The transition from stable to metastable and finally to unstable situations for increasing nuclear charge Z is studied in the adiabatic approximation for the 1 Sigma + g ground state of homonuclear diatomic molecular systems with two or eighteen electrons. Allowing non-integer values for the parameter Z and varying it in small steps, critical values for stability Z c and Z m are determined by means of extensive and accurate ab initio calculations. In addition, the behaviour of various other quantities (equilibrium distances, lowest bound or resonance levels of vibrational motion) is monitored during the transition. The authors' results confirm, in particular, the metastability of the He 2+ 2 ground state, but exclude the possibility of a metastable 1 Sigma + g state for the recently experimentally observed Ne 2+ 2 .
The transition from stable to metastable and finally to unstable situations for increasing nuclear charge Z is studied in the adiabatic approximation for the 1 Sigma + g ground state of homonuclear diatomic molecular systems with two or eighteen electrons. Allowing non-integer values for the parameter Z and varying it in small steps, critical values for stability Z c and Z m are determined by means of extensive and accurate ab initio calculations. In addition, the behaviour of various other quantities (equilibrium distances, lowest bound or resonance levels of vibrational motion) is monitored during the transition. The authors' results confirm, in particular, the metastability of the He 2+ 2 ground state, but exclude the possibility of a metastable 1 Sigma + g state for the recently experimentally observed Ne 2+ 2 .
We present a detailed study of the ground state behaviour of two-electron diatomic molecules. The ground state stability diagram for diatomic molecules in the Born–Oppenheimer approximation is obtained and the behaviour of the ground state near the stability line is studied. Two different cases are analysed: the homonuclear two-centre two-electron molecule with the internuclear distance as a free parameter and the diatomic two-electron molecule (in this case, the internuclear distance is determined by equilibrium conditions). Analytical and numerical results for these systems are presented.
We calculate accurate potential-energy curves for a ground-state He+ ion interacting with a He atom in the lowest-energy metastable 3S electronic state. We employ the full configuration-interaction method, equivalent to exact diagonalization, with results extrapolated to the complete basis set limit. The leading relativistic and adiabatic corrections are included using perturbation theory. We calculate rovibrational levels and spectroscopic constants of the He2+ molecular ion in excited electronic states for three stable isotopologues. We predict the scattering lengths for ultracold ion-atom collisions. The theoretical data are presented with their uncertainties and agree well with previous results for the ground state. The reported results may be useful for the spectroscopy of the He2+ molecular ion in the excited electronic state and collisional studies of He+ ions immersed in ultracold gases of metastable He atoms.
A theoretical analysis of photoassociation in ultracold metastable helium has been undertaken for the 2(^3)S1 + 2(^3)S1 to 2(^3)S1 + 2(^3)P transition. A full multichannel calculation is presented for two aspects of the system, a) the accurate calculation of energies for the bound vibrational levels of the dimer; and b) the non-perturbative calculation of the photoassociation line shapes allowing for abitrary laser intensity and detuning. A strong emphasis is placed on the accuracy of the calculations, and the elimination of approximations that have been used in previous investigations. The results indicate that full multichannel calculations are required rather than approximate single-channel calculations in some important situations, and are especially useful for making assignments between experiment and theory. Bound levels have been previously measured from the photoassociation of cold metastable thermal gases to energies close to the three asymptotes j = 0, 1, 2 of the 2(^3)S1 → 2(^3)Pj atomic transition. Previous analysis of these measurements was made using either approximate accumulated phase techniques based on long-range single-channel potentials, or using multichannel calculations and long-range potentials. Because accurate short-range electronic potentials have been calculated only recently, this thesis presents the first multichannel calculation for the levels near the j = 1, 2 asymptotes. The new short-range potentials had previously been used in an approximate single-channel calculation, but this type of calculation ignores the effects of non-adiabatic and Coriolis couplings. Presented here are the binding energies calculated from a fully multichannel technique which includes these couplings, and some differences of up to 10% from the single-channel calculations are observed. The detailed knowledge of the bound wave functions is then exploited to determine a set of observability criteria that produce a near unique assignment of theoretical levels to experimental observations. From these unique assignments, a 1% correction to the short-range electronic potentials has been implemented that significantly improves the agreement between theory and experiment. Experimental measurements have previously been made of line shifts in the photoassociation spectra of vibrational levels in the 0+u long-range potential that asymptotes to 2(^3)S1 + 2(^3)P0 and their variation with laser intensity. These results were previously analysed by performing an approximate second-order perturbative calculation of the line shift that is valid only for low laser intensities. In this thesis a completely non-perturbative calculation of the spectra and line shapes for abitrary laser intensity is presented for photoassociation to the levels probed in experiment. The techniques of dressed state formalism and a modified radiative coupling are employed to properly treat the laser coupling for large interatomic separations. These calculations produce resonance profiles superimposed on a very significant background, a feature that is not seen in photoassociation calculations of other atomic species. From the calculated line shapes, the line shifts and line widths were determined for varying intensity and a small nonlinear intensity-dependence of up to 2.5% was found for the line shift. The effects of invoking the dipole approximation for the laser coupling for the long-range molecular system are analysed by solving the equations using the complete laser coupling that does not assume the dipole approximation. Important differences are obtained between the profiles with and without the dipole approximation, and the photoassociation resonances are found to be more discernible at larger intensities when the complete laser coupling is used.
A theoretical study is performed for the photoassociation of metastable helium. Combining short-range, high-level, ab initio calculations for 5 Σ g / u + and 5 Π g / u symmetries and long-range behaviour, better described in Hund's case (c), potential-energy curves for attractive, 5 Σ u + and 5 Π g , as well as repulsive, 5 Π u and 5 Σ g + , states of quintet metastable helium molecules dissociating to 2 3 S + 2 3 P are obtained. Taking into account the atomic spin-orbit couplings, vibrational levels are derived for near-dissociation levels at the 3 P 2 asymptote. Comparison with results from three recent photoassociation experiments obtained under different conditions (μK temperatures with spin alignment and mK temperatures without) allowed for an assignation of about three quarters of the observed levels. The robustness of the vibrational numbering is confirmed by testing a modification of the short-range potentials.
The bound states of the fermionic ^3He(2 ^3S_1)+ ^3He(2 ^3P_j)system, where j=0,1,2, are investigated using the recently available ab initio short-range ^{1,3,5}\Sigma^{+}_{g,u} and ^{1,3,5}\Pi_{g,u} potentials computed by Deguilhem et al. (J. Phys. B: At. Mol. Opt. Phys., 2009, 42, 015102). Single-channel and multichannel calculations have been undertaken in order to investigate the effects of Coriolis and non-adiabatic couplings. The possible experimental observability of the theoretical levels is assessed using criteria based upon the short-range character of each level and their coupling to metastable ground states. Purely long-range levels have been identified and 30 short-range levels near five asymptotes are suggested for experimental investigation.
The bound states of the fermionic (3)He(2 (3)S(1)) + (3)He(2 (3)P(j)) system, where j = 0, 1, 2, are investigated using the recently available ab initio short-range (1,3,5)Σ(+)(g,u) and (1,3,5)Π(g,u) potentials computed by Deguilhem et al. (J. Phys. B: At., Mol. Opt. Phys., 2009, 42, 015102). Single-channel and multichannel calculations have been undertaken in order to investigate the effects of Coriolis and non-adiabatic couplings. The possible experimental observability of the theoretical levels is assessed using criteria based upon the short-range character of each level and their coupling to metastable ground states. Purely long-range levels have been identified and 30 short-range levels near five asymptotes are suggested for experimental investigation.