A new probe for local structure: Paramagnetic hyperfine structure in Nd3+ Mössbauer spectra

The⁴I_9/2 ground state of Nd³⁺ (4f³) is split by a crystal field of lower than cubic symmetry into five Kramer doublets. The magnetic hyperfine interactions can be calculated by using an effective magnetic hyperfine tensor Ã, which is obtained from the linear combination coefficients of the ground state doublet eigenvector. The hyperfine tensor à and the line shape depend strongly on the local structure of the system. Nondiagonal magnetic hyperfine interactions produce nonadiabatic relaxation. Corresponding lineshapes are calculated by means of the Clauser-Blume model and the eigenvalue treatment of superoperators. We found for Nd³⁺ in the investigated laser phosphate glass a network-forming function consistent with aC _3h orD _3h point symmetry.     

Tensor interactions and polarization phenomena in heavy-ion scattering

Elastic and inelastic scattering of ⁷Li by ⁵⁸Ni at E_lab = 14.2 and 20.3 MeV is investigated theoretically, special emphasis being laid on polarization phenomena. A parameter-independent study shows second-rank tensor interactions to be the main origin of tensor analyzing powers for both elastic and inelastic scattering. Coupled-channel (CC) calculations using cluster-folding interactions which include the tensor terms are found to be successful in reproducing the data for cross sections and vector and tensor analyzing powers, when projectile excitation effects are sufficiently taken into account. Scattering of ⁶Li by ⁵⁸Ni at E_lab = 20.0 MeV is also investigated by the CC calculation, where successes similar to the ⁷Li case are obtained in understanding experimental data.     

The superfluid as a source of all interactions

The superfluid state of fermion-antifermion fields developed in our previous papers is generalized to include higher orbital and spin states. In addition to single-particle excitations, the system is capable of having real and virtual bound or quasibound composite excitations which are akin to bosons of spinJ ^P equal to0 ^?, 1^?, 2⁺, etc. These pseudoscalar, vector, and tensor bosons can be massive or massless and provide the vehicles for strong, electromagnetic, weak, and gravitational interactions. The concept that the basic (unmanifest) fermion-antifermion interaction can lead to a multiplicity of manifest interactions seems to provide a basis for a unified field theory.     

Nuclear spin relaxation in liquids due to interaction with paramagnetic ions having anisotropic g tensors

Analytical expressions are derived for spin-lattice and spin-spin relaxation times (T_1M and T_2M) of a nucleus arising from magnetic interactions (dipolar and contact) with a paramagnetic ion which has an anisotropic g tensor. The relaxation rates depend on the orientation of the ion-nucleus vector in the principal-axis system of the g tensor. The deviations caused by this angular dependence with reference to the corresponding relaxation rates for an isotropic g tensor are numerically illustrated by considering a case typical for Co (II) complexes.     

Tensor force effect on single-proton energy levels of oxygen isotopes

In the framework of the Hartree-Fock approach the proton spin-orbital splittings of the 1p orbits and the shell gaps in the oxygen isotopes are investigated with the interactions SLy5+T,SLy5+Tw,SGII+Te1,SGII+Te2,SGII+Te3 and many sets of the TIJ interactions.All of the interactions are the Skyrme interactions and contain a tensor component(tensor force).It is shown that the evolution of the single-proton levels for the oxygen isotopes is sensitive to a parameterβTwhich is associated with the tensor force strength of the Skyrme interactions.To understand this phenomenon,we systematically analyze the dependence of the spin-orbit splittings and shell gaps on the parameterβTin terms of the spin-orbit potential and the corresponding wave function.We find that the Skyrme interactions can be classified into two groups:(a)T21,T32,T43,T54,SLy5+T,SLy5+Tw,SGII+Te1 and SGII+Te2,which can roughly reproduce the experimental shell gaps of the oxygen isotopes;(b)T1J and SGII+Te3,which can not reproduce the experimental shell gaps.     

Doubly radiative np capture: A precision evaluation

Our previous prediction σ_2γ=0.12 μb is sharpened by model-independent considerations to σ_2γ=(0.1176±0.0003)μb. The contributions from tensor forces, inner region, retardation, P state interactions, M1-M1 transitions, and exchange currents are all demonstrated to be of order 1:10³ or smaller.     

Quantum dynamics of atomic coherence in a spin-1 condensate: Mean-field versus many-body simulation

We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a “ferromagnetic” state with all spins aligned along the y axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.     

Scattering of polarized 7Li by 120Sn and projectile-target spin-dependent interactions

Scattering of ⁷Li by ¹²⁰Sn targets at E_lab = 44 MeV is investigated in the coupled-channel frame by taking account of the projectile virtual excitations to the lowest three excited states. Calculations are performed by the cluster-folding (CF) interactions and the double-folding (DF) one. Both interactions reproduce very well the experimental data on the cross section, the vector analyzing power, the second-rank tensor ones and the third-rank tensor one in elastic and projectile inelastic scattering, although some differences are found between the CF results and the DF ones. In the calculation, the virtual excitations of the projectile are important for most of the analyzing powers and the spin-orbit interaction is indispensable for the vector analyzing power. These features are in contrast to those in ⁷Li-⁵⁸Ni scattering at 20 MeV and are interpreted as over-Coulomb-barrier effects. The scattering amplitudes and the analyzing powers are investigated by the invariant amplitude method, which provides a key connecting the spin-dependent interactions to the analyzing powers. The method proposes an important relationship between the tensor analyzing powers, which is useful in analyses of both theoretical and experimental results. Finally, it is found that in the elastic scattering the second-rank tensor analyzing powers are proportional to the strength of the second-rank tensor interaction and the vector and third-rank tensor analyzing powers to the square or cube of the strength of this interaction, while in the inelastic scattering the cross section is proportional to the square of the strength of the tensor interaction, other quantities being weakly dependent on the strength.     

Charge-exchange reaction pd → n(pp) within the Bethe-Salpeter approach

The charge-exchange reaction pd → n(pp) at low momentum transfers and low excitation energies of the pp pair is considered within the Bethe-Salpeter approach. The method is proposed for calculating observables in the case where the pp pair is in the ¹ S ₀ state. The results of methodological numerical calculations for the differential cross sections and the tensor analyzing power T ₂₀ are presented. The possibility of using the reaction in question as a basic reaction for creating a deuteron tensor polarimeter at high energies and for obtaining additional information about the elementary amplitude for nucleon-nucleon charge-exchange is predicted.     

N-d elastic scattering and polarization calculations with tensor force and p-wave interaction

Three-body calculations for the n-d elastic scattering are preformed at E_n = 14.1 MeV with s and p-wave N-N interaction and tensor force. The tensor force is not able to reproduce even the order of magnitude of the elastic neutron polarization. It is also shown that the p-wave N-N interactions have an important effect on the neutron polarization.     

A nonperturbative treatment of radiative decays and the relativistic kinetic energy in heavy quarkonia

Using a “regularized potential” we solve the Schrödinger equation including all spin dependent interactions nonperturbatively and calculate the radiative decays of heavy quarkonia. The influence ofS-D mixing due to the tensor term is discussed. Applying the variational approach we investigate the influence of the relativistic kinetic energy on the bound state masses.     

Tensor features and dynamical deformation of the 24Mg(2+) nucleus in the reaction 24Mg(d,dγ)24Mg at E d = 15.3 MeV

The results obtained by reconstructing of the experimental angular dependences of polarization tensors, the tensors of orientation of multipole moments, and the dynamical deformation of ²⁴Mg nuclei produced in the 2⁺ state at 1.369 MeV in inelastic deuteron scattering on ²⁴Mg nuclei at E _d = 15.3 MeV for deuteron scattering angles between 25° and 165° in the laboratory frame are presented. The experimental results are compared with the results of calculations based on various versions of the coupled-channel method. The role of spin-orbit and tensor d ²⁴Mg interactions is discussed along with the influence of the reorientation effect. The correlation features of the 2⁺ state of the ²⁴Mg nucleus at 1.369 MeV that were determined in inelastic deuteron and alpha-particle scattering on ²⁴Mg are compared.     

Tensor polarization of 6Li(2.186 MeV, 3+) states produced in the reaction 9Be(p, α)6Li* at 40 MeV

A consistent theoretical analysis of polarization moments t _kq is performed for the ⁶Li(2.186 MeV, 3⁺) states produced in the reaction ⁹Be(p, α)⁶Li*. The analysis is based on the distorted-wave Born approximation implemented for finite-range forces with allowance for spin-orbit interaction. The calculated tensor moments are compared with relevant experimental data. Particle-particle angular-correlation functions and tensor moments are shown to provide radically new information about reaction mechanisms and about nuclear interactions.     

A new representation for the density matrix: (II). Equations of motion

The equations of motion for the new SU(n) parameters representing the density matrix for arbitrary spin are derived. It is shown that for a class of hamiltonians which are diagonal, the equations are exactly solvable by using the device of combining the SU(n) parameters in pairs using the Pauli spin matrix σ_y. It is also shown that using the correspondence relations between the SU(n) parameters and the spherical tensor moments, it is possible to picture the time evolution of the tensor parameters using the explicit solutions for the SU(n) parameters. This procedure has been illustrated by discussing in detail the problem of spin-1 and $\text{spin}\text{-}\text{3}\text{2}$ systems interacting with an external magnetic field and subjected to quadrupole interactions.     

On the susceptibility of the one-dimensional Ising chain

The elements of the tensor of the susceptibility and the staggered susceptibility of a one-dimensional I Ising chain, with xx couplings between the spins are investigated in the presence of a magnetic field b parallel with or perpendicular to the x direction. Exact expressions are given for all susceptibilities, apart from the parallel susceptibilities in a transverse field which are evaluated by perturbation calculation. Special attention is paid to the conditions under which a susceptibility can have a minimum for b = 0. Furthermore, a system with weakly coupled Ising chains is considered on the basis of a model hamiltonian with separable interchain interactions.     

Nuclear hyperfine interactions in spherical top molecules

The nuclear hyperfine Hamiltonian for XY₄ and XY₆ spherical top molecules in their ground electronic state is built up by a tensor method, and is given by a linear combination of invariant tensor products in the group ^L0(3) × G(G = T_d or 0_h); the case when an external magnetic field is applied is also considered. For the study of a given vibrational state, the appropriate restriction is easily determined; as examples were consider the ground vibronic state and a triply degenerate fundamental state.     

Structure and quadrupole coupling measurements on the NO dimer

Rotational transition frequencies for ¹⁴NO-¹⁴NO, ¹⁴NO-¹⁵NO, and ¹⁵NO-¹⁵NO were measured using a pulsed-nozzle Fourier transform microwave spectrometer. Rotational constants for the different isotopic combinations allowed an unambiguous structure determination. The molecule is in a cis planar structure with a bond between the nitrogen atoms and an NNO angle θ = 99.6(2)°. The NN bond length is 2.236(1) Å and the NO bond length is 1.161(4) Å. Hyperfine structure due to nitrogen quadrupole coupling and spin-rotation interactions was observed and analyzed. Rotation constants, quadrupole coupling tensor, and spin-rotation tensor elements are given.     

Tensor interaction in heavy-ion scattering: (I). The turning-point model

The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power $\text{T}{}_{\mathrm{2q}}$ have certain relations with each other for each type of tensor interaction (T_R, T_P and T_L types). The predicted relations between the $\text{T}{}_{\mathrm{2q}}$ are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for ⁷Li and ²³Na elastic scattering from ⁵⁸Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a T_P? or T_L-type tensor interaction in polarized heavy-ion scattering. The presence of a T_P-type tensor interaction is suggested by measured $\text{T}{}_{20}\text{/}\text{T}{}_{22}$ ratios for ⁷Li+⁵⁸Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail.     

InclusiveK *+(1430),K *0(1430), andf(1270) production inK + p interactions at 32 GeV/c

Results are presented on total and semiinclusive cross sections, longitudinal and transverse momentum distributions of the tensor mesonsK ^*+(1430),K ^*0(1430), andf(1270) observed inK ⁺ p interactions at 32 GeV/c. The data are compared withK ^*+(892).K ^*0(896) and ?⁰ vector meson production in the same experiment. The shapes of inclusive invariantx-spectra for the strange vector and tensor mesons are found to be rather similar, after removal of diffractive and quasi-two-body channels, in agreement with quark-recombination ideas.     

Bures geometry of the three-level quantum systems

We compute — using a formula of Dittmann — the Bures metric tensor (g) for the eight-dimensional state space of three-level quantum systems, employing a newly developed Euler angle-based parameterization of the 3 ×3 density matrices. Most of the individual metric elements (g_ij) are found to be expressible in relatively compact form, many of them in fact being exactly zero.