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arXiv:cond-mat/0401542 · Physical Review A

Excitation spectra of a He3 impurity on He4 clusters

Stefano Fantoni, R. Guardiola, Jesús Navarro

Published Aug 27, 2004• 7 citations
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Abstract

The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of a single $^{3}\mathrm{He}$ atom bound to a cluster with $N$ $^{4}\mathrm{He}$ atoms, with the aim of establishing the most adequate filling ordering of single-fermion orbits to the mixed clusters with a large number of $^{3}\mathrm{He}$ atoms. The resulting ordering looks like the rotational spectrum of a diatomic molecule, being classified only by the angular momentum of the level, although vibrational-like excitations appear at higher energies for sufficiently large $N$.

DOI
10.1103/physreva.70.023206

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The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of a single 3He^{3}\mathrm{He}3He atom bound to a cluster with NNN 4He^{4}\mathrm{He}4He atoms, with the aim of establishing the most adequate filling ordering of single-fermion orbits to the mixed clusters with a large number of 3He^{3}\mathrm{He}3He atoms. The resulting ordering looks like the rotational spectrum of a diatomic molecule, being classified only by the angular momentum of the level, although vibrational-like excitations appear at higher energies for sufficiently large NNN.
The diffusion Monte Carlo technique is used to calculate and analyze the excitation spectrum of 3He atoms bound to a cluster of 4He atoms by using a previously determined optimum filling of single-fermion orbits with well-defined orbital angular momentum L, spin S, and parity quantum numbers. The study concentrates on the energies and shapes of the three kinds of states for which the fermionic part of the wave function is a single Slater determinant: maximum L or maximum S states within a given orbit, and fully polarized clusters. The picture that emerges is that of systems with strong shell effects, whose binding and excitation energies are essentially determined by averages over configuration at fixed number of particles and spin, i.e., by the monopole properties of an effective Hamiltonian.
Optimized variational calculations have been carried out for clusters of He4 between N=20 and N=1000 atoms. For small cluster sizes with less or equal to 112 particles, where comparisons with existing diffusion Monte Carlo results are possible, we find good agreement for the ground state energies and densities. Using a somewhat simpler approximation, we also calculate the bound state energies of He3 atoms attached to these clusters. We then calculate excitations and the dynamic structure function. The complex and nonlocal self-energy introduced for that purpose gives access to the calculation of both elastic and inelastic scattering processes for He4 and He3 atoms impinging on the clusters.
Small helium (4He) clusters containing the lighter isotope He3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang–Tonnies–Yiu (TTY) helium–helium pair potential. The dimer He4–3He is not bound; as well as the trimer He4He23. The smallest cluster containing He3 is He24He3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He34 trimer, is able to bind another He3 atom, forming the tetramer He24He23, which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He4 atom in a pure cluster with a He3 atom leads to an energetic destabilization, as the pair He4–3He is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called “Andreev states” of a single He3 in liquid He4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He4.
The minimal number of 3He^{3}\mathrm{He}3He atoms required to form a bound cluster has been estimated by means of a diffusion Monte Carlo procedure within the fixed-node approximation. Several importance sampling wave functions have been employed in order to consider different shell-model configurations. The resulting upper bound for the minimal number is 32 atoms.
Small and stable drops of 3He^{3}\mathrm{He}3He atoms can only exist above a minimum number of particles, due to the combination of the 3He^{3}\mathrm{He}3He atom Fermi statistics and its light mass. An accurate estimation of this minimum number using microscopic theory has been difficult due to the inhomogeneous and fermionic nature of these systems. We present a diffusion Monte Carlo calculation of 3He^{3}\mathrm{He}3He drops with sizes near the minimum in order to determine the stability threshold. The results show that the minimum self-bound drop is formed by N=30N=30N=30 atoms with preferred orbitals for open shells corresponding to maximum value of the spin.
Many experiments on pure and doped helium clusters result in the production of a broad distribution of charged fragment ions after electron impact or laser ionisation. These ion yield distributions occasionally exhibit distinct stability patterns. We use the diffusion quantum Monte Carlo technique to study these stability patterns and structural features of helium clusters with open shell atomic and molecular dopants. These simulations require reliable many-body potentials which we construct from high level ab initio CCSD(T) calculations for several electronic states mixed by spin-orbit coupling and including non-additive interactions arising from induction. For small clusters numerically exact calculations of rovibrational properties are used to establish the quality of our potential surfaces. The approach is illustrated with applications to Iq^{q}q@Hen_nn​, q=-1,0,+1,+2 clusters which appear in ionisation and photodissociation experiments. Spin-orbit coupling due to the iodine atom is found to have a profound effect on the structure of the mixed clusters. Radial and angular helium density profiles are computed and show that even in the presence of pronounced radial structuring exchange between 'shells' remains possible and angular disorder remains significant. The identification of a well defined ionic snowball core appears incorrect. We present first results for CO+^++ ions in helium clusters. He-CO+^++ is an interesting astrophysical collision system but its interest for helium cluster studies is the similarity of the CO+^++ rotational constant with the one of neutral CO. Our present understanding of rotation inside helium clusters relies on studies of molecules where changing the molecule implies changing dynamical parameters and the interaction potential. The CO/CO+^++ case allows to study the specific effect of changing only the interaction energy. CO+^++@Hen_nn​ should be relatively easy to make by cluster ionisation or aggregation in ion drift tubes and its strong dipole and vibrational transition moment make it an easy target for high resolution spectroscopy. We have computed accurate ab initio surfaces for the two lowest electronic states of He-CO+^++ to predict rovibrational spectroscopic and collisional properties. A many-body model using these surfaces is used to study larger CO+^++Hen_nn​ clusters.