First-order Contribution Research Articles

Quark-diquark contribution to the (56, 0+) mass spectrum

In a quark-diquark model with quark-quark interactions described byO(N) one-body and two-body quark interchange operators, we fit the (56, 0+) and (70, 0+) baryon mass spectra in the limit of no quark-diquark structure. We find that the discrepancies of the fittings set an upper limit of 2.0% for the diquark contribution. The first-order contribution from the quark-diquark structure reduces these discrepancies from 2.0% to 0.67%.

Parity-dependent potentials and exchanged trajectories: A new class of diffracted trajectories

The scattering amplitude of a complex spherical-well potential, perturbed by a parity-dependent term, is evaluated in the semi-classical limit. The first-order contribution of the perturbation to the scattering amplitude is reduced to the sum of a second-order pole contribution with a saddle point one. These two contributions are interpreted as arising from exchanged diffracted and reflected trajectories.

Exact First-Order Electron Self-Energy Contribution to the Decay Rate of Orthopositronium

There is presently a discrepancy between the theoretical and experimental determinations of the purely quantum electrodynamic decay rate for orthopositronium. This Letter presents the first exact calculation of any contribution to the decay rate of orthopositronium to order ..cap alpha../sup 7/.

Natural or orthogonalized magnetic orbitals: Two alternative ways to describe the exchange interaction

The two approaches defined in the title, NMO and OMO, are compared and their advantages discussed. In the OMO approach, the stabilization of the spin singlet arising apparently from the ground configuration-charge-transfer configuration coupling is in fact a black box which implicitly contains a first-order contribution independent of the energy gap between the two configurations.

Phosphite radicals and their reactions. Examples of redox, substitution, and addition reactions

Phosphite radicals HPO/sub 3/- and PO/sub 3//sup 2/-, which exist in an acid-base equilibrium with pK = 5.75, are shown to take part in various types of reactions. In the absence of scavengers, they disappear mainly by second-order disproportionation and combination; a first-order contribution to the decay is also indicated. HPO/sub 3/- and PO/sub 3//sup 2/- are good reductants toward electron acceptors such as tetranitromethane. In this reaction phosphate and C(NO/sub 2/)/sub 3/- are formed. Phosphite radicals can, however, also act as good oxidants, e.g., toward thiols and thiolate ions. These reactions lead to the formation of RS. radicals which were identified either directly, as in the case of penicillamine, through the optical absorption of PenS. or more indirectly through equilibration of RS. with RS- to the optically absorbing RSSR-. disulfide radical anion. A homolytic substitution reaction (S/sub H/2) occurs in the reaction of the phosphite radicals with aliphatic disulfides, yielding RS. radicals and phosphate thioester RSPO/sub 3//sup 2/-. Lipoic acid, as an example of a cyclic disulfide, is reduced to the corresponding RSSR-. radical anion and also undergoes the S/sub H/2 reaction with about equal probability. An addition reaction is observed between phosphite radicals and molecular oxygen. The resultingmore » peroxo phosphate radicals establish an acid-base equilibrium HPO/sub 5//sup -/. reversible PO/sub 5//sup 2 -/. + H+ with a pK = 3.4. Absolute rate constants were determined for all reactions discussed.« less

Multi-centre contributions to the anisotropic hyperfine interactions in the cu(ii) bis(dithiocarbamate) complex. Proton hyperfine couplings

One-, two- and three-centre, first-order contributions to the hyperfine coupling tensors of the central metal atom and of the ligand atoms in Cu(II) bis(N,N-diethyldithiocarbamate) are calculated. Conclusions are drawn on the relative magnitude of the multi-centre and the one-centre contributions The multi-centre contributions are always small and are of importance only if the one-centre contributions are negligible themselves The latter holds especially for the anisotropic coupling tensors of the protons the calculated two- and three-centre contributions agree very well with the experimental values.

Lifting three-dimensional wings in transonic flow

The far field of a lifting three-dimensional wing in transonic flow is analysed. The boundary-value problem governing the flow far from the wing is derived by the method of matched asymptotic expansions. The main result is to show that corrections which are second order in the near field make a first-order contribution to the far field. The present study corrects and simplifies the work of Cheng & Hafez (1975) and Barnwell (1975).

Higher-order instanton effects

We present a formalism for calculating higher-order instanton effects based on a systematic expansion of the functional integrals about multiple instanton-anti-instanton configurations. We consider how various correlation functions may be constructed from the determinants and propagators in a background multiple-instanton field. A multiple-scattering formalism is then developed in order to express these determinants and propagators for a multi-instanton field in terms of the basic single-instanton quantities. The introduction of an improved gluon propagator based on a different choice of zero-mode constraints is required in order to justify the multiple-scattering formalism. As examples of this approach, we consider instanton interactions, which appear as corrections to the dilute-gas approximation for the instanton density, and the first-order quantum contributions to the static quark potential.

An effective Hamiltonian for diatomic molecules: Ab initio calculations of parameters of HCl +

The form of the effective Hamiltonian for a diatomic molecule in an electronic state intermediate between Hund's cases (a) and (b) is reexamined. The derivation is performed in three stages: (i) an electronic contact transformation removes the effects of matrix elements which couple different electronic states; (ii) a vibrational contact transformation removes matrix elements coupling different vibrational states; and (iii) a spin-rotational contact transformation removes indeterminacies in the final Hamiltonian. Expressions for the effective parameters resulting from these transformations are presented. The Hamiltonian is in a convenient form for fitting to experimental data, and the formulas for the parameters assist in the comparison with ab initio calculations. The relations between the present parameters and those employed in the computer program of Zare, Schmeltekopf, Harrop, and Albritton [ J. Mol. Spectrosc. 46, 37–66 (1973)] are given, and make it possible to correct a previous misunderstanding regarding the value of the spin-rotation parameter γ e in the X 2Π state of HCl +. The parameters obtained for this state are compared with ab initio calculations which take account of first-order perturbations within the state and second-order perturbations from the A 2Σ + state and from the four states of the configuration … σ 2π 2σ ∗ . The A 2Σ + state is the dominant perturber, but the contributions from the other states are not negligible. For example, their contribution to γ e is larger than the first-order contribution.

The temperature dependencies of lanthanide-induced NMR shifts: Evaluation of theoretical approaches and experimental evidence

Bleaney's theory represents an excellent approximation in the calculation of the variation of magnetic susceptibility anisotropy as a function of f-electron configuration in complexes of trivalent lanthanide ions. Owing to certain approximations employed in his approach, Bleaney's prediction of a linear dependence of the anisotropy upon T −2 is not strictly correct. The more complete calculational procedure of Horrocks et al. predicts significant deviations from the simple T −2 temperature dependence in some cases. Experimental single-crystal magnetic anisotropy data on two axially symmetric Yb(III) complexes and a nonaxial Yb(III) shift reagent adduct reveal significant deviations from a linear dependence on T −2. Bleaney's assumption of an isotropic Landé splitting factor, g j is shown to be consistent with large g-tensor anisotropies of individual lanthanide ion levels and with large first-order Zeeman contributions to the observed shifts.

Ab initio calculation of the spin-rotation constant for 2Π diatomics : Test of the Van Vleck approximation

Ab initio calculations are carried out to determine γ Π (true), the first-order contribution to the spin-rotation constant, γ Π, for the X 2Π ground states of OH, HF +, and HCl + and their deuterated analogs. These calculations demonstrate that the contribution of this term to the experimentally determined value of γ Π is small, as has been previously conjectured. Furthermore, it is found in the cases under study that the Van Vleck approximation to γ Π (true) significantly overestimates its importance, and a more realistic approximation is presented.

The n??* optical activity of chiral carbonyl compounds predicted to be optically inactive by the octant rule

The “one-electron” model of n→π* optical activity in chiral carbonyl compounds is carried to second-order in perturbation theory and the results are applied to systems which are predicted by the octant rule to yield zero n→π* optical activity. It is shown that second-order contributions to the n→π* rotatory strength lead to sector rules which are qualitatively different from those obtained from first-order contributions. Inclusion of three-way interactions involving the carbonyl chromophore and two different extrachromophoric perturbing groups (or atoms) lead to second-order contributions to the rotatory strength which can account for the n→π* optical activity in chiral carbonyl systems predicted to be optically inactive by the conventional quadrant and octant rules. These results are shown to be in agreement with the conclusions derived by Ruch and Schonhofer from a purely algebraic theory of molecular chirality.

Localized solutions for the massive Thirring model in the presence of an external electrostatic field

We investigate the classical equations of motion for the massive Thirring model in one space and one time dimension in the presence of an external electrostatic field. It is shown that stationary-confined solutions are acceptable for this model if a self-consistency condition is satisfied. We suggest the possibility of solving the equations of motion using a perturbative approach for the electromagnetic interaction. Some properties of the first-order contribution to the solution, which are fully independent of the external potential shape, are exhibited. A specific example is also developed and analyzed.

Exchange interaction between two cobalt ions and a calculation of the g-shift

The form of the exchange interaction between two Co2+ ions, each at a site having octahedral symmetry, is derived using the formalisms of second-quantisation and double-tensor operators. Both first-order contributions, from the two-particle spin-independent Hamiltonian, and second-order contributions, from the one-particle spin-independent Hamiltonian are considered. The changes in the g values of one of the Co2+ ions in a pair are derived and the results obtained are discussed in relation to Co2+ pairs in MgO.

Z−1-expansion calculation of two-particle correlations in atoms

A calculation of the expectation value of the mass-polarization operator $〈{\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}}_{2}〉$ for the two-electron atom is made using the ${Z}^{\ensuremath{-}1}$ perturbation expansion in order to determine the usefulness of this approach in calculating two-particle correlations in atoms. Evaluation of the first-order contribution to $〈{\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}}_{2}〉$ yields a value in good agreement both with an earlier value determined by another method and with the value which may be deduced from calculations using very accurate wave functions. An interesting feature of the calculation is the finding that the summations are dominated by contributions from matrix elements which involve continuum states, with more than 85% of the total coming from these contributions. The second-order contribution is then obtained by demonstrating that both first- and second-order contributions are included in the first-order formula if accurate uncorrelated wave functions for the ground state are used in the matrix elements, rather than the bare hydrogenic orbitals. After observing that most of the greater accuracy of such wave functions arises from inclusion of electronic screening, the first-order calculation is repeated using simple screened hydrogenic orbitals in the matrix elements. The values of $〈{\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{p}}}_{2}〉$ obtained by means of this simple calculation for various $Z$ values agree quite well with those calculated by Hart and Herzberg using accurate 20-term wave functions. The conclusion which is drawn from this calculation is that this method appears to be relatively simple and quite promising for calculating certain types of correlation effects, such as those resulting from double excitation or ionization of valence or inner-shell electrons. As examples of this, qualitative estimates are made of the behavior of the double photoionization cross sections of the remainder of the He isoelectronic sequence ($Z\ensuremath{\ge}3$) and of other closed-shell atoms.

Vacuum polarization in strong, realistic electric fields

Electron-positron vacuum polarization potentials, accurate to all orders $n$ in ${(Z\ensuremath{\alpha})}^{n}$, are calculated using realistic nuclear charge distributions for selected nuclei with $26\ensuremath{\le}Z\ensuremath{\le}114$, and for the quasimolecule U-U. We give further details of the numerical methods used in calculations previously reported, and of the improvements which have led to the present increased accuracy. The vacuum polarization potentials are employed to determine muonic energy-level shifts [order ${(Z \ensuremath{\alpha})}^{n\ensuremath{\ge}1}\ensuremath{\alpha}$] for most relevant states with $l\ensuremath{\le}6$. For the shifts of order ${(Z \ensuremath{\alpha})}^{n\ensuremath{\ge}3}\ensuremath{\alpha}$, interpolation procedures for all values of $Z<137$ and for other exotic particles are noted. Although the effect of finite nuclear size is small for high-lying states (\ensuremath{\sim}10% reduction of the ${(Z \ensuremath{\alpha})}^{n\ensuremath{\ge}3}\ensuremath{\alpha}$ terms in heavy atoms), it yields a reduction by a factor \ensuremath{\gtrsim} 2 for low-lying states. In the case of the quasimolecule U-U, we find that the total vacuum polarization is a minor correction to the dominant Coulomb interaction, with the first-order (Uehling) contribution remaining much larger than the higher-order terms. We also present further details of a previous calculation of order ${(Z \ensuremath{\alpha})}^{2}{\ensuremath{\alpha}}^{2}$ in muonic lead.

Almost-adiabatic collisions of quantum systems

Expressions are derived for corrections resulting from a small variation of the “slow” internal degrees of freedom during an almost-adiabatic quantum collision. First-order non-adiabatic contributions to the scattering wave function and scattering T-matrix element are derived making use of (a) Wronskian surface terms, and (b) converging factors. Advantages of method (a) are indicated. Modifications of the expressions necessary to include a possible projectile intrinsic spin are described. A one-dimensional model illustrating the range of validity of the adiabatic approximation is presented.

Quasi Γ8ground state of titanium-substituted alums

Due to the Jahn-Teller coupling of the Gamma 5g vibrational mode, the first-order contribution to the trigonal splitting is opposite and nearly equal to the second-order contribution. The resulting ground state is a quasi Gamma 8 quartet with a very small trigonal splitting. This model also explains the low-temperature magnetic properties of other titanium-substituted alums.

Many-Body Theory for Hyperfine Fields in Iron-Group Ions—Ferric Ion

The hyperfine constant of ${\mathrm{Fe}}^{+3}$ ion is calculated by the linked-cluster many-body theory procedure. The first-order contribution representing exchange-core-polarization (ECP) effect leads to a hyperfine constant of - 45.46 MHz. Electron-electron interaction effects involving both consistency and correlation contribution are found to be about 12% of the ECP effect. Comparison is made with experimental hyperfine fields in solid state from M\"ossbauer studies, and the relative importance of covalency effects as compared to electron-electron interaction effects on the hyperfine constant are discussed.

Isolating the Two-Reggeon Cut: AnS-Matrix Approach

By separating the n particles of the full unitarity phase space into two bunches, the complete two-Reggeon oontribution to the total cross section is identified. It is shown that the phase space divides into three regions characterized by forward coherent, backward coherent, and incoherent production of the two bunches and that the leading pole is generated at the boundaries between these regions. Further, while the sign of the cut contributions from the coherent regions is positive, that of the incoherent region is quite likely negative, which, for instance, negates multiperipheral arguments concerning the sign since such models include only the coherent regions of phase space. Constraints are obtained on the leading Pomeranchukon and first-order Pomeranchukon cut contributions to the forward particle-Pomeranchukon amplitude; namely, that the former must have a linear zero for vanishing external pomeranchukon mass, and the latter an inverse logarithmic zero. Finaliy, it is shown that the Finkelstei-Kajantie troubles are a result of an improper treatment of the Pomeranchukon renormalization. (auth)