Perturbation theory for the angular correlation function

A perturbation expression for the angular pair correlation function g ⁽²⁾(r ₁₂, ω₁, ω₂) is derived for systems interacting via non central potentials based on the method developed by Gubbins and Gray [1]. The method uses the ‘correct’ (in the sense of Rushbrooke [3] and Cook and Rowlinson [4]) angle-averaged potential as the reference system about which the perturbation is made. A preliminary comparison between the original Gubbins-Gray expression for g ⁽²⁾(r ₁₂, ω₁, ω₂) and the present expression is made for a system of two-dimensional point dipoles.     

Investigations on the g factors of the ground and excited states for Cu2+ ions in ZnO crystal

The g factors g _// and g _⊥ of the ground Γ₆(² T ₂) and excited Γ_4,5(² E), Γ₆(² E) states for trigonal Cu²⁺ centres in ZnO crystals are calculated from three theoretical methods, the complete diagonalization (of the energy matrix) method, the second-order perturbation method (PTM-I) and the simplified second-order perturbation method (PTM-II, this method was described in an earlier paper). These methods are based on the cluster approach in which the spin-orbit coupling parameters ζ, ζ′ and the orbital reduction factors k, k′ are calculated from a semi-empirical molecular orbital method. The crystal-field parameters used in the calculations are obtained from the superposition model and so the defect structure of Cu²⁺ centres in ZnO can be acquired. The calculated g factors from the three methods are in reasonable agreement with the experimental values and the defect structure of Cu²⁺ centres in ZnO is acquired. It appears that in some cases the approximate PTM can be applied in the studies of g factors of various states. The conditions that the PTM are ineffective are discussed.     

Theoretical calculations of spin-Hamiltonian parameters and defect structures for Cu2+ in trigonally-distorted tetrahedral sites of ZnO and GaN crystals

The spin-Hamiltonian (SH) parameters (g factors g _//, g ⊥ and hyperfine structure constants ⁶³ A _//, ⁶³ A ⊥, ⁶⁵ A _//, ⁶⁵ A ⊥) for Cu²⁺ ions in the trigonally-distorted tetrahedral sites of ZnO and GaN crystals are calculated from a complete diagonalization (of energy matrix) method (CDM) based on a two spin-orbit parameter model for d ⁹ ions in trigonal symmetry. In the method, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM. The calculated results are in good agreement with the experimental values. The calculated SH parameters are also compared with those using the traditional diagonalization method or perturbation method only within the ² T ₂ term. It appears that, for exact calculations of SH parameters of d ⁹ ions in trigonal tetrahedral clusters in crystals, the present CDM is preferable to the traditional diagonalization method or perturbation method within the ² T ₂ term. The local structures of Cu²⁺ centers (which differ from the corresponding structure in the host crystal) in ZnO : Cu²⁺ and GaN : Cu²⁺ are obtained from the calculations. The results are discussed.     

Classical Hamiltonian perturbation theory without secular terms or small denominators

We consider perturbation theory in ? for the classical Hamiltonian H = H₀ + ?H₁, where H₀ gives rise to a known motion and ? is small. First we demonstrate how the usual secular terms and small denominators arise from a straightforward expansion in ? and argue that they are artifacts of the method. Then we present an alternative perturbation theory based on an analysis of the operator (s ? L)^?1, where s is a complex number and L is the Liouville operator corresponding to H. This perturbation series contains neither secular terms nor small denominators. In the case of almost multiply periodic systems we show, to lowest non-trivial order in ?, how our series reproduces the standard results both in the resonant and nonresonant regions — all in one analytic formula. As a final exercise we demonstrate that energy is conserved at order ?ⁿ⁺¹ when the accuracy of the theory is order ?ⁿ.     

Measurements of effective delayed neutron fraction in a fast neutron reactor using the perturbation method

A perturbation method is proposed to obtain the effective delayed neutron fraction β_(eff) of a cylindrical highly enriched uranium reactor.Based on reactivity measurements with and without a sample at a specified position using the positive period technique,the reactor reactivity perturbation △ρ of the sample in β_(eff) units is measured.Simulations of the perturbation experiments are performed using the MCNP program.The PERT card is used to provide the difference dκ of effective neutron multiplication factors with and without the sample inside the reactor.Based on the relationship between the effective multiplication factor and the reactivity,the equation β~(eff)=dκ/△ρ is derived.In this paper,the reactivity perturbations of 13 metal samples at the designable position of the reactor are measured and calculated.The average β_(eff) value of the reactor is given as 0.00645,and the standard uncertainty is 3.0%.Additionally,the perturbation experiments for β_(eff) can be used to evaluate the reliabilities of the delayed neutron parameters.This work shows that the delayed neutron data of ~(235)U and ~(238)U from G.R.Keepin's publication are more reliable than those from ENDF-B6.0.ENDF-B7.0,JENDL3.3 and CENDL2.2.     

Theoretical determination of the vibrational levels of NH+ 3 and its isotopomers

The vibrational levels associated with the electronic ground state X²A₂″ of NH⁺ ₃ have been determined up to 5000 cm^?1 by perturbation and variational calculations with full dimensionality of the molecule. For the variational part a new version of MULTIMODE was used which uses the ab initio electronic energy and its first derivative to define the potential energy function. These quantities were generated by the B97-1 density functional and RCCSD(T) approaches. For ND⁺ ₃, ND₂H⁺ and NDH⁺ ₂ the vibrational levels were calculated only by perturbation theory. The rotational constants for all the isotopomers were determined and the first transition dipole moments for NH⁺ ₃ and ND⁺ ₃ were plotted. A critical comparison of the perturbation and variational techniques suggests a possible further modification to the MULTIMODE algorithm for large systems.     

Optimized perturbation theory applied to jet cross sections ine + e − annihilation

The optimized perturbation theory proposed by Stevenson to deal with coupling constant scheme dependence is applied to the calculation ofπ _tot and jet multiplicities ine ⁺ e ^? annihilation. The results are compared with those of simple perturbation theory and with recent experimental cluster multiplicities.     

Nonadiabatic corrections to the rotational energies of the hydrogen molecule

Nonadiabatic corrections to the rotational energies and rotational constants B_ν have been computed by a variational perturbation method for several vibrational levels of the H₂, HD, and D₂ molecules. It is believed that the convergence error in the computed corrections to the energy is less than 10^?3 cm^?1. The corrections improve the agreement of theoretical and experimental rotational quanta, but there are still discrepancies that amount in some cases to a few hundredths of a cm^?1. These discrepancies are irregular and it is argued that they are at least partly due to experimental inaccuracies.     

Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

A method is presented to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei. In such nuclei, always there is a collective low-lying 2⁺ phonon, and a strong mixture of single-particle and particle–phonon states often occurs. As in magic nuclei the so-called g _L ² approximation, where g _L is the vertex of the L-phonon creation, can be used for finding the PC correction δΣ^PC(ε) to the initial mass operator Σ₀. In addition to the usual pole diagram, the phonon “tadpole” diagram is also taken into account. In semi-magic nuclei, the perturbation theory in δΣ^PC(ε) with respect to Σ₀ is often invalid for finding the PC-corrected single-particle energies. Instead, the Dyson equation with the mass operator Σ(ε) = Σ₀ + δΣ^PC(ε) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.     

Perturbative expansions in QCD and analytic properties of α s

It is shown that analytic properties of standard QCD perturbation theory contradict known spectral properties and contain, in particular, infrared-generated Landau ghost poles and cuts. As an outcome, a rigorous background perturbation theory is developed and its analytic properties are shown to be in agreement with general requirements. In the limiting case of large N _c, where QCD amplitudes contain only pole singularities, the strong coupling constant α _s(Q ²) is shown to be a meromorphic function of external momenta as well. Some simple models and examples are given where nonperturbative β function and α _s(Q ²) can be written explicitly. The general form of amplitudes at large N _c is given in the framework of background perturbation theory, and its correspondence with standard perturbation theory at highmomenta is demonstrated in the example of e ⁺ e ^? annihilation. For timelike momenta, the background coupling constant differs drastically from the standard one, but the background series averaged over energy intervals has the same (AF) behavior at high momenta in the Euclidean and in the Minkowskian region.     

Mössbauer Study of the Ni/Ca0.8Sr0.2Ti1−x Fe x O3−α Catalyst System for Partial Oxidation of Methane to Synthesis Gas

The Ni/Ca_0.8Sr_0.2TiO₃ catalyst system prepared by the citrate method shows high activity in partial oxidation of methane to synthesis gas. It is assumed that the interaction of Ni with the perovskite lattice may be responsible for the increased catalytic activity. 1% ⁵⁷Fe dopant substituted for Ti was used in order to see if the presence of Ni has any perturbation effect on the structure of the perovskite. One may expect systematic changes in the Mössbauer parameters of the substitutional Fe impurity as a function of the NiO content if the bulk properties of the perovskite are affected. Samples with different Ni/Ca_0.8Sr_0.2Ti_0.99 ⁵⁷Fe_0.01O_3– ratios from 0:1 to 1:1, and others having Fe substitutions for Ti up to 30%, all prepared by the citrate method, have been investigated. The Mössbauer spectra contained doublets of paramagnetic Fe³⁺ and Fe⁴⁺ species as well as paramagnetically relaxed Fe³⁺. These species were assigned to the bulk perovskite, the perovskite surface and the NiO/perovskite interface. The perturbation of the perovskite structure by Ni could not be verified.     

Investigations of the electron paramagnetic resonance spectra of VO<Superscript>2+</Superscript> in CaO-Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiO<Subscript>2</Subscript> system

The EPR spectra for VO²⁺ in CaO-Al₂O₃-SiO₂ system are calculated using complete diagonalization method (CDM) and perturbation theory method (PTM). The calculated results are in good agreement with the observed values. By comparing the calculated results by CDM and PTM in a wide range of crystal field parameters, the validity of the PTM formulas has been studied. It is shown that, the PTM formulas are reasonable and reliable in a wide range of CF parameters.     

Use of sturmian expansions in calculations of the hyperfine structure of atomic spectra

A procedure for calculating hyperfine structure (HFS) parameters using the basis of Sturmian functions is developed. The procedure is used to calculate the HFS parameter a _4d ⁵ of the 4d ⁵ levels of the niobium atom. The contributions of the continuous spectrum and higher orders of the perturbation theory are quantitatively estimated by comparing the numerical values of the parameter a _4d ¹⁰ obtained in the framework of the perturbation theory with the results of direct calculations by the configuration interaction method. Comparison of the results of relativistic and nonrelativistic calculations allows the contribution of relativistic effects to HFS parameters to be found.     

Perturbation study via rotational-resolved spectrum in the triplet band d3Δ-a3∏(2, 1) of CO

The triplet band d³Δ-a³∏ (2, 1) of the CO molecule in the near infrared region of 12350--12850cm^-1 has been observed and analysed by taking into account the perturbation interaction between the d³Δ(v = 2) and a³∏ (v = 9) states. The most perturbed lines and most precise perturbation parameters, \alpha₂ and \beta₂, and electronic perturbation constants,\xi _\e and \eta _\e , for the d³Δ (v= 2) and ³∏ (v = 9) states have been obtained.     

A double expansion method for calculating molecular properties

Using a form of double perturbation theory we present results of calculations on the ground state energies for the diatomic systems H₂ ⁺, HHe²⁺, H₂ and HHe⁺. For the homonuclear systems the energy values are unexpectedly good. For the heteronuclear cases the results are very encouraging and lead to optimism about the application of the method to larger systems which contain one heavy atom.     

Acoustic perturbations in a pulsedRF-plasma

The response of a stationary weakly ionized plasma to a density perturbation in the neutral gas component was studied in a neon plasma with the following typical properties: electron density ¯N _e≈8×10¹² cm^?3, electron temperature on the axis of the vesselT _e0≈3.0 eV; neutral gas densityN _n≈1×10¹⁷cm^?3 and neutral gas temperatureT _n0≈600 °K. A neutral density perturbation, generated 50 cm apart from the plasma, produces a fluctuation in the ion density and a sharp spike in the differential voltage of a floating double probe. The experimental observations demonstrate the propagation of an ion sheath and of an electric field perturbation together with the neutral density perturbation. An interpretation of the plasma response to acoustic wave pulses has been proposed by Ingard and Schulz in a theory on acoustic wave modes in a weakly ionized gas. The experimental results are in good agreement with the theoretical expectations.     

Modified perturbation series for the anharmonic oscillator using linearization technique

The linearization technique of random phase approximation is applied to the anharmonic oscillator to find a modified perturbation series. It is shown that for the anharmonic termλx ⁴, the ground state energyE ₀ upto the second order of perturbation is given byE ₀=(35/48) (3/4)^1/3 λ ^1/3 asλ→∞.     

ICF分解实验用双介质调制靶的研制

为了研究惯性约束聚变(ICF)实验用靶丸不同密度界面的流体力学不稳定性增长,设计并制备了聚苯乙烯(CH)/碳气凝胶(CRF),CRF/硅气凝胶(SiO2)和CH/Al三种双介质调制靶。采用溶胶-凝胶工艺制备了密度分别为250和800mg/cm3的CRF气凝胶薄片;采用激光微加工工艺分别在两种不同密度的CRF薄片和工业用纯Al箔上引入调制图形;采用旋涂工艺在Al箔和CRF薄片(250mg/cm3)的调制表面制备一层CH薄膜,得到CH/Al和CH/CRF双介质调制靶,采用溶胶-凝胶工艺在CRF薄片(800mg/cm3)表面制备一层低密度SiO2气凝胶,得到CRF/SiO2双介质调制靶。采用电子天平、扫描电子显微镜、工具显微镜和台阶仪对所制备的CH/CRF,CRF/SiO2和CH/Al三种双介质调制靶进行靶参数测量。结果表明:三种双介质调制靶层与层之间结合紧密,界面清晰,调制图形为正弦,靶参数测量准确。     

原子激发态的二体电子关联变分计算

本文将Wilets等人提出并由作者加以改进的二体电子关联变分方法推广到多电子原子一般激发态结构的计算。对He原子及其等电子系列(1s)(nl)电子组态的激发单重态n¹L、三重态n³L,Be原子及其等电子系列(1s)²(2s)(nl)³L和B原子(1s)²(2s)²(nl)²L等激发态进行了计算,结果表明:这种方法的波函数结构简单,便于应用,不仅计算量小, 关键词：