A many-body calculation of the hyperfine interaction in the lowest2S and2P states of li-like systems

A non-relativistic perturbation method of Brueckner-Goldstone type is used to calculate the hyperfine interactions in the lowest² S and² P states of the Li-like systems, Li, Be⁺, B²⁺, C³⁺, N⁴⁺, O⁵⁺ and F⁶⁺. The effect of the polarization of the closed shell is treated to all orders of perturbation, while the correlation effect is calculated in the lowest order, i.e. in the third order of the perturbation expansion. Experimental data are at present available only for Li, Be⁺ and F⁶⁺, and the agreement with the calculated values is in these cases very good, usually within the experimental uncertainties. This implies that the predictions made in the remaining cases should be quite reliable, which may simplify the experimental determination of these quantities. Theoretical values are also given for the quadrupole interaction, which can be used to determine the nuclear quadrupole moments, when accurate experimental information becomes available.     

Theory of hyperfine interactions in lithiumlike systems

The valence, exchange core polarization and correlation contributions to the magnetic hyperfine constants in the ground states of the lithiumlike ions Be⁺, B²⁺, C³⁺, N⁴⁺, O⁵⁺, F⁶⁺, Ne⁷⁺ and Bi⁸⁰⁺ are investigated using relativistic many-body perturbation theory. Radiative corrections have also been studied. Comparison is made with available experimental data and the trends in the various contributions are analyzed.     

On the hyperfine structures of the ground state(s) in the <Superscript>6</Superscript>Li and <Superscript>7</Superscript>Li atoms

The hyperfine structure of the ground 2²S-states of the three-electron atoms and ions is investigated. By using our recent numerical values for the doublet electron density at the atomic nucleus, we determine the hyperfine structure of the ground (doublet) 2²S-state(s) in the ⁶Li and ⁷Li atoms. Our predicted values (228.2058 and 803.5581 MHz, respectively) agree well with the experimental values 228.20528(8) MHz (⁶Li) and 803.50404(48) MHz (⁷Li [R.G. Schlecht and D.W. McColm, Phys. Rev. 142, 11 (1966)]). The hyperfine structures of a number of lithium isotopes with short lifetimes, including ⁸Li, ⁹Li, and ¹¹Li atoms are also predicted. The same method is used to obtain the hyperfine structures of the three-electron ⁷Be⁺ and ⁹Be⁺ ions in their ground 2²S-states. Finally, we conclude that our approach can be generalized to describe the hyperfine structure in the triplet n³S-states of the four-electron atoms and ions.     

Hyperfine structure measurement of the9Be+ 22 s 1/2 ground state by optical pumping

Thermal⁹Be⁺ (I=3/2) ions are polarized by direct optical pumping in He buffer gas. Observation of?gDF=± 1 transitions yields for the hyperfine splitting frequencyv _hfs(⁹Be⁺, 1s ² 2s ² S _1/2)=1250018(5) kHz. The result is discussed with regard to predictions of recent theoretical calculations and of the Fermi-Segré formula for the ground state hfs of the Li isoelectronic sequence.     

Theoretical calculation for the high pressure properties of alkali fluorides

Abstract

The overlap repulsive potentials of ion pairs (Li ⁺?F^?, Na⁺?F^? and K⁺?F^?) are calculated by means of generalized Heitler-London method and the numerical results are fitted in the Born-Mayer form, i.e. Dexp (—αR), Then the parameter D for each pair potential is modified to satisfy the crystal equilibrium condition at the experimentally known lattice constant. The redetermined repulsive potentials are applied to calculate the cohesive energies, bulk moduli, equations of state and NaC1–to-CsC1 structural phase transition pressures of LiF, NaF and KF crystals. The results obtained are compared with some other theoretical values and the available experimental data, and good agreement is reached.     

相对论效应对类锂离子能级结构及辐射跃迁性质的影响

利用基于多组态Dirac-Hartree-Fock(MCDHF) 理论方法的相对论原子结构计算程序包GRASP2K, 细致计算了中性锂原子、类锂Be⁺, C³⁺, O⁵⁺, Ne⁷⁺, Ar¹⁵⁺, Fe²³⁺, Mo³⁹⁺, W⁷¹⁺及U^{89 +} 离子基组态及较低的激发组态1s²nl (n = 2---4, l =s,p,d,f) 的精细结构能级, 以及各能级间发生电偶极(E1) 自发辐射跃迁的能量、概率及振子强度. 同时, 在非相对论极限下, 计算了其相关原子参数. 通过对相对论及非相对论计算结果的比较, 系统研究了相对论效应对类锂等电子系列离子能级结构及E1跃迁性质的影响, 揭示了随原子核电荷数Z变化时, 跃迁能、振子强度强烈依赖于量子数n, l, j变化的规律; 同时, 目前的计算结果与其他已有的理论计算及实验测量结果进行了比较.     

The decay processes Λ8Li → π− + 8Be1 (∼ 17 MeV)

The branching ratio is calculated for _Λ⁸Li decay to the (2⁺) ⁸Be¹ states near 17 MeV, using intermediate coupling wave functions for _Λ⁸Li and for the relevant ⁸Be¹ states. It is pointed out that this ratio is sensitive primarily to a mixing angle ? in the _Λ⁸Li wave function. Within one standard deviation, the data allow two ranges (+0.05 to +0.25 rad and +1.10 to +1.25 rad) for the value of ?. The further requirement that there also be acceptable agreement between the angular distribution expected for the subsequent ${}^8\text{Be}{}^1\text{(? 17}\text{MeV → 2}{}^4\text{He}$ decay and the data, shifts these allowed ranges for ?, to (+0.13 to 0.40) rad and (+0.9 to +1.2) rad. It is predicted that the dominant transition should be to ⁸Be¹ (16.6 MeV), as is observed to be the case, rather than to ⁸Be¹ (16.9 MeV). The interpretation of these values for ? is discussed in some detail and their implications for intermediate coupling shell-model calculations of Λ-hypernuclear wave functions are considered.     

Theoretical study of hyperfine coupling constants and electron spin g factors for X2Σ+ diatomics from Groups 1 and 2

The ESR parameters of the cations Be⁺ ₂, Mg⁺ ₂, Ca⁺ ₂, BeMg⁺, BeCa⁺, MgCa⁺ and the mixed radicals ZBe, ZMg, ZCa (Z = Li, Na, K), all having a X ²Σ⁺ _u(1σ² _g1σ_u)/X ²Σ⁺(1σ²2σ) ground state, have been studied theoretically. The A _iso and A _dip constants have been calculated with UHF, CISD, MP2, B3LYP, PW91PW91 wavefunctions, and 6–311+G(2df) basis sets. The electron spin g factors (magnetic moment μ_s) have been evaluated from correlated (MRDCI) wavefunctions, using a Hamiltonian based on Breit-Pauli theory with perturbation expansions up to second order, and 6–311 + G(2d) basis sets. As expected for s-rich radicals, the hyperfine spectra are governed by the A _iso terms. Both Δg∥ and Δg⊥ values are negative, but Δg∥ lies close to zero. For Δg⊥, the coupling with 1 ²Π_(u) dominates the sum-over-states expansions. Although the singly occupied MOs (SOMO) are mostly of s character, the |Δg⊥| are relatively large, up to 5200 ppm for cationic, and up to 7850 ppm for neutral radicals. These large values are caused by low excitation energies and high magnetic transition moments, the latter due to the fact that the σ?(s-s) SOMO has the same nodal properties as a pσ orbital. Of the radicals considered here, an ESR spectrum is available only for Mg⁺ ₂. Our theoretical A _iso of ?287 MHz reproduces well the matrix result (-291 MHz). Calculated values of ?10 ppm for Δg∥ and of ?1280 ppm for Δg⊥ give an average 〈Δg〉 = ?860 ppm that lies within the experimental range of ?600(±300) ppm in Ne, and of ?1300(±500) ppm in Ar matrices.     

Experimental and theoretical insight into the cooperativity effect in composite wax powder and ternary complex of coronene with CH4 and Mn+ (Mn+ = Li+, Na+, K+, Be2+, Mg2+ or Ca2+)

The experimental infrared (IR) spectrum of composite wax powder was investigated. The frequency shifts of the C=C anti-symmetrical stretching mode were observed and the experimental cooperativity effect involving Na⁺···π interaction was suggested. In order to further reveal the nature of cooperativity effect, the interaction energies in Mⁿ⁺···coronene···CH₄ (Mⁿ⁺ = Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺ or Ca²⁺) as the model systems of composite wax powder were calculated by using the B3LYP, M06-2X and MP2 methods with 6-311++G^** basis set. The results show that the Mⁿ⁺···π interactions were strengthened upon the formation of ternary complexes. Although the changes of absolute values of the interactions between CH₄ and coronene were not obvious, the relative values were considerably significant upon the formation of ternary complexes. The cooperativity effect was perhaps the reason for the formation of notable advantage of composite wax powder upon the introduction of surfactant with cation into wax powder. Reduced density gradient and atoms-in-molecules analysis confirm the cooperativity effect in Mⁿ⁺···coronene···CH₄, and reveal the nature of the formation of the predominant advantage of composite wax powder.     

Calculation of anharmonic effects in the unimolecular dissociation of M2+(H2O)2 (M = Be,Mg, and Ca)

The anharmonic and harmonic rate constants of the unimolecular dissociation of M²⁺(H₂O)₂ (M = Be, Mg, and Ca) were calculated using the Rice–Ramsperger–Kassel–Marcus theory. The anharmonic effects of the reactions were investigated. The results show that the energy barrier of the dissociation of Be²⁺(H₂O)₂ is 68.47 kcal/mol, and the anharmonic (T_4000K = 4.28×10⁸ s^?1) and harmonic (T_4000K = 4.22×10⁸ s^?1) rate constants were close in value in both the canonical and microcanonical systems. The energy barriers of the two steps for the dissociation, Mg²⁺(H₂O)₂ → MgOH⁺+H₃O⁺, were 37.41 and 11.39 kcal/mol, and those for the dissociation, Ca²⁺(H₂O)₂ → CaOH⁺+H₃O⁺, were 21.15 and 26.42 kcal/mol. The anharmonic effect of the two reactions is significant and cannot be neglected in both the canonical and microcanonical systems. The comparison also shows that the rate constants of the dissociation of Ca²⁺(H₂O)₂ have the maximum values, while those of Be²⁺(H₂O)₂ have the minimum values in the three reactions; however, the anharmonic effect also shows the similar trend in the comparison.     

Investigation of the electronic structure of Be2+He and Be+He,and static dipole polarisabilities of the helium atom

The potential energy and spectroscopic constants of the ground and many excited states of the Be⁺He van der Waals system have been investigated using a one-electron pseudo-potential approach, which is used to replace the effect of the Be²⁺ core and the electron-He interactions by effective potentials. Furthermore, the core–core interactions are incorporated. This permits the reduction of the number of active electrons of the Be⁺He van der Waals system to only one electron. Therefore, the potential energy of the ground state as well as the excited states is performed at the SCF level and considering the spin–orbit interaction. The core–core interaction for Be²⁺He ground state is included using accurate CCSD (T) calculations. Then, the spectroscopic properties of the Be⁺He electronic states are extracted and compared with the previous theoretical and experimental studies. This comparison has shown a very good agreement for the ground and the first excited states. Moreover, the transition dipole moment has been determined for a large and dense grid of internuclear distances including the spin orbit effect. In addition, a vibrational spacing analysis for the Be²⁺He and Be⁺He ground states is performed to extract the He atomic polarisability.     

Fine- and hyperfine structure analysis of the odd configurations in the lead atom

The fine- and hyperfine structure (hfs) analysis, on the basis of available experimental data for the configuration 6s ²6p6d+6s ²6p7s+6s ²6p8s in PbI has been performed. The Slater integrals, spin-orbit parameters and the effective hfs one-electron parameters have been determined. We find an off-diagonal core-polarization effect in the 6p6d+6p7s-space. Using the calculated radial parameters, the values of the quadrupole moment for stable and radioactive Pb-nuclei have been determined from measuredB-factors of the 6p7s ³P₁ state. In addition, a repulsion effect on the hfs sublevels with the same quantum numberF has been investigated.     

等电子系列离子的广义振子强度密度之标度关系

利用Born近似可以计算高能电子与原子或离子碰撞激发的微分截面和总截面。微分截面正比于广义振子强度。电子碰撞过程可将靶原子或离子激发到无数个束缚态以及相应的连续态。量子亏损理论能够统一处理这些激发态;因此可定义广义振子强度密度——即每单位激发能内的广义振子强度。我们计算了Li的等电子系列Li,Be⁺,B⁺⁺,C³⁺,Ne⁷⁺,Na⁸⁺,K¹⁶⁺等从基态到S,P,D,F通道的激发的广义振子强度密度,总结了类Li等电子系列离子的广义振子强度密度的标度关系。 关键词：     

The decays of 21.55 min 162gTm and 24.3 s 162Tm (a new isomer)

The decay of the 21.55 min ground state and of the 24.3 s isomeric state of ¹⁶²Tm was investigated with semiconductor detectors. The γ-ray spectrum was investigated with a Compton-suppression Ge(Li)-NaI(Tl) arrangement. A Si (Li) detector, mounted in an electron transport solenoid, was used to investigate the conversion electron spectrum. Three-dimensional coincidence measurements were performed with large-volume Ge(Li) detectors. The ¹⁶²Tm ground state has spin-parity 1^? and Nilsson assignment p[411]↓?n[521]↑. An allowed β-transition (log ft ≈ 6.4) was observed to a 2^?, 2 octupole vibrational level at 1572.84 keV. The Q-value determined from positon-gamma coincidence measurements is 4705 ± 70keV. The discrepancy of the experimental K /β⁺ ratio with theoretical predictions might possibly be explained by a large number of unobserved weak γ-rays besides the total of 315 stronger ones observed in this study. The average β-strength function was calculated to be 1.2 × 10^?5. Among the 50 levels observed in the decay, the 2⁺, 4⁺ and 6⁺ members of the ground-state band, the 2⁺, 3⁺ and 4⁺ members of the γ-band, several 0⁺ and 2⁺ members of the K = 0 β-bands and 1^?, 2^? and 3^? octupole vibrational levels were identified. Parameter values Z_γ(0) and Z_γ(2) determining the mixing between the γ-band and the ground-state band, allow no conclusive evidence about unequalness of the intrinsic quadrupole moments of the ground states and the γ-band. The Z(0) parameters, determining the mixing between the β-bands and the ground-state band, and X parameters determining the ratio of E0 to E2 transition probabilities, were deduced. A previously unreported 24.3 sec isomer in ¹⁶²Tm was observed to decay in 10% of the cases by an allowed unhindered (log ft = 4.7) β-ray transition to a level at 1712.20 keV in ¹⁶²Er. The Nilsson configurations assigned to the isomeric and 1712.20 keV levels are p[523]↑ + n[521]↑₅₊ and n[523]↓ + n[521]↑₄₊ respectively. The isomeric level decays in 90% of the cases by an E3 transition (E_IT < 125 keV) to a p[404]↓ ?n[521]↑_2? level at 66.90 keV in ¹⁶²Tm, which decays by an (M1+ < 40 % E2) to the 21.55 min ¹⁶²Tm 1^? ground state.     

Static quadrupole moments of first 2+ states in the 2s1d shell: A review of experiment and theory

Available experimental information on the static electric quadrupole moments Q₂₊ of the 2⁺ first excited states of even-mass nuclei in the 2s1d shell is tabulated and critically reviewed, and “adopted values” are presented. The results reveal a well defined pattern for the variation of Q_2⁺ through the shell. Predictions of Q_2⁺ made from various nuclear models are tabulated and compared with experiment. For each nucleus the qua ty and quality of the existing data for Q_2⁺, together with the current theoretical significance of the result, are used as criteria to determi whether new experimental work is desirable.     

Theoretical investigations of the EPR parameters and local structure for Cu2+ in BeO

The electron paramagnetic resonance (EPR) parameters (the anisotropic g factors, the hyperfine structure parameters and the quadrupole coupling constant Q) and local structure for Cu²⁺ in BeO are theoretically investigated from the perturbation formulas of these parameters for a 3d⁹ ion under trigonally distorted tetrahedra. The ligand orbital and spin-orbit coupling contributions are included in the basis of the cluster approach, in view of the strong covalency of the [CuO₄]^6? cluster. From the calculations, the impurity Cu²⁺ is suggested not to occupy exactly the ideal Be²⁺ site but to suffer a slight inward displacement (≈0.024 Å) toward the ligand triangle along the C₃ axis. The theoretical EPR parameters show good agreement with the experimental data.     

The F+ center in reactor-irradiated aluminum oxide

A point-ion calculation has been performed for the F⁺ center in α-Al₂O₃ (one electron in an O^2? vacancy). Optical transitions are predicted at 2·26, 3·39 and 5·15 eV. Contact hyperfine interactions with the two nearest pairs of Al³⁺ ions are calculated to be 151 and 39 G. Single crystals of α-Al₂O₃ were reactor-irradiated up to doses of 10²⁰ fast neutrons per cm², and studied by electron spin resonance (ESR). A broad ESR spectrum with 13 resolved components at g=2·0029±0·0005 was interpreted as the interaction of an unpaired electron with two pairs of Al³⁺ nuclei with hyperfine constants of 49·2 and 13·5 G. These values are in the same ratio as the values calculated for the F⁺ center, to which this ESR spectrum is attributed. The discrepancy of a factor of three is typical of point-ion calculations. The optical absorption spectrum for heavily-irradiated samples is not available for comparison with calculated transition energies.     

EPR g factors and tetragonal distortion for the isoelectronic Ni and Cu centers in the CuGaSe2 crystal

The EPR g factors, g_|| and g_⊥, for the isoelectronic 3d⁹ ions Ni⁺ and Cu²⁺ at the tetragonal Cu⁺ site of the CuGaSe₂ crystal are calculated from the high-order perturbation formulas based on a two-spin-orbit-parameter model. In the model, both the contributions to g factors from the spin-orbit parameter of central 3d⁹ ion and that of ligand ion are contained. The calculated results appear to be consistent with the experimental values. The tetragonal distortions (characterized by θ−θ₀, where θ is the angle between the metal-ligand bond and C₄ axis, and θ₀≈54.74° is the same angle in cubic symmetry) of Ni⁺ and Cu²⁺ centers, which are different from the corresponding angle in the host CuGaSe₂ crystal and from impurity to impurity, are obtained from the calculations. The difference of the sign of g_||−g_⊥ between the isoelectronic Ni⁺ and Cu²⁺ centers is found to be due to the different tetragonal distortions of both centers in the CuGaSe₂ crystal.     

化合物和合金中离子投影射程分布矩的计算(Ⅱ)——轻离子(Z1≤10)的射程分布矩

本文根据离子在固体材料中电子阻止截面的实验资料,给出了低能Li⁺,Be⁺,B⁺,C⁺,N⁺,O⁺,F⁺,Ne⁺等离子在固体中电子阻止截面S_e的经验公式。这些经验公式既能够很好地反映电子阻止本领的Z₁和Z₂振荡、又能正确地给出S_e随离子能量E的变化关系。用这种以实验为基础的S_e经验公式和符合于WHB势的核散射函数,计数了从H⁺到Ne⁺十种轻离子在非晶Al₂O₃,SiO₂,20/25/Nb不锈钢,LiNbO₃和UO₂等材料中的投影射程分布的一次至三次矩。将计算值与近几年的实验测量及其他人的计算结果进行了比较,在低能端,我们计算的平均投影射程R_p与实验符合得更好。 关键词：     

Density functional investigation of metal encapsulated X@C12Si8 heterofullerene (X=Li, Na, K, Be, Mg, Ca, Al, Ga)

The stability and the possible application of our recently reported SiC heterofullerenes inspire the investigation of their further stabilization through ion encapsulation. The endohedral complexes X@C₁₂Si₈, where X=Li⁺, Na⁺, K⁺, Be²⁺, Mg²⁺, Ca²⁺, Al³⁺, and Ga³⁺, are probed at the MPWB1K/6-311G? and B3LYP/6-311G* levels of theory. The optimized geometries show the expanding or contracting capability of C₁₂Si₈ in order to accommodate metal ion guests. The inclusion energies indicate the stability of the complexes compared to the components. Meanwhile, the calculated binding energies show the stabilization of C₁₂Si₈ through the inclusion of Be²⁺, Mg²⁺, Al³⁺, and Ga³⁺. The host-guest interaction that is probed through NBO atomic charges supports the obtained results. This study refers to “metal ion encapsulation” as a strategy for stabilization of SiC heterofullerenes.