IBA consistent-Q formalism extended to the vibrational region

Lipas, P.O.; Toivonen, P.; Warner, D. D.

doi:10.1016/0370-2693(85)91573-4

Cited by 132 publications

(60 citation statements)

References 9 publications

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“…All the quantities are given in keV, except for χ i which are dimensionless and for the effective charges, e i , which are given in e·b. The remaining parameters of the Hamiltonian are: ∆ N +2 = 1400 keV and w N,N +2 [74,75] in each subspace. This approach has been shown to be a rather good approximation in many calculations.…”

Section: The Experimental Data In the Even-even Pt Nucleimentioning

confidence: 99%

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The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

García-Ramos

Heyde²

2009

Nuclear Physics A

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The role of intruder configurations in the description of energy spectra and B(E2) values in the Pt region is analyzed. In particular, we study the differences between Interacting Boson Model calculations with or without the inclusion of intruder states in the even Pt nuclei 172−194 Pt. As a result, it shows that for the description of a subset of the existing experimental data, i.e., energy spectra and absolute B(E2) values up to an excitation energy of about 1.5 MeV, both approaches seem to be equally valid. We explain these similarities between both model spaces through an appropriate mapping. We point out the need for a more extensive comparison, encompassing a data set as broad (and complete) as possible to confront with both theoretical approaches in order to test the detailed structure of the nuclear wave functions. 21.60.Fw. PACS

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Section: The Experimental Data In the Even-even Pt Nucleimentioning

confidence: 99%

“…Thus, proton excitations across the Z = 82 closed shell were not taken into account explicitly. In this single-space approach, considering N bosons, McCutchan et al used the ECQF [74,75] with the Hamiltonian [77] …”

Section: The Experimental Data In the Even-even Pt Nucleimentioning

confidence: 99%

The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

García-Ramos

Heyde²

2009

Nuclear Physics A

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“…Calculations for this study were performed using the extended consistent Q [32,33] formalism (ECQF) of the IBA with a Hamiltonian given by [34] (2) , N B is the number of valence bosons, and c is a scaling factor. The above Hamiltonian contains two parameters, ζ and χ, with ζ ranging from 0 to 1, and χ ranging from 0 to − √ 7/2.…”

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confidence: 99%

Simple Empirical Order Parameter for a First-Order Quantum Phase Transition in Atomic Nuclei

et al. 2008

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A simple, empirical signature of a first order phase transition in atomic nuclei is presented, the ratio of the energy of the 6 + level of the ground state band to the energy of the first excited 0 + state. This ratio provides an effective order parameter which is not only easy to measure, but also distinguishes between first and second order phase transitions and takes on a special value in the critical region. Data in the Nd-Dy region show these characteristics. In addition, a repeating degeneracy between alternate yrast states and successive excited 0 + states is found to correspond closely to the line of a first order phase transition in the framework of the Interacting Boson Approximation (IBA) model in the large N limit, pointing to a possible underlying symmetry in the critical region.The study of structural evolution in atomic nuclei has witnessed significant developments in recent years. One of the most important has been the discovery of empirical evidence [1,2] for quantum phase transitions (QPT) in the equilibrium shape as a function of nucleon number. This has led to the proposal [3,4] and empirical verification [5,6] of a new class of models, called critical point symmetries (CPS). These, in turn have spurred an abundance of experimental searches [7,8,9] for nuclei satisfying the predictions of these CPS as well as investigations into the presence of quasidynamical and partial dynamical symmetries at the critical point [10,11].In contrast to the usual thermodynamic phase transitions [12], QPT occur at zero temperature as a parameter in the Hamiltonian is varied [13]. They are attracting much attention in a variety of physical systems, including Josephson-junction arrays and quantum Hall-effect systems [14]. The transition from BardeenCooper-Schrieffer (BCS) pairing correlations [15] to Bose-Einstein condensation (BEC) as a result of increasing the strength of the pairing interaction in ultracold alkali atoms has been recently seen experimentally [16,17,18]. In nonrigid polyatomic molecules, a transition from rigidly-linear to rigidly-bent shapes has also been studied [19]. A relationship between QPT and quantum entanglement has also attracted much attention [20,21]. Central to this active field is the search for simple empirical signatures of QPT and the identification of their order. The properties of QPT in atomic nuclei are therefore of quite broad interest, especially since nuclei are finite-body systems in which the number of constituents can be varied experimentally and theoretically.It is the purpose of this Letter to identify a new, easyto-measure, observable in one such system, atomic nuclei, that acts as an order parameter for QPT in nuclei and which can distinguish first and second order phase transitions. Further, we will show that a particular value of this observable identifies the entire critical region, even for structures not satisfying a specific CPS. Finally we use this value to point to the possible existence of a heretofore undefined new symmetry at the critical point.In the co...

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“…In the sd-IBM-1, we employed a simple schematic Hamiltonian, within the extended consistent Q formalism (ECQF) [13,14], omitting an overall scale and using the standard method of counting valence bosons as pairs of nucleons from the nearest magic shell closure, resulting in N B = 13. The structural parameters ζ and χ were adjusted to reproduce the R 4/2 ratio and the approximate positions of the 0 + 2 and 2 + 2 states, respectively.…”

Section: Standard Ibmmentioning

confidence: 99%

Centrifugal stretching of¹⁷⁰Hf in the interacting boson model

Werner

Pietralla

Smith

2014

EPJ Web of Conferences

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Abstract. We present the results of a recent experiment to deduce lifetimes of members of the ground state rotational band of 170 Hf, which show the effect of centrifugal stretching in this deformed isotope. Results are compared to the geometrical confined beta-soft (CBS) rotor model, as well as to the interacting boson model (IBM). Two methods to correct for effects due to the finite valence space within the IBM are proposed.

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IBA consistent-Q formalism extended to the vibrational region

Cited by 132 publications

References 9 publications

The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

Simple Empirical Order Parameter for a First-Order Quantum Phase Transition in Atomic Nuclei

Centrifugal stretching of¹⁷⁰Hf in the interacting boson model

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IBA consistent-Q formalism extended to the vibrational region

Cited by 132 publications

References 9 publications

The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

The Pt isotopes: Comparing the Interacting Boson Model with configuration mixing and the extended consistent-Q formalism

Simple Empirical Order Parameter for a First-Order Quantum Phase Transition in Atomic Nuclei

Centrifugal stretching of170Hf in the interacting boson model

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Product

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Centrifugal stretching of¹⁷⁰Hf in the interacting boson model