Or acquiring the radial functions and the mixing coefficients. Additional, we performed RCI calculations by considering the Breit and quantum electrodynamic (QED) corrections within the Dirac oulomb Hamiltonian. The transition probabilities are computed in the matrix element of dipole operator in the electromagnetic field.Table 1. Configurations of your initial and final states and the CSFs in non-relativistic notations. Ions Initial State Final State even Xe7+ 4d10 5s 4d9 (5s5p, 4f5s) odd CSFs 4d10 (5s, 5d, 6s, 6d), 4d9 (5s5d, 5s6s, 5s7s, 5s2 , 5p2 ) 4d10 (4f, 5p, 6p), 4d9 (4f5s, 5s5p, 5s5f, 5s6f, 5p5d) 4d10 , 4d9 (5s, 5d, 6s, 6d, 7s, 7d), 4d8 (5s2 , 5p2 , 5d2 ) 4d9 (4f, 5p, 5f, 6p, 6f, 7p, 7f) 4d9 , 4d8 (5s, 5d, 6s, 6d, 7s, 7d), 4p5 4d9 (5p, 5f), 4d7 (5s2 , 5p2 , 5d2 , 5f2 , 5s5d, 5s6s, 5s6d, 5p5f) 4d8 (4f, 5p, 5f, 6p, 6f, 7p), 4d7 (5s5p, 5s5f, 5s6p), 4p5 4d10 , 4d6 4f3 4d8 , 4d7 5d, 4p5 4d8 (5p, 5f), 4d6 (5s2 + 5p2 ) 4d7 (4f, 5p, 5f, 6f), 4p5 4d9 , 4p5 4d8 5d, 4d5 4feven Xe8+ 4d10 4d9 (4f, 5p, 5f, 6p, 6f, 7p) oddeven Xe9+ 4d9 4d8 (4f, 5p), 4p5 4d10 oddeven Xe10+ 4d8 4d7 (4f, 5p), 4p5 4d9 oddWe further use the bound state wavefunctions of the ion within the relativistic distorted wave theory to figure out the electron influence excitation parameters. The T-matrix in theAtoms 2021, 9,four ofRDW approximation for excitation of an N electron ion from an initial state a to a final state b could be written as [22]:RDW Tab (b , Jb , Mb , ; a , Ja , Ma , a ) = – V – Ub ( N + 1)|A+ . a b(two)Right here, Ja(b) , Ma(b) denote the total angular momentum quantum number and its related magnetic quantum number within the initial(final) state, whereas, a(b) represents additional quantum numbers expected for exclusive identification on the state. a(b) refers to the spin projection from the incident(scattered) electron. A could be the anti-symmetrization operator to think about the exchange on the projectile electron using the target electrons and Ub is the distortion potential which is taken to be a function of your radial co-ordinates of the projectile electron only. In our calculations, we select Ub to become a spherically averaged static potential of the excited state of ion. Within the above Equation (2), V will be the Coulomb interaction potential among the incident electron and the target ion. The wave function a(b) represents the solution on the N-electron target wave functions a(b) along with a projectile electron distorted wave function Fa(b) in the initial `a’ and final `b’, states, which is: a(b) = a(b) (1, 2, …, N )) Fa(b) (k a(b) , N + 1).+(-) +(-) +(-) +(-)(3)Here, `+(-)’ sign denotes an outgoing(incoming) wave, even though k a(b) will be the linear momentum from the projectile electron inside the initial(final) state. Equation (two) consists of complete information regarding the excitation method. We, on the other hand, are considering computing only the integrated cross section which can be obtained by taking Phenolic acid Purity square from the mode value from the complex T-matrix with appropriate normalization, as expressed beneath: ab = (2 )four kb 1 k a 2(2Ja + 1)Mb b M a aRDW | Tab (b , Jb , Mb , ; a , Ja , Ma , a )|two d .(four)three. Benefits and Discussion 3.1. Atomic-Structure Calculations We have applied GRASP2K code [21] to execute MCDF and RCI calculations to receive energy levels, wavelengths and transition rates of Xe7+ e10+ ions. Our power values are presented and compared with other theoretical and experimental benefits by means of Tables two for the four ions. The fine-structure states are represented in the relativistic j – j coupling scheme in which all s.
