General Collective Model Research Articles

Microscopically derived potential energy surfaces from mostly structural considerations

A simple procedure to estimate the quadrupole Potential-Energy-Surface (PES) is presented, using mainly structural information, namely the content of the shell model space and the Pauli exclusion principle. Further microscopic properties are implicitly contained through the use of results from the Möller and Nix tables or experimental information. A mapping to the geometric potential is performed yielding the PES. The General Collective Model is used in order to obtain an estimate on the spectrum and quadrupole transitions, adjusting only the mass parameter. First, we test the conjecture on known nuclei, deriving the PES and compare them to known data. We will see that the PES approximates very well the structure expected. Having acquired a certain confidence, we predict the PES of several chain of isotopes of heavy and super-heavy nuclei and at the end we investigate the structure of nuclei in the supposed island of stability. One of the main points to show is that simple assumptions can provide already important information on the structure of nuclei outside known regions and that spectra and electromagnetic transitions can be estimated without using involved calculations and assumptions. The procedure does not allow to calculate binding energies. The method presented can be viewed as a starting point for further improvements.

Boson description of low-lying collective states inBa128

The low-lying collective states in $^{128}\mathrm{Ba}$ are investigated microscopically by means of the boson expansion theory with the self-consistent effective interactions. Calculated level structures and electromagnetic properties are compared with the experimental data. Theoretical structures of the collective wave functions are illustrated in detail for ${0}_{1}^{+},\phantom{\rule{0.16em}{0ex}}{0}_{2}^{+},\phantom{\rule{0.16em}{0ex}}{0}_{3}^{+},\phantom{\rule{0.16em}{0ex}}{2}_{1}^{+},\phantom{\rule{0.16em}{0ex}}{2}_{2}^{+}$, and ${2}_{3}^{+}$ states. In the present results, the main contribution to the ${0}_{2}^{+}$ state of $^{128}\mathrm{Ba}$ comes from the three-phonon component, and the two-phonon component is rather dominant in the ${0}_{3}^{+}$ state. The description of the wave functions is compared to the results of the general collective model.

Electromagnetic properties of100Mo: Experimental results and theoretical description of quadrupole degrees of freedom

The Coulomb excitation experiment to study electromagnetic properties of the heaviest stable Mo isotope, ${}^{100}$Mo, was performed using a 76 MeV ${}^{32}$S beam from the Warsaw cyclotron U-200P. Magnitudes and relative signs of 26 $E1$, $E2$, $E3$, and $M1$ matrix elements coupling nine low-lying states in ${}^{100}$Mo were determined using the least-squares code gosia. Diagonal matrix elements (related to the spectroscopic quadrupole moments) of the 2${}_{1}^{+}$, 2${}_{2}^{+}$, and 2${}_{3}^{+}$ states as well as the 4${}_{1}^{+}$ state were extracted. The resulting set of reduced $E2$ matrix elements was complete and precise enough to obtain, using the quadrupole sum rules approach, quadrupole deformation parameters of ${}^{100}$Mo in its two lowest 0${}^{+}$ states: ground and excited. The overall deformation of the 0${}_{1}^{+}$ and 0${}_{2}^{+}$ states in ${}^{100}$Mo is of similar magnitude, in both cases larger compared to what was found for the neighboring isotopes ${}^{96}$Mo and ${}^{98}$Mo. At the same time, the asymetry parameters obtained for both states strongly differ, indicating a triaxial shape of the ${}^{100}$Mo nucleus in the ground state and a prolate shape in the excited 0${}^{+}$ state. Low-energy quadrupole excitations of the ${}^{100}$Mo nucleus were studied in the frame of the general quadrupole collective Bohr Hamiltonian model (GBH). The potential energy and inertial functions were calculated using the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method starting from two possible variants of the Skyrme effective interaction: SIII and Sly4. The overall quadrupole deformation parameters resulting from the GBH calculations with the SLy4 variant of the Skyrme interaction are slightly closer to the experimentally obtained values than those obtained using SIII.

Yrast electromagnetic transition strengths and shape coexistence in 182Pt

Abstract Using the reaction 170Yb(16O, 4n) at a beam energy of 87 MeV and the Recoil Distance Doppler-Shift Method, five lifetimes in the yrast band of 182Pt have been determined for the first time. For the data analysis, a dedicated version of the Differential Decay Curve Method has been employed. Calculations within the Interacting Boson Model and the General Collective Model indicate shape coexistence in the investigated nucleus.

E0transitions in deformed nuclei

$E0$ transitions are a sensitive indicator of structure in nuclei, reflecting shape transitional regions, deformation, and intruder states. Attention has generally focused on $E0$ transitions to the ground state or low-lying yrast levels. In this paper we look at all $E0$ transitions connecting ${0}^{+}$ states in a rather general collective model. We deduce a new selection rule and map out calculated strengths throughout the spectrum. The distributions of $E0$ strengths for several different collective structures are discussed.

SHAPE EVOLUTION IN HEAVIEST STABLE EVEN-EVEN MOLYBDENUM ISOTOPES STUDIED VIA COULOMB EXCITATION

The quadrupole shape evolution in heaviest stable Mo isotopes is studied in terms of the shape coexistence phenomenon occurrence in this region of nuclear chart. Quadrupole deformation parameters of the 96,98,100 Mo isotopes in the low-lying (ground and excited) 0+ states were deduced using Coulomb excitation method. In all cases rich sets of electromagnetic reduced matrix elements were determined using the GOSIA code and then analysed using the Quadrupole Sum Rules formalism. Discussion of the experimental results in comparison with the predictions of microscopic calculations within the general quadrupole collective Bohr Hamiltonian model is presented for 100 Mo .

MICROSCOPIC STUDY OF COLLECTIVE STATES OF EVEN-EVEN MOLYBDENUM ISOTOPES

Low energy quadrupole excitations of the 84-110 Mo nuclei are studied in the frame of the general Bohr collective model. The potential energy and inertial functions are calculated using the ATDHFB method starting from the Skyrme effective interaction. Obtained energies of the 21, 41, 22 and 02 levels and B(E2) values for the 21 → 0 g . s transitions are in good agreement with experimental data.

Studies of quadrupole collectivity in the γ -soft 106Ru

Various alternative models were used to describe the structure of 106Ru . For example, the General Collective Model (GCM) predicts shape-coexistence for 106Ru with a spherical and a triaxial minimum and strongly mixed structures, while in the IBA-2 calculations, where 106Ru was considered as transitional from vibrational U(5) to γ -soft O(6) , no need was found to include the shape-coexisting configurations. In order to provide additional constraints on the model interpretations, we have applied the Advanced Time-Delayed (ATD) βγγ(t) method to measure the level lifetimes of the excited levels in 106Ru . The new results include the half-lives of T1/2 = 183(3) ps and 7.5(30)ps for the 2+1 and 2+2 states, respectively.

Nonparametric tests of collectively rational consumption behavior: An integer programming procedure

We present an IP-based nonparametric (revealed preference) testing procedure for rational consumption behavior in terms of a general collective model, which includes consumption externalities and public consumption. An empirical application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the practical usefulness of the procedure. Finally, we present extensions of the testing procedure to evaluate the goodness-of-fit (accounting for optimization error as well as measurement error) of the collective model subject to testing.

An Efficient Nonparametric Test of the Collective Household Model

Recently Cherchye et al. (2007a) provided a nonparametric characterization of a general collective model for household consumption which includes externalities and public consumption. This characterization involved different testable necessary and sufficient conditions. We discuss the special case of the household model for which their sufficient conditions are also necessary. We show that verification of this sufficient condition is NP Complete and discuss the relevance of this result for empirical testing. We observe that testing this condition is equivalent to solving the acyclic partitioning problem on a directed graph. We devise an efficient algorithm which approximately solves the minimum acyclic partitioning problem on directed graphs. Hence, we compute an approximate solution to the problem of finding the minimum number K, so that the observed data is consistent with K decision makers. We implement our algorithm on a randomly generated price consumption data set and report the results.

The Revealed Preference Approach to Collective Consumption Behavior: Testing, Recovery and Welfare Analysis

We extend the nonparametric ‘revealed preference’ methodology for analyzing collective consumption behavior (with consumption externalities and public consumption), to render it useful for empirical applications that deal with welfare-related questions. First, we provide a nonparametric necessary and sufficient condition for collectively rational group behavior that incorporates the possibility of assignable quantity information. This characterizes collective rationality in terms of feasible personalized prices, personalized quantities and income shares (representing the underlying sharing rule). Subsequently, we present nonparametric testing tools for data consistency with special cases of the collective model, which impose specific structure on the preferences of the group members (in terms of consumption externalities and public consumption); and we show that these testing tools in turn allow for nonparametrically recovering (bounds on) feasible personalized prices, personalized quantities and income shares that underlie observed (collectively rational) group behavior. In addition, we present formally similar testing and recovery tools for the general collective consumption model, which imposes minimal a priori structure. Interestingly, the proposed testing and recovery methodology can be implemented through integer programming (IP and MILP), which is attractive for practical applications. Finally, while we argue that assignable quantity information generally entails more powerful recovery results, we also demonstrate that precise nonparametric recovery (i.e. tight bounds) can be obtained even if no assignable quantity information is available.

Modeling Collective Rationality: An Nonparametric Test on Experimental Data

We provide a …rst nonparametric (revealed preference) test of the collective consumption model on the basis of experimental data. By using nonparametric testing tools and experimental data, we avoid the usual problems associated with parametric tests (e.g. non-veri…able parametric structure) and the use of ‘real life’data sets (e.g. preference heterogeneity). In addition, our collective rationality test complements the existing nonparametric-experimental evidence on individual rationality. Focusing on dyads, we …nd that all observed consumption choices are consistent with the nonparametric collective rationality conditions. In fact, the consistency results for the parsimonious ‘egoistic’ collective consumption model (as a tool for describing dyads’choice behavior) are closely similar to those for the individual rationality model (as a tool for describing individuals’choice behavior). This suggest that for simple consumption decision settings, such as that considered in our experiment, the egoistic model may be useful for practical analysis. Still, our results also suggest that the more general collective consumption model, which accounts for consumption externalities and public consumption, can be useful even for modeling such simple decision settings. In fact, we can interpret that the appropriate model speci…cation also depends on the speci…c dyad type (e.g. friends or partners; gender composition) and choice setting (e.g. public consumption or not) at hand.

Electromagnetic transition strengths inDy156

Reliable and precise lifetimes of excited states in $^{156}\mathrm{Dy}$ were measured by means of the recoil distance Doppler-shift technique in the coincidence mode. The experiment was performed at the Laboratori Nazionali di Legnaro with the GASP array and the Cologne coincidence plunger apparatus using the reaction $^{124}\mathrm{Sn}$($^{36}\mathrm{S}$,$4n$)$^{156}\mathrm{Dy}$ at a beam energy of 155 MeV. New values of the branching ratios of transitions depopulating the levels of the first excited band have been derived. The measured transition probabilities of $^{156}\mathrm{Dy}$ in the ground-state band and the first excited band as well as the energy spectra are compared to the predictions of the recently proposed X(5) model and to an interacting boson approximation fit. The comparison reveals a different behavior of the intraband transition strengths and indicates a possible coexistence of a normal deformed ground-state band and an X(5)-like first excited band. It also reveals that in $^{156}\mathrm{Dy}$, the \ensuremath{\gamma} degree of freedom plays a more important role than it does in the well-established X(5) nuclei with $N=90$. A fit of the data using the general collective model suggests that a deeper collective potential $V(\ensuremath{\beta},\ensuremath{\gamma})$ may also be a reason for the differences in the spectroscopic properties of $^{156}\mathrm{Dy}$ and those nuclei.

Triaxiality, Chirality and γ-Softness

Current work explores the impact of gamma-softness on partner bands built on the h11/2h11/2 proton-particle-neutron-hole configurations in triaxial odd-odd nuclei. The results of calculations conducted using a core-particle-hole coupling are presented. The model Hamiltonian includes the collective core, the single-particle valence nucleons, and separable quadrupole-quadrupole interactions. The Kerman-Klein method was applied to find eigenstates, which provided a convenient way for exploring core effects. Calculations were made for triaxial cores with various gamma-softness using the General Collective Model keeping the expectation value for the triaxiality parameter fixed at <gamma>=30 deg. The degeneracy in the proton-neutron h11/2h11/2 bands results from the calculations for the gamma-rigid core but is lifted for the gamma-unstable core.

Test of the critical point symmetry X(5) in the mass A = 180 region

Based on the energy spectra and relative transition probabilities 176,178,180Os turned out to be very promising candidates for testing the features of the critical point symmetry X(5). In order to also test absolute transition probabilities predicted in the framework of the X(5) symmetry lifetime measurements were performed at the Cologne FN tandem accelerator. The lifetimes of the first 2+ states in 176,178,180Os were measured using electronic timing and in the case of 178Os with the recoil distance Doppler shift (RDDS) technique using an 16O-induced fusion evaporation reaction. In addition, a coincidence RDDS measurement was performed at the Laboratori Nazionali di Legnaro with the GASP spectrometer using the 154Sm(29Si,5n)178Os reaction. The deduced transition quadrupole moments agree well with the X(5) predictions, thus further supporting an X(5) structure for 178Os. The experimental data for 178Os are compared to calculations in the framework of the interaction boson model (IBM) and of the general collective model (GCM).

The Collective Model of Household Consumption: A Nonparametric Characterization

We provide a nonparametric characterization of a general collective model for household consumption, which includes externalities and public consumption. Next, we establish testable necessary and sufficient conditions for data consistency with collective rationality that only include observed price and quantity information. These conditions have a similar structure as the generalized axiom of revealed preference for the unitary model, which is convenient from a testing point of view. In addition, we derive the minimum number of goods and observations that enable the rejection of collectively rational household behavior.

Opening the Black Box of Intra-Household Decision-Making: Theory and Non-Parametric Empirical Tests of General Collective Consumption Models

We non-parametrically test a general collective consumption model with public consumption and externalities inside the household. We further propose a novel approach to model special cases of the general collective model. These special cases include alternative restrictions on the 'sharing rule' that applies to each household, and which defines the distribution of the household budget over the household members. A limiting case is the unitary model. Our application uses data from the Russia Longitudinal Monitoring Survey (RLMS); the panel structure of this data set allows non-parametric testing of the behavioral models without relying on preference homogeneity assumptions across similar individuals. This application includes test results but also a power analysis for different specifications of the collective consumption model. Our main findings are that the most general collective model, together with a large class of special but still fairly general cases, cannot be rejected by the data, while other, restricted, versions of the general model, including the unitary alternative, are rejected. Since these tests are entirely non-parametric, this provides strong evidence in favor of models focusing on intra-household decision-making.

Lifetimes inTe126from in-beam(n,n′γ)measurements

The excited levels of $^{126}\mathrm{Te}$ have been studied using the $(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction. Excitation functions, $\ensuremath{\gamma}\ensuremath{\gamma}$ coincidences, angular distributions, and Doppler shifts were measured for $\ensuremath{\gamma}$ rays from levels up to an excitation energy of $3.2\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}$; multipole-mixing and branching ratios and transition rates were deduced. Experimental values of electromagnetic transition rates were compared with the anharmonic vibrator model, the general collective model, the neutron-proton interacting boson model with intruder mixing, and particle-core coupling model calculations. No advantage is found in using an intruder description for the low-spin states of $^{126}\mathrm{Te}$. All models used reproduce some features of the level scheme and many transition rates, but the particle-core coupling model was found to have better overall success describing the observed properties of this nucleus.

Transition probabilities inGd154: Evidence for X(5) critical point symmetry

Lifetime measurements in $^{154}\mathrm{Gd}$ were performed by means of the recoil distance Doppler-shift method. Excited states of $^{154}\mathrm{Gd}$ were populated via Coulomb excitation with a $^{32}\mathrm{S}$ beam at $110\phantom{\rule{0.3em}{0ex}}\text{MeV}$ delivered by the FN tandem accelerator of the University of Cologne. The determined transition probabilities as well as the low-spin level scheme of $^{154}\mathrm{Gd}$ demonstrate a good agreement with the predictions of the critical point symmetry X(5). Comparison of specific experimental observables for the $N=90$ rare earth isotones with the calculations of the X(5) model clearly show that $^{154}\mathrm{Gd}$ is one of the good examples of the realization of the X(5) dynamical symmetry. In addition, the experimental data are compared to fits in the framework of the IBA and the general collective model.

The Collective Model of Household Consumption: A Nonparametric Characterization

We provide a nonparametric characterization of a general collective model for multi-person household consumption, which includes externalities and public goods. We derive the minimum number of commodities and observations that enable the falsification of this general model for aggregrate household quantity and price data; these requirements are generally less stringent than the conditions derived by Browning and Chiappori (1998) within a parametric setting. Next, we institute necessary and sufficient conditions for data consistency with collective rationality that only include observed price and quantity information. These conditions are formally similar to the GARP condition for the unitary model (see Varian, 1982); which is particularly convenient from a practical point of view. To illustrate the generality of the collective model, we also discuss a number of interesting special cases, including the traditional unitary model and the collective labor supply a la Chiappori (1988).