Electric Octupole Research Articles

Measurement of the infrared2F7/2−2D5/2transition in a single171Yb+ion

The ${}^{2}{F}_{7/2}(F=3){--}^{2}{D}_{5/2}(F=2)$ 3.43-\ensuremath{\mu}m transition in ${}^{171}{\mathrm{Yb}}^{+}$ has been measured to be 87 366 282 258(91) kHz. This transition is of interest as an infrared frequency standard. A subsidiary measurement of the 3.43-\ensuremath{\mu}m ${(F=4\ensuremath{-}F}^{\ensuremath{'}}=3)$ transition yields a frequency of 87 362 471 500(800) kHz. Taken with a previous measurement of the ${}^{2}{D}_{5/2}$ level hyperfine splitting, a ${}^{2}{F}_{7/2}$ level hyperfine splitting of 3620(2) MHz and an A factor of 905.0(0.5) MHz are deduced. In addition, a 3.43-\ensuremath{\mu}m transition isotope shift of ${v}_{171}--{v}_{172}=+4048(4)\mathrm{MHz}$ is obtained from these experiments and a known value for the transition in the 172 isotope. These measurements taken with previous work give a value for the ${}^{2}{S}_{1/2}(F=0){--}^{2}{F}_{7/2}(F=3)$ electric octupole transition of 642 121 497 308(178) kHz, which will be used as a starting point in the search for this extremely weak transition.

Long-range interactions of metastable helium atoms

The electric dipole, quadrupole, and octupole polarizabilities of a helium atom and the associated dispersion coefficients for the interaction of two helium atoms are calculated for the atomic $n=2$ singlet and triplet states, respectively, $\mathrm{He}(2{}^{1}S)$ and $\mathrm{He}(2{}^{3}S)$. The calculations utilize highly accurate, variationally determined, wave functions composed of doubled basis sets. The effects of retardation due to the finite speed of light are calculated for the dispersion potentials of two $\mathrm{He}(2{}^{1}S)$ or two $\mathrm{He}(2{}^{3}S)$ atoms and for the atom-surface interaction potentials of a $\mathrm{He}(2{}^{1}S)$ or a $\mathrm{He}(2{}^{3}S)$ atom with a perfectly conducting or a dielectric wall.

Yellow InCl as a distorted rock-salt lattice

Because of the subgroup - group relationship which exists between the space group of yellow InCl and that of rock salt , a Landau expansion of the free energy in invariants of the symmetry group of higher order can be performed and a mechanism for distortion arises. The special feature of this hypothetical phase transition is that three lattice modes of different symmetry type and of almost equal force constant bring about the deformation. These three modes, which are apparently nearly degenerate, effect longitudinal displacements of rows of ions, with different amplitudes for the cations and the anions. When these are described by an order parameter, an expansion of the free energy up to the fourth power and containing third-order terms is possible. The cooperation of pseudo-degenerate modes of different symmetry is a hitherto unknown distortion mechanism. Yellow InCl is further characterized by bilinear quantities describing ferrodistortive chirality and electric `' octupoles and antiferrodistortive spiral arrangements. These bilinear quantities are related to fourth-order Landau invariants. Yellow InCl has an electric octupole lattice. In addition, on the basis of the analogy with optical rotatory power, new mechanisms of this effect are predicted.

Time invariance violating nuclear electric octupole moments

The existence of a nuclear electric octupole moment (EOM) requires both parity and time invariance violation. The EOM{close_quote}s of odd Z nuclei that are induced by a particular T- and P-odd interaction are calculated. We compare such octupole moments with the collective EOM{close_quote}s that can occur in nuclei having a static octupole deformation. A nuclear EOM can induce a parity- and time-invariance-violating atomic electric dipole moment, and the magnitude of this effect is calculated. The contribution of a nuclear EOM to such a dipole moment is found, in most cases, to be smaller than that of other mechanisms of atomic electric dipole moment production. {copyright} {ital 1997} {ital The American Physical Society}

Observation of an Electric Octupole Transition in a Single Ion

The $^{2}S_{1/2}\ensuremath{-}^{2}F_{7/2}$ electric octupole $(E3)$ transition in ${}^{172}{\mathrm{Yb}}^{+}$ has been detected by observing quantum jumps in a single laser cooled ion, stored in an electrodynamic trap. The transition frequency is 642 116 785.3(0.7) MHz $(1\ensuremath{\sigma})$. Consideration of the transition rate and laser parameters implies a $^{2}F_{7/2}$ level lifetime of 3700 days. This is the first time an atomic $E3$ transition has been driven. This transition has applications as an optical frequency reference.

Collective T- and P-odd electromagnetic moments in nuclei with octupole deformations.

Parity and time invariance violating forces produce collective P- and T- odd moments in nuclei with static octupole deformation. Collective Schiff moment, electric octupole and dipole and also magnetic quadrupole appear due to the mixing of rotational levels of opposite parity and can exceed single-particle moments by more than a factor of 100. This enhancement is due to two factors, the collective nature of the intrinsic moments and the small energy separation between members of parity doublets. The above moments induce T- and P- odd effects in atoms and molecules. Experiments with such systems may improve substantially the limits on time reversal violation.

Intrinsic reflection asymmetry in atomic nuclei

The experimental and theoretical evidence for intrinsic reflection-asymmetric shapes in nuclei is reviewed. The theoretical methods discussed cover a wide spectrum, from mean-field theory and its extensions to algebraic and cluster approaches. The experimental data for nuclear ground states and at low and high spin, cited as evidence for reflection asymmetry, are collected and categorized. The extensive data on electric dipole transition moments and their theoretical interpretation are surveyed, along with available data on electric octupole moments. The evidence for reflection-asymmetric molecular states in light nuclei is summarized. The application of reflection-asymmetric theories to descriptions of the fission barrier, bimodal fission, superdeformation, and hyperdeformations is reviewed, and some other perspectives in the wider context of nuclear physics are also given. [S0034-6861(96)00102-X]

A new generalization of the Casimir–Polder potential to higher electric multipole polarizabilities

An elementary method for calculating retarded interaction energies for a pair of molecules with electric multipole polarizabilities of arbitrary order is presented. In the multipolar framework of quantum electrodynamics, the interaction energy is viewed as arising from two-photon exchange and calculated using fourth order perturbation theory. It is shown how the energy may be expressed in terms of derivatives of the Casimir–Polder formula written in a special form as an integral over imaginary frequency. Explicit formulas are presented for (a) an electric dipole polarizable molecule interacting with an electric quadrupole polarizable molecule, (b) an electric dipole polarizable molecule interacting with an electric octupole polarizable molecule, and (c) an electric quadrupole polarizable molecule interacting with another electric quadrupole polarizable molecule. The results are expressed in terms of reducible and irreducible components of multipole moments. For case (b) it is shown that in addition to the weight-3 components of the octupole moments, weight-1 components contribute to the interaction energy. For cases (a) and (c) traceless components (weight-2) of the quadrupole moments contribute. The results are compared with other calculations and discrepancies pointed out.

Probabilities for forbidden transitions in atoms and ions: 1989-1995. A commented bibliography

A list is given of references concerning calculated and measured probabilities for forbidden transitions in atoms and ions. The selection is restricted to electric quadrupole (E2), magnetic dipole (M1), magnetic quadrupole (M2) and magnetic octupole (M3) transitions. In particular, spin-forbidden, hyperfine-structure induced and multiphoton transitions are not considered here. Some comments are included on important aspects of recent work in the field. The period covered goes from 1989 to mid-1995. This paper is thus a complement to our previous bibliography on the subject for the period 1968-1989 [Biémont, E. and Zeippen, C. J., J. de Physique IV, C1, 209 (1991)].

Structure of the low-lying intrinsic states in 156Eu.

Microscopic structures of the low-lying nonrotational (intrinsic) states in the odd-odd nucleus $_{63}^{156}\mathrm{Eu}_{93}$ are investigated using the quasiparticle-phonon nuclear model Hamiltonian including the pairing, quadrupole-quadrupole, octupole-octupole, and residual p-n interactions. The extent of vibrational admixtures to the two-quasiparticle configurations and the intrinsic matrix elements of electric octupole operator for the ``same K opposite parity'' bands are examined to conclude that, contrary to some recent suggestions, the low-energy $^{156}\mathrm{Eu}$ spectrum does not contain ``parity doublets'' characteristic of reflection asymmetric shapes, in contrast with the structures seen in $^{152}\mathrm{Eu}$ and $^{154}\mathrm{Eu}$.

Modified random phase approximation for multipole excitations at finite temperature.

The modified finite-temperature random phase approximation (FT-RPA) has been constructed by taking the influence of thermostat on the structure of quasiparticles into account. The modified FT-RPA linear response for electric quadrupole ({lambda}{sup {pi}}=2{sup +}) and octupole ({lambda}{sup {pi}}=3{sup {minus}}) excitations in {sup 58}Ni has been calculated as a function of the nuclear temperature. As compared to the conventional FT-RPA, the modified FT-RPA has given a stronger spreading for the strength distribution of quadrupole excitations at finite temperature {ital T}{le}3 MeV.

Electron-impact excitation of electric octupole transitions in positive ions: Asymptotic behavior of the sum over partial-collision strengths.

An investigation has been made, for the case of octupole transitions, of the dependence of the partial-collision strength on the orbital angular momentum of the colliding electron. It is shown that, similar to the dipole and quadrupole transitions, the sum over partial-collision strengths is asymptotic to a geometric series of common ratio ${\mathit{E}}_{\mathit{j}}$/${\mathit{E}}_{\mathit{i}}$, where ${\mathit{E}}_{\mathit{i}}$ and ${\mathit{E}}_{\mathit{j}}$ are the initial and final energies of the colliding electron, respectively. For large incident energies (${\mathit{E}}_{\mathit{j}}$/${\mathit{E}}_{\mathit{i}}$\ensuremath{\sim}1) the convergence of the sum to the geometric series is rather slow, since the geometric-series method only starts to become valid for large values of angular momentum. This difficulty is overcome by developing an alternative method in which the approximation is made that ${\mathit{E}}_{\mathit{j}}$/${\mathit{E}}_{\mathit{i}}$=1. An analytic formula is then obtained to estimate the contribution to the total-collision strength from large values of angular momentum. Results of partial- and total-collision strengths are presented for direct electric octupole transitions in ${\mathrm{Ca}}^{+}$ and ${\mathrm{Sr}}^{+}$.

The microscopic description of the collective E1, E2 and E3 nuclear excitation through radiationless transitions in actinoid muonic atoms

Microscopic calculations have been made of the probabilities of radiationless E1, E2 and E3 transitions in a muonic atom of 238U. The results obtained are compared with the experimental values for those transitions, the experimental probabilities are available for (2p to 1s, 3p to 1s and 3d to 1s). A considerable probability (10-15%) is predicted in actinoid atoms of E3 radiationless transitions 3d to 2p accompanied by excitation of low-lying electric octupole resonance (LEOR).

Dynamics of collective excitations in 190,192Os and 194Pt observed by 8 MeV neutron scattering.

Differential cross sections have been measured for the scattering of 8 MeV neutrons from $^{190}$,192Os and $^{194}\mathrm{Pt}$. These measurements have been combined with information from other neutron scattering experiments to fix accurately the electric quadrupole and octupole excitations strengths for low-lying levels. Comparison of this information with electromagnetic excitations for these same nuclei elucidates the rapidly evolving behavior of low-lying collective structures in Pt and Os nuclei. The $^{194}\mathrm{Pt}$ excitations are those of a nucleus with a potential energy surface very soft to nonaxial deformations. On the other hand, the scattering cross sections for excited levels of $^{190}\mathrm{Os}$ show evolution of excitations toward those of a nucleus vibrating about a prolate equilibrium shape.

Measurement of Reduced Electric Octupole Transition Probabilities, B(E3; 01??..31), for 118,120,122Sn

Values of reduced electric octupole transition probabilities, B(E3; ot -31), for the nuclides llB,120,122Sn have been determined using Coulomb excitation with 12C projectiles. The results are in good agreement with shell-model calculations made without introducing effective charges but involving core excitations. Values for B(E2; ot -2t) are also presented.

An alternative method to assess the quality of hartree-fock-roothaan wave functions

The different contributions of the Breit Hamiltonian as well as those corresponding to the electric quadrupole and magnetic octupole interactions have been computed using several Slater-Type basis sets. These calculations allow one to assess the quality of the basis sets in regions of configuration space other than those emphasized by the operators appearing in the classical (non-relativistic) Hamiltonian. The results confirm the usefulness of the δ test (L.A.G. Bernardo and J.A. Sordo, J. Chem. Phys. 85 (1986) 1475) for measuring the quality of a given basis set.

Enhanced octupole collectivity at double subshell closure in the96Zr region

A value of 84 ± 44 ps has been established for the half-life of the first 3− state of96Zr, using the centroid shift method. It is shown that the corresponding large electric octupole transition strength is in accordance with systematics, suggesting largest octupole collectivity when both the 1g9/2 Proton and 1h11/2 neutron orbitals are nearly empty due to the Z=40, N=56 double subshell closure.

High-resolution inelastic electron scattering fromO17

Excited states of $^{17}\mathrm{O}$ up to an excitation energy of 15 MeV have been studied by high-resolution electron scattering for momentum transfers between 0.8 and 2.6 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. Previous electron-scattering measurements in this excitation region were confined to momentum transfers below 1.1 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$ and were of lower resolution. Form factors were measured and reduced transition probabilities determined for most excited states below 9.5 MeV. The present data are interpreted within the framework of weak-coupling models to facilitate a simple description of the observed spectrum. Particular emphasis is placed upon understanding states that are excited strongly by electric quadrupole or octupole transitions. Spins and parities have been assigned for several levels that have very narrow widths and, hence, are not amenable to partial-wave analyses involving the $^{16}$O+n and $^{13}$C+\ensuremath{\alpha} reactions. Levels at 5.87 MeV (${(3/2}^{+}$), 6.86 MeV (${(5/2}^{+}$), 7.58 MeV (${(7/2}^{+}$), and 8.47 MeV (${(9/2}^{+}$) are suggested as candidates for predominantly 5p-4h members of a ${K}^{\ensuremath{\pi}}$${=(3/2}^{+}$ rotational band. A narrow state (\ensuremath{\Gamma}\ensuremath{\le}20 keV) at 12.22\ifmmode\pm\else\textpm\fi{}0.02 MeV was observed for the first time and the existence of narrow states at 8.90\ifmmode\pm\else\textpm\fi{}0.02 and 14.72\ifmmode\pm\else\textpm\fi{}0.02 MeV was confirmed.

Coincident electrofission of 238U at q

We have measured the coincidence cross sections $^{238}\mathrm{U}$(e,e'f) at three values of momentum transfer (q\ensuremath{\approxeq}0.26, 0.40, and 0.55 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$) over the range from 5 to 23 MeV in excitation energy; these values of q correspond approximately to the first maxima of the electric dipole, quadrupole/monopole, and octupole form factors, respectively. The angular distribution of fission fragments is peaked along the direction of q near fission threshold, indicating the dominance of K=0 states, but becomes isotropic above 10 MeV. We have integrated our cross sections over fission angle and compared them to recent calculations of multipole strength derived in the quasiparticle random phase approximation. Using model-dependent form factors generated from the Tassie model and the quasiparticle random phase approximation, we have extracted strength functions for the lowest electric multipoles. The deduced E1 strength agrees well with photofission results for reasonable choices of the model form factors. The E2/E0 distribution displays resonant structures at 10 and 13 MeV which agree in position with the collective E2 and E0 strength, respectively, predicted in the quasiparticle random phase approximation. If we make such an assignment for the multipolarity of these two structures, the observed E0 strength agrees with the theoretical prediction, whereas the E2 strength is low by a factor of 2--3. Higher order multipoles also contribute substantially to the cross section at our highest value of q.

Further improvements in a model for 5d electrons in heavy rare earth metals and compounds

A model for 5d electrons in the heavy rare earth metals which takes into account 4f-5d interactions in more detail than most theories is improved in four ways. Firstly, a simpler and more accurate method is found for obtaining a relation between the rectangular equivalents of true 5d subband widths in the model and effective subband widths for calculation of subband occupation numbers when d-d interactions are neglected. Secondly, the effects of d-d Coulomb interactions on the choice of best local basis states to use in the model are considered. Thirdly, more reliable values of Slater parameters are used for the (4f) n 5d(6s) 2 configurations of terbium and dysprosium. Fourthly, a more transparent procedure is found for obtaining approximate solutions of a set of coupled equations determining subband occupation numbers and other parameters. These changed procedures bring about only small alterations in predictions of the model for most properties. Large 5d electric quadrupole and octupole moments are still predicted for rare earths other than gadolinium. However, because of the new method of calculating the best local states, 4f magnetic moments are not reduced so much below their free-ion values as in the 1975 version of the model. Brief comments are made on the applicability of a similar model to the RAl 2 compounds (R ≡ rare earth).