Ground-state Bands Of Even-even Nuclei Research Articles

Discovery of isomers in dysprosium, holmium, and erbium isotopes withN=94to 97

High-spin states in the ${}_{68}^{164}$Er${}_{96}$ region were studied using ${}^{9}$Be $+$ ${}^{160}$Gd reactions. Pulsed beam conditions were exploited for enhanced sensitivity to delayed $\ensuremath{\gamma}$-ray transitions. New isomers were identified in ${}^{161}$Dy, ${}^{163}$Ho, ${}^{162}$Er, and ${}^{165}$Er. The ${}^{162}$Er isomer is interpreted to decay by $E1$ transitions to the ground-state band with a reduced hindrance of ${f}_{\ensuremath{\nu}}=33$. A plot of ${f}_{\ensuremath{\nu}}$ values for all $\ensuremath{\Delta}K=7$, $E1$ transitions from two-quasiparticle isomers to the ground-state bands of even-even nuclei reveals only a small influence from the dynamic to kinematic moment-of-inertia ratio, which provides a measure of Coriolis $K$ mixing within the ground-state band. This is interpreted to imply that the relatively low hindrances are due to $K$ mixing in the isomer, caused by a combination of Coriolis and octupole band mixing.

Nuclear pairing reduction due to rotation and blocking

Nuclear pairing gaps of normally deformed and superdeformed nuclei are investigated using the particle-number-conserving (PNC) formalism for the cranked shell model, in which the blocking effects are treated exactly. Both rotational frequency $\ensuremath{\omega}$ dependence and seniority (number of unpaired particles) $\ensuremath{\nu}$ dependence of the pairing gap $\mathrm{\ensuremath{\Delta}\ifmmode \tilde{}\else \~{}\fi{}}$ are investigated. For the ground-state bands of even-even nuclei, PNC calculations show that, in general, $\mathrm{\ensuremath{\Delta}\ifmmode \tilde{}\else \~{}\fi{}}$ decreases with increasing $\ensuremath{\omega}$, but the $\ensuremath{\omega}$ dependence is much weaker than that calculated by the number-projected Hartree-Fock-Bogolyubov approach. For the multiquasiparticle bands (seniority $\ensuremath{\nu}>2$), the pairing gaps stay almost $\ensuremath{\omega}$ independent. As a function of the seniority $\ensuremath{\nu}$, the bandhead pairing gaps $\mathrm{\ensuremath{\Delta}\ifmmode \tilde{}\else \~{}\fi{}}(\ensuremath{\nu},\ensuremath{\omega}=0)$ decrease slowly with increasing $\ensuremath{\nu}$. Even for the highest seniority $\ensuremath{\nu}$ bands identified so far, $\mathrm{\ensuremath{\Delta}\ifmmode \tilde{}\else \~{}\fi{}}(\ensuremath{\nu},\ensuremath{\omega}=0)$ remains greater than $70%$ of $\mathrm{\ensuremath{\Delta}\ifmmode \tilde{}\else \~{}\fi{}}(\ensuremath{\nu}=0,\ensuremath{\omega}=0)$.

Simple phenomenology for the ground-state bands of even-even nuclei.

It is observed that the even-even nuclei having identical ${\mathit{N}}_{\mathit{p}}$${\mathit{N}}_{\mathit{n}}$/\ensuremath{\Delta} values exhibit identical excitation energies and/or energy ratios (${\mathit{E}}_{\mathit{J}}$/${\mathit{E}}_{2}$,${\mathit{E}}_{\mathit{J}}$/${\mathit{E}}_{4}$) in their ground-state bands (g.s.b.). ${\mathit{N}}_{\mathit{p}}$ (${\mathit{N}}_{\mathit{n}}$) is the valence proton (neutron) number and \ensuremath{\Delta} is the average pairing gap, (${\mathrm{\ensuremath{\Delta}}}_{\mathit{p}}$+${\mathrm{\ensuremath{\Delta}}}_{\mathit{n}}$)/2. It is shown that this correlation is a manifestation of a very simple but uniform dependence of the excitation energies of the g.s.b. of even-even nuclei, spanning a wide mass region (70\ensuremath{\le}A\ensuremath{\le}244), on the ratio of their pairing and n-p interaction energies. An explicit form of this dependence is phenomenologically deduced and subsequently used to study the development of collectivity, existence of subshell closures and some other nuclear systematics.

Reformulation of the variable moment of inertia model in terms of nuclear softness.

The ground-state bands in even-even nuclei are studied by treating the variation of moment of inertia with angular momentum in terms of the relative increase of moment of inertia with angular momentum, called the softness parameter. Such a reformulation of the variable moment of inertia (VMI) model in terms of the various orders of softness of the nuclear softness (NS) model extends the range of validity of the new model, called VMINS, to 2.0\ensuremath{\le}${\mathit{R}}_{42}$\ensuremath{\le}3.33. This gradual softening of the rigid rotator throughout the Periodic Table requires softness parameter to, at least, second order, with the vibrational energy also becoming important for very soft nuclei.

The anharmonic vibrator model and the electromagnetic properties of the ground-state bands of even-even nuclei

It is shown that the model parameters of a phenomenological anharmonic vibrator model, proposed by the authors (see Phys. Rev. C, vol.30, p.1014, 1984), can be related to the electric quadrupole transition moments for 41+ to 21+ and the 21+ to 01+ transitions in even-even nuclei over a wide region which encompasses the so-called spherical, transitional and deformed shapes.

An angular momentum expansion of energy and structure of high spin states

A new angular momentum expansion of level energies of ground-state band of even-even nuclei has been obtained which is found to converge rapidly even for the most back-bending nuclei. Attempts have been made to interpret the parameters and calculate them microscopically. It is found that nuclear structure in the forward bending region is quite different compared to that in the back-bending region.

Validity of a new approach to collective nuclear motions

Morinigo has used the elements of the mass quadrupole tensor as generalized nonredundant variables to describe the nuclear collective motions and has obtained an energy equation which is similar to that of the variable-moment-of-inertia (VMI) model. Applicability of the Morinigo expression to the level energies of the ground-state bands of even-even nuclei is examined and results are presented for 12 representative nuclei. It is found that for the soft nuclei the results are not as good as those from the VMI23 extension of the VMI model.[NUCLEAR STRUCTURE collective models. Even-even nuclei. $^{100}\mathrm{Pd}$, $^{152}\mathrm{Gd}$, $^{128}\mathrm{Xe}$, $^{126}\mathrm{Xe}$, $^{186}\mathrm{Pt}$, $^{184}\mathrm{Pt}$, $^{130}\mathrm{Ce}$, $^{176}\mathrm{Os}$, $^{154}\mathrm{Gd}$, $^{168}\mathrm{Hf}$, $^{166}\mathrm{Yb}$, and $^{242}\mathrm{Pu}$.]

Analysis of Rotational and Quasirotational Ground-State Bands in Even-Even Nuclei

Analysis of Rotational and Quasirotational Ground-State Bands in Even-Even Nuclei

Unified Description of Phenomenological Models of Ground-State Bands in Even-Even Nuclei

Unified Description of Phenomenological Models of Ground-State Bands in Even-Even Nuclei

Quasirotational groundstate bands of even-even nuclei with 50≦N, Z≦82

The quasirotational groundstate bands of140Sm,142Sm,144Gd and136Nd have been determined by studying the prompt γ-decay after (α,xn+yp+zα.) reactions using α-particles of up to 104 MeV and targets of144Sm,142Nd,141Pr,140Ce,136Ce and139La. The new levels continue the trends of the neighbouring even-even nuclides smoothly. These systematics of the groundstate bands in the region 50<N,Z<82 are not disturbed by expected subshell closure effects.

Relationship Between the Transition Moments of Inertia and the Intrinsic Transition Quadrupole Moments

In the "variable-moment-of-inertia" model an empirical relation was established between the transition quadrupole moments and the transition moments of inertia for the levels of ground-state bands in even-even nuclei. Later a modification was proposed in the form of introducing an explicit ${A}^{\frac{1}{4}}$ dependence in this relation, and also an alternative expression for the definition of the transition moment of inertia was adopted. We examine these modifications in comparison with the original assumptions through detailed analysis of the experimental data. No significant improvement in the fit to the data is observed as a result of the modified formulation.

Nuclear-softness model of ground-state bands in even-even nuclei

A nuclear-softness (NS) model for the energy levels of the ground-state bands in even-even nuclei is proposed by treating the variation of the moment of inertia with J in a more generalized manner. The model yields good fits to the observed spectra of all the even-even nuclei, including even the nuclei having only two particles or holes with respect to a closed shell. The idea of considering only the first-order nuclear softness with additional configuration-mixing effects in the ground state has also be tested.

Shape-fluctuation model of ground-state bands in even-even nuclei

A shape-fluctuation (SF) model for the energy levels of the ground-state bands in even-even nuclei is proposed invoking the idea of the J-dependence of the intrinsic wave function. In addition to permitting an excellent fit of the energy levels, the model yields in each state, the contribution to the energy due to shape fluctuation, which provides a measure of the variation of the intrinsic shape in the ground-state band.

Phenomenological Analysis of Ground-State Bands in Even-Even Nuclei

A variable-moment-of-inertia (VMI) model is proposed which permits an excellent fit of level energies of ground-state bands in even-even nuclei. In this model the energy of a level with angular momentum $I$ is given by the sum of a potential energy term $\ensuremath{\propto}{({\mathfrak{g}}_{I}\ensuremath{-}{\mathfrak{g}}_{0})}^{2}$ (where ${\mathfrak{g}}_{0}$ is the ground-state moment of inertia) and a rotational energy term $\frac{{\ensuremath{\hbar}}^{2}I(I+1)}{2{\mathfrak{g}}_{I}}$. It is required that the equilibrium condition $\frac{\ensuremath{\partial}E}{\ensuremath{\partial}\mathfrak{g}}=0$ be satisfied for each state. Each nucleus is described by two adjustable parameters, ${\mathfrak{g}}_{0}$ and $\ensuremath{\sigma}$ (the softness parameter), which are determined by a least-squares fit of all known levels. The calculated level energies and moments of inertia ${\mathfrak{g}}_{I}$, ${\mathfrak{g}}_{0}$, and $\ensuremath{\sigma}$ are tabulated for 88 bands, ranging from Pd to Pt and from Th to Cm. Projections of three-dimensional arrays of ${\mathfrak{g}}_{0}$ and $\ensuremath{\sigma}$ on the ($N,Z$) plane are shown. These parameters are found to vary smoothly as function of $N$ and $Z$. Breaks occur at $N=98, 104, \mathrm{and} 108$. The osmium show a pronounced maximum for ${\mathfrak{g}}_{0}$ and an equally pronounced minimum for $\ensuremath{\sigma}$ at 108 neutrons. In Pt, ${\mathfrak{g}}_{0}$ decreases steeply to 110 neutrons and then more slowly, while $\ensuremath{\sigma}$ increases correspondingly. The stable Pt with $A=190,192, \mathrm{and} 194$ still possess appreciable moments of inertia and large but finite softness parameters. Hence they may be characterized as pseudospherical. For exhibiting a near-harmonic level pattern (like ${\mathrm{Xe}}^{130}$, ${\mathrm{Sm}}^{150}$, and other neutron-deficient rare-earth isotopes), ${\mathfrak{g}}_{0}$ becomes exceedingly small, but already for the 2+ state $\mathfrak{g}$ is several orders of magnitude larger. The parameters of some $K=2$ bands in even-even and of bands found in odd-odd are related to those of appropriate ground-state bands in even-even nuclei. Evidence for a rotational band in ${\mathrm{Ir}}^{194}$ is deduced from recently published experimental results. A plot of $\frac{{E}_{4}}{{E}_{2}}$ versus $A$, presented for the discussion of the region of validity of the model, namely, $2.23l\frac{{E}_{4}}{{E}_{2}}l3.33$, reveals new regularities. The empirical Mallmann curves ($\frac{{E}_{I}}{{E}_{2}}$ plotted versus $\frac{{E}_{4}}{{E}_{2}}$) are deduced from the VMI model within its region of validity. Graphs are presented which allow the determination of ${E}_{I}$ (for $I\ensuremath{\le}16$) and of $\ensuremath{\sigma}$ and ${\mathfrak{g}}_{0}$ for each even-even nucleus for which the first 2+ and 4+ states are known. The model suggested by Harris, which includes the next-higher-order correction of the cranking model, is shown to be mathematically equivalent to the VMI model. The recently discovered appreciable quadrupole moments of 2+ states of spherical nuclei are compatible with the moments of inertia of these states given by the VMI model. The relation between $\frac{B (E2)({2}^{\ensuremath{'}}\ensuremath{\rightarrow}2)}{B (E2)(2\ensuremath{\rightarrow}0)}$ and $\frac{{E}_{4}}{{E}_{2}}$ is explored.