Adiabatic hyperspherical study of the helium trimer

Ultracold state-to-state chemistry for three-body recombination in realistic 3He2-alkaline-earth-metal systems

The ultracold state-to-state chemistry for three-body recombination (TBR) in realistic systems recently could be experimentally investigated with full quantum state resolution. However, many detected phenomena remain challenging to be explored and explained from the theoretical viewpoints because this generally requires computational powers beyond the state-of-the-art. Here, the product-state distributions after TBR of 3He2-alkaline-earth-metal systems, i.e. after the processes 3He+3He+X→3HeX+3He with X being 9Be, 24Mg, 40Ca, 88Sr, or 138Ba, in the zero-collision-energy limit are theoretically studied. Two propensity rules for the distribution of the products found in current experiments have been checked, and the mechanism underlying these product-state distributions is explored. Particularly, two main intriguing transition pathways are identified, which may be responsible for the nonlinear distribution of the products versus their rotational quantum number. In addition, the total TBR rates of these systems are also accounted for by the joint effects of major adiabatic potential energies and relevant nonadiabatic couplings.

Universal Properties of Weakly Bound Two-Neutron Halo Nuclei

We construct an effective field theory of a two-neutron halo nucleus in the limit where the two-neutron separation energy B and the neutron-neutron two-body virtual energy ε_{n} are smaller than any other energy scale in the problem, but the scattering between the core and a single neutron is not fine-tuned, and the Efimov effect does not operate. The theory has one dimensionless coupling which formally runs to a Landau pole in the ultraviolet. We show that many properties of the system are universal in the double fine-tuning limit. The ratio of the mean-square matter radius and charge radius is found to be ⟨r_{m}^{2}⟩/⟨r_{c}^{2}⟩=Af(ε_{n}/B), where A is the mass number of the core and f is a function of the ratio ε_{n}/B which we find explicitly. In particular, when B≫ε_{n}, ⟨r_{m}^{2}⟩/⟨r_{c}^{2}⟩=2/3A. The shape of the E1 dipole strength function also depends only on the ratio ε_{n}/B and is derived in explicit analytic form. We estimate that for the ^{22}C nucleus higher-order corrections to our theory are of the order of 20% or less if the two-neutron separation energy is less than 100 keV and the s-wave scattering length between a neutron and a ^{20}C nucleus is less than 2.8 fm.

Many-Body Dispersion

A broad range of approaches to many-body dispersion are discussed, including empirical approaches with multiple fitted parameters, augmented density functional-based approaches, symmetry adapted perturbation theory, and a supermolecule approach based on coupled cluster theory. Differing definitions of "body" are considered, specifically atom-based vs molecule-based approaches.

Efimov physics: a review

This article reviews theoretical and experimental advances in Efimov physics, an array of quantum few-body and many-body phenomena arising for particles interacting via short-range resonant interactions, that is based on the appearance of a scale-invariant three-body attraction theoretically discovered by Vitaly Efimov in 1970. This three-body effect was originally proposed to explain the binding of nuclei such as the triton and the Hoyle state of carbon-12, and later considered as a simple explanation for the existence of some halo nuclei. It was subsequently evidenced in trapped ultra-cold atomic clouds and in diffracted molecular beams of gaseous helium. These experiments revealed that the previously undetermined three-body parameter introduced in the Efimov theory to stabilise the three-body attraction typically scales with the range of atomic interactions. The few- and many-body consequences of the Efimov attraction have been since investigated theoretically, and are expected to be observed in a broader spectrum of physical systems.

Role of sharp avoided crossings in short hyper-radial range in recombination of the cold 4He3 system

The role of sharp avoided crossings (SACs) in a short hyper-radial range R≤ 50 a.u. in the calculation of recombination for a cold ⁴He₃ system is investigated in the adiabatic hyperspherical representation by "turning off and on" the relevant nonadiabatic couplings. The influence of SACs on the recombination is related with the channels of the system and with the scattering energy. For J^Π = 0⁺ symmetry, the two-body recombination channel has an attractive potential well, which makes radial wave functions of both two-body recombination channel and three-body continuum channels accessible in the short hyper-radial range where SACs are located. The SACs consequently play an important role in coupled-channel calculations and this is particularly the case for lower scattering energies. However, for excited nuclear orbital momenta, i.e., J^Π = 1^-, 2⁺,…, 7^- symmetries, the two-body recombination channel has a repulsive interaction and the radial wave functions are not accessible in the short hyper-radial range. Therefore, omission of SACs in the short range for these symmetries has no effect on the numerical results, which leads to great savings on hyper-radial grid points in the practical numerical calculations. Moreover, to make the nonadiabatic couplings among channels to be continuous in the hyper-radius, different methods associated with the application of consistent phase convention are discussed.

The structure of the asymmetric helium trimer (3)He(4)He2

Despite their apparent simplicity, the properties of the two helium trimers, (4)He3 and (3)He(4)He2, are still not completely understood. In particular, the existence of a bound state of the asymmetric trimer (3)He(4)He2 was established many years ago, using different theoretical approaches, and later it was experimentally detected. However its structural properties have not been thoroughly investigated so far, probably because an accurate theoretical description of this very weakly bound system is computationally quite demanding. In this work we give for the first time an accurate and complete theoretical description of the geometrical structure of this fragile system using quantum Monte Carlo techniques employing the TTY potential and compare its properties with those of (4)He2 and (4)He3. We compute average values of distances and angles, along with the angle-angle distribution function: a two-dimensional probability distribution well suited to discuss the shape of a trimer. Our analysis shows that the lighter isotope is very diffuse and can be found at large distances from the other two atoms, but also close to the center of mass of the system in nearly linear configurations. For this system the concept of "equilibrium structure" is meaningless and all kinds of three-atom configurations must be taken into account in its description.

Approaching universality in weakly bound three-body systems

Atom-dimer scattering below the three-body breakup threshold is studied for a system of three identical bosons. The atom-dimer scattering length and the energy of the most weakly bound three-body state are shown to be strongly correlated. An appropriate rescaling of the observables reveals the subtlety of the correlation and serves to identify universal trends in the unitary limit of divergent two-body scattering length. The correlation provides a new quantitative measure of the degree of universality in three-body systems with short-ranged interactions, as well as a consistency check of effective field theories and other theoretical models.

The weakly bound states and resonances of the BeHe2 triatomic system

In the present study, we carry out a full search of the bound states and resonances of the He(2)Be triatomic system, with its isotopic variants (3)He(2)(9)Be, (3)He(4)He(9)Be, and (4)He(2)(9)Be using the hyperspherical method. Three-body long-range effects are also included in the computation by adding to the additive potential the Axilrod-Teller triple-dipole term. In addition, the possibility of the occurrence of Efimov-type states in these systems is discussed. We have found a bound state for each of the (3)He(2)(9)Be and (3)He(4)He(9)Be trimers, while one weakly bound excited state is also found to exist for the (4)He(2)(9)Be system.

Use of correlated potential harmonic basis functions for the description of the 4He trimer and small clusters

A correlated many-body basis function is used to describe the (4)He trimer and small helium clusters ((4)He(N)) with N = 4-9. A realistic helium dimer potential is adopted. The ground state results of the (4)He dimer and trimer are in close agreement with earlier findings. But no evidence is found for the existence of Efimov state in the trimer for the actual (4)He-(4)He interaction. However, decreasing the potential strength we calculate several excited states of the trimer which exhibit Efimov character. We also solve for excited state energies of these clusters which are in good agreement with Monte Carlo hyperspherical description.

Ground state of small mixed helium and spin-polarized tritium clusters: a quantum Monte Carlo study

We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.

Adiabatic hyperspherical study of weakly bound He(2)H(-), He(2)H, and HeH(2) systems

The He(2)H(-), He(2)H, and HeH(2) triatomic systems are studied using the adiabatic hyperspherical representation. By adopting the best empirical interaction potentials, we search for weakly bound states of (4)He(2) H(-), (4)He(2) H, and (4)HeH(2). We consider not only zero total nuclear orbital angular momentum, J=0, states but also J>0 states. We find no bound state for the (4)He(2) H systems, while the (4)He(2) H(-) and (4)HeH(2) systems are shown to possess three and one bound states, respectively, for J(Pi)=0(+). Interestingly, one bound state has been found each for the J(Pi)=1(-) and 2(+) symmetries of the (4)He(2) H(-) anion. We shall calculate the bound state energies and analyze the molecular structure of these species in detail.

A theoretical study of the rovibrational levels of the bosonic van der Waals neon trimer

The eigenenergies and root mean square radii of the rovibrational levels (J = 0-3) of the weakly bound bosonic van der Waals neon trimer were calculated using a full angular momentum three-dimensional finite element method. The differing results of three previous studies for zero angular momentum are discussed, explained, and compared with the results presented here.

Theoretical progress and challenges in H3+ dissociative recombination

We discuss the Jahn-Teller mechanism for dissociative recombination in low energy collisions between electrons and H3+ ions, in energy ranges relevant to the processes underway in interstellar clouds. While theory has become capable of predicting recombination rates in reasonable agreement with storage ring experiments, some discrepancies remain with them, and a long-standing discrepancy with stationary afterglow measurements remains troubling. Speculations about the desirable improvements in both theory and experiment are presented.

The role of asymptotic vibrational states in H3+

Calculations are discussed which characterize all the vibrational bound states of the H3+ and D2H+ molecular ions using a realistic ab initio potential energy surface. Graphical analysis and calculation of rotational constants show that both ions support a series of atom-diatom-like long-range states: asymptotic vibrational states. The role of these states in the H3+ system and other molecules is discussed. The vibrational calculations are extended above dissociation where the resulting (Feshbach) resonances are shown to be too short-lived to be of importance for the H3+ photodissociation spectrum.

Efimov states and their Fano resonances in a neutron-rich nucleus

Asymmetric resonances in elastic n+19C scattering are attributed to Efimov states of such neutron-rich nuclei, that is, three-body bound states of the n+n+18C system when none of the pairs is bound or some of them are only weakly bound. By fitting to the general resonance shape described by Fano, we extract the resonance position, width, and the "Fano profile index." While Efimov states have been discussed extensively in many areas of physics, there is only one very recent experimental observation in trimers of cesium atoms. The conjunction that we present of the Efimov and Fano phenomena may lead to experimental realization in nuclei.

First principles determination of the bound levels of HeLi-

An analytical potential energy curve is developed from high quality ab initio calculations for the He+Li- interaction. The HeLi- electrostatic complex is found to have an Re of 18.5 bohrs and a De of 0.974 cm(-1). Numerical solution of the rovibrational Schrödinger equation with this potential indicates two bound levels, (v,J)=(0,0) and (0,1), for all naturally occurring isotopologs (i.e., 4He7Li-, 4He6Li-, 3He7Li-, and 3He6Li-). For the common isotopolog, 4He7Li-, a D0 of 0.207 cm(-1) and an R0 of 26.5 bohrs is determined.

Theory of dissociative recombination of d(3h) triatomic ions applied to h+3

We propose a fully quantal description of H+3 dissociative recombination. The new method combines multichannel quantum defect theory, the adiabatic hyperspherical approach, and the techniques of outgoing-wave Siegert pseudostates. The vibrational, rotational, nuclear spin degrees of freedom of the ion, in their full dimensionality, are all taken into account for the first time in any calculation of polyatomic dissociative recombination. Our calculation of the recombination rate confirms that the Jahn-Teller effect is responsible for the large rate in H+3. The resulting theoretical rates for dissociative recombination of H+3 are in good general agreement with experiment.

Formation of atomic tritium clusters and bose-einstein condensates

We present an extensive study of the static and dynamic properties of systems of spin-polarized tritium atoms. In particular, we calculate the two-body |F,m(F)>=|0,0> s-wave scattering length and show that it can be manipulated via a Feshbach resonance at a field strength of about 870 G. Such a resonance might be exploited to make and control a Bose-Einstein condensate of tritium in the |0,0> state. It is further shown that the quartet tritium trimer is the only bound hydrogen isotope and that its single vibrational bound state is a Borromean state. The ground state properties of larger spin-polarized tritium clusters are also presented and compared with those of helium clusters.

Mechanism for the destruction of H+3 ions by electron impact

The rate at which the simplest triatomic ion (H+3) dissociates following recombination with a low-energy electron has been measured in numerous experiments. This process is particularly important for understanding observations of H+3 in diffuse interstellar clouds. But, despite extensive efforts, no theoretical treatment has yet proved capable of predicting the measured dissociative recombination rates at low energy, even to within an order of magnitude. Here we show that the Jahn-Teller symmetry-distortion effect-almost universally neglected in the theoretical description of electron-molecule collisions-generates recombination at a much faster rate than any other known mechanism. Our estimated rate constant overlaps the range of values spanned by experiments. We treat the low-energy collision process as a curve-crossing problem, which was previously thought inapplicable to low-energy recombination in H+3. Our calculation reproduces the measured propensity for three-body versus two-body breakup of the neutral fragments, as well as the vibrational distribution of the H2 product molecules.

Reaction mechanisms for two-neutron halo breakup

We describe a reaction mechanism which is consistent with all available experimental information of high energy three-body breakup processes. The dominating channels are removal of one of the three halo particles leaving the other two either undisturbed or absorbed. We compare with the commonly used deceptive assumption of a decay through two-body resonance states. Our predictions can be tested by measuring neutron-neutron invariant mass spectra.

Determination of the bond length and binding energy of the helium dimer by diffraction from a transmission grating

A molecular beam consisting of small helium clusters is diffracted from a 100 nm period transmission grating. The relative dimer intensities have been measured out to the 7th order and are used to determine the reduction of the effective slit width resulting from the finite size of the dimer. From a theoretical analysis of the data which also takes into account the van der Waals interaction with the grating bars, the bond length (mean internuclear distance) and the binding energy are found to be <r> = 52+/-4 A and |E(b)| = 1. 1+0.3/-0.2 mK.

How to study the elusive efimov state of the 4He3 molecule through a new atom-optical state-selection technique

Excited states and excitation energies of weakly bound systems, e.g., atomic few-body systems and clusters, are difficult to study experimentally. For this purpose we propose a new and very general atom-optical method which is based on inelastic diffraction from transmission gratings. The technique is applicable to the recently found helium trimer molecule 4He3, allowing for the first time an investigation of the possible existence of an excited trimer state and determination of its excitation energy. This would be of fundamental importance for the famous Efimov effect.