Large Orbital Angular Momentum Research Articles

Planar three-coordinate high-spin Fe(II) complexes with large orbital angular momentum: Mössbauer, electron paramagnetic resonance, and electronic structure studies.

Mössbauer spectra of [LFe(II)X](0) (L = beta-diketiminate; X = Cl(-), CH(3)(-), NHTol(-), NHtBu(-)), 1.X, were recorded between 4.2 and 200 K in applied magnetic fields up to 8.0 T. A spin Hamiltonian analysis of these data revealed a spin S = 2 system with uniaxial magnetization properties, arising from a quasi-degenerate M(S) = +/-2 doublet that is separated from the next magnetic sublevels by very large zero-field splittings (3/D/ > 150 cm(-1)). The ground levels give rise to positive magnetic hyperfine fields of unprecedented magnitudes, B(int) = +82, +78, +72, and +62 T for 1.CH(3), 1.NHTol, 1.NHtBu, and 1.Cl, respectively. Parallel-mode EPR measurements at X-band gave effective g values that are considerably larger than the spin-only value 8, namely g(eff) = 10.9 (1.Cl) and 11.4 (1.CH(3)), suggesting the presence of unquenched orbital angular momenta. A qualitative crystal field analysis of g(eff) shows that these momenta originate from spin-orbit coupling between energetically closely spaced yz and z(2) 3d-orbital states at iron and that the spin of the M(S) = +/-2 doublet is quantized along x, where x is along the Fe-X vector and z is normal to the molecular plane. A quantitative analysis of g(eff) provides the magnitude of the crystal field splitting of the lowest two orbitals, /epsilon(yz) - epsilon(2)(z)/ = 452 (1.Cl) and 135 cm(-1) (1.CH(3)). A determination of the sign of the crystal field splitting was attempted by analyzing the electric field gradient (EFG) at the (57)Fe nuclei, taking into account explicitly the influence of spin-orbit coupling on the valence term and ligand contributions. This analysis, however, led to ambiguous results for the sign of epsilon(yz) - epsilon(2)(z). The ambiguity was resolved by analyzing the splitting Delta of the M(S) = +/-2 doublet; Delta = 0.3 cm(-1) for 1.Cl and Delta = 0.03 cm(-)(1) for 1.CH(3). This approach showed that z(2) is the ground state in both complexes and that epsilon(yz) - epsilon(2)(z) approximately 3500 cm(-1) for 1.Cl and 6000 cm(-1) for 1.CH(3). The crystal field states and energies were compared with the results obtained from time-dependent density functional theory (TD-DFT). The isomer shifts and electric field gradients in 1.X exhibit a remarkably strong dependence on ligand X. The ligand contributions to the EFG, denoted W, were expressed by assigning ligand-specific parameters: W(X) to ligands X and W(N) to the diketiminate nitrogens. The additivity and transferability hypotheses underlying this model were confirmed by DFT calculations. The analysis of the EFG data for 1.X yields the ordering W(N(diketiminate)) < W(Cl) < W(N'HR), W(CH(3)) and indicates that the diketiminate nitrogens perturb the iron wave function to a considerably lesser extent than the monodentate nitrogen donors do. Finally, our study of these synthetic model complexes suggests an explanation for the unusual values for the electric hyperfine parameters of the iron sites in the Fe-Mo cofactor of nitrogenase in the M(N) state.

Spin and orbital angular momentum distribution functions of the nucleon

A theoretical prediction is given for the spin and orbital angular momentum distribution functions of the nucleon within the framework of an effective quark model of QCD, i.e., the chiral quark soliton model. An outstanding feature of the model is that it predicts a fairly small quark spin fraction of the nucleon $\ensuremath{\Delta}\ensuremath{\Sigma}\ensuremath{\simeq}0.35,$ which in turn dictates that the remaining 65% of the nucleon spin is carried by the orbital angular momentum of quarks and antiquarks at the model energy scale of ${Q}^{2}\ensuremath{\simeq}0.3$ ${\mathrm{GeV}}^{2}.$ This large orbital angular momentum necessarily affects the scenario of scale dependence of the nucleon spin contents in a drastic way.

A failing of coupled-states calculations for inelastic and pressure-broadening cross sections: Calculations on CO2–Ar

Fully quantal benchmark calculations of pressure-broadening cross sections for infrared and Raman lines of CO2 perturbed by Ar are carried out using both close-coupling (CC) and coupled-states (CS) calculations. CS calculations are found to underestimate the cross sections by up to 15%. The effect occurs even for isotropic Raman cross sections, which are not affected by reorientation contributions. The discrepancy arises mostly for collisions with large orbital angular momenta l, occurring on the long-range part of the potential. It may be attributed to collisions that are adiabatic rather than sudden in nature. A hybrid computational method, employing CS calculations for low l and decoupled l-dominant (DLD) calculations for high l, offers a promising solution.

Relativistic theory of nuclear shielding in one-electron atoms 2. Analytical and numerical results

Non-decomposition theory (Pyper, N. C., 1983, Chem. Phys. Lett., 96, 204; 1999, Molec. Phys., 97, 381) based on the Dirac equation is used to derive fully relativistic analytical expressions for the nuclear shieldings of the 1s, 2[pbar] and 2p states of any one-electron ion having a point charge—point magnetic dipole nucleus. The physically transparent decomposition description of the 1s shieldings is completed by deriving analytical expressions for the two contributions to the relativistic paramagnetic shielding (σ(MPA)). Addition of the relativistic (σ(MD)) and purely relativistic (σ(MPE)) terms in Pyper (1999) yields the total shielding. Further shieldings are computed using the decomposition method with the nuclear charge distributed uniformly throughout a sphere with the nuclear magnetization residing on its surface. Relativity modifies the shieldings by fractions larger than those for the hyperfine structure, enhancing that of a state for which no other has the same m j , large component orbital angular momentum (l A) and principal quantum number (n A). The increases of factors of 3 to 4 for high Z 1s states, originating mainly from σ(MPA), decrease with reduction in Z or increase in l A or n A. The large magnitudes of the shieldings of orbitals in a pair having the same n A, l A and mj but different jA decrease with increasing Z, being positive for j A = l A −1/2 and negative for j A = l A + 1/2. The point nucleus analytical results for the 1s and 2p m = 3/2 shieldings are approximated as the sum of the non-relativistic result plus the lowest order relativistic correction. This perturbation approach fails for high Z 1s levels. The spatial extension of the nuclear charge and magnetization reduces the shieldings of high Zs states by about 20%, those of high Zσ levels by about 1.5%, leaving those of all other states affected only minimally. Even though σ(MPA) is more sensitive to nuclear spatial extension than the hyperfine structure to which σ(MPE) is proportional, the insensitivity of σ(MD) causes the fractional shielding reductions to be slightly less than for the hyperfine interaction.

A quark model analysis of orbital angular momentum

Orbital Angular Momentum (OAM) twist-two parton distributions are studied. At the low energy, hadronic, scale we calculate them for the relativistic MIT bag model and for non-relativistic potential quark models. We reach the scale of the data by leading order evolution using the OPE and perturbative QCD. We confirm that the contribution of quarks and gluons OAM to the nucleon spin grows with Q 2, and it can be relevant at the experimental scale, even if it is negligible at the hadronic scale, irrespective of the model used. The sign and shape of the quark OAM distribution at high Q 2 may depend strongly on the relative size of the OAM and spin distributions at the hadronic scale. Sizeable quark OAM distributions at the hadronic scale, as proposed by several authors, can produce the dominant contribution to the nucleon spin at high Q 2. As expected by general arguments, we obtain, that the large gluon OAM contribution is almost cancelled by the gluon spin contribution.

Magnetic circular dichroism in the soft-x-ray absorption spectra of Mn-based magnetic intermetallic compounds

We have investigated the magnetic electronic structures of PtMnSb, NiMnSb, ${\mathrm{Ni}}_{2}\mathrm{MnSb},$MnSb, MnAlGe, and ${\mathrm{Mn}}_{2}\mathrm{Sb}$ by soft-x-ray absorption spectroscopy (XAS) and magnetic circular dichroism (MCD) measurements in the Mn $2p$ core absorption region. Different degrees of the electron itinerancy of the Mn $3d$ states are discussed. The large orbital angular momentum of the Mn $3d$ electrons is revealed for MnSb by the MCD spectrum. In addition, the XAS and MCD spectra are measured in the Sb $3d,$ Ni $2p,$ and Pt $4f$ core excitation regions. An induced magnetic moment of Sb valence orbitals with the spin antiparallel to that of Mn is clearly indicated for NiMnSb and ${\mathrm{Mn}}_{2}\mathrm{Sb}.$

Discovery of Photospheric Helium in the Ultramassive DA White Dwarf GD 50

Extreme-ultraviolet (EUV) spectroscopy of the hot, hydrogen-rich white dwarf GD 50 reveals an unusual photospheric mixture of hydrogen and helium. This hot DA white dwarf is also remarkable for its mass (≈ 1.2 M☉) near the Chandrasekhar limit. The spectra obtained with the Extreme-Ultraviolet Explorer (EUVE) show a prominent He II resonance line series and constrain its atmospheric parameters to Teff = 40,300 ± 100 K and n(He)/n(H) = (2.4 ± 0.1) × 10-4 (assuming log g = 9.0). We also constrain the local interstellar medium column densities of neutral helium and hydrogen to nHe I = 6 × 1016 and nH I = 9 × 1017 cm-2. The presence of helium in an isolated, massive DA white dwarf is paradoxical. We examine and rule out a couple of scenarios (radiative levitation, accretion from the ISM or a hypothetical companion), but we suggest that if massive white dwarfs do result from stellar mergers, large orbital angular momentum may be preserved and result in a large meridional circulation current, possibly dredging up helium from the envelope. Although we find evidence of large rotational velocity in EUV He II line profiles, we propose additional observational tests of the dredge-up model.

Fast inelastic ion-ion, ion-electron, and ion-positron collisions.

We present scaling relations for the total cross sections and collision strengths of bound-state excitation in positive ions. The colliding particle can be positively or negatively charged and can be a fully ionized atom, an electron, or a positron. We consider collisions in which the kinetic energy of relative motion is large and consequently the adiabaticity parameter \ensuremath{\xi}\ensuremath{\ll}1. We illustrate our general method by calculating collision strengths for proton-impact excitation of fine-structure transitions in hydrogenlike ions. The limiting case of infinite nuclear charge is also included in our calculations. Using a unitarized Coulomb-Born approximation, we show that, for dipole transitions, colliding particles with large orbital angular momenta (l\ensuremath{\gtrsim}2000) make an important contribution (\ensuremath{\sim}70%) to the collision strength of proton-impact excitation. For a nonrelativistic projectile energy ${\mathit{E}}_{\mathit{i}}$\ensuremath{\rightarrow}\ensuremath{\infty}, we use the Born approximation to obtain the scaled collision strengths. These limiting values, dependent only on the particular transition, confirm the correct high-energy behavior of our data. We also use the interactive graphics computer program omeups [Burgess and Tully, Astron. Astrophys. 254, 436 (1992)] to extrapolate our data to higher energies.

Orbital angular momentum, spin fractions, and scenarios for the proton's spin-weighted parton distributions.

New data from the European Muon Collaboration (EMC) on the spin-spin asymmetry in deep-inelastic lepton-proton scattering suggests that the total spin carried by valence quarks in a polarized proton may be approximately canceled by a strong negative polarization of the sea of $\overline{q}q$ pairs. The evolution in ${Q}^{2}$ of the fraction of proton spin carried by gluons depends on the initial spin fractions and it is possible to avoid the introduction of large orbital angular momentum by adopting a "hybrid" quark-Skyrme picture of the proton suggested by the EMC results.

Orbital angular momentum and the parton model

The role of orbital angular momentum is discussed within the framework of the parton model. It is shown that a consistent interpretation of the Altarelli-Parisi equations governing the Q 2-evolution of helicity-weighted parton distributions necessitates the assumption that partons carry a large orbital angular momentum, contrary to popular belief. In developing the arguments presented, the Altarelli-Parisi formalism is extended to include orbital angular momentum dependence.

The temperature dependence of the anomalous effective g value of BiTm:YIG

Bi- and Tm-substituted YIG have shown [V. R. K. Murthy et al., in Digest of INTERMAG Conference (IEEE, New York, 1983)] anomalously low effective g values. The experimentally measured temperature dependence of BiTm:YIG shows that the effective g value decreases with decreasing temperature whereas the simple spin-wave theory predicts the opposite behavior. A recent paper [A. Lehmann-Szweykowska et al., J. Magn. Magn. Mater. 54, 1183 (1986)] predicts that the single ion anisotropy and spin-wave damping also make important contributions to the effective g value. These effects are due to the large crystal field effects of Tm in the garnet crystal host. The ground state of the Tm is J=6, L=5, and S=1. The large orbital angular momentum states enhance the spin-orbit coupling which is related to the crystal field effect. The temperature dependence of the effective g value was measured by FMR (ferromagnetic resonance) on BiTm:YIG. The experimental temperature dependence is fitted to the theoretical model and excellent agreement is obtained.

On the production of Rydberg atoms with large orbital angular momentum

Rydberg atoms are usually produced with large principal quantum numbers, n>10, but with low orbital angular momentum quantum numbers, l<or=3. In this paper the authors show how a careful arrangement of weak electric fields can produce states of large orbital angular momentum, l approximately=n. Specifically, they show how a field which is switched on adiabatically, suddenly rotated through 90 degrees and then suddenly switched off after a specified time interval can produce large l states. The conditions to be satisfied by the field are defined and the effects of other field configurations are discussed. The analysis is based upon a classical model; where possible the significance of quantal effects is assessed.

Gravitational Radiation from a Particle with Orbital Angular Momentum Plunging into a Kerr Black Hole

Using the Sasaki-Nakamura equation, we have computed the energy, linear and angular momentum of the gravitational radiation induced by a particle of mass /1 and angular momentum /1L z plunging in an equatorial plane into a Kerr black hole of mass M(~/1) and angular momentum Ma. It is found that the total energy LlE (/1/ M )/1C 2 is emitted by the particle with sufficient large orbital angular momentum. For the same value of ILzl, a corotating particle emits more energy than a counter-rotating one. We have also calculated the energy from a rotating ring plunging into a Kerr black hole. In this case, we have found' that a corotating ring emits less gravitational energy than a counter-rotating one for the same ILzl. The maximum of the linear momentum is 6 x 102 (/1/ M )/1C, which suggests the recoil velocity of the coalesced black hole is 160 km/s for /1=0.1 M. Since Davis et al. l ) first calculated the energy by a particle of mass f..l falling into a Schwarzschild black hole of mass M (~f..l), many calculations have been performed for the energy, linear and angular momentum radiated by a particle or particles falling into a black hole. 2 )-4) However, for a Kerr black hole case, before the discovery of the Sasaki­ Nakamura equation,5) there existed only the work-by Detweiler 6 ) for the luminosity from a particle in a circular orbit. The Teukolsky equation,7) which governs the perturbations of the Kerr black hole, has a long range potential and divergent source terms, which prevented us from the actual numerical calculations in generic cases. Sasaki and Nakamura got rid of these difficulties by discovering a new transformation. Using the Sasaki -Nakamura equation, Nakamura and Sasaki 5),8) first calculated the energy from a particle falling along the symmetry axis of the Kerr black hole. Nakamura and Haugan 9 ) calculated the linear momentum for the same case. The present authors lO ) have calculated the gravitational radiation from a particle of mass f..l with zero orbital angular momentum plunging in the equatorial plane (e = 7[/ 2 plane) into a Kerr black hole of mass M(~f..l) and angular momentum Ma. They confirmed the quasi-normal modes ll ) of the ,Kerr black hole. The energy for a=O.99M is 4.45xIO- 2 (f..l 2 /M)c2 which is 4.27 times larger than that for a=O case. In this paper, we examine more general cases than those considered in the previous papers. We calculate tpe energy, momentum and angular momentum of gravitational waves radiated, when a test particle of mass f..l with the orbital angular momentum f..lLz plunges in the equatorial plane into a Kerr black hole of mass M(~f..l) and angular momentum Ma. In §2, we show our mathematical formalism briefly. We will use the Sasaki-Nakamura equation instead of the Teukolsky equation. In §3, the numerical results are given. Section 4 is devoted to some discussion and astrophysical implications of the numerical results. Throughout this paper, we will represent a Kerr black hole by Boyer-Lindquist coordinates with (t, r, e, ¢) and use units of c = G = M = 1.

Distorted-wave—Born-approximation study of angular distributions for state-to-state rearrangement collisions: Role of orbital angular momentum

The structures of product angular distributions for the state-to-state rearrangement collision of an atom --- diatomic-molecule system are examined as a function of the orbital (relative) angular momentum and incident kinetic energy. It is found that a coordinated study of the kernel- and radial-overlap distribution is useful for understanding the predicted structures of the angular distributions of the scattered product. The cause of both backward and sideways scattering are explainable from such study. Broadening of the angular distributions in the case of backward scattering is found to occur due to the increased number of partial waves which overlap with the kernel distribution. In addition, we find that the shift of the peak position or the change from the backward to sideways scattering at increased kinetic energies is due to the enhanced radial overlap between the kernel function and partial waves of larger orbital angular momentum.

Monte Carlo simulation of RRKM unimolecular decomposition in molecular beam experiments. II. Application to angular distributions and absolute cross sections for the system K+RbCl

The Monte Carlo simulation algorithm, which we have developed recently, is now applied to one of the well studied alkali—alkali halide systems. The calculations show, that quite good agreement between experiment and theory is found with semiclassical energy distributions and ordinary RRKM theory. This applies also to the branching ratio, which is now found to be around 0.67 instead of the previously reported theoretical value of 1.0–1.3. The good agreement here is due to the exact treatment of angular momentum conservation, the correct evaluation including all initial distributions and the elimination of previous inaccuracies, like the SWHT formulas. By inclusion of three nonstatistical effects, based on trajectory calculations and dynamical arguments, excellent agreement between theory and the absolute experiments is found. One conclusion is, that the usual large orbital angular momentum approximation is not good even in this case with large cross sections.

The autoionisation of high Rydberg atomic states with large orbital angular momentum

The autoionisation of doubly excited atomic states with one electron excited much more than the other is considered in the one-configuration approximation. The theory is asymptotic in the large angular momentum of the highly excited electron. The direct process results in the ejection of the high Rydberg electron whereas in exchange autoionisation the inner excited electron is ejected and the outer electron passes into the low-lying orbital. The multipole expansion of the interaction reduces the calculation of the direct autoionisation to finding the asymptotic behaviour of the one-electron matrix element between highly excited and continuum states for some power of the radial variable. Slater-type or Coulomb wavefunctions are used for the Rydberg electron and plane waves or Coulomb waves are employed for the ejected electron. The asymptotic behaviour of the two-electron matrix element is found for the exchange autoionisation and also for the exchange-type correction to direct autoionisation.

Abstract: Soft-mode behaviour of excitations in praseodymium under pressure

In dhcp Pr, the Pr ions (J=4) experience a crystal field which produces singlet ground states at both the locally hexagonal and locally cubic sites: the coupling between the ions on the hexagonal sites is just below the critical value for the development of a magnetically ordered phase at low temperatures. The magnetic excitations propagating on the hexagonal sites are composed of linear combinations of singlet-doublet transitions. The lowest energy mode is along TM and has a pronounced minimum at a wavevector of 0.25 Å−1. The large orbital angular momentum of Pr leads to a strong magnetoelastic coupling between the spin and lattice systems. From the field dependence of the excitation energies, Jensen1 deduced the strength of this coupling and suggested that magnetic ordering might be induced by an appropriate uniaxial stress. In a series of neutron scattering studies at the Institut Laue-Langevin, we have observed a dramatic stress dependence of the magnetic excitations2. With increasing stress along an a-direction, the lowest energy mode (longitudinal optic) exhibits a clear soft-mode behaviour. Above a critical stress, elastic satellite reflections corresponding to long-range magnetic ordering in a longitudinally modulated structure were observed. This critical stress is 800 bar (80 MPa) at 7.5 K.

Gedanken experiments to destroy a black hole

It is widely believed that the complete gravitational collapse of a body always results in a black hole (i.e., “naked singularities” can never be produced) and that all black holes eventually “settled down” to Kerr-Newman solutions. An important feature of the Kerr-Newman black holes is that they satisfy relation m 2 ⩾ a 2 + e 2 where m is the mass of the black hole, e is its charge, a = J m is its angular momentum per unit mass and geometrized units G = c = 1 are used. (For m 2 < a 2 + e 2 the Kerr-Newman solutions describe naked singularities.) In this paper, we test the validity of the above conjectures on gravitational collapse by attempting to create a spacetime with m 2 < a 2 + e 2 starting with a Kerr-Newman black hole with m 2 = a 2 + e 2. Such a spacetime would either have to be a new black hole solution or a “naked singularity,” in violation of the above conjectures. In the first gedanken experiment we attempt to make the black hole capture a test particle having large charge and orbital angular momentum compared with energy. In the second gedanken experiment we attempt to drop into the black hole a spinning test body having large spin to mass ratio. In both cases we find that bodies which would cause violation of m 2 ⩾ a 2 + e 2 will not be captured by the black hole, and, thus, we cannot obtain m 2 < a 2 + e 2, although we can come arbitrarily close in the sense that m 2 = a 2 + e 2 can be maintained in these processes.

Orbital Angular Momentum in the Theory of Paramagnetic Clusters

The statistical theory of paramagnetic clusters described in the literature to date is largely restricted to ``spin-only'' magnetism for which orbital angular momentum is quenched, or enters the calculations only as a trivially modified g factor. This paper discusses the extension of the theory to magnetic ions for which large unquenched orbital angular momentum is present, rendering the conventional approach completely inoperative. A theory is developed in detail for cobaltous cluster complexes, the cobaltous ion generally being one of the more difficult of the 3d transition metal ions to describe statistically. A preamble into relevant crystal-field theory is followed by the development of a statistical theory valid, to a good approximation, over the entire temperature range. Numerical results are presented to indicate the separate effects of spin—orbital reduction, and inter- as well as intracluster exchange. The full theory is also compared numerically with the results of simpler, but less adequate, approximations to demonstrate the penalty in accuracy paid for algebraically less onerous calculations. The theoretical principles involved are readily extendable for use with other magnetic ions (e.g., ferrous) for which unquenched orbital angular momentum plays an essential role.