Quantum Numbers Research Articles

Space-time description of atoms, part I: Electronic structures, dark matter, and g-factors of electron, muon and tau

The description of atoms is based on 3D time and some relativistic effects about spinning bodies have been published previously. The time displacement of the electrons also plays an important role. While the principal quantum number [Formula: see text] refers to the angular momentum [Formula: see text] observed by external observer, the azimuth quantum number [Formula: see text] refers to the angular momentum [Formula: see text] observed from the electron itself. The intrinsic angular momentum observed by the electron is [Formula: see text] according to Stern–Gerlach experiment, but the angular momentum observed by external observer is about [Formula: see text]. The magnetic quantum numbers are deduced from the mentioned effects and the trajectories of electrons are non-probabilistic and geometrically well determined. The spin quantum number indicates the time arrow toward the future or toward the past. So, the electrons with opposite time arrows can be grouped in pairs, where the nucleus is in the middle. Descriptions of the dark matter particles and the electrons are given. Using the value [Formula: see text] suggested from the QED, the [Formula: see text]-factors of the electron and muon are [Formula: see text]; [Formula: see text], which give excellent agreements with the experiments. So, if we equalize the formulas for [Formula: see text]-factor from QED and this approach, it determines the theoretical value of [Formula: see text], without experiment.

Production of D(*)D¯(*) near the thresholds in e+e− annihilation

It is shown that the nontrivial energy dependencies of DD¯, DD¯*, and D*D¯* pair production cross sections in e+e− annihilation are well described within the approach based on an account of the final-state interaction of produced particles. This statement is valid for the production of charged and neutral particles. Interaction of D(*) and D¯(*) is taken into account using the effective potential method. Its applicability is based on the fact that for near-threshold resonance the characteristic width of peak in the wave function is much larger than the interaction radius. The transition amplitudes between all three channels play an important role in the description of cross sections. These transitions are possible since all channels have the same quantum numbers JPC=1−−. Published by the American Physical Society 2024

Search for baryon junctions in photonuclear processes and isobar collisions at RHIC

During the early development of quantum chromodynamics, it was proposed that baryon number could be carried by a non-perturbative Y-shaped topology of gluon fields, called the gluon junction, rather than by the valence quarks as in the QCD standard model. A puzzling feature of ultra-relativistic nucleus-nucleus collisions is the apparent substantial baryon excess in the mid-rapidity region that could not be adequately accounted for in most conventional models of quark and diquark transport. The transport of baryonic gluon junctions is predicted to lead to a characteristic exponential distribution of net-baryon density with rapidity and could resolve the puzzle. In this context we point out that the rapidity density of net-baryons near mid-rapidity indeed follows an exponential distribution with a slope of -0.61±0.03\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-0.61\\pm 0.03$$\\end{document} as a function of beam rapidity in the existing global data from A+A collisions at AGS, SPS and RHIC energies. To further test if quarks or gluon junctions carry the baryon quantum number, we propose to study the absolute magnitude of the baryon vs. charge stopping in isobar collisions at RHIC. We also argue that semi-inclusive photon-induced processes (γ+p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma +p$$\\end{document}/A) at RHIC kinematics provide an opportunity to search for the signatures of the baryon junction and to shed light onto the mechanisms of observed baryon excess in the mid-rapidity region in ultra-relativistic nucleus-nucleus collisions. Such measurements can be further validated in A+A collisions at the LHC and e+p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e+p$$\\end{document}/A collisions at the EIC.

Derivation of Bose's Entropy Spectral Density from the Multiplicity of Energy Eigenvalues.

The modern textbook analysis of the thermal state of photons inside a three-dimensional reflective cavity is based on the three quantum numbers that characterize photon's energy eigenvalues coming out when the boundary conditions are imposed. The crucial passage from the quantum numbers to the continuous frequency is operated by introducing a three-dimensional continuous version of the three discrete quantum numbers, which leads to the energy spectral density and to the entropy spectral density. This standard analysis obscures the role of the multiplicity of energy eigenvalues associated to the same eigenfrequency. In this paper we review the past derivations of Bose's entropy spectral density and present a new analysis of energy spectral density and entropy spectral density based on the multiplicity of energy eigenvalues. Our analysis explicitly defines the eigenfrequency distribution of energy and entropy and uses it as a starting point for the passage from the discrete eigenfrequencies to the continuous frequency.

Black hole interior quantization: a minimal uncertainty approach

In a previous work we studied the interior of the Schwarzschild black hole implementing an effective minimal length, by applying a modification to the Poisson brackets of the theory. In this work we perform a proper quantization of such a system. Specifically, we quantize the interior of the Schwarzschild black hole in two ways: once by using the standard quantum theory, and once by following a minimal uncertainty approach. Then, we compare the obtained results from the two approaches. We show that, as expected, the wave function in the standard approach diverges in the region where classical singularity is located and the expectation value of the Kretschmann scalar also blows up on this state in that region. On the other hand, by following a minimal uncertainty quantization approach, we obtain 5 new and important results as follows. (1) All the interior states remain well-defined and square-integrable. (2) The expectation value of the Kretschmann scalar on the states remains finite over the whole interior region, particularly where used to be the classical singularity, therefore signaling the resolution of the black hole singularity. (3) A new quantum number is found which plays a crucial role in determining the convergence of the norm of states, as well as the convergence and finiteness of the expectation value of the Kretschmann scalar. (4) A minimum for the radius of the (2-spheres in the) black holes is found (5) By demanding square-integrability of states in the whole interior region, an exact relation between the Barbero-Immirzi parameter and the minimal uncertainty scale is found.

Relativistic energies for the q-deformed Scarf potential with Feynman path integrals formulation

In this paper, the Dirac equation with the q-deformed Scarf potential for spin symmetry is solved for an arbitrary spin-orbit quantum number κ, in the presence of Coulomb-like potential tensor. Using the Feynman path integral formalism and the Pekeris approximation of the centrifugal term, we obtain the bound state energy eigenvalues and the associated spinor of the Dirac particle. Furthermore, this method is used to determine the spectrum of two diatomic molecules Li 2(61Π u ) and KRb(B −1Π). The obtained results are compared to the experimental and numerical ones.

Relativistic energy spectra of diatomic molecules through the solutions of general conformable fractional (GCF) Klein-Gordon equation for Hulthen potential with position-dependent mass (PDM) and the thermodynamic properties

In this study, we investigate the thermodynamic properties of some diatomic molecules modelled by Hulthen potential with PDM. The GCF Klein-Gordon equation in the GCF cylindrical coordinate for the Hulthen potential and the PDM function is solved by using the GCF Laplace method to obtain the GCF energy equation and GCF wave function. The effect of the fractional order, quantum number, potential parameter, and PDM parameter on the energy eigenvalue of the H2, LiH, and HF diatomic molecules is discussed through the corresponding graphs computed using MATLAB software. The results show that the fractional order, quantum number, and potential parameter cause the energy spectrum to increase. In addition, the thermodynamic properties are examined by calculating the partition function. Based on the results, internal energy tends to be constant at lower temperatures, and the specific heat capacity decreases with increasing β . Whereas free energy and entropy increase monotonically with increasing β . To validate our findings, we compare our results with those obtained in the literature.

Accurate ab initio calculation and neural network prediction of the atomic properties of Os LXXIII, Ir LXXIV, Pt LXXV, and Au LXXVI

In this paper, we present an ab initio theoretical calculation of the atomic parameters, including energy levels, wavelengths, lifetimes, and transition parameters, associated with the 1s22snl and 1s22pnl (n= 2–4, l≤n−1) configurations of Be-like sequence: Os LXXIII, Ir LXXIV, Pt LXXV, and Au LXXVI. Our analysis is based on the relativistic wavefunctions derived from the multi-configuration Dirac–Fock (MCDF) method, which are implemented in the relativistic atomic structure package GRASP2018. The correlations within the (principal quantum number) n= 10 complex are accounted for. The Breit interaction and quantum electrodynamical effects are added in the relativistic configuration interaction (RCI) calculation. Our results are compared with the existing data. The uncertainties of the dipole transition line strengths are assessed. In addition, we propose a feed forward neural network to predict the energy levels of Au LXXVI. This is a powerful machine learning tool capable of learning from existing data and predicting unknown data. The network is trained using theoretical energy levels of Os LXXIII, Ir LXXIV, and Pt LXXV obtained from the MCDF method. Our neural network exhibits average relative deviations of approximately 0.01% and 0.02% for trained and predicted energy levels, respectively, when compared to the MCDF results. This level of deviation suggests that our results are reasonably accurate. The data set presented in this study is useful for modeling fusion plasmas.

QUIJOTE discovery of the cation radicals HC5N+ and HC7N+

We present the discovery with the QUIJOTE line survey of the cations HC5N+ and HC7N+ in the direction of TMC-1. Seven lines with half-integer quantum numbers from J = 25/2–23/2 to 37/2–35/2 have been assigned to HC5N+ and eight lines from J = 55/2–53/2 to 71/2–69/2 to HC7N+. Both species have inverted 2Π ground electronic states with very good estimates for their B0 and ASO constants based on optical observations. The lines with the lowest J of HC5N+ exhibit multiple components due to the hyperfine structure introduced by the H and N nuclei. However, these different components collapse for the higher J. No hyperfine structure is found for any of the lines of HC7N+. The derived effective rotational and distortion constants for HC5N+ are Beff = 1336.662 ± 0.001 MHz and Deff = 27.4 ± 2.6 Hz, while for HC7N+ they are Beff = 567.85036 ± 0.00037 MHz and Deff = 4.01 ± 0.19 Hz. From the observed intensities, we derived Trot = 5.5 ± 0.5 K and N = (9.9 ± 1.0) × 1010 cm−2 for HC5N+, while we obtained Trot = 8.5 ± 0.5 K and N = (2.3 ± 0.2) × 1010 cm−2 for HC7N+. The HC5N/HC5N+, C5N/HC5N+, C5N−/HC5N+, HC7N/HC7N+, HC5N+/HC7N+, and C7N−/HC7N+ abundance ratios are 670 ± 80, 4.8 ± 0.8, 1.2 ± 0.2, 1000 ± 150, 4.2 ± 0.5, and 2.2 ± 0.2, respectively. We have run chemical modelling calculations to investigate the formation and destruction of these new cations. We find that these species are mainly formed through the reactions of H2 and the cations C5N+ and C7N+, and by the reactions of H+ with HC5N and HC7N, while they are mostly destroyed through a reaction with H2 and a dissociative recombination with electrons. Based on the underestimation of the abundances of HC5N+ and HC7N+ by the chemical model by a factor ∼20, we suggest that the rate coefficients currently assumed for the reactions of these cations with H2 could be too high by the same factor, something that will be worth investigating.

Probability of He+ Ion at Quantum Number 3 ≤ n ≤ 4 in Momentum Space

Ions resulting from the ionization of helium atoms are known as helium ions. Atom of Helium The probability distribution of the particle locations and velocities inside a helium atom is referred to as probability. Using theoretical study methods, the goal of this research is to find the probability of an electron's position in a helium atom at the quantum number 3 ≤ n ≤ 4. This type of research is non-experimental research by developing previously existing theories. This type of research is non-experimental research by transforming the radial wave function of hydrogenic atoms in position space into a radial wave function in momentum space using the Fourier transformation, then including a number of Gegenbauer functions and using the probability equation of finding an electron in a Helium ion in momentum space. The results of this research provide information regarding the position and probability of the existence of electrons in the helium atom. The probability value for the Helium ion is obtained using the equation P(p) = which is used to indicate the probability of finding an electron in a helium atom is directly proportional to the principal quantum number (n) and the value of the electron's momentum. The larger the electron momentum interval, the greater the probability.

Extended measurements and calculations of CH3C14N-N2 rotational lineshape parameters

Spectroscopic parameters of methyl cyanide are of interest for astrophysical applications because of presence of this molecule in planetary atmospheres, comets, and interstellar medium. For radiative-transfer modeling a key role is played by the pressure-induced linewidths which are strongly influenced by the collision partner and the temperature. To complete the extremely scarce experimental data available, rotational lines of room-temperature CH3C14N in collision with molecular nitrogen have been recorded in a very large (180–1400 GHz) frequency range for J = 9 → 10, 12 → 13, 15 → 16, 21 → 22, 27 → 28, 33 → 34, 42 → 43, 48 → 49, 63 → 64, 69 → 70, 75 → 76 and K = 0–15. The high sensitivity of the frequency-modulated spectrometer has enabled observation of clear deviations of the recorded lineshapes from the usual Voigt profile. Their additional analyses performed with advanced non-Voigt models have demonstrated that the observed lineshapes are mainly governed by the speed dependence of relaxation rates and that the optical diffusion related to velocity changing collisions (Dicke effect) has a nearly negligible role. Compared to infrared-region results available in the literature, our Voigt-profile values lie systematically lower by about 0.5 MHz/Torr, which argues in favor of observable vibrational dependence for the CH3CN-N2 system. Line-broadening parameters have been also evaluated by a semi-empirical method based on the Anderson-Tsao-Curnutte theory. The model parameters determined from fits on some selected experimental values confirm the tendences previously stated for the case of vibrotational transitions and allow better theoretical predictions for extended ranges of rotational quantum numbers. Being temperature-independent, these parameters can be directly used in calculations for other temperatures concerned by radiative transfer models.

The PQN-Code Program Based on Polynomials of Quantum Numbers for Calculating the Centers of Lines in Infrared Spectra of Polyatomic Molecules and Matrix Elements of a Dipole Moment

The PQN-Code Program Based on Polynomials of Quantum Numbers for Calculating the Centers of Lines in Infrared Spectra of Polyatomic Molecules and Matrix Elements of a Dipole Moment

Electronic energy levels and wave-functions evolution from 3-D to 2-D of a hydrogen atom confined by two parallel planes

The compression of an atom produced by two planes induces a change in its electronic structure that evolves from a free atom in 3-D to a 2-D atom. This behavior is of importance in low-dimensional materials and high compression produced by an anvil cell. In this work, we study the evolution of the energy levels and electronic wave-functions of a hydrogen atom placed between two impenetrable planes as a function of the inter-plane separation through a numerical approach. As the inter-plane separation is reduced, the electron motion is restricted along the direction normal to the planes, similar to a particle in a box, while leaving the electron to move unrestricted along the planes, thus, breaking the spherical geometry of the H atom caused by the planes’ compression. The energy levels evolve from 3-D, described by nlm quantum numbers to a 2-D described by n′ml′ , where l′ is the quantum number for a particle in a box along the z direction and n′ is the principal quantum number of the 2-D atom radial direction. We evaluate the energy levels from 3-D to 2-D and the radial average distance 〈ρ〉 in cylindrical coordinates, as a function of the inter-plane separation D along the z-direction. We find that as the inter-plane separation is reduced, the angular momentum quantum number l merges to the z-component of the angular momentum and it produces two branches, a symmetric for l-even and one anti-symmetric for l-odd, connected to a particle in a box quantum number l′ along the z-axis with implications in the atom photo-luminescence, resulting from the symmetry of the system. Furthermore, states with l-odd merge with states with l-even, as they have the same energy and average distance when D → 0. We provide an Aufbau principle for it. Our results agree to the analytical solutions at the 3-D and 2-D limiting cases.

Unveiling the underlying structure of axial-vector bottom-charm tetraquarks in the light of their magnetic moments

The magnetic moment yields an excellent framework to explore the inner structure of particles determined by the quark-gluon dynamics of QCD, as it is the leading-order response of a bound system to a weak external magnetic field. Motivated by this, in this study, the magnetic moments of possible axial-vector Tbcu¯u¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {T}_{bc\\overline{u}\\overline{u}} $$\\end{document}, Tbcd¯d¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {T}_{bc\\overline{d}\\overline{d}} $$\\end{document}, and Tbcu¯d¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {T}_{bc\\overline{u}\\overline{d}} $$\\end{document} tetraquarks are obtained with the help of light-cone QCD sum rules. For this purpose, we assume that these states are represented as a diquark-antidiquark picture with different structures and interpolating currents. The magnetic moment results derived using different diquark-antidiquark configurations differ substantially from each other. This can be translated into more than one tetraquark state with the same quantum number and quark content yet possessing different magnetic moments. From the numerical results obtained, we have concluded that the magnetic moments of the Tbc states can project their inner structure, which can be used for their quantum numbers and quark-gluon organization. The contribution of individual quarks to the magnetic moments is also analyzed for completeness. We hope that our predictions of the magnetic moments of the Tbc tetraquarks, together with the results of other theoretical investigations of the spectroscopic parameters and decay widths of these interesting tetraquarks, may be valuable in the search for these states in future experiments and in unraveling the internal structure of these tetraquarks.

High-Resolution Crossed-Beam Dynamics Studies of the D + Para-H2 → HD + H Reaction at 1.21 eV.

Understanding kinetic isotope effects is important in the study of the reaction dynamics of elementary chemical reactions, particularly those involving hydrogen atoms and molecules. As one of the isotopic variants of the hydrogen exchange reaction, the D + para-H2 reaction has attracted much attention. However, experimental studies of this reaction have been limited primarily due to its strong experimental background noise. In this study, by using the velocity map ion imaging method and the near-threshold ionization technique, together with improvements on the vacuum condition in the vicinity of the collision zone, background noise was reduced significantly, and quantum state-resolved differential cross sections (DCSs) for the D + para-H2 reaction at a collision energy of 1.21 eV were acquired in a crossed molecular beams experiment. Interestingly, clear rotational state-dependent angular distributions were noticed in the quantum state-resolved DCSs. The most intense peak's positions for HD (v', j') products shift to different scattering directions as the product's ro-vibrational quantum number increases. Two different microscopic reaction mechanisms are found to be involved in this reaction for HD products in different vibrational states. The results show a direct correlation between the scattering angle and the product's rotational quantum number, revealing that the contributions of impact parameters are strongly influenced by the corresponding centrifugal barrier.

Origin of regularity in different nuclei from the viewpoint of the effective quadrupole deformation and triaxiality

This paper presents a theoretical investigation of the possible relation between the regularity of nuclei and the quadrupole deformation of different levels (and also triaxiality). The present paper aims to uncover the underlying physical reasons for this regularity. To this aim, we calculated the effective quadrupole deformation of different levels using the interacting boson model. Also, different ratios between the quadrupole deformations of the energy levels in the ground, beta, and gamma bands are defined. The results for the energy levels confirm the correctness of labeling these states by the quantum numbers of U(5) and SU(3) dynamical symmetry limits (and also the extraction processes). Also, we observed a repetition pattern for these ratios for regular nuclei. Of course, the regularity and sameness of repetition patterns for the levels of the rotational bands are more than the levels of the ground band. For further study, we analyzed the effective quadrupole deformation values of different levels of regular nuclei using random matrix theory. The results show a strong statistical correlation for these quantities and confirm the observed repetition pattern. Also, the results of our studies showed that regular nuclei have triaxial properties.

Semi-chiral operators in 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 gauge theories

We discuss the properties of quarter-BPS local operators in four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 supersymmetric Yang-Mills theory using the formalism of holomorphic twists. We study loop corrections both to the space of local operators and to algebraic operations which endow the twisted theory with an infinite symmetry algebra. We classify all single-trace quarter-BPS operators in the planar approximation for SU(N) gauge theory and propose a holographic dual description for the twisted theory. We classify perturbative quarter-BPS operators in SU(2) and SU(3) gauge theories with sufficiently small quantum numbers and discuss possible non-perturbative corrections to the answer. We set up analogous calculations for some theories with matter.

Theory of electric field effect on the optical properties of elliptical quantum wire

In the approximation of the effective mass, the electric field effect on the optical properties of the elliptical quantum wire (EQW) was investigated. In an elliptic coordinate system, exact solutions of the Schrödinger equation for an electron in an EQW with hard walls are obtained. The electron energy spectrum consists of even and odd energies states, whose wave functions are expressed through even and odd Mathieu functions of the first kind. Using these solutions, an orthonormal basis was constructed. The influence of the electric field perpendicular to the quantum wire and parallel to the ellipse’s major axis on the energies and oscillator strength of quantum electron transitions was calculated using the matrix method. It is shown that the ellipticity of the quantum wire leads to the removal of the degeneracy of the energy spectrum of quasiparticles since the energies of even and odd electronic states depend differently on the ratio of the EQW semi-axes. The electron’s ground state is the even state, which is nondegenerate because there is no corresponding odd state. The electric field has a greater effect on energy states with a lower value of the magnetic quantum number. As the electric field strength increases, the energies of even and odd states shift to the region of lower energies.

Новая модель эволюции Вселенной

Experiments and properties of low-energy nuclear reactions are presented.The existence of new ground states in the hydrogen atom, in the helium ion, and other hydrogen-like atoms located in a strong magnetic field at the appearance of third spatial oscillatory quantum number is shown. On the example of a transhelium atom, the possibility of pairing atomic electrons into an orthoboson is considered. The possibility of generating strong and ultra-strong magnetic fields in cosmic absolute plasma in the Photon era has been demonstrated, in which electrons recombine with protons and helium nuclei with the transition to transhydrogen and transhelium atoms. Transatoms combine into transmolecules and enter into multinuclear, radiation-free, low-energy reactions.The time of constant, natural nucleosynthesis has begun.The nucleosynthesis of carbon, nitrogen and oxygen atoms, when they were overwhelmingly surrounded by hydrogen atoms, led after the era of Recombination to intensive organic and bioorganic synthesis, which resulted in the origin of life and filling the entire Universe with that life. Low-energy nuclear reactions that occur in stars have been demonstrated.The possibility of natural nucleosynthesis occurring on Earth is shown.

Understanding Bonding Nature of α‐Keggin Polyoxometalates [XW12O40]n− (X = Al, Si, P, S): A Generalized Superatomic Perspective

α‐Keggin polyoxometalates (POMs) [XW12O40]n− (X = Al, Si, P, S) are widely used in batteries owing to their remarkable redox activity. However, the mechanism underlying the applications appears inconsistent with the widely accepted covalent bonding nature. Here, first‐principles calculations show that XW12 are core–shell structures composed of a shell and an XO4n− core, both are stabilized by covalent interactions. Interestingly, owing to the presence of a substantial number of electrons in W12O36 shell, the frontier molecular orbitals of XW12 are not only strongly delocalized but also exhibit superatomic properties with high‐angular momentum electrons that do not conform to the Jellium model. Detailed analysis indicates that energetically high lying filled molecular orbitals (MOs) have reached unusually high‐angular momentum characterized by quantum number K or higher, allowing for the accommodation of numerous electrons. This attribute confers strong electron acceptor ability and redox activity to XW12. Moreover, electrons added to XW12 still occupy the K orbitals and will not cause rearrangement of the MOs, thereby maintaining the stability of these structures. Our findings highlight the structure–activity relationship and provide a direction for tailor‐made POMs with specific properties at atomic level.