High-precision Theoretical Calculations of the Full Core Plus Correlation Method for the Radial Behaviour of the Lithium-like Systems
|Course||Atomic and Molecular Physics|
|Keywords||the electron density at the nucleus radial expectation values Fermicontact term orbital term the external electric field|
Recently, the high-precision theoretical calculations for the atomic systems havereceived considerable attention. On the one hand, it is necessary for the needs of theother relative research fields. On the other hand, the large scale variationalcalculations for the many-body systems become possible in recent years. Lithium-likeions with a1s2-core are the most fundamental few-body systems, so the structure andproperty of lithium-like systems will be important research object.The full-core plus correlation (FCPC) method has been used to calculate theenergy levels, the fine structure, the dipole polarizability and the gJ–factors et al. oflithium-like systems to a high precision. The calculated results agree with the valuesof theory and experiment very well. The FCPC method not only effectively considersthe correlation effect of electrons, relativistic effect, mass polarization effect andquantum-electrodynamic effect, but also overcomes the difficulty of the slowconvergence rate which appears in the course of dealing with atomic systems with a1s2-core by using the traditional CI method. Thus it has becomed a very effectivetheoretical method to realize high-precision theoretical calculations for the structureand property of lithium-like systems with a1s2-core. In this work, using the FCPCmethod, we have systematically studied some important physical pocess, in which thecorrelation effect is very significant. Except the energy levels and oscillator strength,we also have performed systematically the theoretical investigations for the electroniccharge density, the radial exepctation values, the hyperfine structure parameters andthe electrostatic potential.Based on the numerical results, we have obtained the following conclutions:1. we have calculated the electron density at the nucleus, ρ(0), and radialexpectation values,〈r~k〉(k=-2-10), for the lithium isoelectronic sequence from Z=3-33.At present there are only radial expectation values for the ground state of the lightatomic systems available in the literature. Most of our calculated results agree wellwith those obtained by using other theoretical methods in the literature. By usingthese obtained expectation values, some accurate inequalities of the electron density atthe nucleus, ρ(0), and radial expectation values <rk> derived by Angulo and Dehesafor these systems are examined and extended. On the other hand, these inequalitiescan be again used to examine the precision of radial expectation values. It is foundthat our results accord with these inequalities very well. This shows that FCPC wave function can give satisfactory results whether in long range region or in short rangeregion of the configuration space. It can be said that this wave function is veryaccurate in full configuration space. By using these wave functions we have alsocalculated some expectation values of other operators, and compared with the data inthe literature. The results show that our FCPC wave function is accurate and credibleall the same.2. Considering the fact that the hyperfine structure parameters sensitively denpendon the wave functions used, we have investigated the orbital term and Fermi contactterm in detail and compared with the data in the literature. The results show that ourFCPC wave function is accurate and credible all the same.3. The approach of a slow HCI to a surface presents an unusual experimentalsituation. The electrostatic pull of the HCI can be so great that it begins removingelectrons from the surface even when it is dozens of atomic diameters away. Usingthe FCPC wave fuctions, we have calculated the electrostatic potential of the field,We have found that the potential trend are close to each other as the r increasing.In summary, the studies in this work are very significant for the extension andimprovement of the full core plus correlation method.