Equivalent Electrons Research Articles

Improving the crystal quality and optoelectronic property of GaSb with Al doping

GaSb and Ga1-xAlxSb crystals were prepared with the vertical Bridgman (VB) method. The effects of aluminum atoms (Al) doping on the structure and photoelectric properties of GaSb crystal were investigated. The results show that the GaAlSb crystal maintains the zinc blende crystal structure of the GaSb crystal, and the crystal quality gradually improves with the increase of Al doping concentration, and the effective segregation coefficient keff of Al decreases from 3.69 to 2.83. Furthermore, Al doping significantly inhibits the formation of dislocations, of which density decreases from 3.634 × 103 cm−2 to 1.256 × 103 cm−2. As an element with the same equivalent electrons as Ga, Al doping makes GaSb crystal become into an n-type semiconductor with the free electrons as the main carriers, from a p-type semiconductor with the holes as the main carriers (8.867 × 1017 cm−3). And the carrier concentration, i.e., the free electrons concentration, increases with the doped Al concentration increase, up to the maximum of 1.929 × 1018 cm−3. And the mobility of electron carriers increases with the increase of Al concentration, up to 2.140 × 103 cm2/(V•s), far greater than that of the hole carriers 1.358 × 103 cm2/(V•s). And the resistivity decreases from 7.649 × 10−3 Ω•cm to 1.416 × 10−3 Ω•cm. Moreover, the infrared transmittance spectrum also shows a significant improvement of the crystal quality.

Experimental and theoretical Ritz–Rydberg analysis of the electronic structure of highly charged ions of lead and bismuth by optical spectroscopy

Intra-configuration fine-structure transitions in highly charged ions (HCIs) result in most cases from changes in the coupling of equivalent electrons. They are multipole forbidden to varying degrees and often occur within the optical range. In HCI with semi-filled nd and nf subshells, electrons can in principle couple to states which are energetically close but with very different total angular momenta, e.g. 0⩽J⩽10 . This gives rise to metastable states with very long lifetimes that exhibit particularly interesting clock transitions or, as in the case of orbital level crossings, acquire a considerable sensitivity to a possible variation of the fine-structure constant α. We investigate both experimentally and theoretically connecting the ground state and adjacent states of Pb XXII to Pb XXXIV and Bi X to Bi XV, respectively, covering complex couplings of electrons in the 4f and 5d shells. These and others such as nd and nf , which also contain equivalent electrons, are of interest for frequency metrology using quantum logic spectroscopy, for atomic structure and QED theory tests, and for the search for Dark Matter candidates. We infer their level structure, benchmark calculations from two different electronic structure codes, and lay the groundwork for inferring the wavelengths of forbidden transitions of higher multipolarity in the optical and VUV region.

New Numerical Approach to Calculate Microstates of Equivalent and Non-Equivalent Electrons

A term symbol is used to describe atomic microstate states, which give the multiplicity and total angular momentum of the atomic state. Russel Sauder coupling scheme is used to generate terms of equivalent and non-equivalent electronic configurations. For equivalent electrons, the terms are calculated using Pauli’s principle, and the number of terms is limited and is calculated by the combination rule. The total possible electrons and total available electrons are used in the combination formula. In case of non-equivalent electrons, the number of terms are found by the permutation rule. The number of terms for equivalent electrons is less than the terms for non-equivalent electrons. The number of possible microstates for p2 and d5 configurations are 15 and 252 respectively. While the number of final microstates for 1p2p and 3d4d configurations are 36 and 100. In the proposed study, a Python programme was developed that generates the microstate according to filled and half-filled subshell electronic configurations for equivalent, non-equivalent, and combinations of both. Examples of microstates for non-equivalent electrons of configuration 1s2s, sp, sd, ss, 2p3p, pd, pf, 3d4d, df, 4f5f and for equivalent electrons of configuration su, pv, dx, and f y are presented.

Variational Methods for Atoms and the Virial Theorem

In the case of the one-electron Dirac equation with a point nucleus, the virial theorem (VT) states that the ratio of the kinetic energy to potential energy is exactly −1, a ratio that can be an independent test of the accuracy of a computed solution. This paper studies the virial theorem for subshells of equivalent electrons and their interactions in many-electron atoms. This shows that the linear scaling of the dilation is achieved through the balancing of the contributions to the potential of an electron from inner and outer regions that some Slater integrals impose conditions on a single subshell, but others impose conditions between subshells. The latter slows the rate of convergence of the self-consistent field process in which radial functions are updated one at a time. Several cases are considered. Results are also extended to the nonrelativistic case.

Multiplicity, Parity and Angular Momentum of a Cooper Pair in Unconventional Superconductors of D4h Symmetry: Sr2RuO4 and Fe-Pnictide Materials

Sr2RuO4 and Fe-pnictide superconductors belong to the same point group symmetry D4h. Many experimental data confirm odd pairs in Sr2RuO4 and even pairs in Fe-pnictides, but opposite conclusions also exist. Recent NMR results of Pustogow et al., which revealed even Cooper pairs in Sr2RuO4, require reconsideration of symmetry treatment of its SOP (superconducting order parameter). In the present work making use of the Mackey–Bradley theorem on symmetrized squares, a group theoretical investigation of possible pairing states in D4h symmetry is performed. It is obtained for I4/mmm , i.e., space group of Sr2RuO4, that triplet pairs with even spatial parts are possible in kz direction and in points M and Y. For the two latter cases pairing of equivalent electrons with nonzero total momentum is proposed. In P4/nmm space group of Fe- pnictides in point M, even and odd pairs are possible for singlet and triplet cases. It it shown that even and odd chiral states with angular momentum projection m=±1 have nodes in vertical planes, but Eg is nodal , whereas Eu is nodeless in the basal plane. It is also shown that the widely accepted assertion that the parity of angular momentum value is directly connected with the spatial parity of a pair is not valid in a space-group approach to the wavefunction of a Cooper pair.

Distribution of the total angular momentum in relativistic configurations

This paper is devoted to the analysis of the distribution of the total angular momentum in a relativistic configuration. Using cumulants and generating function formalism this analysis can be reduced to the study of individual subshells with N equivalent electrons of momentum j. An expression as a nth-derivative is provided for the generating function of the J distribution and efficient recurrence relations are established. It is shown that this distribution may be represented by a Gram–Charlier-like series which is derived from the corresponding series for the magnetic quantum number distribution. The numerical efficiency of this expansion is fair when the configuration consists of several subshells, while the accuracy is less good when only one subshell is involved. An analytical expression is given for the odd-order momenta while the even-order ones are expressed as a series which provides an acceptable accuracy though being not convergent. Such expressions may be used to obtain approximate values for the number of transitions in a spin–orbit split array: it is shown that the approximation is often efficient when few terms are kept, while some complex cases require to include a large number of terms.

Angular momentum distribution in a relativistic configuration: magnetic quantum number analysis

This paper is devoted to the analysis of the distribution of the total magnetic quantum number M in a relativistic subshell with N equivalent electrons of momentum j. This distribution is analyzed through its cumulants and through their generating function, for which an analytical expression is provided. This function also allows us to get the values of the cumulants at any order. Such values are useful to obtain the moments at various orders. Since the cumulants of the distinct subshells are additive this study directly applies to any relativistic configuration. Recursion relations on the generating function are given. It is shown that the generating function of the magnetic quantum number distribution may be expressed as an nth derivative of a polynomial. This leads to recurrence relations for this distribution which are very efficient even in the case of large j or N. The magnetic quantum number distribution is numerically studied using the Gram–Charlier and Edgeworth expansions. The inclusion of high-order terms may improve the accuracy of the Gram–Charlier representation for instance when a small and a large angular momenta coexist in the same configuration. However such series does not exhibit convergence when high orders are considered and the account for the first two terms often provides a fair approximation of the magnetic quantum number distribution. The Edgeworth series offers an interesting alternative though this expansion is also divergent and of asymptotic nature.

Strong-field triple ionisation of atoms with p 3 valence shell

The interaction of strong pulsed femtosecond laser field with atoms having three equivalent electrons in the outer shell (p 3 configuration, e.g. nitrogen) is studied via numerical integration of a time-dependent Schrödinger equation on a spatial grid. Single ionisation, double ionisation (DI) and triple ionisation (TI) yields originating from a completely antisymmetric wave function are calculated and extracted using a restricted-geometry model with the soft-core potential and three active electrons. The observed suppression of the ionisation yields for the non-sequential processes, in both DI and TI cases, is attributed to the action of the Pauli principle. Compared against earlier results investigating the s 2 p 1 configuration, we propose that the differences found here might in fact be accessible through electron’s momentum distribution.

Development of a high-performance readout circuit for photoelectric detectors

A high-performance readout circuit for photoelectric detectors is developed in this paper to achieve high-speed low-noise image detection. Here, the W/L ratio of the first-stage P-type following transistor is reduced to decrease the parasitic capacitance of buses, and the bias voltage of the P-type following load transistor is minimized to increase the driving current. These changes increase the sampling frequency of the read-out circuit from its original 2 MHz to 6 MHz, thereby effectively improving the readout frequency of the long-line visible light CMOS detector. Four-sampling is used to achieve true correlated double-sampling and reduce the equivalent input noise of the device, thus, overcoming the original circuit’s non-true correlation cancellation. Testing revealed that the number of equivalent input noise electrons of the CMOS detector decreased from 100e to 50e (rms) when the integral time is 200 µs and the photosensitive area is 20 × 18 μm2. The device could work steadily at a sampling rate of 6 MHz, and its linearity and output swing exceed 99% and 2 V, respectively. Moreover, the sensitivity of the detector could meet the requirements of the system. The development of the proposed CMOS detector lays an important theoretical foundation and provides practical value for future research on ultra-high speed and high-definition image detection technologies.

Coupling: The program for searching optimal coupling scheme in atomic theory

The Coupling program, which is important not only for the Grasp2018 package but for the atom theory in general, is presented in this paper. This program is designed as a part of the Grasp2018 package. The Coupling performs the transformation of atomic state functions (ASFs) from a LSJ-coupled CSF basis into several other configuration state function (CSF) bases such as jj, LK, JK, JJ, and many others. It allows identification of the energy structure of practically any element in different coupling schemes and also allows selection of the most suitable one. In addition, examples of how to use the Coupling program are given in additional file Example_Calculation.pdf listed in source directory grasp2018/src/appl/Coupling/Sample_Runs. Program summaryProgram Title:CouplingProgram Files doi:http://dx.doi.org/10.17632/7tv9n8g24w.1Licensing provisions: MIT licenseProgramming language: Fortran 95.External routines/libraries used:Grasp2018 modules: jj2lsj_data_1_C, jj2lsj_data_2_C, jj2lsj_data_3_C and Atsp2K module: sqlsf.f.Nature of problem: The Coupling program is designed as a part of the Grasp2018 package for the computation of atomic state function transitions and for identification atomic properties in different coupling schemes.Solution method: Spin-angular coupling transformation of multiconfiguration expansions obtained in LS and jj coupling schemes.Additional comments including restrictions and unusual features: The transformations of the configuration state functions is supported for one, two, and three open shell structures including open s, p, d, and f-shells. For shells with l>3 (i.e. beyond the f-shells), however, a proper transformation of the antisymmetrized shell states can be carried out only for the case of one or two equivalent electrons. The jj⟷LS transformation matrices, which are applied internally by the program, are consistent with the previously published definitions of the reduced coefficients of fractional parentage and jj⟷LS transformation matrices. The transformation from LSJ-coupling to all main coupling schemes is performed by the program Coupling. The number and types of coupling schemes depend on the number of coupled shells in LS-coupling.

Structure of the Order Parameter of Topological Superconductors Based on 3d and 4d Transition Metal Oxides

We consider experimental data on the order parameter structure in superconductors with a layered perovskite structure: La2CuO4 and Sr2RuO4. Experimental data are analyzed using the space group approach to two-electron states in crystals. From the crystalline symmetry of Sr2RuO4, we derive two-electron functions with Eu symmetry, having nodal planes consistent with experimental data. In the case of La2CuO4 and high-Tc materials, the order parameter corresponds to the irreducible representation B1g with hidden symmetry D4h. It is also shown that the charge density waves found in pseudogap states of high-Tc materials can be thought of as two-electron states of equivalent electrons with a nonzero momentum.

Bio-regeneration of activated carbon: A comprehensive review

Abstract The use of microorganisms to regenerate activated carbon (AC), bio-generation, can avert costly and logistically challenging ex-situ steam regeneration of carbon normally required to recover its adsorptive capacity. Bio-regeneration employs microbial metabolism in which the microbes use the available organic substrates (contaminants) to generate energy. During this process, they generate equivalent protons and electrons, which are transferred to the substrates to finally break them down to simpler molecules or ions, such as CO2, methane and Cl−. The optimal microbial conditions depend on the temperature, available nitrogen and phosphorus levels, dissolved oxygen levels, and microbe/substrate stoichiometric ratios and the residence time of the AC particles within the reactor. In this review, the authors highlight the most recent development in bio-regeneration including the regeneration mechanism, the relationship between the reversibility of adsorption and the efficiency of bio-regeneration, the general aspects affecting bio-regeneration, the principle and target compounds for bio-regeneration, different established methods for quantifying the bio-regeneration and the efficiency of bio-regeneration. Few case studies of bio-regeneration of activated carbon loaded with different contaminants are presented. Research on microbiology regeneration has gained considerable attention in recent years, but it still needs more contribution from other disciplines including process engineering, biochemistry and material sciences for optimizing the process performance.

Generalized spin-statistic selection rules for atomic transitions with arbitrary number of equivalent photons

Generalized spin-statistic selection rules (SSSR) for the arbitrary number of photons N γ involved in atomic transitions are established. These selection rules are similar to those for systems of many equivalent electrons in atomic theory. The latter are a direct consequence of symmetrization postulate (SP) and the Pauli exclusion principle (PEP) (or its more general formulation is spin-statistics connection (SSC)). In this sense, the SSSR play the role of the exclusion principle for photons: they forbid some particular states for the photon systems. This selection rule represents an extension of the Landau-Yang theorem (LYT) to the photons involved in atomic transitions. The possible experimental test of generalized SSSR are also proposed.

Construction of the energy matrix for complex atoms Part III: Excitation of two equivalent electrons from a closed shell into an open shell or an empty shell

The effects of the second-order configuration interaction perturbations on the energy-level structure of nl N , $$nl^N n_1 l_1^{N_1 }$$ and $$nl^N n_1 l_1^{N_1 } n_2 l_2$$ configurations have been studied. In the previous works (see Part I and II) we presented a method, which allows to analyse complex electronic systems composed of configurations including up to four open shells and the formulae for the first-order electrostatic interaction between sophisticated configurations. In the present paper we consider two-electron core excitations for and between the configurations under study. They constitute the basis for the design of an efficient computer program package allowing large-scale calculations providing accurate wave functions.

Exclusion principle for photons: Spin-statistic selection rules for multiphoton transitions in atomic systems

We establish the existence of spin-statistic selection rules (SSSRs) for multiphoton transitions with equal photons in atomic systems. These selection rules are similar to those for systems of many equivalent electrons in atomic theory. The latter are a direct consequence of the Pauli exclusion principle. In this sense, the SSSRs play the role of the exclusion principle for photons: they forbid some particular states for the photon systems. We established several SSSRs for few-photon systems. (i) First rule: two equivalent photons involved in any atomic transition can have only even values of the total angular momentum, $J$. This selection rule is an extension of the Landau-Yang theorem to the photons involved in atomic transitions. (ii) Second rule: three equivalent dipole photons involved in any atomic transition can have only odd values of the total angular momentum, $J=1,3$. (iii) Third rule: four equivalent dipole photons involved in any atomic transition can have only even values of the total angular momentum, $J=0,2,4$. We also suggest a method for a possible experimental test of these SSSRs by means of laser experiments.

ChemInform Abstract: Novel Aromatic and Antiaromatic Systems

AbstractReview: 48 refs.

Novel aromatic and antiaromatic systems.

We contributed to the field of non-benzenoid aromatic compounds by creating the cyclopropenyl cation and various of its derivatives, including cyclopropenone; it was the first aromatic system with other than six pi electrons in a single ring, and the simplest aromatic system. The pioneering work of Tetsuo Nozoe in tropolone chemistry was celebrated with the founding of ISNA, the International Symposium on Non-Benzenoid Aromatic Compounds, where I described our work in the field. It fit the prediction that aromaticity would be found in systems with 4n + 2 pi electrons, where n is an integer. I was also concerned with the properties of monocyclic systems with 4n cyclically conjugated pi electrons. They were expected not to be aromatic, but the interesting question was whether they were actually antiaromatic, especially destabilized by the cyclic conjugation in such 4n species as the cyclopropenyl anion, cyclobutadiene, and cyclopentadienyl cation. The evidence supports antiaromaticity in these cases. We also examined compounds where 4n cyclic pi systems were fused with aromatic systems, and most interestingly systems in which two 4n pi systems were fused. In these cases the periphery of the molecules had 4n + 2 pi electrons, for aromaticity, but the components were antiaromatic. Recently we have studied electrical conductivities in aromatic molecules such as thiophene and saw that aromaticity added resistance to the systems, so non-aromatic compounds are better conductors and antiaromatic compounds are predicted to be the best of all.

Development of a multi-channel readout ASIC for a fast neutron spectrometer based on GEM-TPC

A multi-channel front-end ASIC has been developed for a fast neutron spectrometer based on Gas Electron Multiplier (GEM)-Time Projection Chamber (TPC). Charge Amplifier and Shaping Amplifier for GEM (CASAGEM) integrates 16+1 channels: 16 channels for anodes and 1 channel for cathode. The gain and the shaping time are adjustable from 2 to 40 mV/fC and from 20 to 80 ns, respectively. The prototype ASIC is fabricated in 0.35 μm CMOS process. An evaluation Print Circuit Board (PCB) was also developed for chip tests. In total 20 chips have been tested. The integrated nonlinearity is less than 1%. The equivalent noise electrons is less than 2000e when the input capacitor is 50 pF. The time jitter is less than 1 ns. The design and the test results are presented in the paper.

Beta particles sensitivity of an all-carbon detector

The response of high quality polycrystalline diamond pixel detectors to 90Sr beta particles is reported. Laser induced surface graphitization was used to realize 36 conductive contacts with 1mm×1mm area each, pitch 1.2mm, on one detector side whereas a 8mm×8mm large area graphite contact was realized on the other face for grounding or biasing. A proximity board was used to hold the matrix, the amplifiers and to bond nine pixels to test homogeneity of response among 36 detector pixels. Two configurations were used to test charge collection uniformity and signal dependence on voltage. Both configurations showed noise pedestal fitted with a Gaussian curve of 1150 equivalent electrons (1σ) and typical beta source particles spectrum. Reversing the bias polarity the pulse height distribution does not change and the saturation of most probable value of charge collection was observed around ±200V (0.4V/μm) with reasonable pixel response uniformity equal to a most probable value 1.28±0.05fC. The charge collection efficiency (CCE) measurement was implemented using coincidence mode acquisition with an external trigger made by a commercial polycrystalline diamond slab. The detector shows a CCE=0.59 estimated using the 1mm2 large graphite pixel. The information earned with this first prototype will be used to design the new board with amplifying electronics for reading all 36 pixels at a time and perform experiments with monochromatic high energy electrons.

Diamond-graphite pixel array for particles detection

The response of graphite-diamond pixel detectors to90Sr β-particles is reported. Laser induced graphitization was used torealize 200 μm × 200 μm square conductive graphite pads onone detector side whereas a large area graphite contact was realized on theother face for biasing. A board with nine hybrid charge sensitivepre-amplifier channels was used to test homogeneity of response of ninepixels at a time. In the dark the current is Ohmic up to 100 V where thecurrent increases with a power law. While the bulk pixel resistance is2.5 × 1012 Ω, the resistance betweenadjacent pixels depends on voltage following a power law. Under irradiationa resolved β-spectrum well separated from the noise contribution was observedon each pixel. The most probable value of the collected charge distributionis voltage dependent and saturates around ±300 V (0.6 V/μm) with avalue of 0.70±0.05 fC (4300±300 equivalent electrons charge).