Optimisation of the dipole-Coulomb approximation for high-l Rydberg states of polar molecules

ABSTRACT

The present work deals with the question of the origin choice to get the maximal accuracy of the dipole-Coulomb approximation in the theory of molecular Rydberg states with high orbital momentum l. Concerning birefringence in polar molecules, the question of adequate origin choice has first been raised in the classical work by Buckingham & Longuet-Higgins in 1968, where it has been taken into account that the dipole moment of a polar molecular core (cation) depends on the origin choice. This dependence also leads to inseparability of dipole and quadrupole corrections to the Rydberg electron spectra in polar molecules. In the present work a new option for the problem is proposed as applied to the dipole-Coulomb approximation. Considering a simplified model of a molecular core as a system of N effective fixed point charges, we show both analytically and numerically that the optimal choice of origin, at least for a linear core, is the geometric centre of the core. On the other hand, results of the present work as well as previous publications show that the problem raised by Buckingham and Longuet-Higgins does not have a universal solution.

Abbreviations: RS: Rydberg state; RSs: Rydberg states; ZEKE: zero electron kinetic energy; MATI: mass-analysed threshold ionisation; QDT: quantum defect theory; DCA: dipole-Couloumb approximation; CD: centre of dipole; CC: centre of charge; GC: geometric centre; DCAGC: dipole-Couloumb approximation with origin in the geometric centre; DCACD: dipole-Couloumb approximation with origin in the centre of dipole     

Mechanisms of organelle division and inheritance and their implications regarding the origin of eukaryotic cells

Mitochondria and plastids have their own DNAs and are regarded as descendants of endosymbiotic prokaryotes. Organellar DNAs are not naked in vivo but are associated with basic proteins to form DNA-protein complexes (called organelle nuclei). The concept of organelle nuclei provides a new approach to explain the origin, division, and inheritance of organelles. Organelles divide using organelle division rings (machineries) after organelle-nuclear division. Organelle division machineries are a chimera of the FtsZ (filamentous temperature sensitive Z) ring of bacterial origin and the eukaryotic mechanochemical dynamin ring. Thus, organelle division machineries contain a key to solve the origin of organelles (eukaryotes). The maternal inheritance of organelles developed during sexual reproduction and it is also probably intimately related to the origin of organelles. The aims of this review are to describe the strategies used to reveal the dynamics of organelle division machineries, and the significance of the division machineries and maternal inheritance in the origin and evolution of eukaryotes.     

Distribution of Lattice Points Visible from the Origin

Let Ω be a region in the plane which contains the origin, is star-shaped with respect to the origin and has a piecewise C ¹ boundary. For each integer Q≥ 1, we consider the integer lattice points from which are visible from the origin and prove that the 1 ^st consecutive spacing distribution of the angles formed with the origin exists. This is a probability measure supported on an interval [m _Ω,∞), with m _Ω >0. Its repartition function is explicitly expressed as the convolution between the square of the distance from origin function and a certain kernel. Received: 2 November 1999 / Accepted: 2 March 2000     

S-wave inverse problem and sum rules for potentials with a simple pole at the origin

In a previous paper (F. Calogero and A. Degasperis, J. Math. Phys.9 (1968), 90) an approach to the inverse problem for the nonrelativistic S-wave potential scattering has been developed with the aim of obtaining explicit and exact expressions of the potential in terms of the phase shift and of the bound states parameters. Since this method, based on the high energy asymptotic expansion, yields the expression of the potential and of all its derivative at the origin only if these quantities are bounded, physically interesting interactions such as the Yukawa potential could not be considered. In this paper this approach has been generalized to potentials with a simple pole at the origin and the expression of the Laurent coefficients of the potential in a neighborhood of the origin has been obtained as an explicit functional of the experimental data. Furthermore the general structure of the high energy expansion of the phase shift has been derived and discussed. The requirement that the potential has only a simple pole at the origin turns out to imply strong constraints on the experimental data. These conditions on the experimental data have been explicitely expressed as a set of infinitely many nonlinear sum rules involving only the phase shift and the energies of the bound states.     

Lack of magnetoacoustic emission in iron with 6.5% silicon

The phenomenon of magnetoacoustic emission (MAE) has been ascribed usually to one of two origins: either (1) motion of non-180° domain walls or (2) creation or annihilation of domains. In this paper, we present strong evidence for the argument that the only origin for MAE is motion of non-180° domain walls. The proof is evident as a result of measurements of zero MAE for a wide range of stress in the isotropic zero magnetostrictive polycrystalline alloy of iron with 6.5% silicon. We also explain why it was that the alternative origin was proposed and how the data in that same experiment can be reinterpreted to be consistent with the non-180° wall motion origin.     

A new light on a first example of lustred majolica in Italy

A study has been realised to elucidate the first step of lustre production in Italy. With this aim in mind, an investigation was carried out on an emblematic lustred object: Baglioni’s albarello. It is conserved at Louvre museum and it is considered as one of the very first examples of lustred object produced in Italy. The characteristics of the lustred film have been determined, identifying interesting aspects that may be used to scientifically confirm the origin of this object. This study was completed by the investigation of other objects: a not lustred albarello, still decorated with the coat of arms of Baglioni’s family and a lustred plate with the coat of arms of the Montefeltro family. The two Baglioni’s albarelli are stylistically and historically considered as produced in one of the numerous workshops of Deruta. The origin of the Montefeltro’s plate, although from central Italy, is not precisely attested. In order to acquire more information, clarifying the origin and place of production of these objects, a comparison of their physico-chemical characteristics with results obtained and already published on different well-attested productions, such as Islamic, Hispano-Moresque and Italian, was carried out. For what concerns the museum objects, the use of non-destructive investigation techniques was mandatory. For this reason, ion beam techniques as PIXE and RBS have been used at AGLAE facility, as well as a new X-ray micro-diffraction equipment, at C2RMF. Moreover, the results were compared with data obtained on shards of certain production origin, by means of chemometric techniques. Some hypothesis concerning the place of production of the examined objects have been formulated.     

Origin of cosmic rays

Cosmic rays were discovered in 1911 but it is only now that some ideas are beginning to emerge as to their origin. This paper will examine the present evidence concerning the origin question over the whole energy range, from 10⁹ eV to 10²⁰ eV. At the lowest energies, (10⁹–10¹⁰ eV), the new subject of gamma ray astronomy plays a crucial role and a galactic origin is favoured. At higher energies (10¹²–10¹⁷ eV) recent measurements of the anisotropies in arrival directions also suggest a galactic origin, although the evidence is not as strong. At the very highest energies it seems likely that some, at least, of the particles come from outside the galaxy although the non-existence of the cut-off at about 6 × 10¹⁹ eV arising from interactions with the cosmological relict radiation provides a paradox. The likely future areas of advance in this fascinating subject will be indicated. Based on the B. B. Roy memorial lectures delivered at Calcutta University, February 1–3, 1978.     

Structural and magnetic investigations in the vicinity of first-order transformations in Ni–Mn–Ga–Co ferromagnetic shape memory alloys

Among the series of alloys derived from Ni₅₀Mn₂₉Ga₂₁ on selective substitution of Co for Ni and Mn, two alloys Ni_49.8Mn_27.2Ga_21.2Co_1.8 and Ni_46.9Mn_28.8Ga₂₁Co_3.3 referred to as CoMn-1.8 and CoNi-3.3, respectively, are found to exhibit an additional first-order transformation below their martensitic transformation temperatures. Systematic studies on temperature and field dependence of magnetic properties of these alloys are carried out, through the transformations, to understand their origin. An examination of these results in conjunction with those from structural investigations reveals that the transformation in the CoMn-1.8 alloy is an intermartensitic transformation and has a structural origin, while that in the CoNi-3.3 alloy is not of the structural origin and is attributed to local spin inversion of Co moments, which is of the magnetic origin.     

ASYMPTOTIC FREEDOM AND THE WAVE FUNCTIONS AT THE ORIGIN AND THE ENERGY LEVELS OF THE J/ψ AND THEY

On the basis of phenomenological quantum chromodynamics (QCD), a nonre-lativistic linear and Coulomb-like potential describtion of the strong interaction be-tween quarks is assumed and it is considered that the effective quark-gluon coup-ling constant approaches the asymptotically free limit of QCD. The cloice of thepotential parameters is so made as to fit the experimental values of the wave func-tions at the origin as well as the masses of the J/ψ and the γ Following the calcu-lation referring to the ψ′and the γ′, we acquire a consistent explanation for boththe relative values of the wave functions at the origin and the experimental mass asdifferences of these particles.     

Some evidences of multiple particle sources from nuclear matter jets in He+AT collisions at relativistic energies

Searching for interesting variables which contains information about the compression stage of a relativistic A + A collision, the concept of “nuclear matter jets” is an interesting tool for selecting different event structures as: single-jet events, two-jet events, three-jet events, and non-jet events. We found a relation between the number of jets and the centrality of the collision. The analysis of the jet properties allowed us to make assumptions about their origin. The founded jets in these interactions have a hadronic origin and not a partonic one.     

Hyperfine fields and neutron scattering in ferromagnetic metals

The origin of ferromagnetism in the transition metal ferromagnets, iron, cobalt, and nickel is discussed, from an ab initio band structure point of view, with proper attention to the explicit roles of exchange, correlation and hybridization effects. The influence of these effects and all the mechanisms such as direct, exchange core polarization and many-body effects that have been found important for the hyperfine properties of atomic systems are included in attempting to understand the experimentally observed hyperfine fields at the nuclei in these metals. Spin-density distributions using calculated spin polarized band wave-functions are used to make comparisons with experimental neutron scattering data. The impact of the results of analyses of hyperfine fields at the nuclei and spin density distributions on the origin of hyperfine fields at muon sites is discussed. This talk, and the corresponding article for the proceedings of this conference, will deal with the theoretical understanding of the hyperfine fields at the nuclei and neutron scattering form factors in the three ferromagnetic metals, iron, cobalt and nickel and the impact of this understanding on that of the origin of the hyperfine fields at positive muon sites in these metals. With these aims in mind, the plan of my talk will be the following.

1. Discussion of a first-principle principle procedure to obtain the energy bands and electronic wave-functions in these metals and the understanding of the origin of their ferromagnetism from a band point of view.
2. Mechanisms contributing to hyperfine fields in atomic systems and their relevance for ferromagnetic metals.
3. The mechanisms for the origin of hyperfine fields in these metals, corresponding theoretical results and comparison with experiment.
4. Comparison between calculated spin-density distributions and experimental results from neutron scattering data.
5. Remarks on the origin of hyperfine fields at muon sites in these metals.

     

Hyperbolic Low-Dimensional Invariant Tori¶and Summations of Divergent Series

We consider a class of a priori stable quasi-integrable analytic Hamiltonian systems and study the regularity of low-dimensional hyperbolic invariant tori as functions of the perturbation parameter. We show that, under natural nonresonance conditions, such tori exist and can be identified through the maxima or minima of a suitable potential. They are analytic inside a disc centered at the origin and deprived of a region around the positive or negative real axis with a quadratic cusp at the origin. The invariant tori admit an asymptotic series at the origin with Taylor coefficients that grow at most as a power of a factorial and a remainder that to any order N is bounded by the (N+1)-st power of the argument times a power of N!. We show the existence of a summation criterion of the (generically divergent) series, in powers of the perturbation size, that represent the parametric equations of the tori by following the renormalization group methods for the resummations of perturbative series in quantum field theory. Received: 9 July 2001 / Accepted: 26 October 2001     

Raman spectroscopic investigations of structural aspects of the different phases of lithium sodium and potassium nitrate

Raman spectra have been obtained for LiNO₃, NaNO₃ and KNO₃ as oriented single crystals and polycrystalline solids over a wide range of temperatures up to the melting points. The anomalous component previously observed in the symmetric stretching region and attributed to a disordered nitrate group has been studied as a function of temperature. The results suggest that the peak may have a hot band origin such that transitions 0001 → 1001 and 0100→ 1100 may occur in addition to the ground state transition, 0000→ 1000 of nitrate. In the symmetric stretching region the shift of the hot band is sufficiently large to ensure that the modes of this origin are not coupled to the ground state lattice in the usual way. Hot bands with an external mode origin could not be detected. KNO₃(II), KNO₃(III), NaNO₃(II) and LiNO₃, have ordered structures with small amounts of disorder of a hot band origin. KNO₃(I) and NaNO₃(I) have similarly disordered structures but exhibit minor differences due to different relative populations and symmetries of the disordered sites. Raman studies of the disordered phases suggest that the crystal symmetry is lower than the “average” structure deduced from X-ray diffraction methods. A number of bands previously reported have not been detected while several bands were reassigned on the basis of ¹⁵N substitution.     

基于PCA-SVM的仿刺参产地溯源在线系统研究

仿刺参是具有极高经济价值的水产资源,是海水养殖产业的重要组成部分,研发出一种灵活、稳定、高效的仿刺参产地溯源方法对于水产养殖产业具有极强的现实意义。仿刺参主要有三种养殖方式,分别是底播增殖、圈养养殖和筏式养殖。不同产地采用不同的养殖方式,仿刺参的营养价值、药用价值和经济价值都存在着明显差异。不同产地初级生产者的构成不同,作为初级生产者的不同藻类与浮游生物体内的脂肪酸特征也各不相同,通过食物链的传递,不同产地的仿刺参具有了不同的脂肪酸特征。气相色谱指纹图谱法是一种快速准确地食品产地溯源技术,碳稳定同位素质谱法不仅可以鉴别产地还可以区分出食品的营养价值。采集9个最具代表性产地的仿刺参样品,先利用Folch法对样品进行总脂提取,再通过气相色谱仪测定出各种脂肪酸的种类及其相对含量;最后使用稳定同位素质谱仪测定出每种脂肪酸各自的碳稳定同位素组成数据。使用单因素方差分析法对脂肪酸相对含量和脂肪酸碳稳定同位素组成数据进行显著性检验,各筛选出17种脂肪酸数据作为两个模型的输入。主成分分析(PCA)法可以降低数据的维度,聚合不同种脂肪酸数据的溯源特征,提高产地溯源的精度。支持向量机(SVM)是一种以结构化风险最小为目标的分类识别算法,具有优秀的泛化能力。研究结果表明,不同产地仿刺参的脂肪酸相对含量和脂肪酸碳稳定同位素组成数据存在明显差异。通过主成分变换后,脂肪酸数据的聚类特征更加明显,运用随机交叉验证法确定前6个主成分作为两个支持向量机分类器的输入。采用基于遗传交叉因子改进的粒子群优化算法(GPSO),以粒子不同K值各100次交叉验证的平均准确率作为其适应度,寻找支持向量机分类器模型的最优参数组合。最终计算得到脂肪酸相对含量产地溯源模型的最优参数组合为σ=6.247 599和C=14.313 042,平均准确率为79.49%;脂肪酸碳稳定同位素组成产地溯源模型的最优参数组合为σ=7.626 194和C=2.193 410,平均准确率为98.33%。对比交叉验证的结果,脂肪酸碳稳定同位素组成产地溯源模型具有更高的准确率和更强的泛化性能。在两个模型的识别结果不一致时,采用脂肪酸碳稳定同位素组成模型的识别结果。将实验室检测与互联网技术进行整合,构建了仿刺参产地溯源在线系统。实现了“互联网+产地溯源”的一体化溯源模式,为进一步开展食品产地溯源研究提供了科学依据和技术支撑。     

Identifying an extraZ 0 boson with a new model

According to the principle of minimality, we find a newSU(6) model. ThisSU(6) model, and other models, can be identified as a theoretical origin of an extra Z⁰ boson. We apply the strategy of Boudjemaet al. (BLRV) which is very effective in identifying the theoretical origin of an extra Z⁰ boson in the newSU(6) model, and compare the model with six other models.     

Spin relaxation in the quasi-one-dimensional conductor Rb2Pt(CN)4(FHF)0.4

We analyze the electron paramagnetic resonance linewidth in Rb₂Pt(CN)₄(FHF)_0.4 as a function of temperature. Above 60 K, the results are interpreted as a superposition of spin-phonon and spin-spin relaxation effects. The dominant contribution to the relaxation rate l/T₂ has a dipolar origin in contrast to the spin-phonon origin observed in K₂Pt(CN)₄Br_0.3 · H₂O. This difference could arise from different anisotropy ratios of the transfer integrals. The influence of the interchain coupling is also discussed.     

Ferromagnetic resonance investigation of nanocrystalline FeCuNbSiB

An elaborate line-shape analysis of the ferromagnetic resonance (FMR) spectra taken in the temperature range 100 K to 350 K on amorphous FeCuNbSiB alloys before and after nanocrystallizing them reveals that in the nanocrystalline state, (i) spin wave stiffness (D) is enhanced while the saturation magnetization,M _S, is reduced, (ii) both the ‘in-plane’ anisotropy field,H _K, as well as the FMR line-width scale with MS, (iii) the single-ion anisotropy of spin-orbit plus crystal field origin dominates over the twoion anisotropy of dipolar origin and (iv) multi-magnon scattering contributions to FMR line-width become important in some cases     

Metal-insulator transition in the In/Si(1 1 1) surface

The metal-insulator transition observed in the In/Si(1 1 1)-4 × 1 reconstruction is studied by means of ab initio calculations of a simplified model of the surface. Different surface bands are identified and classified according to their origin and their response to several structural distortions. We support the, recently proposed [C. González, J. Ortega, F. Flores, New J. Phys. 7 (2005) 100], combination of a shear and a Peierls distortions as the origin of the metal-insulator transition. Our results also seem to favor an electronic driving force for the transition.     

On the quantum dynamics of a point particle in conical space

A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a δ-function potential, which appear naturally in the model. These pathological potentials are treated with the self-adjoint extension method which yields the correct boundary condition (not necessarily a null wavefunction) at the origin. We show that the usual boundary condition requiring that the wavefunction vanishes at the origin is arbitrary and drastically reduces the number of bound states if used. The situation studied here is closely related to the problem of a dipole moving in conical space.     

Aesthetic fields—Null theory II

We have again studied a null theory within the complex aesthetic field theory. This time we required that the spatially inverted origin point data represent the imaginary part of the complex origin point data. This was not the case in our previous studies of the null aesthetic field theory. However, this procedure did not lead to effects not previously observed as far as we could tell. Adding an additional term to the origin point data that presented the null character of the theory also did not lead to new effects. We also investigated a real null theory that led to constant fields. This theory was then made complex by a procedure discussed in the early part of the paper. We found that the resulting complex theory remained trivial nevertheless. Again, we found that it was not necessary for the theory to be null to find confluence type solutions.