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Register a new userThe hydrogen molecule $rm{H}_{2}$ in inclined configuration in a weak magnetic field
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Highly accurate variational calculations, based on a few-parameter, physically adequate trial function, are carried out for the hydrogen molecule hh in inclined configuration, where the molecular axis forms an angle $theta$ with respect to the direction of a uniform constant magnetic field ${bf B}$, for $B=0,, 0.1,, 0.175$ and $0.2,$a.u. Three inclinations $theta=0^circ,,45^circ,,90^circ$ are studied in detail with emphasis to the ground state $1_g$. Diamagnetic and paramagnetic susceptibilities are calculated (for $theta=45^circ$ for the first time), they are in agreement with the experimental data and with other calculations. For $B=0,, 0.1$ and $0.2,$a.u. potential energy curves $E$ vs $R$ are built for each inclination, they are interpolated by simple, two-point Pade approximant $Pade[2/6](R)$ with accuracy of not less than 4 significant digits. Spectra of rovibrational states are calculated for the first time. It was found that the optimal configuration of the ground state for $B leq B_{cr}=0.178,$a.u. corresponds always to the parallel configuration, $theta=0$, thus, it is a $^1Sigma_g$ state. The state $1_g$ remains bound for any magnetic field, becoming metastable for $B > B_{cr}$, while for $B_{cr} < B < 12$,a.u. the ground state corresponds to two isolated hydrogen atoms with parallel spins.
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A compact, few-parametric, physically adequate, 3-term variational trial function is used to calculate with high accuracy the energy of the ground state ${}^3Pi_u$ of the hydrogen molecule ${rm H}_2$ in strong magnetic field ${bf B}$ in the range $5times10^{10}, {rm G} leq B leq 10^{13},$G. The nuclei (protons) are assumed as infinitely massive (BO appproximation of zero order) and situated along the magnetic field line (parallel configuration).
We present an accurate quantum mechanical study of molecule-molecule collisions in the presence of a magnetic field. The work focusses on the analysis of elastic scattering and spin relaxation in collisions of O2(3Sigma_g) molecules at cold (~0.1 K) and ultracold (~10^{-6} K) temperatures. Our calculations show that magnetic spin relaxation in molecule-molecule collisions is extremely efficient except at magnetic fields below 1 mT. The rate constant for spin relaxation at T=0.1 K and a magnetic field of 0.1 T is found to be as large as 6.1 x 10^{-11} cm3/s. The magnetic field dependence of elastic and inelastic scattering cross sections at ultracold temperatures is dominated by a manifold of Feshbach resonances with the density of ~100 resonances per Tesla for collisions of molecules in the absolute ground state. This suggests that the scattering length of ultracold molecules in the absolute ground state can be effectively tuned in a very wide range of magnetic fields. Our calculations demonstrate that the number and properties of the magnetic Feshbach resonances are dramatically different for molecules in the absolute ground and excited spin states. The density of Feshbach resonances for molecule-molecule scattering in the low-field-seeking Zeeman state is reduced by a factor of 10.
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