Total Spin Angular Momentum Research Articles

Role of spins in molecular photoionization: Spectroscopy and dynamics of autoionizing Rydberg states of ortho-H2

A combined experimental and theoretical investigation of the role of electronic and nuclear spins in molecular photoionization is reported. Photoionization spectra of autoionizing $p$ Rydberg states belonging to series converging on the $X$ $^{2}\ensuremath{\Sigma}_{g}^{+}({v}^{+}=0,{N}^{+}=3)$ level of ortho-${\mathrm{H}}_{2}^{+}$ have been measured in the range of principal quantum number $n=50--200$ from the long-lived $H$ $^{1}\ensuremath{\Sigma}_{g}^{+}(v=0,J=3)$ level. The use of a pulsed near-Fourier-transform-limited laser with a bandwidth of less than $10\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ resulted in a Doppler-limited linewidth of $25\phantom{\rule{0.3em}{0ex}}\mathrm{MHz}$ which sufficed to partially resolve the hyperfine structure of the Rydberg states. Below $n\ensuremath{\approx}70$, the exchange interaction between the ion core and Rydberg electrons is larger than the hyperfine interactions in the ion core and the observed levels can be understood in terms of Hund's angular momentum coupling case (d). With increasing value of $n$, the hyperfine interactions in the core lead to a mixing of singlet and triplet characters of the Rydberg states and eventually to a complete decoupling of the Rydberg electron spin from the core spins that results in distinct series converging on the hyperfine components of the ion. Several intermediate coupling cases have been identified and two of them completely characterized. Most interestingly, the total spin angular momentum has been found to be a good quantum number up to $n\ensuremath{\approx}150$ at least, i.e., far beyond the region where the ionic hyperfine structure starts dominating the coupling hierarchy. Multichannel quantum defect theory including nuclear and electron spins has been extended to treat autoionization and predict spectral intensities. The comparison with the experimental spectra has revealed a satisfactory agreement between calculated and measured line positions, linewidths, and intensities and has enabled us to extract, by extrapolation, a more accurate term value for the $H$ $^{1}\ensuremath{\Sigma}_{g}^{+}(v=0,J=3)$ level. The calculations have been used to characterize the role of hyperfine, spin-rotational, and pf interactions in rotational autoionization and have revealed a very strong dependence of the autoionization lifetimes of high Rydberg states on the value of the total angular momentum quantum number $F$.

Electrically and magnetically controlled optical spanner based on the transfer of spin angular momentum of light in an optically active medium

An optical spanner is a light beam that can exert a torque on an object. It is demonstrated in this Rapid Communication that, with the aid of applied electric and magnetic fields, a light beam with initially linear polarization and initially zero total spin angular momentum can interact with an optically active medium, resulting in a change of the ratio of left-handed circularly polarized photons to right-handed ones. Thus the total spin angular momentum of the light is changed, which leads to a torque, creating an electrically and magnetically controlled optical spanner on the medium. For a linearly polarized $632.8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ laser beam incident on a $100\ensuremath{-}\ensuremath{\mu}\mathrm{m}$-long $\mathrm{Ce}:{\mathrm{Bi}}_{12}\mathrm{Ti}{\mathrm{O}}_{20}$ whisker crystal with $5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ radius, if the magnetic field is fixed at $\ensuremath{-}1.8\phantom{\rule{0.3em}{0ex}}\mathrm{T}$, both the left- (right-)handed circularly polarized photon number and the total spin angular momentum vary with the applied electric field in a sinusoidal way, which means the torque exerted by the optical spanner on the crystal also varies sinusoidally with the electric field. It is found that at 50 $(\text{or}\ensuremath{-}50)\phantom{\rule{0.3em}{0ex}}\mathrm{kV}∕\mathrm{cm}$, 56% right- (left-)handed circularly polarized photons are translated into left- (right-)handed ones, which corresponds to a transfer of $0.56\ensuremath{\hbar}$ spin angular momentum contributed by each photon.

The universal cut function and type II metrics

In analogy with classical electromagnetic theory, where one determines the total charge and both electric and magnetic multipole moments of a source from certain surface integrals of the asymptotic (or far) fields, it has been known for many years—from the work of Hermann Bondi—that the energy and momentum of gravitational sources could be determined by similar integrals of the asymptotic Weyl tensor. Recently, we observed that there were certain overlooked structures, defined at future null infinity, that allowed one to determine (or define) further properties of both electromagnetic and gravitating sources. These structures, families of complex ‘slices’ or ‘cuts’ of Penrose's , are referred to as universal cut functions. In particular, one can define from these structures a (complex) centre of mass (and centre of charge) and its equations of motion—with rather surprising consequences. It appears as if these asymptotic structures contain, in their imaginary part, a well-defined total spin-angular momentum of the source. We apply these ideas to the type II algebraically special metrics, both twisting and twist free.

Comment on “Legendre-transform functionals for spin-density-functional theory” [J. Chem. Phys. 124, 224108 (2006)

In this Comment the authors propose an alternative formulation of the starting point to the analysis performed in the commented paper [P. W. Ayers and W. Yang, J. Chem. Phys.124, 224108 (2006)]. An important role of the z component of the vector of the total spin angular momentum operator for the considered many-electron system is indicated. The authors believe their approach to be mathematically cleaner and conceptually easier than the original treatment.

Deep, Low Mass Ratio Overcontact Binary Systems. VI. AH Cancri in the Old Open Cluster M67

CCD photometric light curves in the B and V bands obtained in 2001 and in the V band obtained in 2002 of AH Cnc in the old open cluster M67 are presented. It is shown that AH Cnc is a total-eclipsing binary and its light curves correspond to a typical A type according to Binnendijk's classification. The variations of the light curve around the primary minimum and second maximum were found. Our nine epochs of light minimum monitored from 2001 to 2005, including others collected from the literature, were used to create the first study of the period changes of the binary system. A cyclic oscillation with a period of 36.5 yr and an amplitude of 0.0237 days was discovered to be superposed on a continuous period increase (dP/dt = 3: 99; 10(-7) days yr(-1)). Weak evidence indicates that there exists another small-amplitude period oscillation (A(4) = 0: 0035 days, P-4 = 7.75 yr). The symmetric light curves in the B and V bands obtained in 2001 were analyzed with the 2003 version of the Wilson-Devinney code. It is confirmed that AH Cnc is a deep overcontact binary system with a high degree of overcontact f = 58.5%+/- 4.5% and a low mass ratio of q = 0.1682 +/- 0.0012. The existence of the third light and the cyclic period oscillation both may suggest that AH Cnc is a triple system containing an unseen third body. The tertiary component may have played an important role in the origin of the overcontact binary star by removing angular momentum from the central system, which would cause it to have a short initial orbital period and thus evolve into an overcontact configuration by angular momentum loss. The long-term period increase can be interpreted as a mass transfer from the less massive component to the more massive one. As the orbital period increases, the decrease of the mass ratio will cause it finally to evolve into a single rapid-rotating star when the system meets the more familiar criterion that the orbital angular momentum be less than 3 times the total spin angular momentum. Therefore, AH Cnc may be a progenitor of the blue straggler stars in M67.

Deep, Low Mass Ratio Overcontact Binary Systems. V. The Lowest Mass Ratio Binary V857 Herculis

Charge-coupled device (CCD) photometric light curves in the B, V, and R bands of the complete eclipsing binary star V857 Her are presented. It is shown that the light curves of the W UMa-type binary are symmetric and of A type according to Binnendijk's classification. Our four epochs of light minimum along with others compiled from the literature were used to revise the period and study the period change. Weak evidence indicates that the orbital period of V857 Her may show a continuous increase at a rate of dP/dt = +2.90 x 10(-7) days yr(-1). The photometric parameters of the system were determined with the 2003 version of the Wilson-Devinney code. It is shown that V857 Her is a deep overcontact binary system with f = 83.8% +/- 5.1%. The derived mass ratio of q = 0.06532 +/- 0.0002 suggests that it has the lowest mass ratio among overcontact binary systems. As the orbital period increases, the decrease of the mass ratio will cause it to evolve into a single rapidly rotating star when it meets the more familiar criterion that the orbital angular momentum be less than 3 times the total spin angular momentum. To understand the evolutionary state of the system, long-term photometric monitoring and spectroscopic observations will be required.

High-resolution millimeter wave spectroscopy and multichannel quantum defect theory of the hyperfine structure in high Rydberg states of molecular hydrogen H2

Experimental and theoretical methodologies have been developed to determine the hyperfine structure of molecular ions from detailed studies of the Rydberg spectrum and have been tested on molecular hydrogen. The hyperfine structure in l=0-3 Rydberg states of H2 located below the X 2Sigmag+(v+=0,N+=1) ground state of ortho H2+ has been measured in the range of principal quantum number n=50-65 at sub-MHz resolution by millimeter wave spectroscopy following laser excitation to np and nd Rydberg states using a variety of single-photon and multiphoton excitation sequences. The np1(1), nd1(1), and the nf1(0-3) Rydberg states were found to be metastable and to have lifetimes of more than 5 micros beyond n=50. Members of other series, such as the nd1(2), nd1(3), and the np1(0) series, were found to have lifetimes of more than 1 mus. Local perturbations induced by low-n Rydberg states belonging to series converging on rovibrationally excited levels of H2+ reduce the lifetimes in narrow ranges of n values. The hyperfine structure is strongly dependent on the value of the orbital angular momentum l. In the penetrating s and p states at n approximately 50 the exchange interaction dominates over the hyperfine interaction and the levels can be labeled by the total electron spin angular momentum quantum number S (S=0 or 1). In the less penetrating d and f Rydberg states, the hyperfine interaction between the core nuclear and electron spins is larger than the exchange interaction and the Rydberg states are of mixed singlet and triplet character. A procedure based on the Stark effect and on the systematic analysis of selection rules and combination differences was developed to determine the orbital and the total angular momentum quantum numbers l and F and to construct an energy map of p and f Rydberg levels between n=54 and 64 with relative positions of an accuracy of better than 1 MHz. Multichannel quantum defect theory (MQDT) was extended to treat the hyperfine structure in molecular Rydberg states and was used to analyze the observed hyperfine structure of the p and f Rydberg states of H2. The frame transformation between the Born-Oppenheimer channels described by the angular momentum coupling scheme (abetaJ) and the asymptotic channels described by the (e[bbetaS+]) coupling scheme was derived and enables an elegant treatment of all intermediate coupling cases. Purely ab initio quantum defect theory reproduced the experimentally determined positions to within 40 MHz for the p levels and 13 MHz for the f levels. By slight adjustments of the quantum defect functions and their energy dependences and by consideration of the p-f interaction, of the singlet-triplet splittings of the f levels, and of the departure of the ionic levels from pure coupling case (bbetaS+), the agreement between theory and experiment could be improved to 600 kHz. By comparing the results of MQDT calculations of the hyperfine structure of f Rydberg levels with those of coupled equations calculations, the frame transformation approximation of MQDT was shown to be accurate to within 300 kHz. The extrapolated ionic hyperfine structure of the X 2Sigmag+(v+=0,N+=1) ionic level corresponds to the ab initio prediciton of Babb and Dalgarno [Phys. Rev. A 46, R5317 (1992)] within the experimental error.

Phase transitions in magnetic multilayers; statics and dynamics

Magnetic multilayers which incorporate ultrathin ferromagnetic films are physical realizations of classical, one dimensional spin systems, with spins coupled via exchange mediated by spacer layers or interactions at interfaces, and subject to anisotropy. Here by `spin', we refer to the total spin angular momentum of an ultrathin film in the structure. Such systems can undergo a rich range of phase transitions, in reponse to an external magnetic field, or change in temperature. Since interfilm exchange is weak, modest magnetic fields can induce spin reorientation phase transitions. We thus have a new and diverse class of magnetic materials, with phase diagrams subject to design, since both thickness, composition, or growth conditions. The paper reviews selected examples, including recent studies of the dynamic response (AC susceptibility) of an antiferromagnetically coupled Fe/Cr system which undergoes the surface spin-flop transition.

The use of one-electron quantum numbers to describe polyelectronic systems

Atomic states are rigorously characterized by the total orbital angular momentum and the total spin angular momentum, but chemists persist in the use of electron configurations based on one-electron quantum numbers and simplified rules for predicting ground state configurations. This practice is defended against two lines of criticism, and its use in teaching chemistry is encouraged with the claim that the inductive approach of Mendeleev and the deductive approach initiated by Schrodinger compose the consummate example of that interaction of empirical and rational epistemologies that defines how chemists think.

Optically Detected Electron Spin Echo Envelope Modulation on a Photoexcited Triplet State in Zero Magnetic Field—A Comparison between the Zero-Field and High-Field Limits

Electron spin echo envelope modulation (ESEEM) has been studied at zero and low magnetic fields (B≤ 100 G) by means of optically detected magnetic resonance. Qualitative differences of the ESEEM effect for an electronic triplet state (S= 1) under low-field and high-field conditions are observed and discussed. They are related to the different properties of the total spin angular momentum operatorŜand the hyperfine interaction at zero and high magnetic field. The novel method was applied to the photoexcited triplet state of acridine-d9in a fluorene-h10matrix. An analysis of the observed nitrogen quadrupole splitting is done by a quantitative description of the ESEEM effect in zero field.

Theory of photoluminescence from modulation-doped self-assembled quantum dots in a magnetic field

We study the effect of free carriers on photoluminescence from modulation-doped self-assembled quantum dots. Exact diagonalization studies of up to N=8 electrons and a single exciton in InAs self-assembled dots, and a Hartree-Fock calculations for up to N=20 electrons, are carried out. The total spin and total angular momentum are found to oscillate with the number of electrons. The photoluminescence spectrum is calculated and the band-gap renormalization in zero-dimensional systems is discussed. The tendency of electrons in degenerate, partially filled electronic shells to maximize the total spin leads to a strong dependence of the spectrum on the number of electrons N, the magnetic field B, and the polarization of light.

First Post-Newtonian Angular Momentum In Relativistic Celestial Mechanics

With a new theory on the 1PN celestial mechanics recently developed by Damour, Soffel and Xu (1991,1992,1993,1994), definitions and expressions of the 1PN spin angular momentum are investigated and analysed. The total spin angular momentum of a system of extended bodies such as the solar system is calculated and expressed as the function of local parameters and observables under reasonable assumptions, which would find its application in the evolution and dynamics of systems of celestial bodies.

Experimental determination of orbital and spin orientation of (Ar+)* formed in collisions.

We have experimentally obtained the state multipoles up to rank two for {ital J}-resolved {sup 2}{ital F}{sub 7/2,5/2} states of Ar{sup +} for the two-electron process He{sup +}+Ar{r_arrow}He(1{ital s}{sup 2})+Ar{sup +}(3{ital p}{sup 4}[{sup 1}{ital D}]4{ital p}{sup 2}{ital F}{sup {ital o}}{sub 7/2,5/2}) by measuring the Stokes parameters of the fluorescence light from (Ar{sup +}){asterisk} in coincidence with the scattered He. By expanding the state multipoles of each {ital J} state in terms of total orbital and total spin multipole moments, we have determined the contributions to the experimentally determined state multipoles of each {ital J} state due to total orbital and total spin angular momenta. When the process is spin dependent, it is possible to extract magnetic octupole moments of the excited state due to the orbital charge circulation. {copyright} {ital 1996 The American Physical Society.}

Selection rule in resonant photoemission in rare earths

The difference in 4 f, 5 p and 5 s photoemission (PE) spectra under off-resonant and various on-resonant conditions is systematically discussed for 4 f rare earths at the 4 d core threshold and is compared with the case of 3 d core threshold on the basis of an ionic model including the full multiplet. Due to the 3 d or 4 d core spin-orbit interaction, the higher energy multiplets with lower total spin or orbital angular momentum are shown to be produced in 4 f, 5 p and 5 s PE spectra by tuning the photon energy, which is not seen in off-resonant process.

Selection rule in resonant photoemission in rare earths

The difference in 4 f , 5 p and 5 s photoemission (PE) spectra under off-resonant and various on-resonant conditions is systematically discussed for 4 f rare earths at the 4 d core threshold and is compared with the case of 3 d core threshold on the basis of an ionic model including the full multiplet. Due to the 3 d or 4 d core spin-orbit interaction, the higher energy multiplets with lower total spin or orbital angular momentum are shown to be produced in 4 f , 5 p and 5 s PE spectra by tuning the photon energy, which is not seen in off-resonant process.

Skyrmion excitations in quantum Hall systems

Using finite size calculations on the surface of a sphere we study the topological (skyrmion) excitation in quantum Hall system with spin degree of freedom at filling factors around $\nu=1$. In the absence of Zeeman energy, we find, in systems with one quasi-particle or one quasi-hole, the lowest energy band consists of states with $L=S$, where $L$ and $S$ are the total orbital and spin angular momentum. These different spin states are almost degenerate in the thermodynamic limit and their symmetry-breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electron interaction and the skyrmion shrinks to a spin texture of finite size. We have calculated the energy gap of the system at infinite wave vector limit as a function of the Zeeman energy and find there are kinks in the energy gap associated with the shrinking of the size of the skyrmion. breaking ground state is the state with one skyrmion of infinite size. In the presence of Zeeman energy, the skyrmion size is determined by the interplay of the Zeeman energy and electron-electron

Forbidden singlet–singlet transitions in collisional processes

In an atomic collision in which total spin angular momentum is conserved, retention of singlet status by either collision partner is strictly forbidden when the other collision partner undergoes a change in multiplicity. The absence of such forbidden transitions appears to be the only stringent test of spin conservation. This is strikingly manifested in the translational energy spectra of boron ions, B+, scattered off CO molecules, with suppression of the interaction channel B+(1S)+CO(X 1Σ+)→B+(1S)+CO (a 3Πrf). For projectile ions in nonsinglet ground states, the singlet–triplet X 1Σ+→a 3Πr excitation of CO is an unusually prominent feature.

Spin symmetry and interaction mechanisms in free radical reactions

The principles underlying the spin-allowed and spin-forbidden free radical reactions are sought. Based on symmetry, the interactionmechanism and the corresponding transmission matrix elements for the mixing of reactant/product hyperpotential surfaces ar elucidated. Magnetic multipole, electrostatic, spin-orbit and spin-spin interactions are considered. Four examples are used to illustrate various cases: (1) Xe ( 3P u) + N 2 ( 1Σ g +) → Xe( 1S g) + N 2 ( 3II g), which satisfies Wigner's selection rule for the conservation of total spin angular momentum and for which spin and orbital interactions must be compatible, all of the above interactions are found. (2) The perpendicular mode of photodissociation in O 3 * ( 1B 1) → O( 3P g) + O 2( 3E g −), which is orbitally forbidden and for which only spin-spin interaction is found. (3) The hypothetical reaction CH( 4Σ −) + CH( 2Σ +) → C 2H 2 (Ã 1A u), which is spin forbidden but is made allowed by the C 2h geometry of the reaction coordinate. Only spin interactions are found. (4) The triplet cyclopropylidene to orthogonal singlet allene transformation, which is a Hückel to Möbius transformation, and the reaction coordinate produces orbital angular momentum changes to compensate for the spin change. The detailed interaction matrix elements shown for each channel of reaction give a qualitative indication of the branching ratios for different reaction paths and may be compared with future experimental measurements.

Optically pumped atomic spin orientation and the law of mass action for 2Cs⇄Cs2

The effect of optically pumped atomic spin orientation on the atom–dimer equilibrium in cesium vapor has been observed. Such a shift in equilibrium was predicted over two decades ago and is due to the redistribution of spin-determined bonding and antibonding collision trajectories. Orientation of the total spin angular momentum of 6 2S1/2 ground state Cs atoms in the vapor phase was produced by optical pumping with a tunable cw dye laser. A decrease in the equilibrium molecular density resulted and was measured using laser induced fluorescence from the B 1Πu state. The shift in equilibrium is a function of the degree of atomic orientation and could be observed in the temperature range 383–421 K for cesium vapor in a glass cell which also contained a He–N2 buffer gas mixture with a composition ratio of 9:1.

Effective three-body magnetic operators in the d shell

The three-body magnetic effective operators acting within the d shell are discussed. These operators are classified and orthogonalised through the use of continuous Lie groups. These operators are of the form T(kk) where k represents the rank of the total spin and orbital angular momentum. For the three-body operators there are 16 operators with k equal to one, ten with k equal to two, and two with k equal to three. In many cases the transformation properties with respect to the available groups do not provide enough information to completely resolve all the operators. The author shows how the group label multiplicities can be handled by direct reference to the operator matrix elements. An analysis of the second-order electrostatically correlated spin-spin effect is performed and reveals that only six of the spin-spin-type operators (k=2) appear in this order.