Static electric quadrupole and hexadecapole moments of nuclei

Ground-state static electric quadrupole and hexadecapole moments of even nuclei are calculated microscopically. Rare-earth, actinide and neutron-deficient nuclei with 50 <Z, N < 82 and neutron-rich nuclei with 28 < Z < 50, 50 < N < 82 are studied. Fairly good agreement with experiment is found. In the actinide region, the electric moments of fission isomers are also examined.     

Current electric quadrupole moments of atoms and nuclei

It is shown that current electric multipoles exist. Their field is electrostatic and it is unrelated to the existence of a net electric charge. At long range, it is the same as the field of the corresponding charge electric multipoles. Current electric multipoles arise during the motion of magnetic multipoles. An orbital motion of magnetic dipoles, a precession of a current-carrying loop, and the motion of magnetic quadrupoles all lead to current electric quadrupole moments. Expressions for the current electric quadrupole moments of atoms and nuclei are derived.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1991.The author wishes to thank S. A. Kuten' and V. I. Rapoport for useful comments offered during the writing of this paper and for a discussion of the results.     

The neutron-proton pairing and the moments of inertia of the rare earth even-even nuclei

In this study, the possible effect of the neutron-proton pairing interaction in the heavy nuclei has been investigated in the framework of the BCS model by making a simple approximation. This effect has been searched realistically by calculating the moments of inertia of deformed even-even nuclei. Calculations show that the moments of inertia of rare earth nuclei changed dramatically and approached the experimental values.     

On the hexadecapole anomaly at the border of the rare earth region

Theoretical calculations of equilibrium deformations and multipole moments of rare earth nuclei are presented. Good agreement with experiment for the centre of the rare earth region is found, but there are large discrepancies for the heavy Hf, W and Os isotopes and some light Sm and Gd nuclei. These discrepancies are related to hexadecapole moments and deformations. The assumption of a “partial bubble” like density distribution, as suggested by electron scattering measurements, is found to be insufficient to explain this hexadecapole anomaly. The inclusion of non-axial and hexadecapole degrees of freedom in processing the experimental data, as well as in performing theoretical calculations, is found to be the most promising approach to explaining the hexadecapole anomaly.     

Electric quadrupole moments of neutron-rich nuclei 32Al and 31Al

The electric quadrupole moments for the ground states of ³²Al and ³¹Al have been measured by the β ray-detected nuclear quadrupole resonance method. Spin-polarized ³²Al and ³¹Al nuclei were obtained from the fragmentation of ⁴⁰Ar projectiles at E/A?=?95 MeV/nucleon, and were implanted in a single crystal α-Al₂O₃ stopper. The measured Q moment of ³²Al, |Q(³²Al)|?=?24(2) mb, is in good agreement with a conventional shell-model calculation with a full sd model space and empirical effective charges, while that of ³¹Al is considerably smaller than the sd calculations.     

Relativistic description of deformed rare earth nuclei

Ground state properties of heavy deformed nuclei in the rare earth region are described in the framework of the relativistic Hartree approximation. Both linear and non-linear parameter sets of the lagrangian are used. The non-linear sets reproduce the experimentally observed binding energies, the charge radii and the quadrupole moments, with the same quality as non-relativistic density dependent mean field calculations with Skyrme forces.     

Magnetic and quadrupole interactions of rare earth in bone crystals

From emission Mössbauer spectra performed on¹⁶¹Tb-bone samples, the Mössbauer and hyperfine parameters are obtained. The lattice components of the EFG acting at Dy in bone crystals are evaluated. These values show that the rare earth ions are fixed on hydroxyapatite crystallites in a hydroxyde environment.     

Magnetic dipole response in rare earth nuclei

Experimental observations in certain rare earth nuclei have established the presence of sizeable B(M1) strength of two peak structure lying in the 5–10 MeV region. The character of the states concerned, studied within a self-consistent Random Phase Approximation using Skyrme forces, are identified to be that of proton and neutron giant spin-flip resonances. Received: 14 July 1997 / Revised version: 20 October 1997     

Neutron strength functions in rare earth nuclei

The coupling of the single particle motion of the neutron to other degrees of freedom is studied by the (d, p) reaction leading to highly excited states in rare earth nuclei. Experimental spectra have been obtained with a telescope counter system for 13 rare earth isotopes of Gd, Dy, Er and Yb. The results are compared with calculations based upon the single particle model in a deformed Saxon-Woods potential. The spreading of the single particle strength resulting from the coupling to other degrees of freedom is taken into account in a simple phenomenological way. A qualitative similarity between the experimental and calculated spectra is observed, and the total integrated (d, p) cross section up to the neutron binding energy is reproduced quite closely by the calculations. For a given excitation energy, the amount of structure in the experimental spectrum seems to decrease with neutron number for each element investigated.     

Magnetic coupling of rare earth moments in amorphous alloys

Several amorphous Gd alloys containing about 75 at % Gd were prepared, the second component being Al, Cu, Ga, Rh or Pd. All these alloys were found to be ferromagnetic with quite similar ordering temperatures. Possible coupling mechanisms between the localized moments are discussed. It is shown that the RKKY coupling scheme can only be of minor importance in these alloys.     

Microscopic treatment of the coupled monopole and quadrupole vibrations in light nuclei

The coupled monopole and volume-conserving quadrupole oscillations in ⁴He, ¹²C, ¹⁶O, ²⁰Ne and ⁴⁰Ca have been studied within the framework of the Hill-Wheeler generator coordinate method.     

Measurement of electric quadrupole moments of neutron-rich nuclei14B and15B

The experimental study of nuclear moments of several neutron-rich nuclei, using the phenomenon of ejectile spin polarization in the projectile fragmentation reaction, is reported. The spin-polarized fragments¹⁴B and¹⁵B were produced in the fragmentation of¹⁸O projectiles on a Nb target at 64.7 MeV/u. They were implanted into a Mg single crystal, and the quadrupole momentsQ were determined by the-NMR method. The results, ¦Q(¹⁴B)¦ =29.84 ±0.75 mb and ¦Q(¹⁵B)¦=38.01 ±1.08 mb, are compared with theoretical models. Shell model calculations in a 0 model space, using effective charges commonly accepted in this mass region, predict values about 40% larger than the experimentalQ(¹⁵B). Agreement is obtained when a much smaller effective charge for neutrons is employed. The method was also applied to the measurement of the magnetic moments of¹⁷N and¹⁷B. The result reveals an important contribution of configurations with excess neutrons coupled to formJ =2⁺.     

Saturation magnetic moments,magnetic hyperfine fields and electric field gradients at nuclei in the heavy rare earth metals

The contributions of 4f, 5d and 6s electrons to the saturation magnetic moments and magnetic hyperfine fields in the heavy rare earth metals are calculated using the model described in the previous paper. It is found that 4f shell moments are reduced from their free ion values by amounts varying from 0.05µ _B in Gd to several tenths of a Bohr magneton in Tb and Dy, in qualitative agreement with a recent published analysis of neutron diffraction results in Tb, but that the calculated total saturation moments in Tb and Dy are slightly larger than commonly accepted experimental values. After 6s contributions to magnetic hyperfine fields are determined by fitting observations in Gd, the predicted differences between the fields for metals and those for free ions are such that the estimated uncertainty ranges of the theoretical values overlap the experimental ranges. The 5d contribution in the model is negative, varying from about –40 kOe in Tb to –200 kOe in Er. Electric field gradients are also analysed. Observed results can be fitted if the average effective Sternheimer screening factorR _d ^* for 5d electrons in the metals satisfies (1 —R _d ^* )0.7.     

Level density and thermal properties in rare earth nuclei

A convergent method to extract the nuclear level density and the γ-ray strength function from primary γ-ray spectra has been established. Thermodynamical quantities have been obtained within the microcanonical and canonical ensemble theory. Structures in the caloric curve and in the heat capacity curve are interpreted as fingerprints of breaking of Cooper pairs and quenching of pairing correlations. The strength function can be described using models and common parametrizations for the E1, M1, and pygmy resonance strength. However, a significant decrease of the pygmy resonance strength at finite temperatures has been observed.     

Systematic investigation of hexadecapole collectivity in even-even nuclei

Energies of the first 2⁺, 3⁻ and 4⁺ states of even-even nuclei are plotted against proton and neutron number. Using this systematics, shell effects and the corresponding quadrupole and hexadecapole collectivity and deformation effects are compared and contrasted. Also, the correspondingB(E2),B(E3) andB(E4) values are plotted against neutron number and their very different systematics compared. Among the new results are the presence of hexadecapole collectivity at the 82 proton and neutron closed shells and the presence of the maximum values ofB(E4) at neutron numbers 10, 90–92 and 140–146. Finally, the systematics of the hexadecapole (K=4⁺) vibrations is compared with that of the quadrupole (K=2⁺) gamma vibrations in the quadrupole deformed rare earth region. This research has been supported by the National Sciences and Engineering Research Council of Canada at McMaster University and by the Department of Atomic Energy, Government of India, at Banaras Hindu University.     

Concentration dependence of the Fe moments in rare earth iron compounds

A linear relationhip has been found between the hyperfine fields observed at the various Fe sites in rare earth iron compounds R_xFe_y and the relative number of near neighbour Fe atoms corresponding to these sites. From these results it is concluded that the concentration dependence of the magnitude of the Fe moments in these compounds is largely determined by the local environment.     

On the hexadecapole collective motion in spherical nuclei

The hexadecapole-collective motion in spherical nuclei is discussed. Numerical calculations are presented and compared with available experimental data.