Ultracold helium trimers

We summarize the results on binding energies and scattering observables for ⁴He-⁴He₂ and ³He-⁴He₂ collisions obtained with the Tang-Toennies-Yiu potential.     

Binding energies and scattering observables in the 4He3 atomic system

The ⁴He₃ system is investigated using a hard-core version of the Faddeev differential equations. Realistic ⁴He-⁴He interactions are employed, among them the LM2M2 potential by Aziz and Slaman and the recent TTY potential by Tang, Toennies and Yiu. We calculate the binding energies of the ⁴He trimer, but concentrate in particular on scattering observables. The scattering lengths and the atom-diatom phase shifts are calculated for center of mass energies up to 2.45 mK. It is found that the LM2M2 and TTY potentials, although of quite different structure, give practically the same bound-state and scattering results. Received 19 June 2000     

The determination of interatomic potentials from the extrema in differential cross sections

A new method for determining interaction potentials from the positions of the extrema in interference patterns in atomic scattering is applied to ⁴He-⁴He and ⁴He⁺-⁴He scattering. The new computed potentials for ⁴He⁺-⁴He confirm that in most collisions the atoms follow the diabatic rather than the adiabatic potential.     

Stability of 3He2 4He M and 3He3 4He M L = 0,1 Clusters

We have studied the stability of mixed ³He/⁴He clusters in L = 0 and L = 1 states by the diffusion Monte Carlo method, employing the Tang-Toennies-Yiu (TTY) He-He potential. The clusters ³He⁴He_M ( ) and ³He₂⁴He_M (L = 0, S = 0) are stable for M > 1, while to bind two ³He in a triplet state the minimum number of ⁴He is four. Considering clusters with three ³He, ³He₃⁴He₄ is the smallest stable system in the L = 1 state, while ³He₃⁴He₈ is the smallest stable system in the L = 0 state.     

Ultracold collisions in the system of three helium atoms

The Faddeev differential equations for a system of three particles with a hard-core interaction are described. Numerical results on the binding energies of the ⁴He₃ and ³He⁴He₂ trimers and on ultracold collisions of ^3,4He atoms with ⁴He₂ dimers obtained with the help of those differential equations are reviewed. The results obtained for the hard-core model using the Faddeev equations are compared with analogous results obtained by alternative methods.     

Binding Energies and Scattering Observables in the 4He3 and 3He4He2 Three-Atomic Systems

The asymmetric ³He⁴He₂ three-atomic system is studied on the basis of a hard-core version of the Faddeev differential equations. Binding energy and scattering observables for this system are compared to previous results for the symmetric ⁴He₃ problem.     

The concentration susceptibility in He3He4 mixtures near the superfluid transition

We report direct measurements of the concentration susceptibility in He³He⁴ mixtures by observing the gravity-induced concentration change δX₃ over a height of 2 mm in the mixture. The predicted peak at the superfluid transition is observed for the investigated mixtures, 0.60 ? X₃ ? 0.67.     

Metastable helium cluster He<Stack><Subscript>4</Subscript><Superscript>*</Superscript></Stack>

The existence of a metastable cluster He ₄ ^* with total spin S = 2 is predicted. The cluster consists of two covalently bound excited spin-polarized triplet He ₂ ^* molecules and is rectangular in shape. The electron wavefunctions, the dependence of the energy He ₄ ^* system on the distance between the He ₂ ^* triplet molecules, the atomic spacing, the frequency spectrum of natural oscillations of the cluster, and other characteristics are calculated from first principles. It is shown that the metastable state is formed if one of the excited He ₂ ^* molecules is in the ³Σ _u ⁺ state, while the other is in the ³Π_g state. The radiation lifetime τ of the metastable cluster He ₄ ^* is calculated; it is found to range from 100 to 200 s, which is much longer than the lifetime τ ≈ 20 s of the triplet molecule He ₂ ^* (³Σ _u ⁺ ). The height U ≈ 0.5 eV of the potential barrier preventing the departure from the local energy minimum is determined. The energy E_acc ≈ 9 eV/atom accumulated in the He ₄ ^* cluster is calculated; this energy considerably exceeds the energy of known chemical energy carriers. It is shown that the accumulated energy is released virtually completely during decomposition of the He ₄ ^* cluster into individual helium atoms. This means that helium clusters are a promising material with a high accumulated energy density (HEDM).     

Screening effects in secondary electron production by equal velocity H+, H+2, He+, He++ions

Electron spectra produced by equal velocity (0.75 MeV/amu) H⁺, H⁺₂, He⁺ and He ⁺⁺ ions are shown. Screening effects are observed for He⁺ ions but not for H⁺₂. He⁺⁺ cross sections scale like Z² = 4 when compared to H⁺ cross sections.     

Exit angle dependence of charge-state distribution of backscattered He ions

Exit angle and energy dependences of the charge-state distribution of backscattered He ions were investigated when 500 keV He⁺ ions were incident on SiO₂. The energy dependence of the He⁺ fraction was estimated by comparing the measured He⁺ spectra with the simulated spectra of He ions in all charge states at the exit angles of 5-25° with respect to the SiO₂ surface. We found that the He⁺ fraction is almost independent of the exit angle at energies higher than 250 keV and the observed energy dependence of the He⁺ fraction is in good agreement with that for the carbon-foil-transmission experiment. In the low energy region (<250 keV), however, the He⁺ fraction decreases as the exit angle decreases.     

Theoretical Study of Triatomic Systems Involving Helium Atoms

The triatomic ⁴He system and its isotopic species ${^4{\rm He}_2^3{\rm He}}$ are theoretically investigated. By adopting the best empirical helium interaction potentials, we calculate the bound state energy levels as well as the rates for the three-body recombination processes: ⁴He + ⁴He + ⁴He → ⁴ He₂ + ⁴He and ⁴He + ⁴He + ³He → ⁴He₂ + ³He. We consider not only zero total angular momentum J = 0 states, but also J > 0 states. We also extend our study to mixed helium-alkali triatomic systems, that is ⁴He₂ X with X = ⁷Li, ²³Na, ³⁹K, ⁸⁵ Rb, and ¹³³Cs. The energy levels of all the J ≥ 0 bound states for these species are calculated as well as the rates for three-body recombination processes such as ⁴He + ⁴He + ⁷Li → ⁴ He₂ + ⁷Li and ⁴He + ⁴He + ⁷Li → ⁴ He⁷Li + ⁴He. In our calculations, the adiabatic hyperspherical representation is employed but we also obtain preliminary results using the Gaussian expansion method.     

Charged cores in ionized $\mathsf{{^{4}He}}$ clusters III: A quantum modeling for the collisional relaxation dynamics

When a pure ⁴He droplet is ionized by electron impact, the most abundant fragment detected in mass spectra after ionization is He₂ ⁺ . All the models that have been proposed thus far to explain the experimental evidence therefore involve the formation of the He₂ ⁺ molecular ion. The understanding of the interactions between this ion and the surrounding He atoms in the cluster and of their dynamical behavior during cluster break-up is an important element for the modeling of the cluster evolution after the ionization event. In previous works [1,2] we have computed and described the Potential Energy Surface (PES) of the electronic ground state for the He₃ ⁺ system that provides the required forces between He₂ ⁺ and He. After ionization He₂ ⁺ is presumably formed by association of an He ⁺ and any of the neutral atoms in the cluster via a 3-body collision process. The ensuing vibrational quenching of the hot molecular ion may release the energy necessary to evaporate the entire droplet, or most of it, and give the fragmentation patterns detected by experiments. We present here a model quantum dynamics that generates vibrational deexcitation cross-sections and the corresponding rate coefficients for the collision of He₂ ⁺ with He. A timescale of the cluster evaporation due to vibrational relaxation is estimated and the present findings are compared with earlier studies on the same system.Received: 15 June 2004, Published online: 24 August 2004PACS: 31.15.Qg Molecular dynamics and other numerical methods - 34.50.Ez Rotational and vibrational energy transfer - 36.40.Wa Charged clusters     

He5 scattering states in the refined cluster function representation

As a first application of the refined cluster model reaction theory we calculated the scattering states of He⁵ using a specific ansatz for the nucleon-nucleon forces. He⁴-n and H³-d channels are considered only. Our results agree qualitatively with the experimental values if available; in particular we were able to explain the narrow resonance in theD _3/2 He⁴-n channel as a consequence of the strong coupling to theS _3/2 T-d channel.     

Investigation of the reaction D(<Superscript>4</Superscript>He, γ)<Superscript>6</Superscript>Li at ultralow energies

The cross section of the reaction D(⁴He, γ)⁶Li with titanium and zirconium deuterides as targets is measured for incident ⁴He⁺ ion energies of 30 and 36 keV, respectively. The ion beam is generated by a Hall pulsed plasma accelerator. For the first time, upper limits on the cross section of the reaction D(⁴He, γ)⁶Li at ultralow energies are imposed (at 90% confidence level): σ ≤ 1.2 × 10^?35 cm² for the TiD₂ target and E(⁴He⁺) = 30 keV, and σ ≤ 7 × 10^?36 cm² for the ZrD₂ target and E(⁴He⁺) = 36 keV     

Spectroscopic evidence for superfluidity in liquid He droplets

A beam of liquid He _N droplets (N≈5000) is prepared by a cryogenic free jet expansion, doped with single molecules and studied via laser spectroscopy. The spectra consist of sharp lines (Δν?0.003–0.1 cm^?1) and show rotational structure (for SF₆), providing the first information on the droplet temperature, which is 0.37 K for⁴He _N and 0.14 K for³He _N . The rotational constants give information on the microscopic interaction of the molecule with the He environment. Each of the sharp vibronic lines of the elecronic S₁←S₀ transition in glyoxal (C₂O₂H₂) is accompanied by a phonon sideband, showing a distinct gap followed by a sharp peak at the roton energy (8.1 K) and a second weaker maxon peak followed by a broad multiphonon wing. These provide the first evidence for superfluidity in⁴He _N predicted theoretically.     

On the π3He3He coupling

A critical discussion of different methods of estimation of the coupling constant f_π³He³He² is given. It is claimed that at present the best way of obtaining information on this coupling constant is to extrapolate certain differential cross sections, in particular, of the elastic ³He³H scattering, to the pion pole. The resulting value f_π³He³He² = 0.055 ± 0.020 is smaller than the corresponding pion-nucleon value. It supports the expected shadowing effects inside the nucleus but disagrees with other more model-dependent estimations.     

钠分子同位素替代对低温下的He-Na2冷碰撞体系转动激发积分散射截面的影响

用多体刚性椭球模型计算了不同能量下氦的同位素原子⁴He,¹⁰He与钠的同位素分子¹⁸Na₂,²³Na₂,³⁷Na₂ 替代碰撞体系的转动激发积分散射截面.通过分析⁴He,¹⁰He-¹⁸Na₂,²³Na₂,³⁷Na₂各转动激发积分散射截面的差异,总结出在钠分子的对称同位素替代情形下⁴He,¹⁰He -¹⁸Na₂,²³Na₂,³⁷Na₂碰撞体系转动激发积分散射截面随钠分子转动量子数和体系约化质量变化的规律.结果表明,体系的约化质量及入射原子相对碰撞能量的变化均给体系的碰撞截面带来不同程度的影响.另外,计算了相对入射能量为100 meV时,相互作用势的不同区域对¹⁰He-¹⁸Na₂,²³Na₂,³⁷Na₂各碰撞体系转动激发积分散射截面的贡献情况. 关键词： 多体刚性椭球模型 转动激发积分散射截面 钠同位素分子 椭球等势面     

Exchange and nuclear symmetry interference in He+-He scattering

A method is described to determine the potential difference, V _g-V _u, that will accurately reproduce the exchange and nuclear symmetry oscillations observed by Aberth et al. in their experimental work on He⁺-He differential scattering. It is demonstrated that at higher energies and angles the experimental results for ⁴He⁺-⁴He, ⁴He⁺-³He and ³He⁺-³He appear incompatible with one another when investigated in terms of a two-state scattering theory. This is an indication that at these energies and angles the theory may require modification to include the effects of coupling to higher states.     

Frequency stabilization and measurements of 543 nm HeNe lasers

In this paper we report our investigations on the frequency stabilization and frequency measurements of 543 nm HeNe laser. It contains following four different works. (1) Using a metal laser tube we have built an iodine-stabilized 543 nm HeNe laser by the Frequency-Modulation (FM) spectroscopy. The signal-to-noise ratio of the hyperfine spectrum reached 2 × 10^–12 at 1 s sampling time. (2) We have built a compact iodine-stabilized 543 nm HeNe laser system using the third-harmonic locking technique. Stability better than 1 × 10^–12 for sampling time >1 s is obtained. We also suggest the b₁₀ line for the future recommendation. (3) We constructed the Lamb-dip stabilized He-²⁰Ne and He-²²Ne lasers and measured their frequency stability, reproducibility, and absolute frequencies. The results suggest that the Lamb-dip stabilized lasers are appropriate for secondary wavelength standards. We have also deduced the isotope shift of Ne atom at 543 nm. (4) We have developed two two-mode stabilized 543 nm HeNe lasers using the bang-bang control method. The Allan variance is 1 × 10^–11 at 1 s sampling time.     

4He+在Al和Si单晶晶面沟道中的半波长及阻止本领

采用高分辨探测系统,在不同的入射角θ_in和出射角θ_out的条件下,测量了1—2MeV⁴He⁺入射在Al(100)面和Si(110),(100)面中的背散射能谱。得到了背散射能谱振荡峰的间距ΔE与cosθ_in/cosθ_out的直线关系,从而获得了1—2MeV⁴He⁺在这三个晶面中的振荡半波长及阻止本领。实验得到的半波长与理论计算值在误差范围内一致,晶面沟道方向的阻止本领略大于随机方向的阻止本领。 关键词：