Total angular momentum quantum number

In quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). If s is the particle's spin angular momentum and ℓ its orbital angular momentum vector, the total angular momentum j is \mathbf j = \mathbf s + \boldsymbol {\ell} ~. The associated quantum number is the main total angular momentum quantum number j. It can take the following range of values, jumping only in integer steps: \vert \ell - s\vert \le j \le \ell + s where ℓ is the azimuthal quantum number (parameterizing the orbital angular momentum) and s is the spin quantum number (parameterizing the spin). The relation between the total angular momentum vector j and the total angular momentum quantum number j is given by the usual relation (see angular momentum quantum number) \Vert \mathbf

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Spin-orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3

Jean-Sebastien Caux, Martin Mourigal, Henrik Moodysson Rønnow, Thorsten Schmitt

When viewed as an elementary particle, the electron has spin and charge. When binding to the atomic nucleus, it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies. Even if electrons in solids form bands and delocalize from the nuclei, in Mott insulators they retain their three fundamental quantum numbers: spin, charge and orbital(1). The hallmark of one-dimensional physics is a breaking up of the elementary electron into its separate degrees of freedom(2). The separation of the electron into independent quasi-particles that carry either spin (spinons) or charge (holons) was first observed fifteen years ago(3). Here we report observation of the separation of the orbital degree of freedom (orbiton) using resonant inelastic X-ray scattering on the one-dimensional Mott insulator Sr2CuO3. We resolve an orbiton separating itself from spinons and propagating through the lattice as a distinct quasi-particle with a substantial dispersion in energy over momentum, of about 0.2 electronvolts, over nearly one Brillouin zone.

2012

Fully spin-polarized bulk states in ferroelectric GeTe

Jan Hugo Dil, Mauro Fanciulli

By measuring the spin polarization of GeTe films as a function of light polarization we observed that the bulk states are fully spin polarized in the initial state, in strong contrast with observations for other systems with a strong spin-orbit interaction and the surface derived states in the same system. In agreement with state-of-the-art theory, our experimental results show that fully spin-polarized bulk states are an intrinsic property of the ferroelectric Rashba semiconductor α-GeTe(111). The fact that the measured spin-polarization vector does not change with light polarization can be explained by the absence of a mixing of states with a different total angular momentum J

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Product energy partitioning in the unimolecular decomposition of vibrationally and rotationally state‐selected hydrogen peroxide

Thomas Rizzo

Infrared-optical double resonance prepares HOOH molecules in single rotational levels of the 6-nu(OH), 5-nu(OH) + nu(OOH), 5-nu(OH) + nu(OO), and 4-nu(OH) + nu(OH), vibrational states which range from 3 to 2287 cm-1 of excess energy above the unimolecular dissociation threshold. Laser-induced fluorescence probes the nascent OH rotational state distributions from the decomposition of rovibrationally selected reactants. The nascent rotational state distributions reveal that both OH spin-orbit states can be populated by the decomposition of a single molecule and hence that electronic angular momentum is not conserved throughout the dissociation process. The product state distributions from reactants excited to the 6-nu(OH) and 4-nu(OH) + nu(OH), vibrational levels are generally in good agreement with the predictions of phase-space theory provided electronic angular momentum is treated statistically. Reactants decomposing from single rotational states in the 5-nu(OH) + nu(OOH) combination level (and to a lesser extent the 5-nu(OH) + nu(OO) level) show product state distributions which are systematically colder than phase-space theory predictions. This observation indicates that energy redistribution in vibrationally excited HOOH is not complete on the time scale of unimolecular decomposition.

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