Planck Mass Plasma Analog of String Theory

In recent years there had been a growing interest in analog models of general relativity, with certain superfluid solutions simulating black hole solutions of Einstein's gravitational field equation. The quantization of a superfluid, composed of discrete particles (helium atoms), treated as a nonrelativistic many body problem does not lead to divergencies as the quantization of Einstein's field equations. Quantization of gravity is possible in string theory, but only if one introduces the daring hypothesis of higher dimensions. But if the gravitational field is made up of discrete elements as superfluid helium is made up of helium atoms, then gravity can be quantized without difficulty in three space and one time dimension. Such a hypothesis, of course, implies that Lorentz invariance is a dynamic symmetry caused by real rod and clock deformations, as it was assumed in the pre-Einstein theory of relativity by Lorentz and Poincaré, which required the existence of an aether. Making the hypothesis that this aether is a kind of superfluid plasma made up of positive and negative Planck mass particles interacting with the Planck force over a Planck length, one obtains an analog of the standard model, including gravity, which can be quantized as a nonrelativistic many body problem. In this model nonrelativistic vortex rings in three space dimensions and one time dimension simulate the relativistic theory of closed strings in ten space-time dimensions. But because in the vortex lattice, one obtains a large dimensionless number conceivably advancing our understanding of the finestructure constant.     

A semi-empirical method for the calculation of spin—orbit splitting in degenerate electronic states of linear polyatomic molecules

A semiempirical method for the calculation of spin—orbit coupling constants in linear polyatomic molecules is discussed. The method uses the readily available output from a CNDO/2 calculation and a set of effective atomic coupling constants obtained from observed spectroscopic data on atoms. Two procedures for obtaining the spin—orbit splitting are discussed: one based on a closed shell CNDO/2 calculation and one based on an open shell calculation.The average error for the molecules studied was 6.8% and 7.7% for the two procedures used in the calculations, the easier closed shell procedure giving the lower percentage error. It should be noted that the largest errors occurred in the case of diatomic molecules where the error would be expected to be the greatest. Thus, the average error involved in the values of the spin—orbit splitting for polyatomic molecules is much less than 3.7% for the closed shell procedure. The method used appears to be extendable to non-linear molecules in which the only atoms off the principle symmetry axis of the molecules are hydrogen. The method should be useful in the interpretation of photoelectron spectra.     

A semi-empirical method for the calculation of spin—orbit splitting in degenerate electronic states of linear polyatomic molecules

A semiempirical method for the calculation of spin—orbit coupling constants in linear polyatomic molecules is discussed. The method uses the readily available output from a CNDO/2 calculation and a set of effective atomic coupling constants obtained from observed spectroscopic data on atoms. Two procedures for obtaining the spin—orbit splitting are discussed: one based on a closed shell CNDO/2 calculation and one based on an open shell calculation.The average error for the molecules studied was 6.8% and 7.7% for the two procedures used in the calculations, the easier closed shell procedure giving the lower percentage error. It should be noted that the largest errors occurred in the case of diatomic molecules where the error would be expected to be the greatest. Thus, the average error involved in the values of the spin—orbit splitting for polyatomic molecules is much less than 3.7% for the closed shell procedure. The method used appears to be extendable to non-linear molecules in which the only atoms off the principle symmetry axis of the molecules are hydrogen. The method should be useful in the interpretation of photoelectron spectra.     

Equation of state of metallic helium

The effective ion-ion interaction, free energy, pressure, and electric resistance of metallic liquid helium have been calculated in wide density and temperature ranges using perturbation theory in the electron-ion interaction potential. In the case of conduction electrons, the exchange interaction has been taken into account in the random-phase approximation and correlations have been taken into account in the local-field approximation. The solid-sphere model has been used for the nuclear subsystem. The diameter of these spheres is the only parameter of this theory. The diameter and density of the system at which the transition of helium from the singly ionized to doubly ionized state occurs have been estimated by analyzing the pair effective interaction between helium atoms. The case of doubly ionized helium atoms has been considered. Terms up to the third order of perturbation theory have been taken into account in the numerical calculations. The contribution of the third-order term is significant in all cases. The electric resistance and its temperature dependence for metallic helium are characteristic of simple divalent metals in the liquid state. The thermodynamic parameters—temperature and pressure densities-are within the ranges characteristic of the central regions of giant planets. This makes it possible to assume the existence of helium in the metallic state within the solar system.     

Quantum reflection

Recent experimental and theoretical results concerning the sticking coefficient at ultralow energy are described. The need for an accurate treatment of long range forces, including retardation, is emphasized. The system involving H atoms incident on liquid helium provides the first clear evidence of quantum reflection. New results are reported for the sticking of D atoms incident on helium. The energy upper bound for the regime of quantum reflection for alkali atoms is found to be extremely low, but ultimately achievable.     

Relaxation mechanisms of multi-quantum coherences in the Zeeman structure of atomic Cs trapped in solid He

This paper extends our previous work on near-degenerate magnetic resonance transitions in alkali ground states involving the simultaneous absorption of multiple radio-frequency quanta. New experimental results with an improved spectral resolution were obtained with cesium atoms trapped in the cubic phase of a helium crystal. The main objective of the paper is a theoretical study of the influence of stochastic perturbations of given multipole orders on the various multi-photon coherences. Algebraic and numerical results for perturbations of both dipolar and quadrupolar symmetry are presented. The present experimental resolution does not yet allow us to distinguish between these two most likely relaxation mechanisms. Nonetheless, the experimental spectra are very well described when allowing in the calculations for a magnetic field inhomogeneity of 2×10^-5. PACS 76.70.Hb; 32.80.Wr; 32.30.Dx; 32.60.+i     

Self-consistent quantum structure of diffuse helium atom clusters

Diffuse clusters of arbitrary numbers of helium atoms are treated in a mean-field theory of the many-body system. The nonlinear Hartree self-consistent-field equations are solved numerically to give their energy eigenvalues and eigenfunctions. Both isotopes ⁴He and ³He are treated according to their bosonic and fermionic statistics and symmetry requirements. Clusters of all sizes of ⁴He atoms are stable, but there is a minimum threshold of ～70 atoms for the formation of ³He clusters. All the excited states in addition to the ground state were found. The wave functions are seen to have interesting differences from electronic wave functions in atoms.     

非相对论性和相对论性原子组态相互作用理论——激发能量和辐射跃迁几率

我们建立的非相对论性和相对论性原子组态相互作用理论计算方法可用来计算低度激发态的激发能量和辐射跃迁几率(包括允许跃迁和禁戒跃迁)。为了检查我们的计算程序,分别用两种方法计算了氦原子N=2激发态的激发能和相应的辐射跃迁几率。结果表明:非相对论性理论和相对论性理论计算结果基本一致。原子激发能量的精度为千分之几,振子强度的精度为百分之几。上述原子组态相互作用理论方法可用于计算任何原子或离化态原子。 关键词：     

The role of collision cascades and helium atoms in cavity nucleation

Abstract

The simultaneous production of helium atoms and collision cascades during irradiation may enhance the nucleation of cavities. The influence of parameters such as helium generation rate and recoil energy on the possibility of cavity nucleation is investigated. The three most likely mechanisms by which cascade nucleation might occur are considered. Firstly, helium atoms that are present within the cascade may succeed in preventing the collapse of cascades into dislocation loops. Secondly, helium atoms in the cascades may be swept together during the cooling of the cascade to form cavity embryos. Thirdly, more distant helium atoms may be able to reach an uncollapsed vacancy aggregate in a cascade by diffusion before thermal annealing of the cascade.

Calculations indicate that it is unlikely that a sufficient number of helium atoms would be present in a cascade to prevent its collapse. The probability of several helium atoms being swept together within the volume of a cascade is also found to be rather small. Calculations suggest, however, that the cavity nucleation in cascades might become significant if helium atoms were to diffuse much faster than the substitutional diffusion rate during irradiation. The selfinterstitial replacement mechanism, for instance, would yield such a fast diffusion rate of helium.     

Discovery of dumbbell-shaped Cs*Hen exciplexes in solid 4He

We have observed several new spectral features in the fluorescence of cesium atoms implanted in the hcp phase of solid helium following laser excitation to the 62P states. Based on calculations of the emission spectra using semiempirical Cs-He pair potentials the newly discovered lines can be assigned to the decay of specific Cs*Hen exciplexes: an apple-shaped Cs(APi3/2)He2 and a dumbbell-shaped Cs(APi1/2)Hen exciplex with a well-defined number n of bound helium atoms. While the former has been observed in other environments, it was commonly believed that exciplexes with n>2 might not exist. The calculations suggest Cs(APi1/2)He7 to be the most probable candidate for that exciplex, in which the helium atoms are arranged on a ring around the waist of the dumbbell-shaped electronic density distribution of the cesium atom.     

Application of combined Hartree-Fock-Roothaan theory to atoms with an arbitrary number of closed and open shells of any symmetry

The applicability of a combined open-shell Hartree-Fock theory of atomic-molecular and nuclear systems to the states of a single configuration which has the arbitrary symmetry of open shells is explicitly demonstrated by calculations based on the combined Hartree-Fock-Roothaan equations for atoms. As examples of an application of the combined theory using single-zeta Slater-type basis sets, the calculations have been performed for the lowest states of the lowest and excited electronic configurations of carbon and nitrogen atoms containing one-, two- and three-open shells. For the case of single-open shells for carbon and nitrogen atoms, the double-zeta basis-set calculations are also presented. The results of computer calculations for the orbitals, kinetic and total energies, linear combination coefficients and virial ratios are given.     

Analysis of the fractal intrinsic quality in the ionization of Rydberg helium and lithium atoms

We study the fractal rhythm in the ionization of Rydberg helium and lithium atoms in an electric field by using the semiclassical method. The fractal structures present a nested relationship layer by layer in the initial launch angles of the ionized electrons versus the escape time, which is defined as the rhythm attractor, and exhibit similar rhythm endings. The gradually enhanced chaotic regions of the escape time plots tend to broaden as the scaled energy increases. In addition,the fractal rhythm changes synchronously with the oscillations of the kinetic energy spectrum. We note that the intrinsic quality of the fractal rhythm is closely related to the kinetic energy distribution, that is, the inherent dynamic properties of the Hamiltonian equations have an impact on the fractal regularities. In addition, different ionizing closed trajectories exhibit iterate properties and the inherent beauty of symmetry. Our results and analysis can not only reveal new laws in the ionization of Rydberg atoms, but also promote the establishment of the dynamic mechanism of fractals.     

相对论离子与氦二聚体碰撞电离的理论研究

基于对称程函近似,从理论角度研究了相对论离子与氦二聚体碰撞双电离的直接碎裂通道：由入射离子与两个原子的作用造成的双电离。从不同的近似角度出发,建立了两个理论模型,第一个模型将氦二聚体的两个原子看做一个整体,而另外一个模型完全忽略了两个氦原子之间的相互作用。模型的数值计算结果表明,总截面与氦二聚体的空间取向有很强的依赖关系,当氦二聚体与入射离子束流平行时,总截面达到最大值,在垂直时为最小值。进一步研究发现,模型一的结果在氦二聚体核间距较小时更为合理,核间距较大时,模型二更为精确。     

Irreducible spin precession theory applied to some topics in atomic and nuclear radio-frequency spectroscopy

Several problems from radio-frequency spectroscopy of atoms and nuclei are treated with irreducible spin precession theory. In the first part, effective field techniques are used to derive analytically single and multiple quantum double resonance lineshapes for atoms with a hyperfine structure in a high magnetic field. In the second part (as an extension to previous work), nuclear resonance signals are calculated for oriented nuclei subject to an electric hexadecapole interaction. Lineshapes of acoustically driven hexadecapole transitions are derived in closed form and compared to experiment. Further, multiple quantum NMR transitions within a hexadecapole shifted nuclear Zeeman structure are calculated, and some distinct features of hexadecapole effects on NMR lineshapes are pointed out. This last case is of current interest due to recent progress in NMR-line narrowing techniques. — In the Appendix, we give lineshape equations for single and double quantum NMR transitions on oriented (I=1)-nuclei subject to an electric quadrupole interaction; these equations are also being used in the atomic rf-spectroscopy calculations. The equations are exact to all orders of the interaction with the external fields.     

Interpretation of intensities in electron-momentum and photoelectron spectroscopiesag

Relative intensities for the photoelectron reaction on atoms and molecules are not related to structure calculations in the same way as those for the noncoplanar symmetric (e, 2e) reaction. The photoelectron dipole matrix element is dependent on recoil momentum only through the unique relationship of recoil momentum to the photon energy and is much harder to calculate for chemically-interesting momenta. Relative intensities for binary (e, 2e) reactions are independent of total energy at high enough energies and strongly dependent on symmetry and recoil momentum, for which an intensity profile can be measured for values starting at zero. In comparing with structure calculations, binary (e, 2e) intensities for low recoil momentum may be compared directly with pole strengths in calculations of the one-electron Green's function. In the case of states within a single symmetry manifold the relative intensities will be independent of recoil momentum up to some maximum, usually at least a few atomic units.     

Microwave spectroscopy measurements of the hyperfine structure in antiprotonic 3He

We shall present here the first experimental results for microwave spectroscopy of the hyperfine structure of antiprotonic He-3 and a comparison to numerical simulations of the measurement. Due to the helium nuclear spin, antiprotonic He-3 has a more complex hyperfine structure than antiprotonic He-4 which has already been studied before. Thus a comparison between theoretical calculations and the experimental results will provide a more stringent test of the three-body quantum electrodynamics (QED) theory. The comparison of measured data to simulations allows to investigate the collisional processes between the helium atoms of the target medium and the antiprotonic helium atomcules. The collision rates can not be calculated exactly, but estimated by comparison of numeric simulations with the experimental results. Two out of four super-super-hyperfine (SSHF) transition lines of the (n, L)?=?(36, 34) state were observed. The measured frequencies of the individual transitions are 11.12559(14)?GHz and 11.15839(18)?GHz, less than 1?MHz higher than the current theoretical values, but still within their estimated errors. The frequency difference between the two lines also agrees with theoretical calculations.     

Control of dissipation of energy via reservoirs of coherent states

Dynamic profiles of various chemical reactivity indices like chemical potential, chemical hardness, electrophilicity, susceptibility, etc., within a confined environment during the interaction of atoms with strong oscillating time dependent magnetic fields have been studied. In the present study hydrogen and helium atoms in ground state (n = 1), as well as in excited state (n = 20) are considered. Time-dependent Schrödinger equations are solved for the ground and excited states of hydrogen atom and the Rydberg state of the helium atom while a generalized nonlinear Schrödinger equation is solved for the ground state of the helium atom. Dirichlet type boundary condition has been used to implement confinement to the systems. With an increase in the degree of confinement the system gets harder and hence becomes more stable. Keeping the confinement radius fixed, systems get more stabilized in strong field compared to weak field.     

弹性反冲探测分析技术在材料氦行为研究中的应用

弹性反冲探测分析技术（ERDA）对轻元素的测定具有灵敏度高、包含深度信息的优势,因此在材料氦行为研究中发挥着重要作用。镍基哈氏N合金被认为是未来熔盐堆的结构材料,氦脆是其服役性能下降的主要因素之一。利用掠入射模式的ERDA,解析了哈氏N合金样品中的氦原子浓度及其分布,但仅局限于0~175 nm深度范围内。结果表明:在800℃的退火条件下,距离样品辐照表面~33 nm深度区域内,出现了氦原子逃逸现象。更高温度的退火（1 050℃）可加剧氦原子的逃逸,但样品中仍有氦原子滞留。另外,采用透射式的ERDA,极大地扩大了对氦原子分析的深度范围,得到了纯镍薄膜在0~950 nm深度区域内的氦原子浓度分布。这表明将块体材料制备成薄膜样品,利用透射模式的ERDA,将可以得到氦原子在更大范围内的扩散、逃逸行为。Since the elastic recoil detection analysis (ERDA) technique has the advantages of high sensitivity and deep information in analyzing the light elements, it plays an important role in the study of helium behavior in materials. Helium embrittlement is one of the main reasons for the degradation of the Hastelloy N alloy, which has been considered as the promising candidate structural material for the further molten salt reactor. In this work, the profile of helium concentrationin sample of Hastelloy N alloy was analyzed by ERDA experiments applying grazing-incidence geometry. However, the result was limited within the depth range of 0~175 nm, and it shown that helium atoms escaped in the range from the irradiated surface of the sample to the depth of ~33 nm when annealing the sample at 800℃ The annealing at higher temperature (1 050℃) increased the escape of helium atoms, but a small fraction of helium atoms still trapped in the sample. In addition, the profile of helium concentration was obtained in the helium-irradiated pure nickel film in the depth range of 0~950 nm, using the ERDA experiments in transmission geometry. This indicates that the diffusion behavior of helium atoms in bulk samples can be completely obtained using the ERDA experiments in tranmission geometry if the bulk material can be prepared into a thin film sample.     

对理想条件下Rn及其子体垂直运移实验数据的再分析

当1个Rn与8个以上的He原子结合成团簇后,该团簇可以克服重力向上运移;当与1个Rn结合的He原子少于8个时,该团簇将向下运移.因此向上运移的RnHe团簇的平均原子数要明显大于向下运移的RnHe团簇的平均原子数.对Rn及其子体的长距离运移实验数据进行分析表明：在不考虑扩散的情况下,平均每个Rn需要与7.5个He原子结合,则铀矿石源所能提供的He原子数量可能不够;如果考虑扩散的情况,平均每个Rn只需与4.26—5.57个He原子结合,则铀矿石源可以提供足够数量的He.这一推导结果说明,在采用团簇运移机制解释Rn及其子体垂直运移实验结果时,不能忽略扩散运移的存在. 关键词： Rn 垂直运移 RnHe团簇     

The system of differential equations in the momentum space for the three-body problem: Continuous spectrum

A system of differential equations in the momentum space for describing three-body scattering is obtained. Preliminary calculations of the length of boson scattering on a bound bosonic pair are performed. The data obtained are in good agreement with the results of calculations of helium atom scattering on a helium dimer.