Part Of Angular Momentum Research Articles

Inelastic neutrino–nucleus reaction cross sections at low neutrino-energies

Differential and integrated inelastic neutrino–nucleus reaction cross sections are studied, focusing on the neutral current processes of even–even nuclear systems. Contributions coming from all types of interactions, both for the vector and axial-vector components of the corresponding hadronic currents, have been included. The necessary nuclear wave-functions for J -projected final states have been deduced in the context of Quasi-particle Random Phase Approximation (QRPA), and tested on the reproducibility of the low-lying energy spectrum (up to about 5 MeV), and the nuclear magnetic moments (by calculating separately the orbital angular momentum and spin parts) of the studied nucleus. Subsequently, the corresponding total cross sections are evaluated by summing-over-partial-rates and the results are compared with those obtained by other methods. The results presented refer to the nuclei 40Ar, the target of the ICARUS neutrino-experiment at Gran Sasso, and 56Fe, which, among others, plays a significant role in supernova neutrino phenomena.

H ULLAC, an integrated computer package for atomic processes in plasmas

We describe H ULLAC, an integrated code for calculating atomic structure and cross sections for collisional and radiative atomic processes. This code evolved and has been used over the years, but so far, there was no coherent, comprehensive, and in-depth presentation of it. It is based on relativistic quantum mechanical calculations including configuration interaction. The collisional cross sections are calculated in the distorted wave approximation. The theory and code are presented, emphasizing the various novel methods that has been developed to obtain accurate results very efficiently. In particular we describe the parametric potential method used for both bound and free orbitals, the factorization–interpolation method applied in the derivation of collisional rates, the phase amplitude approach for calculating the continuum orbitals and the N JGRAF graphical method used in the calculation of the angular momentum part of the matrix elements. Special effort has been made to insure the simplicity of use, which is demonstrated in an example.

Orbital and spin photon angular momentum transfer in liquid crystals.

All-optical angular control of the molecular alignment in liquid-crystal films is demonstrated using a laser beam having an elliptically shaped intensity profile. The material birefringence is unimportant, as proven by the fact that good alignment is obtained with unpolarized light. This raises the possibility of achieving optical angular control of transparent isotropic bodies. A general theoretical approach, based on light and matter angular momentum conservation, shows that the optical alignment is due to the internal compensation between the transfer of the orbital and the spin part of angular momentum of the incident photons to the material.

Effect of liquid to solid phase transition on rotational and vibrational broadening of vibrational bands of CF 3CL in Xe solutions

Fundamental and second order bands of CF 3Cl dissolved in Xe solutions have been studied near the melting point by using technique of transparent solid sample growth from the liquid rare gas solution. The widths at half maximum 2 Γ of the bands were noticeably decreased after crystallization, especially in the case of the broadest 2 ν 4( E) band. Experimental data have been interpreted in the framework of Debye limit (〈 ω〉 τ J ≪1) for the J-model of a heavy symmetrical top rotation. Additional broadening, caused by fluctuational mechanisms of vibrational relaxation, was taken into account. Angular momentum correlation times ( τ J⊥ and τ J∥ ) and parts of widths, originated from vibrational relaxation, were estimated for the liquid and solid Xe solutions near the melting point. The results obtained have shown decreasing effect of fluctuational broadening and increasing disturbance of rotational motion of CF 3Cl when going from the liquid Xe solution to the crystal state.

Coefficients of fractional parentage of a boson system with F-spin

Wavefunctions of bosons each with angular momentum I and F-spin 1/2 are classified according to the group chain U(2N) contains/implies (U(N) contains/implies O(N) contains/implies O(3))*SU(2). The boson number, seniority, reduced F-spin, total angular momentum, and total F-spin quantum numbers are used to label the wavefunctions. The corresponding coefficients of fractional percentage (CFP) are factorized into F-spin and angular momentum parts. The F-spin parts are calculated by an analytical formula and the angular momentum parts are calculated by recursion technique. The isoscalar factors of U(2N) contains/implies U(N) contains/implies O(N) and the F-spin part of the CFP for the cases F= Fmax and F=Fmax-1 are given explicitly.

Simultaneous Implosive Accretion and Jet Formation in Quasars: Correlation of Optical Outbursts by VLBI Jets

A model and simulation code have been developed for time-dependent axisymmetric disk accretion onto a compact object including for the first time the influence of an ordered magnetic field and magnetically driven outflow of energy and angular momentum in (±z) directions (see also Lovelace et al., 1993). It was shown that the system behaviour crucially depends on the amplitude of the poloidal magnetic field fluctuation Bp, compared to the critical value Bcr ∼ (α2T1/2σ/R3/2)1/2, where T(r, t) is the temperature, σ(r, t) the surface density of the disk, R the radial distance, α the alpha coefficient of Shakura-Sunyaev disk model. If the fluctuation is small, Bp < Bcr, then it diffuses outwards with decreasing the amplitude and eventually disappears. In the opposite case Bp > Bcr, a soliton-like structure forms in the disk density, temperature, and magnetic field and propagates implosively inward. In this case the radial accretion speed u(r, t) is shown to be the sum of the usual viscous contribution and magneitic contribution ∼ R3/2B2p/σ. The essential part of angular momentum and energy is going to the jet from the region of fluctuation. Compression of matter in the propagating wave leads to enhancement of magnetic field and more effective angular momentum outflow. This leads in turn to accelerated accretion and subsequent enhancement of magnetic field. It gives the implosive nature of the process, which can be observed as: simultaneous burst in the radiation and outflow. The model is pertinent to the formation of discrete components observed in VLBI jets which appear to originate at times of optical outbursts at some quasars.

Fermion wave-mechanical operators in curved space-time.

In the context of a general wave-mechanical formalism, we derive explicit forms for the Hamiltonian, kinetic energy, and momentum operators for a massive fermion in curved space-time. In the two-spinor representation, the scalar products of state vectors are conserved under the Dirac equation, but the time-development Hamiltonian is in general not Hermitian for a nonstatic metric. A geodesic normal coordinate system provides an economical framework in which to interpret the results. We apply the formalism to a closed Robertson-Walker metric, for which we find the eigenvalues and eigenfunctions of the kinetic energy density. The angular momentum parts turn out to be simpler than in the usual four-spinor representation, and the radial parts involve Jacobi polynomials.

Dynamo magnetic field-induced angular momentum transport in protostellar nebulae - The 'minimum mass' protosolar nebula

Magnetic torques can produce angular momentum redistribution in protostellar nebulas. Dynamo magnetic fields can be generated in differentially rotating and turbulent nebulas and can be the source of magnetic torques that transfer angular momentum from a protostar to a disk, as well as redistribute angular momentum within a disk. A magnetic field strength of 100-1000 G is needed to transport the major part of a protostar's angular momentum into a surrounding disk in a time characteristic of star formation, thus allowing formation of a solar-system size protoplanetary nebula in the usual 'minimum-mass' model of the protosolar nebula. This paper examines the possibility that a dynamo magnetic field could have induced the needed angular momentum transport from the proto-Sun to the protoplanetary nebula.

Magnetic properties of interstitial 3d impurities in silicon

Using self-consistent Green's function calculations, we (i) discuss the magnetism of interstitial 3d impurities in silicon, (ii) makes a comparison of the theory with EPR data, (iii) discuss a mechanism of covalent reduction of both the hyperfine coupling constant and the orbital angular momentum part of the g-values, and (iv) propose a new type of “negative effective U”, induced by exchange-correlation.

Electronic and Magnetic Properties of Interstitial 3d Impurities in Silicon

AbstractSelf-consistent spin-unrestricted all-electron Green's function calculations are reported for the first time for a series of interstitial 3d impurities in silicon. The calculations, performed within the selfinteraction- corrected local-spin-density fromalism show: (i) not all 3d impurities follow Hund's rule: Tio, Ti−, Vo, V+ and Co2+ have a low-spin ground state, (ii) the angular momentum part gL of g-value is quenched due to p-d hybridization effects, (iii) covalency explains also the chemical trends in the central hyperfine coupling constants, (iii) chemical trends in donor andacceptor transitions are reproduced and are consistent with a high-spin to lowspin transition at the low-Z end and high-Z end of the 3d series, (iv) A number of predictions are offered.

Δ-isobar effects onM2strength inPb208

The strength distribution of the 2/sup -/ states in /sup 208/Pb is calculated including the ..delta..-isobar quenching effects. The theoretical B(M2) values up to 8 MeV are dominated by the orbital angular momentum part of the M2 operator. Therefore we find only little quenching in this energy region owing to the ..delta..-particle nucleon-hole admixtures.

First-order formalism in gauge field theory

A description of gauge fields based on symmetric second-order spinors is considered. The Lagrange function and the equations of motion are found. The gravitational field in vacuum and in the presence of matter is studied, as well as the interaction of the gravitational and an arbitrary tensor fields. It is shown that in this approach, the source of the gravitational field is the tensor of the density of the spin part of angular momentum.

Optimized polynomial expansions: Potentials andppphase shift analyses

We have examined the Cutkosky-Deo-Ciulli-Chao optimized polynomial expansion as applied to the proton-proton scattering amplitudes. We found that we could not reproduce Chao's positive numerical results for intermediate energy scattering data. Instead, we reached a negative conclusion as to the method's usefulness for that application. We also examined the method's ability to predict the higher angular momentum parts of the amplitudes for three different potentials having realistic parts. Again we found the method to have very meager successes.NUCLEAR REACTIONS Optimal polynomial expansions in nucleon-nucleon scattering; potential models, phase analyses; previous errors.

Relaxation parameters for power-broadened microwave line shapes. II. Sudden approximation

A sudden approximation, utilizing linear trajectories and a dipole–dipole potential as developed by Cross [J. Chem. Phys. 55, 510 (1971)], is extended to enable calculation of collisional relaxation parameters of arbitrary tensor order. Expressions are given for linear rotors and symmetric tops. The relaxation parameters factorize into a dynamical part and an angular momentum part and are expressible as linear combinations of collisional transition probabilities out of the j = 0 rotational level. This is in agreement with previous discussions of the infinite order sudden approximation to the coupled states equations. An experiment is proposed which would enable the determination of all polarization relaxation times of a given transition. The results of such an experiment would help to define the validity of the sudden approximation in calculating relaxation cross sections. Finally, application of the sudden approximation to four-level double resonance experiments is discussed.

Melosh transformation in interacting quark theories

We make a general study of the existence of a Melosh-type transformation in interacting quark field theories quantized on the null plane. Following Carlitz and Tung this transformation is required to decompose the total angular momentum operators of these theories into mutually commuting orbital angular momentum and spin parts. This allows the identification of a U(6) \ifmmode\times\else\texttimes\fi{} U(6) \ifmmode\times\else\texttimes\fi{} O(3) classification group in these theories. It is shown that the requirement of commutativity between the generators of the U(6) \ifmmode\times\else\texttimes\fi{} U(6) subgroup and the three momentum operators ${P}^{+}$, ${\stackrel{\ensuremath{\rightarrow}}{P}}^{\ensuremath{\perp}}$ generating translations on the null plane, when combined with the spin properties of the former, automatically assures the exact conservation of the entire U(6) \ifmmode\times\else\texttimes\fi{} U(6) algebra in a Poincar\'e-invariant theory. A part of this transformation which is bilinear in the quark field is shown to exist in these theories. This part commutes with the operators ${P}^{+}$ and ${\stackrel{\ensuremath{\rightarrow}}{P}}^{\ensuremath{\perp}}$ showing that the breaking of U(6) \ifmmode\times\else\texttimes\fi{} U(6) symmetry can take place only through the quark pair terms appearing in the transformation.

On the two-body decays of the higher boson resonances

Tile assignment of the higher boson resonances to SU~ multiplets followed two different lines. On the one hand, it was proposed to use one of the symmetric representations (189 or 4()5) contained in the direct (two-meson) product 35| 35 (i). This corresponds, in the quark language, to describing the higher bosons as systems of four quarks (two quark-antiquark pairs), all in relative S-waves. On the other hand, BORCHI and GATTO (2) proposed a representation of dimension 105, which behaves like 35 under SU 6 and like P-wave under orbital rotations. 'Ihis corresponds to a quark-ant iquark system in relative P-wave. The relativistic completion of the 189 representation has been performed by DELBOURGO et al. (3), in the frame of the ~,2 scheme. The known higher resonances have been accomodated in the 4212 representation of ~12 (4); in this scheme the decays of the 2 + mesons in the available two-meson channels are forbidden, so tha t they are entirely due to a symmetry-breaking interaction. We propose here a possible (,boosting,)(5) of the P-wave two-quark model. We start from an SU 0 | R 3 structure and assume that, in the absence of spin-orbit interaction, the (~ boosting ,> is carried out indipendently on the SL~ part and on the angular momentum (R3) part, giving an ~,~Q~f structure. We give here the prescriptions, without discussing the foundation of such a procedure. We use, in the following, the notat ion of SAKITA and WALI (6). ~he pseudo-

Implications of parity nonconservation and time reversal noninvariance in electromagnetic interactions: Part II. Atomic energy levels

The implications of the parity nonconserving and time reversal noninvariant theory of electromagnetic interactions (which has been developed in a previous paper) with regard to the properties of atoms and their associated spectra, are investigated. In the first part of this paper, the modified Dirac equation for the hydrogen atom, in which the extra pseudovector part of the four potential ( B ν ) is included, is solved exactly. The solutions are found to depend on a new constant of the motion which replaces the conventional angular momentum operator. This new constant is made up in part of the conventional pseudovector angular momentum (particle) variable and in part of a vector function of the particle and field variables. The results are applied to a determination of new selection rules for magnetic and electric dipole transitions (which are forbidden in the conventional theory) and the calculation of the associated transition probabilities. The contribution of the pseudovector four potential to the measured value of the Lamb shift is calculated. It is found that, analogously to the linear Stark effect in hydrogen, there is a non-Zeeman type linear magnetic field effect in the first excited state of hydrogen. This effect is linear in the mixing parameter ξ. The value of ξ required to account for the present-day discrepancy between the calculated value of the Lamb shift and its measured value, would still insure compatibility with other experimental data. It is also found that the lifetimes of atomic states depend on ξ 2, thus having much less affect on the metastability of the 2S 1 2 state of hydrogen. The second part of this paper deals with the spectra of constituent magnetic ions of paramagnetic crystals. The relationship between the crystalline field interactions with the magnetic ions and time reversal invariance is emphasized. A sample perturbation calculation of the pseudoscalar interaction implied by this theory is then carried out for the case in which a magnetic ion is subjected to a crystalline field (whose symmetry group lacks an inversion center) and/or an externally applied uniform electric field.