Intrinsic Quadrupole Moment Research Articles

Measurements of lifetimes and feeding times for high spin states in 156Dy

The inverse reaction 24 Mg( 136Xe, 4n) 156Dy at 595 MeV has been used to populate high spin states in 156Dy. A recoil distance technique was applied to measure lifetimes and feeding times in both the ground state band and a band of anomalously high moment of inertia. Values for the intrinsic quadrupole moments, Q 0, were derived to spin 22 +. The limit of centrifugal stretching appeared to be reached at spin 14 +. The results are discussed in terms of band mixing.

Shell structure of collective states inFe56,Fe58, andFe60

Conventional shell-model calculations of the iron isotopes with $A=56\ensuremath{-}60$ are discussed. The calculated level spectra are in good agreement with experiment. The calculations of $E2$ observables are in reasonable agreement with experiment when added effective charges of $1.0e$ are used for both neutrons and protons. The neutron effective charge is significantly different from one appropriate ($1.9e$) for $^{56}\mathrm{Ni}$. There is a strong state dependence in the effective $M1$ operator, and calculations of $M1$ observables are in general disagreement with experiment. An analysis of the structure of ground-state bands and yrast levels is made in terms of a simple rotational model. In all even isotopes, the intrinsic quadrupole moments in the ground-state "band" shrink dramatically with increasing $J$. There is evidence of a band crossing in all three even isotopes, but no evidence is found for an abrupt shape change in the ground-state bands of these nuclei. It is concluded that no simple rotational model gives a good description of the low-lying states of the iron isotopes.NUCLEAR STRUCTURE $^{56}\mathrm{Fe}$, $^{57}\mathrm{Fe}$, $^{58}\mathrm{Fe}$, $^{59}\mathrm{Fe}$, $^{60}\mathrm{Fe}$, calculated levels. $^{56}\mathrm{Fe}$, $^{58}\mathrm{Fe}$, $^{60}\mathrm{Fe}$, calculated $B(M1)$, $B(E2)$, $\ensuremath{\mu}$, branching ratios. Shell model, Vervier interaction, Horie-Ogawa interaction, effective operators. Comparison with experiment and rotational model.

Giant resonance in transitional nuclei: Photoneutron cross sections for osmium isotopes

Photoneutron cross sections, including $\ensuremath{\sigma}[(\ensuremath{\gamma},n)+(\ensuremath{\gamma},pn)]$, $\ensuremath{\sigma}[(\ensuremath{\gamma},2n)+(\ensuremath{\gamma},p2n)]$, and $\ensuremath{\sigma}(\ensuremath{\gamma},3n)$, were measured for $^{188}\mathrm{Os}$, $^{189}\mathrm{Os}$, $^{190}\mathrm{Os}$, and $^{192}\mathrm{Os}$ from 7 to 30 MeV and for $^{186}\mathrm{Os}$ from 11 to 20 MeV, with a photon energy resolution of about 300 keV. The source of radiation was the monoenergetic photon beam obtained from the annihilation in flight of fast positrons. The partial photoneutron cross sections were determined by neutron multiplicity counting, and the average neutron energies for each multiplicity were determined simultaneously with the cross-section data by the ring-ratio technique. Nuclear information extracted from the data includes parameters of the giant dipole and giant quadrupole resonances, integrated cross sections and their moments, nuclear symmetry energies, and nuclear deformation parameters and intrinsic quadrupole moments. No fewer than eight kinds of evidence point to a sudden change of behavior between $^{189}\mathrm{Os}$ and $^{190}\mathrm{Os}$, which could be interpreted as a phase transition from a statically deformed prolate nucleus to a $\ensuremath{\gamma}$-unstable one, in general (but not detailed) agreement with the prediction of a dynamic-collective-model calculation.

Determination of the effective quadrupole moment in 181Ta with pionic X-rays

From the hyperfine splitting of the 5g → 4f and the 6g → 4f pionic X-rays in 181Ta, an effective quadrupole moment of Q eff = 3.58±0.03 b was determined. The strong interaction monopole shift ε 0 and the width Γ 0 of the 4f level were measured to be ε 0 = 540±100 eV and Γ 0 = 225±57 eV. in good agreement with the values obtained with the standard optical potential description of the pion-nucleus interaction. Estimating the influence of the finite nuclear size, the deformation induced through the strong interaction between the pion and the finite nucleus, and the relative magnitude between the strong and the electromagnetic quadrupole coupling constants, we arrive at a value for the spectroscopic quadrupole moment of Q = 3.30±0.06 b, and for the intrinsic quadrupole moment of Q 0 = 7.06±0.12 b. This result is in good agreement with earlier values and with recent results reported from kaonic and muonic atoms as well as with the value obtained from Nilsson model calculations.

Nuclear charge distributions deduced from the muonic atoms ofTh232,U235,U238, andPu239

The muonic x rays from four highly deformed actinide nuclei /sup 2/32Th, /sup 2/35U, /sup 2/38U, and /sup 2/39Pu have been measured. A four parameter Fermi charge distribution with distortion terms of the form ..beta../sub 2n/Y/sub 2n/0, n < or = 2, was used to characterize the nuclear charge distribution. A least squares fit was made to the energies of the 2p-1s and 3d-2p muonic x rays and their fine and hyperfine structure splitting. The 4f-3d and 5g-4f muonic x rays were measured for the four nuclei as well as the 5-3, 4-2, and 3-1 muonic transitions for /sup 2/32Th and /sup 2/38U. The intrinsic electric quadrupole moments were deduced. Our results are compared with those from earlier muonic experiments, as well as with proton, ..cap alpha.., and electron inelastic scattering.

Coupled-channel α-decay theory for odd-mass nuclei: 253Es and 255Fm

An exact numerical coupled-channel integration treatment has been applied to the α-decay of odd-mass spheroidal nuclei. The only noncentral coupling of importance between an emitted α-particle and rotational final states in the daughter nucleus involves the intrinsic quadrupole moment of the daughter. The nuclei 253Es and 255Fm are ideal cases to examine since α-transitions to the favored bands are well known and angular distribution data from low-temperature nuclear alignment are available. We examined in detail two commonly used approximations: first, that near the nuclear surface there is zero projection of orbital angular momentum of favored α-waves along the cylindrical symmetry axis of the daughter nucleus and second, that the intensity of each α-particle l-wave is proportional to the product of a squared Clebsch-Gordan coefficient and the (calculated) spherical barrier penetrability factor. It is found that neither approximation holds within experimental error, and m l ≠ 0 α-wave components must be introduced at the nuclear surface to give agreement with experimental intensities for both l = 2 and l = 4 waves.

Short-range correlations and pseudopotentials. V

Deformed Hartree-Fock-Bogoliubov calculations have been carried out with an effective interaction derived from the different Hamada-Johnson, Yale, Tabakin, and Reid potentials and from the potential $A$ calculated by us. Short-range pseudopotentials are introduced to these potentials to achieve healing in the correlated wave functions and to produce zero-phase shift in the pair state. The deformed Hartree-Fock-Bogoliubov method has been applied to the $2p\ensuremath{-}1f$ shell even-even nuclei. Intrinsic quadrupole moments $〈Q_{0}^{}{}_{}{}^{2}〉$, quadrupole moments of the first excited states ${Q}_{2+}$, and the reduced transition probabilities $B(E2) ({0}^{+}\ensuremath{\rightarrow}{2}^{+})$ have been calculated. The angular momentum projected spectra for these nuclei have also been obtained. The present calculations of quadrupole moments, transition probabilities, and angular momentum spectra for the different Ti, Cr, Fe, and Ni isotopes are in good agreement with the experimental results.NUCLEAR STRUCTURE $^{44,46,48,50}\mathrm{Ti}$, $^{48,50,52,54}\mathrm{Cr}$, $^{52,54,56,58}\mathrm{Fe}$, $^{58,60,62,64}\mathrm{Ni}$; calculated intrinsic quadrupole moments, quadrupole moments of the first excited states, reduced transition probabilities, projected angular momentum spectra and energy levels; pseudopotentials. Hartree-Fock-Bogoliubov method.

Ho165by muonic x rays

The $K$ and $L$ transitions of muonic atoms of $^{165}\mathrm{Ho}$ were measured. A modified Fermi distribution of three parameters was assumed for the charge distribution for purposes of the analysis. Correction for nuclear polarizations and extended space of the hydrogenlike atom were included in the calculation. It was possible to find a range of values for the half radius, the surface thickness, and the intrinsic quadrupole moment to give acceptable fits to the experimental data.NUCLEAR STRUCTURE Energies of $K$ and $L$ transitions of muonic $^{165}\mathrm{Ho}$ presented. Data fitted by three parameter modified Fermi distribution of electrical charge.

High-spin states in even Hg nuclei and rotation alignment inHg198

High-spin states in even Hg isotopes populated in ($\ensuremath{\alpha}, \mathrm{xn}$) reactions were investigated by in-beam $\ensuremath{\gamma}$-ray and conversion electron spectroscopy. Several new excited states in the ground state band of $^{198}\mathrm{Hg}$ and in the negative parity bands of $^{198,200}\mathrm{Hg}$ were identified. Half-lives of a number of levels in $^{194,196,198}\mathrm{Hg}$ were measured. In particular we obtain ${T}_{\frac{1}{2}}=1.38(4) \mathrm{and} 1.85(16)$ ns for the ${12}^{+}$ and ${10}^{+}$ states in $^{198}\mathrm{Hg}$, respectively. Intrinsic quadrupole moments ${Q}_{0}$ derived from these data and the $B(E2,{0}^{+}\ensuremath{\rightarrow}{2}^{+})$ agree within the limits of error. These data together with the excitation energies of the ground state band are interpreted within the rotationalignment model.NUCLEAR REACTIONS $^{194,196,198}\mathrm{Pt}(\ensuremath{\alpha}, xn)$, $E=28, 31, 34, 48$ MeV; measured ${E}_{\ensuremath{\gamma}}$, ${I}_{\ensuremath{\gamma}}$, $\ensuremath{\gamma}(\ensuremath{\theta})$, $\ensuremath{\gamma}(t)$, $\ensuremath{\gamma}\ensuremath{\gamma}$ coin, ${I}_{\mathrm{c}\mathrm{}\mathrm{e}}$, $\mathrm{ce}(t)$. $^{194,196,198,200}\mathrm{Hg}$ deduced levels, $I$, $\ensuremath{\pi}$, ${T}_{\frac{1}{2}}$, ICC, $\ensuremath{\Lambda}$, $B(\ensuremath{\Lambda})$, Rotation-alignment model.

A precision determination of the radial charge parameters and the quadrupole moment of 181Ta using muonic X-rays

We report the measurement of the energies of the 4f → 3d, 3d → 2p and 2p → 1s atomic transitions in muonic 181Ta. Using transitions to and from the 1s and 2p levels, as well as the hyperfine splittings of the 2p and 3d states, we obtained the radial charge parameters assuming deformed Fermi distributions. We found the intrinsic static quadrupole moment Q 0 = 6.82 ± 0.06 e · b, in excellent agreement with Coulomb excitation results. We verified that the dynamic (corresponding to transitions to the first excited state) and the static (ground state) E2 moments were equal to within 1.1 %. The intrinsic hexadecapole moment was determined to be Π 0 = −0.12 ± 0.40 e · b 2.

Gravitational radiation from n-body systems

An expression for the quadrupole moment of any two-body system with structure is derived from a “paralel axes” theorem. Within the weak-field limit of the theory of general relativity, expressions for the gravitational radiation flux of energy and angular momentum from two particles or two spherically symmetric bodies in arbitrary plane motion arising from any type of forces are consequently obtained in terms of time derivatives of the relative coordinates of the system. An estimate of the gravitational flux from any plane motion follows. In particular, the flux from systems with Keplerian and straight-line motion are deduced as special cases. For the general problem of a two-body system with intrinsic quadrupole moment (due to deviation from spherical symmetry), it is found that in addition to the flux from the orbital and the spin motion there is another source of flux—the interaction flux. This is shown explicitly in two special cases—the system of a particle moving in the plane of symmetry of a Jacobi ellipsoid, and that of two spinning rigid rods in plane circular motion with parallel spin and orbital angular momentum. The interaction flux is regarded as the result of interaction of the bodies with gravitational waves. An outline of the method for the calculation of gravitational radiation flux from an n-body system is given. For a three-body system—an astrophysically interesting situation—this is worked out in detail. It is seen that the presence of an unsuspected third body can, by virtue of the interaction power term, increase the generation of gravitational waves significantly.

(α, 2nγ) Studies of γ-vibrational and other side-bands in 162, 164, 166Er

Levels in 162, 164, 166Er have been studied using the (α, 2nγ) reaction at an energy of 24 MeV. Singles spectra, γ-γ coincidence spectra, and angular distributions were obtained using Ge(Li) detectors. Transitions from levels in the γ-vibrational bands up to the 8 +' in 162, 164Er and 10 +' in 166Er were observed and M1/E2 mixtures were determined for many of these transitions. There is a relative shifting upward of the even-spin levels in the γ-band of 166Er while the analogous levels of 162, 164Er are shifted downward with the effect being most pronounced for 162Er. The standard phenomenological band-mixing parameters z 2 and z 02 were obtained from γ-ray branching ratio data and the values are probably correlated with the staggering of levels in the γ-bands. The ratios of the intraband and interband E2 transition strengths which are related to the intrinsic quadrupole moments of the ground-state and γ-bands are discussed. A number of other levels are observed in 162, 164Er and some of these correspond to negative parity states reported in decay studies.

Collective states in 48V

The low-lying positive parity states of 48V have been studied in the framework of deformed configuration mixing model calculations based on projected Hartree-Fock theory, within the full fp shell space. The modified Kuo-Brown effective interaction has been used. The calculated spectrum and the electromagnetic properties of these states are in good agreement with the experiment. The calculation predicts an excited low-lying collective K = 2 + band in the spectrum of 48V and accounts for the observed breakdown of the “signature” selection rule arising in the shell-model calculation within the ( f 7 2 ) nd space. It does not favour a 5 + assignment to the observed 1.099 MeV level. Two sets of proton and neutron effective charges (i) e p = 1.32 e and e n = 0.89 e and (ii) Kuo and Osnes charges e p = 1.25 e and e n = 0.47 e were employed. The observed decay properties appear to favour the latter charges. Our model also explains in a semiquantitative way the observed K-value, moment of inertia parameter and the intrinsic quadrupole moment of the K = 1 −1 rotational band.

Deformed states of high spin in42Ca

The42Ca levels at 4,715 and 6,633 keV excitation energy have been investigated using the39K(α,pγ reaction atEα=14 and 15 MeV. From particle-γ-ray angular correlations the spin assignmentsJ(4,715)=6, 4 andJ(6,633)=8, 6, 4 have been obtained. Lifetime measurements using the Doppler-shift attenuation method yieldedτ (4,715)=120±46 fs andτ(6,633)=52±21 fs. Both levels have positive parity and decay by enhancedE2 transitions. They are interpreted as theJπ=6+ and 8+ members, respectively, of theKπ=0+ rotational band which has theE x =1,837, 2,423 and 3,250 keV states as further members. The enhancement of inbandE2 transitions is 50 −16 +35 W.u. (6→4) and 63 W.u. (8→6) respectively. The intrinsic quadrupole moments which have been derived on the basis of the coexistence model, areQ0=1.13−0.16/+0.37b(8→6) andQ0=1.36±0.25b(6→4), respectively. TheJπ=10+ member of the rotational band has possibly been observed as a level at 8,856±5 keV excitation energy.

The feeding times and lifetimes of high-spin levels in ytterbium doubly even isotopes

The intensities, lifetimes and feeding times of rotational bands with spins up to 10–20ħ have been measured for four doubly even isotopes, 160–166Yb, formed in the reactions 124–130 52Te ( 40 18Ar, 4n), using the recoil-distance Doppler-shift method. The obtained values of rotational level lifetimes, τ I , are compared with the predictions of the rigid-rotor model. For the isotopes 164, 166Yb a small retardation (by a factor of 1.2–1.4) of transitions in the backbending region is found. Intrinsic quadrupole moments and deformation parameters are deduced as a function of spin for all the four isotopes. The results are discussed in terms of different backbending concepts. The meansquare angular momenta of the levels populated are obtained. Some conclusions on the nature of the γ-ray cascade leading to the feeding of rotational bands are drawn.

Survey of electromagnetic properties of positive parity states in odd [formula omitted] shell nuclei

Experimental transition rates B(M1) and B(E2) for in-band K π = 3 2 + transitions in 43, 45, 47Sc, 45Ti and 47, 49V have been systematically compared. In the framework of the pure rotational model, intrinsic quadrupole moments ¦Q 0¦ and ¦g K − g R¦ ratios have been derived. Band mixing calculations have been performed for the positive parity states. It turns out that the experimental data are well reproduced in these calculations with a deformation parameter corresponding to a minimum of the static potential energy.

Distribution of electrical charge in the nucleus ofTa181

The $K$ and $L$ transitions of muonic atoms of $^{181}\mathrm{Ta}$ were measured. A comparison of the experimental values with calculated values was made. A modified Fermi distribution of charge of three parameters was assumed for the calculation. The calculations include corrections for nuclear polarization and extended space of the Dirac hydrogenlike atom. A range of values for the half radius, the surface thickness, and the intrinsic quadrupole moment was obtained. A description of the analysis is included.NUCLEAR STRUCTURE Energies of $\ensuremath{\gamma}$ rays of $K$ and $L$ transitions of muonic $^{181}\mathrm{Ta}$ measured. Data fitted by three parameter modified Fermi distribution of charge.

Charge parameters, isotope shifts, quadrupole moments, and nuclear excitation in muonic 170–174,176Yb

Muonic X-rays and nuclear γ-rays from separated isotopes of Yb with mass numbers 170–174 and 176 were measured. The parameters of the nuclear charge distribution were determined for each isotope. From the 2p splitting, intrinsic quadrupole moments were found with the following values: Q 0(170) = 7.80 (4) b, Q 0 (171) = 7.95 (4) b, Q 0 (172) = 7.91 (4) b, Q 0 (173) = 7.92 (5) b, Q 0 (174) = 7.82 (5) b and Q 0(176) = 7.59 (5) b, the quoted errors being statistical. These errors can be used for differences or ratios of the quadrupole moments. The total errors are 0.3 b. For the ground state of 173Yb a spectroscopic quadrupole moment of Q 0 = 2.80 (04) b was derived from the observed 3d splitting. The combined analysis of the 2p and 3d splittings provided a sensitive test of the nuclear charge model in 173Yb. The isotope shifts were determined and interpreted in terms of a model independent parameter. The isomer shifts of the first excited 2 + states in 170Yb and 172Yb were found, as well as the isomer shift of the 1.039 MeV 0 + state in 172Yb. In 172Yb evidence was found for a pronounced resonance between the 3d 1 2 −1s 1 2 transition and a nuclear state at 6.9314 (12) MeV. Several n scheme for the 6.931 MeV state in 172Yb was proposed.

Correction to Muonic X-Ray Spectra for Nuclear Polarization and Extended Space.

The nuclear-polarization and extended-space corrections are calculated for x-ray transitions of muonic atoms of $sup 169$Tm, $sup 181$Ta, and $sup 165$Ho for acceptable values of the three parameters: the half-radius of the charge distribution, the surface thickness, and the intrinsic quadrupole moment. It is shown that there is enough variation in the values of the corrections for the transitions in a given nuclide to preclude the assignment of a constant amount to all the transitions.

The level structure of 189Os

The level structure of 189Os has been studied by (d, p), (d, t) and (d, d') reaction spectroscopy at E d = 12.1 MeV. Assignments of a number of levels at excitation energies below ≈ 1700 keV are given. The assignments are discussed in terms of a unified model based on the Nilsson model including pairing, rotational motion and attenuated Coriolis coupling. Deviations between predicted and experimental excitation energies and wave functions are generally found to be consistent with trends observed in 187Os and in the odd W isotopes. Evidence for the existence of collective non-rotational states is found from the (d, d') reactions. Results of ( 3He, α) and high resolution γ-ray and conversion electron studies were also included at various stages of the investigation to supplement the data from the deuteron induced reactions. Comparisons between calculated and measured B(E2) values are found to indicate an intrinsic quadrupole moment of the ground-state band of ≈ 5.0 b, in agreement with values in adjacent even Os isotopes. Details of the Coriolis coupling calculations are given.