The general collective model applied to the chains of Pt, Os and W isotopes

Excited low-spin, nonyrast states in 170,172,174 Hf were populated in β + / decay and studied through off-beam γ -ray spectroscopy. New coincidence data allowed for a substantial revision of the level schemes of 170,172 Hf and a confirmation of the level scheme of 174 Hf. The Hf isotopes represent a unique situation in which a crossing of collective intrinsic excitations occurs, enhancing significantly the effects of mixing. Using branching ratios from excited 2 + states, this mixing is followed and studied. The resulting mixing matrix elements are found to be ∼30 keV-an order of magnitude larger than estimated previously for nearby nuclei. In the case of 170 Hf, the 2 + β and 2 + γ level are shown to be completely mixed.

“…In the present work, we identify a level at 1158.95 (8) keV that we associate with the reported 1155-keV level. This identification is based on two depopulating transitions.…”

Section: (4 + ) Level At 1155 Kevsupporting

confidence: 74%

“…Initial studies [7,8] involving a variety of different models indicated a small mixing between the γ and β bands. In addition, later calculations, based on improved measurements of B(E2) transition strengths, yielded absolute matrix elements between the 2 + γ and 2 + β states in 182 W on the order of ∼2 keV [9,10].…”

Section: Introductionmentioning

confidence: 99%

Enhanced mixing of intrinsic states in deformed Hf nuclei

McCutchan¹,

Casten²,

Werner³

et al. 2008

“…Electromagnetic transition strengths can be calculated from the matrix elements of the collective multipole operators. The general E2 operator for the geometric model [27,28,29] may be expanded in laboratory frame coordinates α 2µ as [30] …”

Section: Consider the Bohr Hamiltonian [4]mentioning

confidence: 99%

Consequences of wall stiffness for aβ-soft potential

Caprio

2004

“…Many GCM studies have retained the secondorder term [7], but inclusion of this or other higher-order terms destroys the simple invariance of B(E2) ratios, since the different terms in (3) scale by different powers of a under dilation. The second-order term usually provides only a relatively small correction to the linear term, and the correct coefficient by which it should be normalized is highly uncertain [4,8]. Comparative studies by Petkov, Dewald, and Andrejtscheff [16] have shown no clear benefit to its inclusion for the nuclei considered.…”

Section: Scaling Propertiesmentioning

confidence: 99%

“…Once wave functions for the nuclear eigenstates are calculated, electromagnetic matrix elements can be evaluated. The most commonly used expression for the electric quadrupole operator is deduced using the assumption that the nuclear charge is uniformly distributed within a radius R = R 0 (1 + µ α 2µ Y * 2µ ) [4,8], which leads to a series expression…”

Section: Introductionmentioning

confidence: 99%

Simplified approach to the application of the geometric collective model

Caprio

2003

The predictions of the geometric collective model (GCM) for different sets of Hamiltonian parameter values are related by analytic scaling relations. For the quartic truncated form of the GCMwhich describes harmonic oscillator, rotor, deformed γ-soft, and intermediate transitional structures -these relations are applied to reduce the effective number of model parameters from four to two. Analytic estimates of the dependence of the model predictions upon these parameters are derived. Numerical predictions over the entire parameter space are compactly summarized in twodimensional contour plots. The results considerably simplify the application of the GCM, allowing the parameters relevant to a given nucleus to be deduced essentially by inspection. A precomputed mesh of calculations covering this parameter space and an associated computer code for extracting observable values are made available through the Electronic Physics Auxiliary Publication Service. For illustration, the nucleus 102 Pd is considered.