Calculated Quadrupole Moments Research Articles

Low-lying states of heavy nuclei within the nucleon pair approximation

In this article we perform systematic calculations on low-lying states of 33 nuclei with A=202-212, using the nucleon pair approximation of the shell model. We use a phenomenological shell-model Hamiltonian that includes single-particle energies, monopole and quadrupole pairing interactions, and quadrupole-quadrupole interactions. The building blocks of our model space include one J=4 valence neutron pair, and one J=4,6,8 valence proton pair, in addition to the usual S and D pairs. We calculate binding energies, excitation energies, electric quadrupole and magnetic dipole moments of low-lying states, and E2 transition rates between low-lying states. Our calculated results are reasonably consistent with available experimental data. The calculated quadrupole moments and magnetic moments, many of which have not yet been measured for these nuclei, are useful for future experimental measurements.

Electric moments of carbon dichalcogenides

The dipole and quadrupole moments and parallel dipole polarizabilities of the carbon dichalcogenides XCY (X, Y = O, S, Se and Te) are evaluated at the level of the CCSD(T) approximation with HyPolX basis sets. The relativistic effects are taken into account by using the scalar version of the two-component Douglas–Kroll method. The reported calculations provide a systematic study of the electron correlation and relativistic effects in the investigated series of carbon dichalcogenides and their results agree well with best-known experimental data. Particular attention has been given to the OCS molecule and the present calculations combined with recent studies by other authors may help to resolve the ambiguities concerning its quadrupole moment. Changes of dipole and quadrupole moments in the studied series of molecules are interpreted in terms of the electronegativities of the chalcogene atoms and their changes due to relativistic effects. The latter have been found to lead to significant changes in the calculated quadrupole moments of the heavy members of the series of molecules. Study of the basis set dependence of the calculated data shows that both the earlier PolX and the recently developed HyPolX basis sets are suitable for calculations of reliable values of the low-multipole moments and dipole polarizabilities of molecules containing heavy elements.

Relativistic mean field model for isotopic shifts of odd-ABi isotopes

The results of relativistic mean field (RMF) calculations for the ground-state properties of odd-$A$ Bi isotopes are presented using the most successful nonlinear sets of Lagrangian parameters. The calculated quadrupole moments are found to increase as neutrons are added or removed from the $N=126$ shell. However, no corresponding increase is revealed in the calculated charge radii. This observation is consistent with recent experimental findings.

Cation-aromatic π interaction in the gas phase: an experimental study on relative silver (I) ion affinities of polyaromatic hydrocarbons

Abundant silver (I) ion bound asymmetric dimers of polyaromatic hydrocarbons (PAHs) were easily generated by electrospray ionization. Based on the unimolecular decomposition of the Ag(I) ion bound asymmetric dimers, the relative Ag(I) ion affinities of nine PAHs in the gas phase has been established­as: benzene? <? naphthalene? <? phenanthrene? <? anthracene? <? fluoranthene? <? pyrene? <? triphenylene? <­chrysene < benz[a]anthracene. The observed Ag(I) ion affinities were found to correlate with calculated quadrupole moments of PAHs, indicating that electrostatic charge–quadrupole interaction is important in the cation–aromatic π binding of the polyaromatic systems being studied. However, secondary effects, such as surface area of the aromatic π electrons or intermolecular electronic repulsion and steric repulsion between bay region hydrogens, could also affect the magnitude and relative order of Ag(I) ion affinities of PAHs. © 1998 John Wiley & Sons, Ltd.

Quadrupolar effects in the temperature dependence of the lattice parameters of HoP1-xVxO4.

Powder-neutron-diffraction techniques have been used to investigate the temperature dependence of the structural properties of ${\mathrm{HoP}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{V}}_{\mathit{x}}$${\mathrm{O}}_{4}$ for x values of 0.0, 0.33, 0.52, 0.71, and 1.0. The diffraction data confirm the tetragonal zircon-type crystal structure for all of the samples in the temperature range between 12 and 300 K. The temperature dependence of the lattice parameters of the pure ${\mathrm{HoPO}}_{4}$ and ${\mathrm{HoVO}}_{4}$, however, exhibits significant anomalies below about 100 K. In ${\mathrm{HoPO}}_{4}$, the lattice parameter a increases with decreasing temperature while c decreases. In ${\mathrm{HoVO}}_{4}$ this behavior is reversed. These anomalies can be explained in terms of quadrupolar interactions of the ${\mathrm{Ho}}^{3+}$ ion with the crystalline lattice. In particular, the calculated quadrupole moments for ${\mathrm{HoPO}}_{4}$ and ${\mathrm{HoVO}}_{4}$ reproduce the observed temperature dependence and the inverse behavior. The anomaly in the thermal expansion is reduced in the case of the mixed phosphate vanadate materials (0x1) because of the competing ${\mathrm{Ho}}^{3+}$ quadrupole contributions.

The natural atomic orbital point charge model for PM3: Multipole moments and molecular electrostatic potentials

AbstractThe natural atomic orbital/point (NAO‐PC) model originally developed to calculate molecular electrostatic potentials (MEPs) and multiple moments based on the AM1 wave function has been extended to PM3. As for AM1, NAO‐PC/PM3 reproduces dipole moments calculated by the standard PM3 method very well. There is also a surprisingly good correlation between experimental and calculated quadrupole moments. The MEPs calculated using PM3/NAO‐PC are found to be in better agreement with those given by RHF/6‐31G* than those obtained from the PM3 wave function using Coulson charges. On the other hand, the NAO‐PC model is often slightly worse then the method implemented in MOPAC‐ESP. The MEPs calculated using our model based on the PM3 wave function are often in better agreement with those given by RHF/6‐31G* than those obtain with AM1. © 1994 by John Wiley &amp; Sons, Inc.

Electric properties of diatomic interhalogens. A study of the electron correlation and relativistic contributions

The recently developed polarized basis sets for halogen atoms are used to calculate several basic electric properties of diatomic interhalogen molecules. In the valence approximation the electron correlation contribution is treated at the level of the fourth-order many-body perturbation theory approximation. The corresponding results are corrected for the core-polarization and relativistic effects. It is shown that the dipole moments of heavy interhalogen diatomics are considerably affected by the relativistic contribution, while the core-polarization effects are of lesser importance. The calculated, relativistically corrected, dipole moments are in agreement with experimental data and are used to discuss the reliability of the effective core potential approximation. The calculated quadrupole moments and parallel components of the dipole polarizability tensor are only marginally affected by contributions due to core-polarization and relativistic terms. The geometry derivatives of dipole moments and dipole polarizabilities computed in this study can be used for the evaluation of intensities in infrared and Raman spectra of interhalogen diatomics.

Quadrupole moments as measures of electron correlation in two-electron atoms.

We have calculated quadrupole moments, ${\mathit{Q}}_{\mathit{z}\mathit{z}}$, of helium in several of its doubly excited states and in two of its singly excited Rydberg states, and of the alkaline-earth atoms Be, Mg, Ca, Sr, and Ba in their ground and low-lying excited states. The calculations use well-converged, frozen-core configuration-interaction (CI) wave functions and, for interpretive purposes, Hartree-Fock (HF) atomic wave functions and single-term, optimized, molecular rotor-vibrator (RV) wave functions. The quadrupole moments calculated using RV wave functions serve as a test of the validity of the correlated, moleculelike model, which has been used to describe the effects of electron correlation in these two-electron and pseudo-two-electron atoms. Likewise, the quadrupole moments calculated with HF wave functions test the validity of the independent-particle model. In addition to their predictive use and their application to testing simple models, the quadrupole moments calculated with CI wave functions reveal previously unavailable information about the electronic structure of these atoms. Experimental methods by which these quadrupole moments might be measured are also discussed. The quadrupole moments computed from CI wave functions are presented as predictions; measurements of ${\mathit{Q}}_{\mathit{z}\mathit{z}}$ have been made for only two singly excited Rydberg states of He, and a value of ${\mathit{Q}}_{\mathit{z}\mathit{z}}$ has been computed previously for only one of the states reported here. We present these results in the hope of stimulating others to measure some of these quadrupole moments.

Negative parity rotational bands in28Si: A cluster model approach

Brink's alpha cluster model is used for the description of negative parity intrinsic states in28Si. The existence of a 3− and 5− rotational band is predicted in accordance with experimental results. The calculated quadrupole moments agree with the data within the error bars.

Structure calculations for 25Mg- 25Al

The results of a shell model calculation for 25Mg- 25Al are presented in which the Hamiltonian for the system was taken to be that of an inert 16O core plus nine s-d shell particles interacting through the usual one-body l 2 and l · s terms plus general two-body residual interactions of the Kuo-Brown type. The basis was truncated to include nine favored representations of SU(3) in each of the two leading spatial symmetries ([441]: (66), (93), (74), (82) 2, (55) 2, (28), (90); [432]: (10,1), (74), (82) 2, (55) 2, (28), (47), (90)). It is found that a (λμ)-dependent renormalization of the type proposed by Harvey but empirically modified for axially asymmetric shape distributions is required to reproduce the experimentally observed ordering of the three lowest rotational bands. The goodness of K J as a band label for the calculated eigenstates is investigated by comparing calculated quadrupole moments with simple rotational model predictions. Calculated B(E2) and B (M1) rates are compared with the available data. Results for relative spectroscopic factors from (d, p) stripping on the ground state of 24Mg are also presented.

The use of generalized sum rules in many-body theory: (I). Microscopic description of nuclear rotation

Following a recent paper of Marumori et al. the idea of using sum rules expressing different single-particle transition operators in terms of higher powers of other operators is extended to the general case. With the help of these generalized sum rules a new microscopic method is developed to calculate energies and transition probabilities for nuclei within the rotational region. For simplicity we restrict ourselves to the single j-shell case with a quadrupole two-body interaction. The mass region where rotational phenomena may be expected is determined and is interpreted by a simple Hartree model. The calculated quadrupole moments and transition probabilities show excellent agreement with the exact calculations of Mulhall and Šips.

Corrections to the reorientation effect of Coulomb excitation in deformed doubly even nuclei

The reorientation of the lowest 2 + rotational state is influenced by 5–12% in general, depending on the energy of the incident ion. The resulting corrections of the calculated quadrupole moments of excited nuclear states are due to both the giant resonances and the β- and γ-vibrations. The quadrupole moment of the γ-band cannot be determined by Coulomb excitation, because the contribution of the reorientation effect to the cross section cancels against the second-order contribution via the first rotational state.

Equilibrium deformations of the odd-mass nuclei in the rare-earth region

Previous calculations of the ground-state equilibrium deformations and quadrupole moments for the even nuclei in the rare earth region have been extended to the case of the odd-mass nuclei. These calculations were performed in the framework of the Nilsson model including pairing force. The calculated quadrupole moments are generally found to be in agreement with experiment to better than 10 %, with exception of the neighbourhood of the Eu and Sm nuclei, where the transition takes place between spherical and deformed shapes. The density deformation parameter corresponding to the calculated quadrupole moments overlaps within 10 % difference with the deformation of the nuclear potential. The influence of the blocking effect on the equilibrium deformation is also discussed.

Molecular Quadrupole Moments of N2 and O2

Molecular orbital calculations of the quadrupole moments of N2 and O2 have been made. Models assuming 20 percent s—p hybridization for N2 and 5–10 percent s—p hybridization for O2 give calculated quadrupole moments agreeing with those deduced from microwave line broadening data (0.27e×10−16 esu for N2 and &amp;lt;0.09e×10−16 esu for O2).