Three-body decays: structure, decay mechanism and fragment properties

We discuss the three-body decay mechanisms of many-body resonances. R-matrix sequential description is compared with full Faddeev computation. The role of the angular momentum and boson symmetries is also studied. As an illustration we show the computed $\alpha$-particle energy distribution after the decay of 12C(1^+) resonance at 12.7 MeV.Comment: 4 pages, 3 figures. Proceedings of the workshop "Critical Stability of Few-Body Quantum Systems" 200

Momentum distributions of α\alpha-particles from decaying low-lying 12^{12}C-resonances

The complex scaled hyperspherical adiabatic expansion method is used to compute momentum and energy distributions of the three $\alpha$-particles emerging from the decay of low-lying $^{12}$C-resonances. The large distance continuum properties of the wave functions are crucial and must be accurately calculated. We discuss separately decays of natural parity states: two $0^+$, one $1^{-}$, three $2^+$, one $3^-$, two $4^+$, one $6^+$, and one of each of unnatural parity, $1^{+}$, $2^-$, $3^+$, $4^-$. The lowest natural parity state of each $J^{\pi}$ decays predominantly sequentially via the $^{8}$Be ground state whereas other states including unnatural parity states predominantly decay directly to the continuum. We present Dalitz plots and systematic detailed momentum correlations of the emerging $\alpha$-particles.Comment: 11 pages, 7 figures, accepted for publication in Physical Review

Few-body decay and recombination in nuclear astrophysics

Three-body continuum problems are investigated for light nuclei of astrophysical relevance. We focus on three-body decays of resonances or recombination via resonances or the continuum background. The concepts of widths, decay mechanisms and dynamic evolution are discussed. We also discuss results for the triple $\alpha$ decay in connection with $2^+$ resonances and density and temperature dependence rates of recombination into light nuclei from $\alpha$-particles and neutrons.Comment: 9 pages, 8 figures. Proceedings of the 21st European Few Body Conference held in Salamanca (Spain) in August-September 201

Few-body quantum method in a dd-dimensional space

In this work we investigate the continuous confinement of quantum systems from three to two dimensions. Two different methods will be used and related. In the first one the confinement is achieved by putting the system under the effect of an external field. This method is conceptually simple, although, due to the presence of the external field, its numerical implementation can become rather cumbersome, especially when the system is highly confined. In the second method the external field is not used, and it simply considers the spatial dimension $d$ as a parameter that changes continuously between the ordinary integer values. In this way the numerical effort is absorbed in a modified strength of the centrifugal barrier. Then the technique required to obtain the wave function of the confined system is precisely the same as needed in ordinary three dimensional calculations without any confinement potential. The case of a two-body system squeezed from three to two dimensions is considered, and used to provide a translation between all the quantities in the two methods. Finally we point out perspectives for applications on more particles, different spatial dimensions, and other confinement potentials.Comment: To be published in Physics Letters

Package wsbackfit for Smooth Backfitting Estimation of Generalized Structured Models

A package is introduced that provides the weighted smooth backfitting estimator for a large family of popular semiparametric regression models. This family is known as generalized structured models, comprising, for example, generalized varying coefficient model, generalized additive models, mixtures, potentially including parametric parts. The kernel-based weighted smooth backfitting belongs to the statistically most efficient procedures for this model class. Its asymptotic properties are well-understood thanks to the large body of literature about this estimator. The introduced weights allow for the inclusion of sampling weights, trimming, and efficient estimation under heteroscedasticity. Further options facilitate easy handling of aggregated data, prediction, and the presentation of estimation results. Cross-validation methods are provided which can be used for model and bandwidth selection.

alpha particle momentum distributions from 12C decaying resonances

The computed $\alpha$ particle momentum distributions from the decay of low-lying $^{12}$C resonances are shown. The wave function of the decaying fragments is computed by means of the complex scaled hyperspherical adiabatic expansion method. The large-distance part of the wave functions is crucial and has to be accurately calculated. We discuss energy distributions, angular distributions and Dalitz plots for the $4^+$, $1^+$ and $4^-$ states of $^{12}$C.Comment: 6 pages, 4 figures. Proceedings of the SOTANCP2008 conference held in Strasbourg in May 200

Decay of low-lying 12C resonances within a 3alpha cluster model

We compute energy distributions of three $\alpha$-particles emerging from the decay of $^{12}$C resonances by means of the hyperspherical adiabatic expansion method combined with complex scaling. The large distance continuum properties of the wave functions are crucial and must be accurately calculated. The substantial changes from small to large distances determine the decay mechanisms. We illustrate by computing the energy distributions from decays of the $1^{+}$ and $3^-$-resonances in $^{12}$C. These states are dominated by direct and sequential decays into the three-body continuum respectively.Comment: 5 pages, 3 figures. Proceedings of the Clusters '07 conference held in Stratford-upon-Avon in September 200

Structure and three-body decay of 9^9Be resonances

The complex-rotated hyperspherical adiabatic method is used to study the decay of low-lying $^9$Be resonances into one neutron and two $\alpha$-particles. We investigate the six resonances above the break-up threshold and below 6 MeV: $1/2^\pm$, $3/2^\pm$ and $5/2^\pm$. The short-distance properties of each resonance are studied, and the different angular momentum and parity configurations of the $^8$Be and $^5$He two-body substructures are determined. We compute the branching ratio for sequential decay via the $^8$Be ground state which qualitatively is consistent with measurements. We extract the momentum distributions after decay directly into the three-body continuum from the large-distance asymptotic structures. The kinematically complete results are presented as Dalitz plots as well as projections on given neutron and $\alpha$-energy. The distributions are discussed and in most cases found to agree with available experimental data.Comment: 12 pages, 10 figures. To appear in Physical Review

A game theory model to explore the role of cooperation and diversity in community food security: the case of Southern Malawi

The Sustainable Development Goals aim at ending food insecurity by 2030. Therefore, civil society needs to understand the inherent complexities of both socio-economic and ecological dynamics and their interdependencies. In particular, the behavioural dynamics that underpin human agents are crucial in driving the final outcomes in terms of community food security and require further attention. Using household behaviour within a rural village of Southern Malawi as an example, we describe a game theory model representing cropping strategies: (1) cooperation, as driven by other-regarding preferences, and (2) conformation, the tendency to converge to similar crop planting choices as opposed to differentiation (and thus crop diversity). We find that the latter plays a crucial role in driving the system towards successful strategies: how individuals relate to social norms has greater effect. Cooperation is only necessary for community success when the community converges on crop planting choices. On the contrary, differentiation, the affirmation of the individual unique identity, can succeed with or without cooperation. We further elaborate on the idea that community level sustainability can be reached through different pathways, which might require food exchange mechanisms within and beyond the system boundaries. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.This research is supported by the Basque Government through the BERC 2018-2021 program and by the Ikertzaile Doktoreentzako Hobekuntzarako doktoretza-ondoko Programa and by Spanish Ministry of Economy and Competitiveness MINECO through BC3 María de Maeztu excellence accreditation MDM-2017-0714 and by the Leverhulme TrustResearch Fellowship “CREATE: the network components of creativity and success. This work was also inspired and partially funded by the ASSETS (Attaining Sustainable Services from Ecosystems) project (NERC/ESPA NE-J002267-1)