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Register a new userThe molecule ${rm H}_2$ in a strong magnetic field revisited
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Daniel Julian Nader
Publication date
2020
fields
Physics
and research's language is
English
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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).
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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.
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.
The formation of positive ions of antihydrogen $bar{rm{H}}^+$ via the three body reaction (i) $rm{e}^+ + rm{e}^- + bar{rm{H}} rightarrow rm{e}^- + bar{rm{H}}^+$ is considered. In reaction (i), free positrons $rm{e}^+$ are incident on antihydrogen $bar{rm{H}}$ embedded in a gas of low-energy ($sim $ meV) electrons and, due to the positron-electron interaction, a positron is attached to $bar{rm{H}}$ whereas an electron carries away the energy excess. We compare reaction (i) with two radiative attachment mechanisms. One of them is (ii) spontaneous radiative attachment, in which the ion is formed due to spontaneous emission of a photon by a positron incident on $bar{rm{H}}$. The other is (iii) two-center dileptonic attachment which takes place in the presence of a neighboring atom B and in which an incident positron is attached to $bar{rm{H}}$ via resonant transfer of energy to B with its subsequent relaxation through spontaneous radiative decay. It is shown that reaction (i) can strongly dominate over mechanisms (ii) and (iii) for positron energies below $0.1$ eV. It is also shown that at the energies considered reaction (i) will not be influenced by annihilation and that the reaction $rm{e}^+ + rm{e}^+ + bar{rm{H}} rightarrow rm{e}^+ + bar{rm{H}}^+$ has a vanishingly small rate compared to reaction (i).
We have carried out calculations of the triple-differential cross section for one-photon double ionization of molecular hydrogen for a central photon energy of $75$~eV, using a fully {it ab initio}, nonperturbative approach to solve the time-dependent Schro equation in prolate spheroidal coordinates. The spatial coordinates $xi$ and $eta$ are discretized in a finite-element discrete-variable representation. The wave packet of the laser-driven two-electron system is propagated in time through an effective short iterative Lanczos method to simulate the double ionization of the hydrogen molecule. For both symmetric and asymmetric energy sharing, the present results agree to a satisfactory level with most earlier predictions for the absolute magnitude and the shape of the angular distributions. A notable exception, however, concerns the predictions of the recent time-independent calculations based on the exterior complex scaling method in prolate spheroidal coordinates [Phys.~Rev.~A~{bf 82}, 023423 (2010)]. Extensive tests of the numerical implementation were performed, including the effect of truncating the Neumann expansion for the dielectronic interaction on the description of the initial bound state and the predicted cross sections. We observe that the dominant escape mode of the two photoelectrons dramatically depends upon the energy sharing. In the parallel geometry, when the ejected electrons are collected along the direction of the laser polarization axis, back-to-back escape is the dominant channel for strongly asymmetric energy sharing, while it is completely forbidden if the two electrons share the excess energy equally.
Some time ago we have derived from the QCD Lagrangian an equation of state (EOS) for the cold quark matter, which can be considered an improved version of the MIT bag model EOS. Compared to the latter, our equation of state reaches higher values of the pressure at comparable baryon densities. This feature is due to perturbative corrections and also to non-perturbative effects. Later we applied this EOS to the study of compact stars, discussing the absolute stability of quark matter and computing the mass-radius relation for self-bound (strange) stars. We found maximum masses of the sequences with more than two solar masses, in agreement with the recent experimental observations. In the present work we include the magnetic field in the equation of state and study how it changes the stability conditions and the mass-radius curves.
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