arXiv subjects
Publications and source records attributed to Kevin K. Lehmann.
A short GAP computer program is presented for computing nuclear spin statistical weights of rovibronic symmetry species in polyatomic molecules. As examples, benzene dimer and methane dimer are discussed.
Evaporative cooling of helium nanodroplets is studied with a statistical rate model that includes, for the first time, angular momentum conservation as a constraint on the accessible droplet states. It is found that while the final temperature of the droplets is almost identical to that previously predicted and later observed, the distribution of total droplet energy and angular momentum states is vastly more excited than a canonical distribution at the same temperature. It is found that the final angular momentum of the droplets is highly correlated with the initial direction, and that a significant fraction of the alignment of the total angular momentum should be transferred to the rotational angular momentum of an embedded molecule.
The ro--vibrational spectra of molecules dissolved in liquid $^4$He nanodroplets display rotational structure. Where resolved, this structure has been used to determine a temperature that has been assumed to equal that of the intrinsic excitations of the helium droplets containing the molecules. Consideration of the density of states as a function of energy and total angular momentum demonstrates that there is a small but significant bias of the rotor populations that make the temperature extracted from a fit to its rotational level populations slightly higher than the temperature of the ripplons of the droplet. This bias grows with both the total angular momentum of the droplet and with the moment of inertia of the solute molecule.
The energy and angular momentum of both straight and curved vortex states of a helium nanodroplet are examined as a function of droplet size. For droplets in the size range of many experiments, it is found that during the pickup of heavy solutes, a significant fraction of events deposit sufficient energy and angular momentum to form a straight vortex line. Curved vortex lines exist down to nearly zero angular momentum and energy, and thus could in principle form in almost any collision. Further, the coalescence of smaller droplets during the cooling by expansion could also deposit sufficient angular momentum to form vortex lines. Despite their high energy, most vortices are predicted to be stable at the final temperature (0.38 K) of helium nanodroplets due to lack of decay channels that conserve both energy and angular momentum.
The density of states and other thermodynamic functions of helium nanodroplets are calculated for a microcanonical ensemble with both energy and total angular momentum treated as conserved quantum numbers. These functions allow angular momentum conserving evaporative cooling simulations. As part of this project, a recursion relationship is derived for the reduction to irreducible representations of the n'th symmetric power of the irreducible representations of the rotation group. These give the distribution of total angular momentum states generated by putting multiple quanta into a ripplon or phonon mode of the droplet, each of which is characterized by a angular momentum quantum number.
In this article, recent developments in HElium NanoDroplet Isolation (HENDI) spectroscopy are reviewed, with an emphasis on the infrared region of the spectrum. Topics discussed include experimental details, comparison of radiation sources, symmetry issues of the helium solvation structure, sources of line broadening, changes in spectroscopic constants upon solvation, and applications including formation of novel chemical structures.
The increase in moment of inertia of SF$_6$ in helium nanodroplets is calculated using the quantum hydrodynamic approach. This required an extension of the numerical solution to the hydrodynamic equation to three explicit dimensions. Based upon an expansion of the density in terms of the lowest four Octahedral spherical harmonics, the predicted increase in moment of inertia is $170 {\rm u Å^2}$, compared to an experimentally determined value of $310(10) {\rm u Å^2}$, i.e., 55% of the observed value. The difference is likely in at least part due to lack of convergence with respect to the angular expansion, but at present we do not have access to the full densities from which a higher order expansion can be determined. The present results contradict those of Kwon et al., J. Chem. Phys. {\bf 113}, 6469 (2000), who predicted that the hydrodynamic theory predicted less than 10% of the observed increase in moment of inertia.
We present a simple numerical procedure for calculating the irrotational hydrodynamic flow in a helium solvation structure around a spherical solute in linear motion through superfluid helium. The calculation requires only the radial helium density around the impurity as input. From the resulting irrotational flow, the helium contribution to the effective mass of the solute is calculated. The results for alkali cations are compared to recent many-body Variational Monte Carlo (VMC) calculations by M. Buzzacchi, D. E. Galli, and L. Reatto (Phys. Rev. B., {\bf 64} 094512 (2001)). The helium contribution to the effective masses calculated by the two methods are 12.9(4.6) versus 9.4 u for Li$^+$, 48.2(5.6) versus 52.1 u for Na$^+$, 69.6(4.8) versus 70.1 u for K$^+$, and 6.4(8.8) versus 6.8 for Cs$^+$, with the VMC result listed first (with one $σ$ statistical error estimate) and the hydrodynamic result listed second. For the cases of Na$^+$ and K$^+$, the hydrodynamic calculation treated the first helium solvation shell as a rigid solid, as suggested by the VMC calculations; treating the first solvent layer as part of the superfluid lead to considerable underestimate, $\approx 50%$, of the mass increase in both cases. In all cases, the agreement of the two results are in within the error estimate of the VMC calculation, demonstrating the accuracy of hydrodynamic treatment of helium motion even on the atomic length scale.
This paper presents an analysis of a model problem, consisting of two interacting rigid rings, for the rotation of molecules in liquid $^4$He. Due to Bose symmetry, the excitation of the rotor corresponding to a ring of N helium atoms is restricted to states with integer multiples of N quanta of angular momentum. This minimal model shares many of the same features of the rotational spectra that have been observed for molecules in nanodroplets of $\approx 10^3 - 10^4$ helium atoms. In particular, this model predicts, for the first time, the very large enhancement of the centrifugal distortion constants that have been observed experimentally. It also illustrates the different effects of increasing rotational velocity by increases in angular momentum quantum number or by increasing the rotational constant of the molecular rotor. It is found that fixed node, diffusion Monte Carlo and a hydrodynamic model provide upper and lower bounds on the size of the effective rotational constant of the molecular rotor when coupled to the helium.
This paper presents an analysis of the motion of an neutral impurity species in a nanometer scale $^4$He cluster, extending a previous study of the dynamics of an ionic impurity. It is shown that for realistic neutral impurity-He potentials, such as those of SF$_6$ and OCS, the impurity is kept well away of the the surface of the cluster by long range induction and dispersion interactions with He, but that a large number of `particle in a box' center of mass states are thermally populated. It is explicitly demonstrated how to calculate the spectrum that arises from the coupling of the impurity rotation and the center of mass motion, and it is found that this is a potentially significant source of inhomogeneous broadening in vibration-rotation spectra of anisotropic impurities. Another source of inhomogeneous broadening is the hydrodynamic coupling of the rotation of the impurity with the center of mass velocity. A quantum hamiltonian to describe this effect is derived from the classical hydrodynamic kinetic energy of an ellipsoid. Simple analytic expressions are derived for the resulting spectral line shape for an impurity in bulk He, and the relevant matrix elements derived to allow fully quantum calculations of the coupling of the center of mass motion and rotation for an impurity confined in a spherical He cluster. Lastly, the hydrodynamic contribution to the impurity effective moment of inertia is evaluated and found to produce only a minor fractional increase.
This paper presents an analysis of the motion of an impurity ion in a nanometer scale $^4$He cluster. Due to induction forces, ions are strongly localized near the center of the cluster, with a root mean squared thermal displacements of only a few Å. The trapping potential is found to be nearly harmonic, with a frequency of 2.3(1.0) GHz for a positive (negative) ion in a He cluster of radius 5 nm. The anharmonicity is small and positive (energy increases slightly faster than linear with quantum number). It is suggested that by using frequency sweep microwave radiation, it should be possible to drive the ion center of mass motion up to high quantum numbers, allowing the study of the critical velocity as a function of cluster size.
Microwave detected, microwave-optical double resonance was used to record the A state electronic spectrum of NH3, NH2D, and NHD2 with both vibrational and rotational resolution. To investigate ND3 with the same resolution as we had with our hydrogen containing isotopomers, a strip-line cell was constructed allowing the simultaneous passage of radio-frequency and ultraviolet radiation. Rotational constants were obtained as a function of nu2 excitation and an A state equilibrium bond length was estimated at 1.055(8) angstroms. In addition, the harmonic force field for the A state has been experimentally determined. fhh, falpha,alpha-falpha,alpha', and frr were found to be 1.06(4)aJ/angstrom2, 0.25(2)aJ, and 4.9aJ/angstrom^2 respectively. This calculated harmonic force field predicts that the asymmetry observed in the NH3 2(4) band is due to a strong anharmonic interaction with the 4(3) level and the broad feature observed in the dispersed fluorescence spectrum previously assigned to the 1(1) band is more likely attributable to the 4(2) level.
Using microwave detected, microwave-optical double resonance, we have measured the homogeneous linewidths of individual rovibrational transitions in the à state of NH3, NH2D, NHD2, and ND3. We have used this excited state spectroscopic data to characterize the height of the dissociation barrier and the mechanisms by which the molecule uses its excess vibrational and rotational energies to help overcome this barrier. To interpret the observed vibronic widths, a one dimensional, local mode potential has been developed along a N-H(D) bond. These calculations suggest the barrier height is roughly 2100cm-1, approximately 1000cm-1 below the ab initio prediction. The observed vibronic dependence of levels containing two or more quanta in nu2 is explained by a Fermi resonance between nu2 and the N-H(D) stretch. This interaction also explains the observed trends due to isotopic substitution. The rotational enhancement of the predissociation rates in the NH3 2(1) level is dominated by Coriolis coupling while for the same level in ND3, centrifugal effects dominate.