Modern Physics Letters A

The automorphism group of the spinor space of the standard model introduces the permutations of S₃ in addition to the gauge groups in a unified theory of the elementary particle interactions. The ${\mathrm{\text{S}}}_3$ symmetry will be the basis of a theoretical explanation of the inclusion of a fermion term, which transforms under the spin-$\frac{1}{2}$ representation of the symmetric permutation group, in the Koide relation for charged leptons. This field is identified with the sterile neutrino, and the mass is compatible with experimental bounds.

A normalizable static supersymmetric bound ground state annihilated by the super-generators has got zero number of internal nodes in the framework of one-dimensional supersymmetric quantum mechanics. The super-generator transformations between excited super-partner bound states as combined with the standard technique of Wronskian provide an elegant and self-sufficient way to derive the equality of internal nodes amount to the number of consequent excitations.

In the Robe’s restricted three-body problem, we have considered the motion of the test particle which is moving inside the outermost layer of the heterogeneous body. This heterogeneous body has N layers with different densities and is filled with viscous fluid. The test particle which is taken as the third (or infinitesimal) body is moving under the influence of the heterogeneous body (primary) and point mass (secondary). We are motivated from Ansari, where the linear stability and other important properties of this specific model have been discussed. In this paper, we have extended their work and discussed here the nonlinear stability of the non-collinear stationary points $L_4$ and $L_5$. Therefore, using the Arnold–Moser theorem (Kolmogorov–Arnold–Moser theory), we have done our analysis on the nonlinear stability and obtained significant results.

This research paper examines the feasibility and stability of compact stars in the context of $f(\mathcal{𝒬})$ theory, where $\mathcal{𝒬}$ represents the non-metricity scalar. To achieve this objective, a static spherical line element is assumed in the interior region and the Schwarzschild spacetime is used in the exterior region of the star. The unknown constants are determined by using the Darmois junction conditions. We consider a specific model of this theory to investigate the viability of compact stars through various physical quantities such as matter contents, energy bounds, anisotropy and state parameters. The stability states for the stellar objects under consideration are determined by the speed of sound and adiabatic index, respectively. The resulting data indicate that the compact stars in this modified framework are physically viable and stable.

In this paper, we systematically investigate the cluster decay half-lives of heavy nuclei using the Wentzel–Kramers–Brillouin method and Bohr–Sommerfeld quantization condition for the Morse molecular potential. We determine the optimal nuclear potential parameters that best fit the experimental data of known cluster decay half-lives. Subsequently, we theoretically calculate the cluster decay half-lives for the heavy nuclei lacking experimental decay half-lives. Our findings reveal that the Morse model is highly effective in explaining the decay half-lives of the heavy nuclei, particularly when utilizing two degrees of freedom. This approach produces results that match the accuracy of empirical models found in the existing literature. Theoretical determinations of cluster decay half-lives with optimally derived model parameters are expected to guide future experimental studies.

Singularities in Newton’s gravitation, in general relativity (GR), in Coulomb’s law, and elsewhere in classical physics, stem from two ill conceived assumptions: (a) there are point-like entities with finite masses, charges, etc., packed in zero volumes, and (b) the non-quantum assumption that these point-likes can be assigned precise coordinates and momenta. In the case of GR, we argue that the classical energy–momentum tensor in Einstein’s field equation is that of a collection of point particles and is prone to singularity. In compliance with Heisenberg’s uncertainty principle, we suggest to replace each constituent of the gravitating matter with a suitable quantum mechanical equivalent, here a Klien–Gordon (KG) or a Yukawa-ameliorated version of it, YKG field. KG and YKG fields are spatially distributed entities. They do not end up in singular spacetime points nor predict singular blackholes. On the other hand, YKG waves reach infinity as $\frac{1}{r}{e}^{-(\kappa \pm ik)r}$. They create the Newtonian $r^{-2}$ term as well as a non-Newtonian $r^{-1}$ force. The latter is capable of explaining the observed flat rotation curves of spiral galaxies, and is interpretable as an alternative gravity, a dark matter scenario, etc. There are ample observational data on flat rotation curves of spiral galaxies, coded in the Tully–Fisher relation, to support our propositions.

In this paper, we study the nuclear charge radius for 804 nuclei with $Z,N\ge 12$ in the CR2013 database (excluding the isotopic chains of Tb, Tm, Lu and Cm). By adding the Casten factor for the $Z^{1/3}$ law empirical formula to calculate the charge radii of these nuclei, the root mean square deviation (RMSD) between calculated and experimental values is 0.0530fm. A new empirical formula is then obtained by correcting using neutron–proton ratio factor $N/Z$ and the neutron factor $1/N$. The RMSD between the calculated values obtained using this new empirical formula and experimental values is 0.0197fm. The new empirical formula reproduces well not only the factors’ (i.e. the $N/Z$ and $1/N$ factors) dependence on charge radii, but also the kinks of charge radii at the neutron magic numbers N = 82 and 126 for some isotope chains. Furthermore, this paper introduces the Back propagation (BP) neural network approach using the Casten factor, the $N/Z$ factor and the $1/N$ factor as input variables to train the model. The RMSD between the calculated values obtained by the neural network model II and the experimental values is only 0.0098fm. Compared to the empirical formula, the RMSD of the neural network model is reduced by 50%. The above research results based on the improvement of the $Z^{1/3}$ law formula indicate that the relation and models proposed in this paper have accuracy and reliability.

Based on the widely recognized Karmarkar condition, or embedding class 1 technique, this work searches for charged wormhole solutions with spherical symmetry for the Einstein field equations. With charged traversable wormhole geometry, we use the Karmarkar condition to derive a wormhole shape function. The obtained shape function satisfies the necessary traversability conditions. In addition, we discuss the embedding diagram in Euclidean space, in both two and three dimensions, and verify the proper radial distance to display the wormhole configurations. Next, we examine a model with a quintessence field and a second field that represents regular matter and has an anisotropic pressure, providing energy for developing wormhole spacetime. Then, we obtain the Einstein field equations to verify the energy conditions. After that, we take three density profiles, which are the pseudo-isothermal density profile, the Navarro–Frenk–White density profile, and the density profile of Einasto Dark Matter of the galactic halo, and observe that for all of these density profiles, the NEC is violated. Hence, wormhole structures are firmly maintained by the composition of exotic matter within them. Furthermore, we use the volume integral quantifier to determine the necessary quantity of exotic matter near the wormhole throat.