Lithium-like Atoms Research Articles

High pressure effects on the excitation spectra and dipole properties of Li, Be+, and B2+ atoms under confinement

Properties of atoms and molecules undergo significant changes when subjected to spatial confinement. We study the excitation spectra of lithium-like atoms in the initial 1s22s electronic configuration when confined by an impenetrable spherical cavity. We implement Slater’s X-α method in Hartree–Fock theory to obtain the excitation spectrum. We verify that as the cavity size decreases, the total, 2s, 2p, and higher excited energy levels increase. Furthermore, we confirm the existence of crossing points between ns–np states for low values of the confinement radius such that the ns → np dipole transition becomes zero at that critical pressure. The crossing points of the s–p states imply that instead of photon absorption, one observes photon emission for cavities with radius smaller than the critical radius. Hence, the dipole oscillator strength associated with the 2s → 2p transition becomes negative, and for higher pressures, the 2s → 3p dipole oscillator strength transition becomes larger than unity. We validate the completeness of the spectrum by calculating the Thomas–Reiche–Kuhn sum rule, as well as the static dipole polarizability and mean excitation energy of lithium-like atoms. We find that the static dipole polarizability decreases and exhibits a sudden change at the critical pressure for the absorption-to-emission transition. The mean excitation energy increases as the pressure rises. However, as a consequence of the critical transition from absorption to emission, the mean excitation energy becomes undetermined for higher pressures, with implications for material damage under extreme conditions. For unconfined systems, our results show good to excellent agreement with data found in the literature.

Applications of four-body exponentially correlated functions

We demonstrate the applicability of four-body exponentially correlated functions for the accurate calculations of relativistic effects in lithium-like atoms and present results for matrix elements of various operators which involve negative powers of interparticle distances.

Crossover phenomena and resonances in quantum systems

tonian that exhibit resonances. We show the existence of a crossover phenomenon for the energy spectrum; the transition from a bound state to a continuum is a ‘‘second-order phase transition’’ in one region and a ‘‘firstorder phase transition’’ in another region. As the parameters varied, the numerical value of the critical exponent of the energy levels changed from two to one. In the zone where the critical exponent equals one, the system has narrow resonances and they disappear when the exponent is two. The method has potential applicability in predicting stable and metastable atomic and molecular states. We also show that finite-size scaling methods are capable of detecting multicritical points. DOI: 10.1103/PhysRevA.64.062502 PACS number~s!: 31.15.2p The finite-size scaling method ~FSS! was formulated in statistical mechanics to extrapolate information obtained from a finite system to the thermodynamic limit @1,2# .I n quantum mechanics, when using variation methods, one encounters the same finite-size problem in studying the critical behavior of a quantum Hamiltonian H(l 1 , . .., l k )a s a function of its set of parameters $l i%. In this context, critical means the values of $l i% for which a bound-state energy is nonanalytic. In this paper, a critical point l c is defined as the point where a bound-state energy becomes absorbed or degenerate with a continuum. In the variational calculations, the finite-size corresponds to the number of elements in a complete basis set used to expand the exact wave function of a given Hamiltonian @3#. The problem of what happens when the continuum ‘‘swallows’’ a bound state has a long history with many important results and was reviewed in Ref. @3#. Recently, Neirotti, Serra, and Kais have developed the FSS method to calculate atomic and molecular critical parameters @4,5#. In particular, FSS calculations for two and three electron atoms gave very accurate results for the critical nuclear charges @6,7#. These results have shown that the analytical behavior of the energy as a function of the nuclear charge for lithiumlike atoms is completely different from that of heliumlike atoms. Analogy with standard phase transitions show that for helium, the transition from a bound state to a continuum is ‘‘first-order,’’ while lithium exhibits a ‘‘secondorder phase transition.’’ For the helium sequence, the question of whether or not the radius of convergence, of the 1/Z expansion for the energy, is the same as the variational critical energy was discussed by several authors @ 8‐1 0#. The coincidence between the critical point and the radius of convergence was conjectured by Reinhardt using arguments based on dilatation analyticity @11# and later rigorously confirmed, analytically and numerically, by Baker et al. @12#. Our results for the helium sequence using the finite-size scaling method were in complete agreement with the Reinhardt

Data collapse for the Schrödinger equation

We present a data-collapse study for quantum few-body problems. Our data strongly support a recent hypothesis for the application of the finite-size scaling approach for the calculation of the critical parameters for the few-body Schrödinger equation. We test the data collapse using very accurate calculations of the one-body Yukawa potential. This powerful tool is used to obtain an estimation of the critical exponents for the lithium-like atoms.

Nuclear recoil corrections to the 2p3/2 state energy of hydrogen-like and high-Z lithium-like atoms in all orders in alpha Z

The relativistic nuclear recoil corrections to the energy of the 2p3/2 state of hydrogen-like and the (1s)22p3/2 state of high-Z lithium-like atoms in all orders in alpha Z are calculated. The calculations are carried out using the B-spline method for the Dirac equation. For low Z the results of the calculation are in good agreement with the alpha Z-expansion results. It is found that the total nuclear recoil contribution to the energy of the (1s)22p3/2-(1s)22s transition in lithium-like uranium constitutes -0.09 eV.

Hyperfine structure of hydrogenlike and lithiumlike atoms.

The hyperfine splitting values of the ground state of the hydrogenlike atoms $^{13}\mathrm{C}^{5+}$, $^{14}\mathrm{N}^{6+}$, $^{17}\mathrm{O}^{7+}$ and the lithiumlike atoms $^{7}\mathrm{Li}^{0}$, $^{14}\mathrm{N}^{4+}$, $^{19}\mathrm{F}^{6+}$, $^{23}\mathrm{Na}^{8+}$, $^{25}\mathrm{Mg}^{9+}$, $^{27}\mathrm{Al}^{10+}$, $^{29}\mathrm{Si}^{11+}$, $^{35}\mathrm{Cl}^{14+}$, $^{57}\mathrm{Fe}^{23+}$ are calculated. The calculations of the lithiumlike ions (Z\ensuremath{\ge}7) are based on a combination of the 1/Z perturbation theory and the configuration interaction Hartree-Fock method. The relativistic corrections are calculated in the zeroth and first orders in 1/Z. The nuclear charge and magnetization distribution corrections and the radiative corrections are taken into account. The uncertainty of the calculations is estimated to be \ensuremath{\sim}0.02% for the hydrogenlike ions and \ensuremath{\sim}0.06% for the lithiumlike ions, except $^{57}\mathrm{Fe}^{23+}$, for which the uncertainty is about 0.15%. The hyperfine structure constant of the ground state of Li is calculated to be A=401.5(4) MHz. The results of the calculations are compared with the theoretical values obtained with other methods and with experiment.

Relativistic nuclear recoil corrections to the energy levels of hydrogenlike and high-Z lithiumlike atoms in all orders in alpha Z.

The relativistic nuclear recoil corrections to the energy levels of low-lying states of hydrogenlike and high-Z lithiumlike atoms in all orders in \ensuremath{\alpha}Z are calculated. The calculations are carried out using the B-spline method for the Dirac equation. For low Z the results of the calculation are in good agreement with the \ensuremath{\alpha}Z-expansion results. It is found that the nuclear recoil contribution, in addition to Salpeter's contribution, to the Lamb shift (n=2) of hydrogen is -1.32(6) kHz. The total nuclear recoil correction to the energy of the (1s${)}^{2}$${\mathit{p}}_{1/2\mathrm{\ensuremath{-}}}$(1s${)}^{2}$2s transition in lithiumlike uranium constitutes -0.07 eV and is largely made up of QED contributions.

Possible modes of angular motion in 4S degrees triply excited states

A model where the radial freedoms are frozen is used to simulate the 4S degrees triply excited states of lithium-like atoms with all electrons in the same shell. It is confirmed by direct observation of the wavefunction that the 4S degrees states prefer the equilateral triangle configuration. However, since the coplanar structure is prohibited by the 4S degrees symmetry, the plane of this triangle does not contain the nucleus. Besides, the sharp isosceles and the flattened isosceles shapes are found to appear in higher states. Different modes of motion are found around the equilateral triangle shape, and they are coupled in a specific manner. Accordingly, different types of collisions are found, namely the three-body head-on collision, planar two-body collision, and the quasi-three-body collision. Repeated occurrence of three-body head-on collisions is a basic mode and exists in all 4S degrees states. It was shown that this mode is associated with a periodic solution of the corresponding classical mechanisms system.

EFFECTIVE ACTION AND THE ATOMIC ENERGY LEVELS

Applying the recently developed method of the on-shell expansion of the effective action, a compact equation is derived in the framework of the quantum electrodynamics which determines the energy levels of the hydrogen-, helium- and lithium-like atoms. Since they are derived systematically, our method provides a transparent formal derivation of the equations which includes the full order corrections.

Electron-impact ionization cross sections for highly ionized hydrogen- and lithium-like atoms

Electron-impact ionization cross sections for highly ionized atoms in the hydrogen and lithium isoelectronic sequences have been computed in several variants of the Coulomb-Born and distorted-wave approximations. Electron exchange in the transition matrix element and Coulomb distortion of the partial waves were found to be important. The results are compared to recent crossed-beam experimental data and to other theoretical predictions.

Doublet and Triplet Separations in Optical Spectra as Evidence whether Orbits penetrate into the Core

Landé has indicated a connection between the “relativity” doublets of X-ray spectra, and the doublets and triplets of optical spectra, and so has obtained a formula for the separation of optical doublets and triplets. This formula can only be expected to hold if the orbit of the series electron penetrates into the core, so it may be possible to obtain evidence on the question whether an orbit penetrates from the doublet or triplet separation of the corresponding term.From this evidence it is concluded that, except for lithium-like atoms, p terms of all known spectra correspond to penetrating orbits; this disagrees with Bohr's assignment of quantum numbers for those terms of the spectra of neutral atoms of the Cu and Zn sub-groups. For d terms the evidence is not so definite, but it seems possible that for Cs I and Tl I the d terms correspond to penetrating orbits, in disagreement with Bohr's assignment. It is shown that the Landé formula seems to hold approximately for separations in multiplet spectra when the terms belong to a sequence of the Rydberg type.Ideas suggested by Heisenberg in a recent paper would involve some modifications of the interpretation of the magnitudes of doublet separations, but at least the conclusions as to the p orbits penetrating still stand.

The Spectra of some Lithium-like and Sodium-like Atoms

It is possible to obtain approximate theoretical relations between the spectra of different atoms ionised to such an extent that they possess the same electron structure. In this paper these relations are used to extrapolate values of the terms of the spectra of various lithium-like and sodium-like atoms.From the terms so estimated lines can be calculated, and in many cases correlated with lines observed by Millikan and Bowen in the hot spark spectrum of the corresponding element. Revised term values can then be calculated from the lines so identified.The spectra of lithium-like atoms treated in this way include those from Be II up to O VI, and those of sodium-like atoms, the spectra P V and S VI.