Bose-Einstein condensation of incommensurate solid 4He

It is pointed out that the simulation computation of energy performed so far cannot be used to decide if the ground state of solid 4He has the number of lattice sites equal to the number of atoms (commensurate state) or if it is different (incommensurate state). The best variational wave function, a shadow wave function, gives an incommensurate state, but the equilibrium concentration of vacancies remains to be determined. We have computed the one-body density matrix in solid 4He for the incommensurate state by means of an exact ground state projector method in which incommensurability occurs spontaneously. We find a vacancy induced Bose-Einstein condensation of about 0.23 atoms per vacancy at a pressure of 54 bar. This means that bulk solid 4He is supersolid at low enough temperature if the exact ground state is incommensurate.     

Vacancy excitation spectrum in solid 4He and longitudinal phonons

The first microscopic ab initio calculation of the excitation spectrum of a vacancy in solid 4He is reported. The energy-wave vector dispersion relation has been obtained at melting density within a development of the shadow wave function variational technique. The calculation of the excitation spectrum of a vacancy gives a bandwidth which ranges from 6 to 10 K in the hcp solid 4He, depending on the particular direction of the wave vector of the excitation. The effective mass of the vacancy turns out to be about 0.35 4He masses. We have also computed the spectrum of longitudinal phonons and we find rather good agreement with recent experimental results.     

Theory for the ground state of quantum crystals

We propose a new variational method for treating the ground state of quantum crystals which is free from the ills associated with cluster expansion procedures. Its application to solid ⁴He and neutron star matter produced satisfactory results.     

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.     

Ab Initio NCSM/RGM for Three-Body Cluster Systems and Application to 4He+n+n

We introduce an extension of the ab initio no-core shell model/resonating group method (NCSM/RGM) in order to describe three-body cluster states. We present results for the ⁶He ground state within a ⁴He+n+n cluster basis as well as first results for the phase shifts of different channels of the ⁴He+n+n system which provide information about low-lying resonances of this nucleus.     

氦原子和类氦离子基态能量的变分计算及相对论修正

采用一个包含坐标伸缩系数的简单有效的变分波函数,同时考虑到核的运动,利用Mathematic a语言开发了一个用变分法计算三体问题的程序,对氦原子和类氦离子(H^-,He,Li ⁺,Be⁺⁺,B³⁺,C⁴⁺,N⁵⁺,O ⁶⁺)的非相对论基态能量和解析波 函数进行了变分计算.在此基础上,对非相对论哈密顿量进行相对论和辐射修正,并考虑到有 限核电荷半径的影响,得到了氦原子和类氦离子高精度的基态能量值. 关键词： 氦原子 类氦离子 变分法 基态能量 相对论修正     

Stochastic solution of the Schrödinger equation for finite Fermi systems

We apply the Green function Monte Carlo method to model ground states for the atomic nucleus ¹⁶O and for a droplet of eight ⁴He atoms assumed to obey Fermi statistics. Ground-state properties of the two systems are obtained by means of projection onto antisymmetric trial functions. The Monte Carlo process is stabilized by allowing the generation size to grow sufficiently fast. The variational method using refined backflow Jastrow-Slater wave functions is shown to be reasonably accurate.     

Variational Calculation of 4He Tetramer Ground and Excited States Using Realistic 4He–4He Potentials

We calculated binding energies and wave functions of the ⁴He tetramer ground and excited states employing various realistic ⁴He?⁴He potentials which includes the currently most accurate one with the adiabatic, relativistic, QED and residual retardation corrections. We used our Gaussian expansion method (GEM) for ab initio variational calculations of few-body systems. We found that precisely the same shape of the short-range correlation (r _ij < 4Å) in the dimer appear in the ground and excited states of trimer and tetramer. The four kinds of the binding energies of the trimer and tetramer ground and excited states, ${B_3^{(0)}, B_3^{(1)}, B_4^{(0)}}$ and ${B_4^{(1)}}$ , for the different potentials exhibit perfect linear correlations over the range of binding energies relevant for ⁴He atoms; namely, six types of the generalized atomic Tjon lines were observed.     

Equilibrium concentration of point defects in crystalline4He at O K

We calculate the concentrations of vacancies and intersitials in the ground state of a Bose solid which models⁴He. Because ground-state boson wave functions are nodeless, their probability densities correspond to classical Boltzmann factors, and properties of Bose solids, such as the concentration of vacancies and interstitials, can be calculated using classical statistical mechanics. We model the ground-state wave function of⁴He with the product (Jastrow) form that corresponds to a classical 1/r ^b pair potential, and use a quasiharmonic approximation to calculate the concentrations of vacancies and interstitials in an fcc lattice with this potential. We find that the fractional concentration of vacancies at the melting point is 1.60×10^–5 for 1/r ⁹ and 6.36×10^–6 for 1/r ⁶, while the interstitial fractional concentrations are 1.32×10^–3 and 1.08×10^–5, respectively; the defect concentrations decrease by 7–16 orders of magnitude when the crystal density increases by 50%. At the same density, and with the same 1/r ⁹ potential, the concentration of vacancies in an hcp lattice is essentially the same as in an fcc lattice, but the interstitial concentration is much lower, apparently because the fcc lattice contains a more favorable split-interstitial site than does hcp. Therefore, our fcc vacancy results should be directly relevant for (hcp)⁴He, providing what we think is a lower bound on the vacancy concentration, while the interstitial concentration in⁴He is probably much lower than our results.     

Brueckner theory and Jastrow approach for finite nuclei

The results of Jastrow variational calculations and of Brueckner theory in lowest order (Brueckner-Hartree-Fock) are compared. The comparison is made for the calculations of ground state properties like binding energy and charge-radius of light and medium weight, closed shell nuclei (⁴He, ¹⁶O, ⁴⁰Ca). For the nucleon-nucleon interaction rather simple forces are used (Brink-Boeker potential B1, Afnan-Tang potential S3). For all cases considered it turns out that the results of the two different methods are in fairly good agreement, with the binding energy calculated in the Brueckner-Hartree-Fock approximation being always slightly below the corresponding upper bounds calculated in the Jastrow variational approach. This good agreement between the two methods indicates, that for light and medium weight nuclei the Jastrow variational approach and the Brueck-ner-Hartree-Fock approximation can be considered as reasonable approximations to a complete solution of the many-body problem.     

Neutron scattering study of the excitation spectrum of solid helium at ultra-low temperatures

There has been a resurgence of interest in the properties of solid helium due to the recent discovery of non-classical rotational inertia (NCRI) in solid ⁴He by Chan and coworkers below 200 mK which they have interpreted as a transition to a ‘supersolid’ phase. We have carried out a series of elastic and inelastic neutron scattering measurements on single crystals of hcp ⁴He at temperatures down to 60 mK. While we have found no direct evidence of any change in the excitation spectrum at low temperatures, we have found that the excitation spectrum of solid ⁴He shows several interesting features, including extra branches in addition to the phonon branches. We interpret these extra branches as single particle excitations due to propagating vacancy waves, which map on to the famous ‘roton minimum’ long known in the excitation spectrum of superfluid liquid ⁴He. The results show that in fact solid ⁴He shares several features in common with the superfluid.      

TDHF study of the He+ collision on atomic He targets at the8Be ground state energy

Experimentally the⁸Be ground state resonance has been studied in He⁺ collisions on atomic He atoms. The nuclear resonance manifests itself by satellite resonance lines corresponding to different electron configurations of the Be ion. Experimentally a large probability for the emission of one electron has been deduced. We study the atomic He⁺+He collision within a model in which the evolution of the electron wavefunction is treated dynamically in the TDHF scheme, and the motion of the nuclei is treated classically. In agreement with experiment we find a large probability for one electron to be emitted into the continuum during the lifetime of the⁸Be ground state resonance.     

An atomic linear Stark shift violating P but not T arising from the electroweak nuclear anapole moment

We propose a direct method of detection of the nuclear anapole moment. It is based on the existence of a linear Stark shift for alkali atoms in their ground state perturbed by a quadrupolar interaction of uniaxial symmetry around a direction and a magnetic field. This shift is characterized by the T-even pseudoscalar ( ^. )(∧ ^. )/B ². It involves on the one hand the anisotropy of the hyperfine interaction induced by the quadrupolar interaction and, on the other, the static electric dipole moment arising from electroweak interactions inside the nucleus. The case of ground state Cs atoms trapped in a uniaxial (hcp) phase of solid ⁴He is examined. From an explicit evaluation of both the hyperfine structure anisotropy and the static dipole deduced from recent empirical data about the Cs nuclear anapole moment, we predict the Stark shift. It is three times the experimental upper bound to be set on the T-odd Stark shift of free Cs atoms in order to improve the present limit on the electron EDM. Received 20 December 2000     

Lifetime of the Cs 6P1/2 state in bcc and hcp solid 4He

We present the first experimental study of time-resolved fluorescence from laser-excited Cs(6P_1/2) atoms isolated in a solid ⁴He matrix. The results are compared to the predictions of the bubble model including the interaction of the atomic dipole with its radiation reflected at the bubble interface. Our results show that in liquid He as well as in the body-centered cubic (bcc) crystalline phase of He the lifetime of excited Cs atoms does not depend on He pressure, in agreement with our theory. When going from the bcc to the hexagonally close-packed (hcp) phase of ⁴He the lifetime is reduced by ≈10% and decreases further with increasing He pressure. We assign this effect to the formation of Cs^*He_n exciplexes, and determine the pressure dependence of the probability that the 6P_1/2 state decays via this nonradiative channel.     

X-ray diffraction study of thermal vacancies in solid helium-3

Thermal vacancy concentrations in solid ³He have been directly measured by x-rays over a wide range of molar volumes in the bcc phase and one molar volume in the hcp phase. Values of the vacancy free energies and free volumes of formation have been obtained, and comparison with NMR and ultrasonic studies yields information about vacancy motion in the two phases of the solid.     

On the Choice of the Wavefunction of the Ground State of He for Precision Calculations of Autoionization State Parameters above the Excited Ion Formation Threshold

The necessity of choosing multiparametric wavefunctions for describing the ground state of an atom in the problems of ionization of atoms by photons and electrons has been substantiated for the He atom as an example. Comparative analysis of application of different ground-state wavefunctions for this atom has been performed. The energies, widths, and partial widths of the lower autoionization state ¹P of the He atom above the excited ion formation threshold has been performed. It is shown that in contrast to total widths of quasi-stationary states, which differ insignificantly for different wavefunctions of the ground state, the partial widths are substantially different.     

An EPR Study of Cu2+ Doped Sodium Hydrogen Oxalate Monohydrate Single Crystal

The EPR spectra of Cu²⁺ in Sodium hydrogen oxalate monohydrate, NaHC₂O₄.H₂O(SHOMH hereafter) single crystal was studied at room temperature. The angular variation of EPR spectra showed that the Cu²⁺ ion in SHOMH single crystal substitutes with Na⁺ monovalent cation together with a monovalent vacancy to compensate oxygen in the crystal. Since the crystal symmetry is triclinic, only one site is observed in the EPR spectra in three perpendicular axis. The spin Hamiltonian parameters were obtained, and the ground state wave function of Cu²⁺ ion in the lattice was constructed.     

A Clear Atomic Example for the Surface Sensitivity of Penning Ionization: He*(23S) + Yb

Using a crossed-beam apparatus with a double hemispherical electron spectrometer, we have studied the spectrum of electrons released in thermal energy ionizing collisions of metastable He*(2³S) atoms with ground state Yb(4f¹⁴ 6s^{2 1}S₀) atoms, thereby providing the first Penning electron spectrum of an atomic target with 4f-electrons. In contrast to the Hel (58.4 nm) and NeI (73.6/74.4 nm) photoelectron spectra of Yb, which show mainly 4f- and 6s-electron emission in about a 5:1 ratio, the He*(2³S) Penning electron spectrum is dominated by 6s-ionization, accompanied by some correlation-induced 6p-emission (8% Yb⁺(4f¹⁴ 6p ²P) formation) and very little 4f-ionization (?2.5%). This astounding result is attributed to the electron exchange mechanism for He*(2³S) ionization and reflects the poor overlap of the target 4f-electron wavefunction with the 1s-hole of He*(2³S), as discussed on the basis of Dirac-Fock wave functions for the Yb orbitals and through calculations of the partial ionization cross sections involving semiempirical complex potentials. The presented case may be regarded as the clearest atomic example for the surface sensitivity of He*(2³S) Penning ionization observed so far.     

Metastability range of the Bose condensate in 7Li-fermion mixtures at T = 0

We evaluate the ground state of a mixture of bosons and spin-polarized fermions in the case of attractive boson-boson interactions, using a variational Ansatz for the Bose condensate wave function and the Thomas-Fermi approximation for the fermions in the mean field of the condensate. Within this approximation we show that the presence of the fermions tends to restrict the metastability range of the condensate, irrespectively of the sign of the boson-fermion interactions. Numerical illustrations are reported for mixtures of ⁷Li atoms with fermions having the ⁶Li mass.     

Resonance inelastic scattering of an x-ray photon by a Ne-like atomic ion

The absolute values and the shape of the double differential cross sections of the resonance inelastic scattering of a linearly polarized x-ray photon in the energy region of the ionization threshold of the deep 1s shell of the Ne atom and the Si⁴⁺ and Ar⁸⁺ neon-like ions are calculated in the nonrelativistic approximation for the wave functions of one-electron states and in the dipole approximation for the scattering probability amplitude. The multiparticle effects of radial relaxation of electronic shells in the field of a deep vacancy and of stabilization of the deep vacancy as a neutral atom transforms to a multiply charged positive ion, as well as the effect of the spin-orbit splitting of the 2p valence shell, are taken into account. The calculation results are predictive in character.