,65).The correlation effects of valence–valence(VV)and core–valence(CV)electrons were systematically considered.In addition,we have taken into account transverse-photon(Breit)interaction and quantum electrodynamics(QED)corrections to treat accurately the atomic state wave functions in the final relativistic configuration interaction(RCI)calculations.Our calculated energy levels and transition wavelengths are in excellent agreement with the available experimental and theoretical results.Most importantly,we predicted some new transition parameters that have not yet been reported.These data would further provide critical insights into better analyzing the physical processes of various astrophysical plasmas.

Saturable Absorption Enchantment of Au Nanorods Based on Energy Transfer between Longitudinal and Transverse Energy Levels

Four kinds of Au nanorods（NRs）with different aspect ratios are designed to adjust the relationship between resonance energy level of longitudinal（L）and transverse（T）modes.During the femto-second Z-scan experiments,huge saturable absorption phenomena are observed while the energy level T is located between one to two times of the energylevel L.This means that the energy may transfer between longitudinal and transverse energylevels in the same and/or different Au NRs.It effectively depresses the production of revised saturated absorption and increases the saturable absorption efficiency.This method is significant for the preparation of high-efficiency saturable absorption devices.

Relativistic calculations of fine-structure energy levels of He-like Ar in dense plasmas

The fine-structure energy levels of 1 s2s and 1 s2p atomic states for the He-like Ar ion immersed in dense plasmas are calculated. The ion sphere model is used to describe the plasma screening effect on the tested ion. The influences of the hard sphere confinement and plasma screening on the fine-structure energy levels are investigated respectively. The calculated results show that the confined effect of the hard sphere on the fine-structure energy levels increases with decreasing hard sphere radius, and the plasma screening effect on the fine-structure energy levels increases with the increase of free electron density. In dense plasmas, the confined effect of the hard generally, compared with the contribution from free electron crossing is found among 1 s2s （1 So） and 1 s2p （3P0,1） atomic plasma diagnostics. sphere on the fine-structure energy levels can be neglected screening. An interesting phenomenon about the energy level states. The results reported at the present work are useful for

Improved Calculation of Vibrational Energy Levels in F2 Molecule using the RKR Method

The potential energy curves of the ground state X2∑＋g of the fluorine molecule have been accurately reconstructed employing the Ryderg-Klein-Rees （RKR） method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the corresponding radial one-dimensional Schr？dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimental data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm？1 and the relative deviation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F2 ground state.

Red Organic Light-Emitting Diodes Based on Energy Levels Matching of Dopant with the Host Materials

By doping red dye 4 dicyanomethylene 2 ( tert butyl) 6 methyl 4H pyran(DCJTB) in the tris (8 hydroxyquinolinato) metal Mq 3(where M = Al, Ga, In) chelate complexes, a series of red dopant organic light emitting diodes with different doping concentrations have been fabricated. The electroluminescence efficiency of these red diodes with a DCJTB doped Mq 3 emitting layer is found to be decreased markedly with the increasing of doping concentration. Electroluminescence characteristics of these devices are studied in terms of energy levels matching of red dopant with the host materials and carrier transporting layers.

Relativistic Reduction of the Electron-Nucleus Force in Bohr’s Hydrogen Atom and the Time of Electron Transition between the Neighbouring Quantum Energy Levels

The aim of the paper is to get an insight into the time interval of electron emission done between two neighbouring energy levels of the hydrogen atom. To this purpose, in the first step, the formulae of the special relativity are applied to demonstrate the conditions which can annihilate the electrostatic force acting between the nucleus and electron in the atom. This result is obtained when a suitable electron speed entering the Lorentz transformation is combined with the strength of the magnetic field acting normally to the electron orbit in the atom. In the next step, the Maxwell equation characterizing the electromotive force is applied to calculate the time interval connected with the change of the magnetic field necessary to produce the force. It is shown that the time interval obtained from the Maxwell equation, multiplied by the energy change of two neighbouring energy levels considered in the atom, does satisfy the Joule-Lenz formula associated with the quantum electron energy emission rate between the levels.

The Effect of Energy Levels of the Electron Acceptor Materials on Organic Photovoltaic Cells

Organic photovoltaic cells have been fabricated using copper phthalocyanine CuPc as electron donor and C60 or PCBM as electron acceptor. We have investigated the I-V measurements of two different structures: ITO/PEDOT: PSS/(CuPc:C60 or CuPc:PCBM)/BCP/Al. We have observed that the substitution of PCBM by C60 scales up the photocurrent and the efficiency of the devices. As for the open-circuit voltage and the fill factor, we have seen that Voc and FF depend on the energy difference between the highest occupied molecular orbital (HOMO) of CuPc and the lowest unoccupied molecular orbital (LUMO)of C60 or PCBM.

Solving Energy Levels for SSH Hamiltonian Describing Peierls Phase Transition by Virtue of Invariant Eigen-operator Method

We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.

Energy levels and states of parabolic cylindrical lens shaped quantum dots

The parabolic cylindrical lens shaped quantum dot is investigated theoretically. The Schrǒdinger equation for an electron confined in this structure is solved in the parabolic cylindrical coordinate system. The wavefunctions for the electron are presented in terms of confluent hypergeometric functions, and the electron energy spectra are also obtained.

Calculation of Rydberg energy levels for the francium atom

Based on the weakest bound electron potential model theory, the Rydberg energy levels and quantum defects of the nP^2P^o1/2 （n=7-50） and np^2P^o3/2 （n=7-50） spectrum series for the francium atom are calculated. The calculated results are in excellent agreement with the 48 measured levels, and 40 energy levels for highly excited states are predicted.

Energy levels and magnetic dipole transition parameters for the nitrogen isoelectronic sequence

Theoretical calculations of the energy levels and magnetic dipole transition parameters for the 1s^(2)2s^(2)2p^(3) and 1s^(2)2p^(5) configurations of nitrogen isoelectronic sequence with Z=21-30 are performed using multi-congfiguration Dirac-Fock(MCDF)method.Based on the relativistic computational code GRASP2k compiled within the framework of MCDF method,the electron correlations,Breit interaction and QED effects are well treated in detail.The energy levels,line strengths and transition rates of magnetic dipole transition are obtained and compared with the experimental data avail-able.For most cases,good agreements are achieved and the relative differences of them are less than 0.114%,8.43% and 9.80%,respectively.The scaling laws of the fine structure splitting and transition rate are obtained on the isoelec-tronic sequence and the corresponding physical mechanisms are discussed.The data sets for tables are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00022.

Energy Levels of Highly Ionized Ar XIV

With the Breit interaction and quantum electrodynamics corrections considered, relativistic configuration interaction calculations have been carried out in the extended optimal level scheme using multi-configuration Dirac-Fock wave functions on the 204 energy levels and electric dipole transitions of Ar XIV. The results of electric dipole transitions are in good agreement with experiments. Among the energy levels calculated, the lowest 125 levels are in good agreement with available experimental and other theoretical ones, and the other 79 levels are new ones obtained by the present work. This wide range of atomic energy levels is useful in astrophysics and plasma physics.

Theoretical study on the potential energy surface and vibrational energy levels of HXeI

The potential energy surface for the electronic ground state of the HXeI molecule is constructed by using the internally contracted multi-reference configuration interaction with the Davidson correction（icMRCI＋Q）method and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces.The three-body dissociation channel is found to be the dominate dissociation channel for HXeI.Based on the obtained potentials,vibrational energy levels of HXeI are calculated using the Lanczos algorithm.Our theoretical results are in excellent agreement with the available observed values.

An ab initio potential energy surface and vibrational energy levels of HXeBr

A three-dimensional global potential energy surface for the electronic ground state of HXeBr molecule is constructed from more than 4200 ab initio points. These points are generated using an internally contracted multi-reference configuration interaction method with the Davidson correction （icMRCI ＋ Q） and large basis sets. The stabilities and dissociation barriers are identified from the potential energy surfaces. The three-body dissociation channel is found to be the dominate dissociation channel for HXeBr. Based on the obtained potentials, low-lying vibrational energy levels of HXeBr calculated using the Lanczos algorithm is found to be in good agreement with the available experimental band origins.

The Relationship Between the Energy Levels of Shock Waves and the Degree of Renal Damage After ESWL:A Prospective Clinical Matching Trail

In an attempt to understand the effects of high energy shock wave (HESW)on renal function, we studied prospectively 40 patients with nephrolithiasis in 4 groups,using same voltage with different numbers of shock wave therapy to identify the difference of effects on renal function. Stone burdens and posit ion were similar in these groups. Each group received 1500, 2000, 2500 or 3000 puises at 12. 5 KV on JT-3lithotripotor respectively. All the groups had significantly increased the levels of urinary NAG, β2MG, ALB and serum β2MG, which reached the highest values on 1-3days after ESWL (P<0. 001), and then decreased to the pre-ESWL levels except urinary NAG in group Cand D and serum β2MG which were still significantly higher (P<0.05) than those before-ESWL on the 7th day after ESWL. There was significant correlation between either urinary NAG (γ=0. 977, P<0. 05) or β2MG (γ=0. 933, P<0. 001) with the number of shock wave. In addition, urinary NAG and β2MG increased significantly when the number of shock waves was over 2500 shots.These above findings suggest that shock wave had induced acute changes in renal functions and transient renal tubular damages, although these functional changes recovered within one week, and the tubular damage might last longer than 7 days , In order to avoid serious renal damage, it’s necessary to limit the energy level of shock waves under 12. 5 KV×2500 shots by using JT-3 lithotriptor.