Energy calculations of the (2P2 1D); (3D2 1G) and (4F2 1I) doubly excited states of helium isoelectronic sequence (z ≤ 20) via the modified atomic orbital theory

We report in this paper the total energies of the 2p2 1D, 3d2 1G, 4f2 1I doubly excited states of Helium isoelectronic sequence with nuclear charge Z ≤ 20. Calculations are performed using the Modified Atomic Orbital Theory (MAOT) [1;2] in the framework of a variational procedure. The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function [3] combining with Hylleraas-type wave function [4]. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This proposed MAOT variational procedure, leads to accurate results in good agreement as well as with available other theoretical results than experimental data. In the present work, a new correlated wave function is presented to express analytically the total energies for each 2p2 1D, 3d2 1G, 4f 2 1I Doubly Excited States (DES) in the He-like systems. The present accurate data may be a useful guideline for future experimental and theoretical studies in the (nl2 ) systems.

COMPLEX-ROTATION CALCULATIONS FOR DOUBLY EXCITED STATES (Nℓ N’ℓ’) 2S+1L ᴨ [(2≤N≤ 3 ) ; ( 3 ≤N’≤4); (0 ≤ ℓ ≤ 2 ) AND ( 0 ≤ ℓ’ ≤ 2)] OF HELIUM ISOELECTRONIC SERIES

In this paper, we report the energies and resonant widths of the [(2s3s 1Se and 2s3s 3Se) (2s4s 1Se and 2s4s 3Se) (2s3p 1P0 and 2s3p 3P0) (2s4p 1P0 and 2s4p 3P0) (2p3p 1De and 2p3p 3De) (2p4p 1De and 2p4p 3De) (3s4s 1Se and 3s4s 3Se) (3s4p 1P0 and 3s4p 3P0) (3p4p 1De and 3p4p 3De) (3d4d 1Ge and 3d4d 1Ge)] Doubly Excited States of Helium isoelectronic series with nuclear charge Z (2 ≤ Z ≤ 10).Calculations are performedusing the Complex Rotation Method (CRM) in the framework of a variational procedure. The purpose of this study required a new correlated hydrogenic radial wave function combined with a Hylleraas wave function. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This proposed variational procedure, leads to accurate results in good agreement with available other theoretical results.The present accurate data may be a useful guideline for future experimental and theoretical studies in the (Nℓ Nℓ) 2S+1Lᴨsystems.

On the Macroscopic Response and Field Statistics in Particulate Composites With Elasto-Plastic Phases and Random Microstructures

In this article, we carry out a theoretical investigation of the macroscopic response and field statistics in two-phase particulate composites with elasto-plastic constituents and random microstructures under cyclic loading conditions. To this end, we make use of the “incremental variational homogenization” (IVH) procedure of Agoras et al. (2016, “Incremental Variational Procedure for Elasto-Viscoplastic Composites and Application to Polymer- and Metal-Matrix Composites Reinforced by Spheroidal Elastic Particles,” Int. J. Solid Struct., 97–98, pp. 668–686) and corresponding unit cell finite element simulations. Results are obtained for statistically isotropic distributions of spherical particles and for “spheroidal distributions” of spheroidal particles. It is shown analytically that the IVH estimate of Agoras et al. and that of Lahellec and Suquet (2013, “Effective Response and Field Statistics in Elasto-Plastic and Elasto-Visco-Plastic Composites Under Radial and Non-Radial Loadings,” Int. J. Plasticity, 42, pp. 1–30) are equivalent. In addition, it is illustrated by means of specific numeral comparisons that the IVH estimate is also equivalent (to within numerical accuracy) to the corresponding estimates of Idiart and Lahellec (2016, “Estimates for the Overall Linear Properties of Pointwise Heterogeneous Solids With Application to Elasto-Viscoplasticity,” J. Mech. Phys. Solids, 97, pp. 317–332) and Lucchetta et al. (2019, “A Double Incremental Variational Procedure for Elastoplastic Composites With Combined Isotropic and Linear Kinematic Hardening,” Int. J. Solid Struct., 158, pp. 243–267). Furthermore, it is shown in the context of specific exact results for composite materials with lamellar microstructures that the elastic–plastic coupling and the Bauschinger effect are the macroscopic manifestations of the incompatibility of the local elastic strains. Local strain hardening is incorporate in the IVH model. The predictions of the IVH model for the macroscopic response of particulate composites are found to be in good agreement with the corresponding numerical results, in general. For the extreme cases of rigidly reinforced composites and porous materials, however, the IVH model fails to capture the elastic–plastic coupling and the Bauschinger effect. The underlying reasons for this shortcoming are discussed and a strategy toward the improvement of the IVH model is proposed.

Variational procedure leading from Davidson potentials to the E(5)and X(5) critical point symmetries

Davidson potentials of the form β^2 + β0^4/β^2, when used in the original Bohr Hamiltonian for γ-independent potentials bridge the U(5) and 0(6) symmetries. Using a variational procedure, we determine for each value of angular momentum L the value of β0 at which the derivative of the energy ratio RL = E(L)/E(2) with respect to β0 has a sharp maximum, the collection of RL values at these points forming a band which practically coincides with the ground state band of the E(5) model, corresponding to the critical point in the shape phase transition from U(5) to Ο(6). The same potentials, when used in the Bohr Hamiltonian after separating variables as in the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational procedure leading to a band which practically coincides with the ground state band of the X(5) model, corresponding to the critical point of the U(5) to SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

Computational analysis of the far infrared spectral region of various deuterated varieties of ethylene glycol

The FIR spectrum of three deuterated isotopologues of ethylene glycol are studied using highly correlated ab initio methods, VPT2 theory and a variational procedure of reduced dimensionality.

Critical point for the Deformation Dependent Mass model through a variational procedure

The recently introduced Deformation-Dependent Mass model is combined with a variational approach to the Bohr Hamiltonian in order to describe transitional nuclei. The results of this procedure are demon- strated for the ‘spherical to γ-unstable’ and the ‘spherical to deformed’ transitional classes, which corre- spond to the E(5) and X(5) solutions.