Spin-orbit Distortion Research Articles

Analyzing power and cross section distributions of theC12(p,pα)Be8cluster knockout reaction at an incident energy of 100 MeV

The ($p,p\ensuremath{\alpha}$) reaction on $^{12}\mathrm{C}$ was investigated experimentally using polarized incident protons of 100 MeV. The scattered proton and $\ensuremath{\alpha}$ particle, from the knockout reaction, were detected in coincidence. Coincident data, which were obtained at ten quasifree angle pairs for proton angles ranging from ${25}^{\ifmmode^\circ\else\textdegree\fi{}}$ to ${110}^{\ifmmode^\circ\else\textdegree\fi{}}$, were analyzed in terms of the distorted-wave impulse approximation (DWIA). Calculated energy-sharing cross section and analyzing power distributions reproduce the data reasonably well, indicating that a quasifree knockout mechanism dominates the reaction. Since measurements of analyzing powers were made, spin-orbit distortions were included in the DWIA calculations. The effects of this were found to be very small near zero recoil momentum and did not destroy the validity of the factorization approximation where the two-body $p\text{\ensuremath{-}}\ensuremath{\alpha}$ cross section enters as a multiplicative factor in the three-body ($p,p\ensuremath{\alpha}$) cross section expression. Spectroscopic factors derived from the data are consistent with theoretical predictions. Analyzing power data also follow the trend of free $p\text{\ensuremath{-}}^{4}\mathrm{He}$ scattering data, and comparisons with DWIA predictions are in reasonable agreement. Because the two-body interaction response between the projectile and the $\ensuremath{\alpha}$ cluster was found to resemble the scattering of protons from a free $\ensuremath{\alpha}$ particle to a remarkable degree, the present results would strongly imply the existence of preformed $\ensuremath{\alpha}$ clusters in $^{12}\mathrm{C}$.

The spectral fine structure, zero-field splitting parameters and Jahn-Teller effect of LiNbO3∶Fe3+crystals

The 252 rank completely diagonalized Hamiltonian matrix of the 3d5 configuration with trigonal symmetry have been established by group theory, crystal field theory and irreducible tensor operator method. The spectral fine structure, zero-field splitting parameters, and Jahn-Teller effect, as well s the influence of spin doublet state and spin quartet state on the ground-state energy levels in LiNbO3∶Fe3+ crystals were studied with this matrix. The results show that the contribution of spin quartet state on the ground- state energy levels is the most important, the contribution of spin doublet state is weak but can not be neglected. The calculated results are in good agreement with the experiments. On their basis, the influence of spin-orbit interaction and spin-spin interaction on the spectra fine structure and zero-field splitting parameters were further studied, and we found that the influence of spin-orbit interaction is dominant, but the influence of spin-spin interaction can not be neglected. The research shows this substance has J-T effect in the spectral structure of spin quartet state. The reason is the combined action of spin-orbit interaction and trigonal distortion.

Polarization observables and spin-dependent distortion effects in single-nucleon knockout reactions

A formalism is developed and predictions are made for selected polarization observables in one-nucleon knockout reactions within the transfer-to-the-continuum direct reaction model. The effects of nucleon-target spin-orbit distortions are also included and their importance is quantified. The calculated knockout reaction analyzing powers reach an appreciable fraction of their maximum allowed values. They are also found to be quite sensitive to the different approximation schemes used for the transfer probability amplitude within the transfer-to-the-continuum model. In contrast, they are shown to be insensitive to details of the two-body interactions assumed, including the nucleon-target spin-orbit interaction. The angular distributions of \ensuremath{\gamma}-rays, arising from the decay of heavy reaction residues produced in excited final states, are shown to be strongly anisotropic.

The microwave spectrum of cobalt monoxide: Hyperfine interactions in the X 4Δ state

The rotational spectrum of CoO in the Δ4 ground state was observed using a source-modulated submillimeter-wave spectrometer. A direct current sputtering method using cobalt powder placed in the hollow cathode electrode was used to generate the CoO radical in an atmosphere of oxygen and helium. In total 84 spectral lines were precisely measured in the frequency region of 255–465 GHz for eight rotational transitions of the two lowest spin substates. Each rotational transition consists of eight components due to the Co59 (I=7/2) hyperfine interaction. A least squares analysis of the measured frequencies gave a new set of molecular parameters: rotational constant, hyperfine coupling constants, a, bF, c, and eQq, centrifugal distortion corrections to rotation and spin–orbit interaction, and the less well known higher-order spin–orbit distortion term to the Fermi contact interaction, bS. A comparison of the determined molecular hyperfine coupling constants was made with those of atomic/ionic Co in order to assess the inherent characteristics of the molecular orbitals around the Co nucleus.

Spin-dependent scattering of deeply bound nucleons

Exclusive measurements of the analyzing power and two spin-transfer observables for nucleon knockout from an ${}^{16}\mathrm{O}$ target are presented, at kinematic conditions chosen to emphasize interactions in the nuclear interior. The analyzing power data are substantially reduced in comparison with values calculated in the distorted wave impulse approximation (DWIA) using the free nucleon-nucleon interaction, particularly for knockout of the deeply bound ${1s}_{1/2}$ nucleons. Inclusion of density dependence for the interaction in the calculations improves the agreement with the data, but does not provide a satisfactory description for nucleon knockout from ${}^{16}\mathrm{O}.$ Spin-orbit distortions are shown to strongly affect the DWIA predictions of the ${1s}_{1/2}$ analyzing powers over most of the experimental kinematic range, but notably not near the points of negligible recoil momentum. Hence these data offer constraints on the optical potentials and independently on the two-body effective interaction.

Microwave spectrum of the MnO radical in the X 6Σ+ state

The microwave spectrum of MnO in the Σ+6 ground electronic state was detected using a source-modulated submillimeter-wave spectrometer. The MnO radical was efficiently generated by dc sputtering of manganese flakes placed inside a hollow cathode in the presence of an oxygen and helium mixture. In total, 283 spectral lines were measured in the frequency region of 210–450 GHz for nine rotational transitions, each of which showed six fine structure line groups consisting of several hyperfine structure components due to the Mn55 nucleus (I=5/2). A least-squares analysis of the measured line frequencies resulted in the determination of rotational, fine, and hyperfine coupling constants including higher-order spin–orbit distortion terms for the spin–spin, spin–rotation interactions and the Fermi contact interaction of the Mn nucleus. The hyperfine coupling constants were used to assess plausible molecular orbital bonding models.

Rotational and Hyperfine Structure in the B4Π-X4Σ− (0,0) Band of VO at 7900 Å: Perturbations by the a2Σ+, v = 2 Level

The (0,0) band of the B4Π-X4Σ− system of VO near 7900 Å has been analyzed from Doppler-limited Fourier transform emission spectra, together with wavelength-resolved laser-induced fluorescence and sub-Doppler intermodulated fluorescence spectra. The B4Π, ν = 0 level is heavily perturbed by the a2Σ+, ν = 2 level. Because the 3dδ2 4sσ a2Σ+ and 3dδ2 3dπ B4Π states have very different hyperfine parameters, the hyperfine patterns of the rotational lines vary dramatically with J at the perturbations. The observed hyperfine structure of the band, including the lowest-J perturbation, near J = 3812, could be explained in detail by a model Hamiltonian that takes the interactions into account: 3211 hyperfine line frequencies have been fitted with an rms error of 11 MHz. The b parameter (the coefficient of I·S in the magnetic hyperfine Hamiltonian) is well determined for the a2Σ+ state and provides the evidence for its electron configuration. The hyperfine structure of the B4Π state shows no effects of spin-orbit distortion and is well explained by the standard case (aβJ) model. Only the spin-orbit operator is needed to describe the interaction between the a and B states; the parameter for the direct dipolar interaction between them is too small to be determined. A fit to the higher-J rotational data showed that the spin-orbit interaction matrix element, which arises as a result of configuration interaction in the two states, has an apparent J dependence; this presumably means that the mixing is r dependent. Improved values for the ground state hyperfine parameters have been obtained from the new data, supplemented by the three very precise microwave frequencies measured by Suenram et al. (J. Mol. Spectrosc.148, 114, 1991).

Hyperfine structure in high spin multiplicity electronic states: Analysis of the B 4Π–X 4Σ− transition of gaseous NbO

The (0,0) band of the B 4Π–X 4Σ− transition of NbO, near 6600 Å, has been analyzed from spectra taken at sub-Doppler resolution. The transition is notable for the great width of its Nb nuclear hyperfine structure, which is caused principally by the unpaired 5sσ electron in the ground state interacting with the large magnetic moment of the 4193Nb nucleus (I=9/2). A fit to the ground-state combination differences, including four very precise microwave lines measured by Suenram et al. [J. Mol. Spectrosc. 148, 114 (1991)], has given a comprehensive set of rotational, spin, and hyperfine parameters. Prominent among these are the third-order spin–orbit distortions of the spin-rotation interaction and the Fermi contact interaction, which are large and well determined, reflecting different degrees of spin–orbit contamination of the the 4Σ1/2− and 4Σ3/2− components of the ground state. The δ 2π B 4Π state was hard to fit, for a number of reasons. First, its spin–orbit structure is asymmetric, because of strong perturbations by a 2Π state which has been identified in this work, from among the various weak bands in the NbO spectrum near 7000 Å; the result is that many high order centrifugal distortion terms are needed in an effective Hamiltonian model for the rotation. Second, the hyperfine structure is perturbed, not only by this 2Π state, but by distant Σ and Δ states at higher energy. The δ 2σ* C 4Σ− state at 21 350 cm−1 appears to be one of these. The distant states generate large apparent nuclear spin-rotation interactions, both within and between the Λ components of the Π state, as a result of cross terms between matrix elements of the operators −2BJ⋅L and aI⋅L. Similar cross terms arising from the operators AL⋅S and aI⋅L produce corrections to the Fermi contact matrix elements and are responsible for the unexpected negative sign of the magnetic hyperfine parameter d. The ‘‘off-diagonal’’ quadrupole parameter e2Qq2 is very large, and causes some of the higher J line shapes of the B–X system to be noticeably asymmetric at Doppler limited resolution; its value is consistent with the electron configuration of the B 4Π state being δ 2π.

Analysis of [Dtilde]2A1-[Ctilde]2T2emission bands of CF+4under high resolution

High-resolution emission spectra of [Dtilde] 2A1-[Ctilde] 2T2 transitions in CF+ 4 were obtained from a hollow cathode discharge in CF4/He mixtures. The partly resolved rotational structures of the 0-0, 10 1 and 10 2 bands were analysed on the basis of a model Hamiltonian developed by Watson for tetrahedral molecules. Spectroscopic constants were determined via computer simulations and relations for intervals between heads of branches. Spin-orbit coupling, Coriolis interaction and Jahn-Teller distortion in the lower electronic state were found to be relatively small but to show a vibrational dependence on v 1.

Relativistic effects on polarization transfer observables for quasielastic proton-nucleus scattering.

Within the relativistic plane-wave impulse approximation, the sensitivity of complete sets of quasielastic proton-nucleus spin observables is investigated with respect to relativistic effects, the importance of exchange contributions to the [ital NN] amplitudes, the form of the [pi][ital N] vertex, and spin-orbit distortions. Calculations are performed at laboratory energies ranging from 135 to 500 MeV and for target nuclei ranging from [sup 12]C to [sup 208]Pb at a fairly large fixed momentum transfer of 1.97 fm[sup [minus]1]. Of all the spin observables, only [ital A][sub [ital y]] exhibits a clear relativistic effect at the highest energy, as has been previously found. However, at the lower energies (200 MeV and below) the relativistic effect shifts to two other polarization transfer observables, mainly [ital D][sub [ital s][prime][ital s]] and to a lesser extent [ital D][sub [ital l][prime][ital s]]. In addition, it is found that [ital D][sub [ital n][prime][ital n]] is extremely sensitive to the pseudoscalar versus pseudovector ambiguity of the [pi][ital N] vertex, whereas [ital D][sub [ital s][prime][ital l]] and [ital D][sub [ital l][prime][ital l]] are sensitive to exchange contributions to the [ital NN] amplitudes. Compared to the latter, the effects of spin-orbit distortion are not insignificantly small and had to bemore » corrected for. This investigation stresses the urgent need for measurements of the quasielastic spin observables at these low energies.« less

Distorted wave impulse approximation calculations of 6Li(p,pd)4He reaction at 8 and 9 MeV.

The distorted wave impulse approximation is used for an analysis of experimental data of the {sup 6}Li({ital p},{ital pd}){sup 4}He reaction measured at 8 and 9 MeV. Potential coupling and kinematic coupling approximations for the description of the final state were examined. The effects of spin-dependent distortions are also studied. Satisfactory agreement between the experimental results and the calculations is achieved only when potential coupling approximation is used and spin-orbit distortions are included.

Spin–orbit distortion of the hyperfine structure in heavier molecules: Breakdown of the case (aβ) formalism in the B 3Φ–X 3Δ system of gaseous NbN

A detailed analysis of the rotational and hyperfine structure of the (0,0) band of the B 3Φ–X 3Δ electronic transition of NbN has been performed from sub-Doppler spectra taken with linewidths of about 50 MHz. The Nb hyperfine structure is impressively wide in both states, but particularly so in X 3Δ where one of the unpaired electrons occupies a σ orbital derived from the metal 5s orbital. The electron spin and hyperfine structures do not follow the expected case (aβ ) coupling because of extensive second order spin-orbit effects. It is shown that the asymmetry in the spin–orbit structure of X 3Δ is explained almost quantitatively by interaction with a 1 Δ state from the same electron configuration (which lies at 5197 cm−1); also cross terms between the spin–orbit and Fermi contact interactions in the matrix element 〈3Δ2‖H‖1Δ〉 produce a large correction to the apparent coefficient of the I⋅L magnetic hyperfine interaction in X 3Δ2. The hyperfine structure in a triplet state turns out to be extremely sensitive to the details of the electron spin coupling, and reversals in the sense of the hyperfine structure in the 3Φ4–3Δ3 and 3Φ2–3Δ1 subbands are shown to be consistent with the3Δ state being a regular spin–orbit multiplet (A>0). Particular care has been taken with the calibration, which has meant that extra terms have needed to be added to the magnetic hyperfine Hamiltonian to account for the spin–orbit distortions: instead of the usual three parameters needed in case (aβ ) coupling, the B 3Φ state has required four parameters and the X 3Δ state has required five. The model explains the data very well, and the standard deviation in the least-squares fit to more than 1000 hyperfine line frequencies was 0.000 58 cm−1 (17 MHz).

J dependence in the reaction 16O( pi +,2p)14N at 116 MeV.

A distorted wave impulse approximation formalism is described for (${\ensuremath{\pi}}^{+}$,2p) reactions. The reaction is assumed to proceed via absorption on a deuteron-like p-n pair projected from shell-model wave functions. The spin dependence of this primary interaction is assumed to be dominated by s-wave \ensuremath{\Delta}-nucleon terms. Spin-orbit distortions of the emitted protons, and the coherent addition of different orbital angular momentum transfers, L, are properly taken into account. For L=2, the calculations show a significant dependence on the total angular momentum transfer, J${=1}^{+}$, ${2}^{+}$, or ${3}^{+}$. These new calculations are compared with experimental data for the $^{16}({\ensuremath{\pi}}^{+}$,2p${)}^{14}$N reaction.

The 116Si(d, p) 117Sn l=0 reaction mechanism at intermediate energies

We report measurements of the cross section, proton polarization, and deuteron vector ( A y ) and tensor ( A yy ) analyzing powers for the 116S(d, p) 117)Sn reaction to the 1 2 + ground state of 117Sn at E d = 79.0 MeV. The polarization was observed as the analyzing power in the time-reversed 117Sn(p, d) 116Sn reaction. Adiabatic model calculations of the deuteron elastic channel reveal significant 3D-wave breakup contributions to the elastic cross section. Satisfactory agreement with the transfer reaction data is nevertheless obtained using adiabatic calculations which include only 3 S-wave breakup and the bound deuteron D-state. The influence of the deuteron spin-orbit distortions on the polarization and vector analyzing power is reduced through a combination of the effects of angular momentum mismatch and deuteron channel absorption.

The effects of far-side dominance on the j-dependence of the medium energy 116Sn(d, p) 117Sn reaction

We report measurements of the 116Sn(d, p) 117Sn reaction to the d 3 2 , g 7 2 , and h 11 2 low-lying states at 79.0 MeV. Transfer reaction calculations which include an adiabatic deuteron channel wavefunction, finite range including the deuteron S- and D-state, and non-locality corrections are performed for these transitions. A separation of the reaction amplitude into the near- and far-side components shows that the g 7 2 and h 11 2 reaction calculations are far-side dominated. In this context, the proton channel spin-orbit distortions modify the j-dependence of the A y vector analyzing power and introduce a strong j-dependence in the A yy tensor analyzing power.

Erratum: Relativistic effects on spin observables in quasielastic proton scattering

The spin observables in quasielastic proton scattering are calculated in a simple relativistic model where the NN interaction is assumed to depend on the enhancement of the lower components of nucleon wave functions (because of strong nuclear potentials). This enhancement is characterized by an average effective mass M( of (0.8--0.9)M which is calculated in an eikonal model. The M( dependence of the NN interaction is taken from relativistic impulse approximation calculations. The polarization is found to decrease by 40 percent compared to the free NN value at 500 MeV. Next, simple formulas are provided to estimate the effects of spin-orbit potential distortions on spin observables. At 500 MeV and 18.5/sup 0/ in /sup 208/Pb, the polarization is decreased by 5 percent while D/sub l/'l and D/sub s/'s are decreased by 15 percent and D/sub n/n is almost unchanged.

Magnetism in the linear-chain antiferromagnet RbCoCl3

The magnetism in ${\mathrm{RbCoCl}}_{3}$\ensuremath{\cdot}${2\mathrm{H}}_{2}$O (${T}_{N}$=2.97 K) is studied by high-temperature dynamic susceptibility and low-temperature electron-spin resonance. In order to describe the experiments a Hamiltonian is derived that includes spin-orbit coupling, tetragonal and rhombic distortions, exchange in the mean-field approximation, and an external magnetic field. A simultaneous fit to three mutual perpendicular susceptibilities yields consistent values for the crystal-field parameters and an intrachain exchange constant of J/${k}_{B}$=-5.0 K. The final Hamiltonian in the effective-spin s=(1/2) formalism is more or less of the planar type. The zero-field electron-spin-resonance spectra are described in terms of magnon bound states, i.e., the elementary excitations of the proposed Hamiltonian. The frequency independence and the angular dependence of both microwave and external fields are explained by the model. The temperature variations of the absorption intensity and linewidth are qualitatively discussed using simplified models.

Separation of projectile and ejectile spin-orbit distortions in an L = 0 (d, 3He) reaction

Analysing powers of the l tr = 0, 31P( d, 3He) 30Si , reaction and its inverse reaction have been measured. Quantities which are proportional to the entrance and exit-channel spin-orbit distortions have been constructed from these analysing powers. From these quantities the relative importance of the two spin-orbit distortions was ascertained. A DWBA analysis including D-state contributions in the 3He wave function was conducted in order to fit the spin-separated quantities. Optical-model potential parameters used in the DWBA analysis were deduced from a study of the entrance- and exit-channel elastic scattering data.

Spin orbit effects in quasifree knockout reactions

An efficient calculational method for distorted wave impulse approximation analyses of quasifree knockout reactions is described. Since the usual Racah algebra is eliminated, it is straightforward to include spin-orbit distortions. Results are presented for 150 MeV (p,2p) and (p,pn) reactions. In some cases the effects of the spin-orbit terms are large.

Sequential and simultaneous transfer in the reactions 18O(p, t) 16O, 48Ca(t, p) 50Ca and 90Zr(t, p) 92Zr

The effects of sequential transfer of a pair of neutrons in the reactions 18O(p, t) 16O, 48Ca(t, p) 50Ca and 90Zr(t, p) 92Zr are found to be sizeable. Channel spin-orbit distortion is an important feature of the calculations of the 18O and the 48Ca reactions.