Relativistic multi-configuration calculations of Kα and Kβ X-ray transitions for highly ionized Mo ions

A relativistic multi-configuration Dirac-Fock technique has been used for computing the transition wavelengths, transition probabilities, absorption oscillator strengths, and line strengths for the Kα and Kβ line transitions of He-like to Ne-like molybdenum ions. The contributions from the Breit interaction, quantum electrodynamic corrections, and nuclear mass corrections to the initial and final levels have been taken into account. Transitions from the ground state to the n = 2 and 3 states of He-like and Li-like molybdenum have been calculated using two sets of configuration-interaction wavefunctions. One set of wavefunctions was generated using the fully relativistic GRASPVU code and the other was obtained using GRASP², the calculated transition wavelength, transition probabilities, and absorption strengths obtained by these two independent methods are in very good agreement and there is good agreement between these results and recent theoretical and experimental results. These data provide reference values for the level lifetimes, charge state distributions, and average charge of molybdenum plasmas.     

Theoretical L-shell Coster-Kronig energies 11 ≤ Z ≤ 103

Relativistic relaxed-orbital calculations of L-shell Coster-Kronig transition energies have been performed ab initio for all possible transitions in atoms with atomic numbers 11 ≤ Z ≤ 103. Hartree-Fock-Slater wavefunctions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order approximation to the local approximation was thus included. Quantum-electrodynamic corrections were made. Each transition energy was computed as the difference between results of separate self-consistent-field calculations for the initial, singly ionized state and the final two-hole state. The following quantities are listed: total transition energy, “electric” (Dirac-Hartree-Fock-Slater) contribution, magnetic and retardation contributions, and contributions due to vacuum polarization and self energy.     

Gamma-ray transition probabilities in deformed nuclei (150 < A ≤ 190)

Experimental data on absolute γ-ray transition probabilities in deformed nuclei (150 < A ≤ 190) are presented together with information on the initial and final states as well as energies, multipolarities, and total conversion coefficients of the transitions involved. For comparison with model predictions, Weisskopf and Nilsson hindrance factors, the latter with the pairing effect taken into account, are listed. Data available up to May 1975 have been included.     

The energy levels and radiative transition probabilities for electric quadrupole and magnetic dipole transitions among the levels of the ground configuration, [Kr]4d4f, of W

Large-scale multiconfiguration Hartree-Fock and Dirac-Fock calculations have been performed for the ground configuration, [Kr]4d¹⁰4f⁴, energy levels of the W²⁴⁺ ion. The relativistic corrections were taken into account in the quasirelativistic Breit-Pauli and fully relativistic Breit (taking into account QED effects) approximations. The role of correlation, relativistic, and QED corrections is discussed. Line strengths, oscillator strengths, and transition probabilities in the Coulomb and Babushkin gauges are presented for the electric quadrupole (E2) transitions among these levels. The magnetic dipole transitions are also investigated. Dependence of the E2 transition probabilities on the gauge condition of the electromagnetic field potential is studied as well.     

Precise Measurement of Gamma-Ray Emission Probabilities for 187W by Using a Two-Dimensional 4πβ-γ Coincidence System

Gamma-ray emission probabilities for ¹⁸⁷W have been determined with uncertainties less than 1% from measurement of absolute γ-ray intensities and disintegration rate. The measured emission probabilities are larger than those previously reported by about 20% and hence the β-ray branching ratio to the ground state has to be smaller than about 40%. The decay scheme of ¹⁸⁷W calculated by using the present results is given as a final result.     

Stopping power of swift neon ions in dependence on the charge state in the non-equilibrium regime

We report on measurements of charge changing cross-sections and energy losses in dependence on the initial and final charge state of Ne ions at an incident energy of 2 MeV/u penetrating thin carbon foils. Different initial charge states could be separated in energy by applying a high voltage in front of the carbon foils; the final charges and their energy loss were measured with a high-resolution magnetic spectrometer. We derived a consistent evolution of the charge state distribution solving the corresponding rate equations for the measured cross-sections. Including the charge state dependent energy losses, ΔE(q_i,q_f), stopping power values for frozen charge states, S(q), could be extracted. The experimental data are compared with different theoretical predictions.     

An absolute determination of the U fission cross section at 964 keV

An absolute measurement of the ²³⁵U fission cross section has been carried out using a ²⁴Na---Be photoneutron source with median neutron energy of 964 keV. A symmetric two-foil experiment was set up to measure the fission rate in a low-albedo laboratory, and variations in the source-to-foil spacing used to determine the room background. Fission fragments passing through a limited solid angle aperture were recorded from each foil by solid state tracketch techniques. The photoneutron source was calibrated after each run using the manganese bath method and the secondary national standard source NBS-II. A computed neutron source spectrum with 32 keV FWHM was derived by the Monte Carlo method and used in reducing the data to a cross section at 964 keV. The final value of 1.21 ± 0.025 barns is absolute in that, except for small corrections, its determination was independent of any other cross section data.     

Energy-level scheme and transition probabilities of Cl-like ions

Theoretical energy levels and transition probabilities are presented for 31 low-lying levels of chlorine-like ions. The multiconfiguration Dirac-Fock technique is used to calculate energy levels and wave functions. The Breit interaction and Lamb shift contributions are calculated perturbatively as corrections to the Dirac-Fock energy. The E1 transitions between excited and ground levels and the M1 and E2 transitions between the two levels of the ground-state configuration are presented.     

Energy-level scheme and transition probabilities of P-like ions

Theoretical energy levels and transition probabilities are presented for 41 low-lying levels of phosphorus-like ions. The multiconfiguration Dirac-Fock technique is used to calculate energy levels and wave functions. The Breit interaction and Lamb shift contributions are calculated perturbatively as corrections to the Dirac-Fock energy. The M1 and E2 transitions between the five levels of the ground-state configuration and the E1 transitions between excited and ground levels are presented.     

The lamb shift in hydrogen-like atoms, 1 ⩽ Z ⩽ 110

Theoretical energy levels and energy-level separations for n = 1 and n = 2 states of hydrogen-like atoms with nuclear charge numbers in the range 1 ? Z ? 110 are tabulated. Quantum electrodynamical corrections of first and second order in the fine-structure constant α are included, together with finite nuclear size corrections, reduced mass corrections, and recoil corrections.     

Energy-level scheme and transition probabilities of Si-like ions

Theoretical energy levels and transition probabilities are presented for 27 low-lying levels of silicon-like ions from Z = 15 to Z = 106. The multiconfiguration Dirac-Fock technique is used to calculate energy levels and wave functions. The Breit interaction and Lamb shift contributions are calculated perturbatively as corrections to the Dirac-Fock energy. The M1 and E2 transitions between the five levels of the ground-state configuration and the E1 transitions between excited and the ground levels are presented.     

Probability-based design criteria for shear walls in nuclear power plants

The development of probability-based criteria for the design of reinforced concrete shear walls subjected to dead load, live load and in-plane earthquake forces in nuclear plants is described. These criteria are determined for flexure and shear limit states in a load and resistance factor design (LRFD) format. The flexure limit state is defined according to traditional principles of ultimate strength analysis, while the shear limit state is established from experimental results. Resistance factors for shear and flexure, load factors for dead and live load, and a load factor for effect of Safe-Shutdown Earthquake are determined for target limit state probabilities of 1.0 × 10⁻⁶ and 1.0 × 10⁻⁵ over a a period of 40 years. Comparisons among the proposed design criteria, ACI 349 and US NRC Standard Review Plan 3.8.4 are included.     

Reliability analysis of nuclear containment without metallic liners against jet aircraft crash

The present study presents a methodology for detailed reliability analysis of nuclear containment without metallic liners against aircraft crash. For this purpose, a nonlinear limit state function has been derived using violation of tolerable crack width as failure criterion. This criterion has been considered as failure criterion because radioactive radiations may come out if size of crack becomes more than the tolerable crack width. The derived limit state uses the response of containment that has been obtained from a detailed dynamic analysis of nuclear containment under an impact of a large size Boeing jet aircraft. Using this response in conjunction with limit state function, the reliabilities and probabilities of failures are obtained at a number of vulnerable locations employing an efficient first-order reliability method (FORM). These values of reliability and probability of failure at various vulnerable locations are then used for the estimation of conditional and annual reliabilities of nuclear containment as a function of its location from the airport. To study the influence of the various random variables on containment reliability the sensitivity analysis has been performed. Some parametric studies have also been included to obtain the results of field and academic interest.     

L-subshell ionization cross sections of Lu,W, Au,Tl, Pb,Th and U by protons of 0.5—0.9 MeV energy

The L-subshell ionization cross sections for 0.5—0.9 MeV protons on thin Lu, W, Au, Tl, Pb, Th and U targets were extracted from the L X-ray production cross sections. The experimental cross sections were compared with other recent experimental data as well as with the results predicted by the plane wave Born approximation (PWBA) and by the perturbed stationary state theory (PSS) with the relativistic and Coulomb deflection corrections included (CPSSR). Experimental data are, on the average, still about 30% higher than those predicted by the CPSSR theory.     

Transition probabilities and oscillator strengths of E1 transitions in Fe XII and Fe XIV

Non-orthogonal orbitals in the multiconfiguration Hartree-Fock approach are used to calculate line strengths, oscillator strengths and transition probabilities for E1 transitions among the fine-structure levels of the 3s²3p³, 3s3p⁴, 3s²3p²3d, 3s3p³3d, 3p⁵ and 3s²3p3d² configurations in Fe XII and 3s²3p, 3s3p², 3s²3d, 3p³, 3s3p3d, 3p²3d, 3s3d², 3p3d², 3s²4s, 3s²4p, 3s3p4s and 3s²4d configurations in Fe XIV. The lifetimes of excited levels belonging to these configurations of Fe XII and Fe XIV are also presented. An accurate representation of the levels has been obtained using spectroscopic and correlation radial functions. The wavefunctions exhibit large correlations and significant dependence of one-electron valence orbitals due to both the total and intermediate terms. The relativistic corrections are included through the one-body and two-body operators in the Breit-Pauli Hamiltonian. Progressively larger calculations are performed to check for important electron correlation contributions and for convergence of results. The atomic wavefunctions give excitation energies which are in close agreement with experiment. The present oscillator strengths and transition probabilities compare very well with previous large scale calculations.     

类镁离子磁四极3s~2 ~1S_0-3s3p ~3P_2(Z=20~103)禁戒跃迁

采用全相对论多组态Dirac-Fock方法,对高离化类镁离子的磁四极3s2 1 S0-3s3p 3 P2(Z=20~103)自旋禁戒跃迁的能级间隔、跃迁波长、跃迁概率和振子强度等光谱跃迁参数进行了系统计算,计算中考虑了重要核的有限体积效应、Breit修正和QED修正,所得结果和最近已有的实验数据进行了比较。结果表明,高原子序数的高电荷离子(Z≥70)磁四极自旋禁戒跃迁几乎可与中性原子的光学允许跃迁相比拟,不仅在天体等离子体中,在ICF和MCF高温激光等离子体中,磁四极自旋禁戒跃迁和其他自旋禁戒跃迁(磁偶极、电四极)一样不容忽视,在双电子复合、不透明度、自由程等理论计算中应考虑其影响。     

Transition probabilities and branching ratios for electric-dipole transitions between arbitrary levels of hydrogen-like atoms

Transition probabilities and branching ratios in hydrogen-like atoms due to electric-dipole transitions are tabulated for the initial principal and angular-momentum quantum numbers n′l′, and final principal and angular-momentum quantum numbers nl. The electric-dipole matrices are evaluated in parabolic coordinates, and by a transformation their values in spherical coordinates are found. In Table I transition probabilities for transitions n′l′ → n and n′ → n given.Branching ratios are tabulated in Table II for transitions n′l′ → n and n′ → n, while in Table III these ratios are tabulated for transitions n′l′ → nl and n′ → nl.The lifetime of an excited state nl can be expressed as (μZ⁴)^?1c_nln³l², where μ and Z are the reduced mass and nuclear charge of the hydrogen-like atom, and c_l is a slowly varying coefficient of n and l, approaching a constant as n,l → ∞. Values of c_nl are given in Table IV.     

The study of reduced transition probabilities for E2 transitions in the decays of Os and Pt nuclei

The ratios of E2 transition rates, i.e., B(E2; I_i − I_f)/B(E2; I_i − I_f) were computed for gamma to ground state band transitions in ¹⁹²Os and ¹⁹²Pt. The reduced transition probabilities for the E2 transitions evaluated on the basis of Interacting Boson Approximation (IBA-I) model and those measured experimentally are compared. The SU(3) symmetry of IBA-I is not strictly obeyed by the nuclei in which T(E2; I_i − I_f) transitions are observed, i.e., the symmetry SU(3) is broken. The percentage sum coincidence corrections are applied to marginalise contributions from crossover transitions and the intensities of affected transitions are found to agree fairly well with earlier sum peak method applications to the decay of ¹⁹²Ir.     

Improvement to the Calculation of Collision Probabilities in Annular System and Its Application to Cluster Geometry

A new method of calculating first-flight collision probabilities in cluster geometry is developed. The collision probabilities in an annular system as well as the transition probabilities for a neutron escaping from one subcell to reach other subcells are calculated and combined. The former is an improvement on Bonalumi's approximation and the latter is an extension of the Dancoff correction to subcells containing fuel rods and coolant. As applications of the present method, we calculate the collision probabilities in a hexagonal cluster with 7 fuel rods and in a square cluster with 28 fuel rods. Fairly good agreement is obtained by comparing the probabilities obtained from our method with the results obtained by the exact method. One-group calculations of the flux distribution are carried out in these systems.     

Pu-H2相互作用的反应机理及电子密度分析

通过量子力学中密度泛函理论的相关方法和相对论有效原子实模型(RECP),应用Gaussian09程序对钚与氢气的相互作用进行了计算和分析。计算得到了钚与氢气的详细微观反应机理：Pu+H2→FC→TS→PuH2,优化了沿反应路径的特殊结构（能量极小点及过渡态）,并通过能量分析画出了势能剖面图。基于优化的几何结构,通过多种拓扑分析方法分析了反应路径中所有特殊结构的电子密度相关性质,如自旋密度分析、Mulliken自旋布居分析、电子定域泛函理论分析,得到了电子密度在反应过程中的详细变化。