Particle number projection with effective forces

The particle number projection method is formulated for density dependent forces and in particular for the finite range Gogny force. Detailed formula for the projected energy and its gradient are provided. The problems arising from the neglection of any exchange term, which may lead to divergences, are throughly discussed and the possible inaccuracies estimated. Numericala results for the projection after variation method are shown for the nucleus 164Er and for the projection before variation approach for the nuclei 48-50Cr. We also confirm the Coulomb antipairing effect found in mean field theories.Comment: 33 pages, 8 figures. Submit to Nuc. Phys.

Coulomb exchange and pairing contributions in nuclear Hartree-Fock-Bogoliubov calculations with the Gogny force

We present exact Hartree-Fock-Bogoliubov calculations with the finite range density dependent Gogny force using a triaxial basis. For the first time, all contributions to the Pairing and Fock Fields arising from the Gogny and Coulomb interactions as well as the two-body correction of the kinetic energy have been calculated in this basis. We analyze the relevance of these terms in different regions of the periodic table at zero and high angular momentum. The validity of commonly used approximations that neglect different terms in the variational equations is also checked. We find a decrease of the proton pairing energies mainly due to a Coulomb antipairing effect.Comment: 32 pages, 12 figures. In press in Nucl. Physics

Mean-field Based Approaches to Pairing Correlations in Atomic Nuclei

The evolution of the pairing correlations from closed shell to middle shell nuclei is analyzed with a Finite Range Density Dependent interaction in the Sn isotopes. As theoretical approaches we use the Hartree-Fock-Bogoliubov, the Lipkin-Nogami, their particle number projected counterparts and the full variation after particle number projection method. We find that whereas all approaches succeed rather well in the description of the total energy they differ significantly in the pairing correlation content of the wave functions. The description of the evolution from the weak to the strong pairing regime is also approach dependent, specially at shell closure.Comment: 14 pages, 5 figure

GNSS reflectometry for land remote sensing applications

Soil moisture and vegetation biomass are two essential parameters from a scienti c and economical point of view. On one hand, they are key for the understanding of the hydrological and carbon cycle. On the other hand, soil moisture is essential for agricultural applications and water management, and vegetation biomass is crucial for regional development programs. Several remote sensing techniques have been used to measure these two parameters. However, retrieving soil moisture and vegetation biomass with the required accuracy, and the appropriate spatial and temporal resolutions still remains a major challenge. The use of Global Navigation Satellite Systems (GNSS) reflected signals as sources of opportunity for measuring soil moisture and vegetation biomass is assessed in this PhD Thesis. This technique, commonly known as GNSS-Reflectometry (GNSS-R), has gained increasing interest among the scienti c community during the last two decades due to its unique characteristics. Previous experimental works have already shown the capabilities of GNSS-R to sense small reflectivity changes on the surface. The use of the co- and cross-polarized reflected signals was also proposed to mitigate nuisance parameters, such as soil surface roughness, in the determination of soil moisture. However, experimental evidence of the suitability of that technique could not be demonstrated. This work analyses from a theoretical and an experimental point of view the capabilities of polarimetric observations of GNSS reflected signals for monitoring soil moisture and vegetation biomass. The Thesis is structured in four main parts. The fi rst part examines the fundamental aspects of the technique and provides a detailed review of the GNSS-R state of the art for soil moisture and vegetation monitoring. The second part deals with the scattering models from land surfaces. A comprehensive description of the formation of scattered signals from rough surfaces is provided. Simulations with current state of the art models for bare and vegetated soils were performed in order to analyze the scattering components of GNSS reflected signals. A simpli ed scattering model was also developed in order to relate in a straightforward way experimental measurements to soil bio-geophysical parameters. The third part reviews the experimental work performed within this research. The development of a GNSS-R instrument for land applications is described, together with the three experimental campaigns carried out in the frame of this PhD Thesis. The analysis of the GNSS-R and ground truth data is also discussed within this part. As predicted by models, it was observed that GNSS scattered signals from natural surfaces are a combination of a coherent and an incoherent scattering components. A data analysis technique was proposed to separate both scattering contributions. The use of polarimetric observations for the determination of soil moisture was demonstrated to be useful under most soil conditions. It was also observed that forests with high levels of biomass could be observed with GNSS reflected signals. The fourth and last part of the Thesis provides an analysis of the technology perspectives. A GNSS-R End-to-End simulator was used to determine the capabilities of the technique to observe di erent soil reflectivity conditions from a low Earth orbiting satellite. It was determined that high accuracy in the estimation of reflectivity could be achieved within reasonable on-ground resolution, as the coherent scattering component is expected to be the predominant one in a spaceborne scenario. The results obtained in this PhD Thesis show the promising potential of GNSS-R measurements for land remote sensing applications, which could represent an excellent complementary observation for a wide range of Earth Observation missions such as SMOS, SMAP, and the recently approved ESA Earth Explorer Mission Biomass.La humedad del suelo y la biomasa de la vegetaci on son dos parametros clave desde un punto de vista tanto cient co como econ omico. Por una parte son esenciales para el estudio del ciclo del agua y del carbono. Por otra parte, la humedad del suelo es esencial para la gesti on de las cosechas y los recursos h dricos, mientras que la biomasa es un par ametro fundamental para ciertos programas de desarrollo. Varias formas de teledetección se han utilizado para la observaci on remota de estos par ametros, sin embargo, su monitorizaci on con la precisi on y resoluci on necesarias es todav a un importante reto tecnol ogico. Esta Tesis evalua la capacidad de medir humedad del suelo y biomasa de la vegetaci on con señales de Sistemas Satelitales de Posicionamiento Global (GNSS, en sus siglas en ingl es) reflejadas sobre la Tierra. La t ecnica se conoce como Reflectometr í a GNSS (GNSS-R), la cual ha ganado un creciente inter es dentro de la comunidad científ ca durante las dos ultimas d ecadas. Experimentos previos a este trabajo ya demostraron la capacidad de observar cambios en la reflectividad del terreno con GNSS-R. El uso de la componente copolar y contrapolar de la señal reflejada fue propuesto para independizar la medida de humedad del suelo de otros par ametros como la rugosidad del terreno. Sin embargo, no se pudo demostrar una evidencia experimental de la viabilidad de la t ecnica. En este trabajo se analiza desde un punto de vista te orico y experimental el uso de la informaci on polarim etrica de la señales GNSS reflejadas sobre el suelo para la determinaci on de humedad y biomasa de la vegetaci on. La Tesis se estructura en cuatro partes principales. En la primera parte se eval uan los aspectos fundamentales de la t ecnica y se da una revisi on detallada del estado del arte para la observaci on de humedad y vegetaci on. En la segunda parte se discuten los modelos de dispersi on electromagn etica sobre el suelo. Simulaciones con estos modelos fueron realizadas para analizar las componentes coherente e incoherente de la dispersi on de la señal reflejada sobre distintos tipos de terreno. Durante este trabajo se desarroll o un modelo de reflexi on simpli cado para poder relacionar de forma directa las observaciones con los par ametros geof sicos del suelo. La tercera parte describe las campañas experimentales realizadas durante este trabajo y discute el an alisis y la comparaci on de los datos GNSS-R con las mediciones in-situ. Como se predice por los modelos, se comprob o experimentalmente que la señal reflejada est a formada por una componente coherente y otra incoherente. Una t ecnica de an alisis de datos se propuso para la separacióon de estas dos contribuciones. Con los datos de las campañas experimentales se demonstr o el bene cio del uso de la informaci on polarim etrica en las señales GNSS reflejadas para la medici on de humedad del suelo, para la mayor a de las condiciones de rugosidad observadas. Tambi en se demostr o la capacidad de este tipo de observaciones para medir zonas boscosas densamente pobladas. La cuarta parte de la tesis analiza la capacidad de la t ecnica para observar cambios en la reflectividad del suelo desde un sat elite en orbita baja. Los resultados obtenidos muestran que la reflectividad del terreno podr a medirse con gran precisi on ya que la componente coherente del scattering ser a la predominante en ese tipo de escenarios. En este trabajo de doctorado se muestran la potencialidades de la t ecnica GNSS-R para observar remotamente par ametros del suelo tan importantes como la humedad del suelo y la biomasa de la vegetaci on. Este tipo de medidas pueden complementar un amplio rango de misiones de observaci on de la Tierra como SMOS, SMAP, y Biomass, esta ultima recientemente aprobada para la siguiente misi on Earth Explorer de la ESA

On the origin of the anomalous behaviour of 2+ excitation energies in the neutron-rich Cd isotopes

Recent experimental results obtained using $\beta$ decay and isomer spectroscopy indicate an unusual behaviour of the energies of the first excited 2$^{+}$ states in neutron-rich Cd isotopes approaching the N=82 shell closure. To explain the unexpected trend, changes of the nuclear structure far-off stability have been suggested, namely a quenching of the N=82 shell gap already in $^{130}$Cd, only two proton holes away from doubly magic $^{132}$Sn. We study the behaviour of the 2$^+$ energies in the Cd isotopes from N=50 to N=82, i.e. across the entire span of a major neutron shell using modern beyond mean field techniques and the Gogny force. We demonstrate that the observed low 2$^+$ excitation energy in $^{128}$Cd close to the N=82 shell closure is a consequence of the doubly magic character of this nucleus for oblate deformation favoring thereby prolate configurations rather than spherical ones.Comment: 10 pages, 4 figures, to be publised in Phys. Lett.

Approximate particle number projection with density dependent forces: Superdeformed bands in the A=150 and A=190 regions

We derive the equations for approximate particle number projection based on mean field wave functions with finite range density dependent forces. As an application ground bands of even-A superdeformed nuclei in the A=150 and A=190 regions are calculated with the Gogny force. We discuss nuclear properties such as quadrupole moments, moments of inertia and quasiparticle spectra, among others, as a function of the angular momentum. We obtain a good overall description.Comment: 31 pages, 10 figures, 3 appendices. In press in Nucl. Phy

Changes in quantity and quality of time for children: United States, 1981-1997.

This paper tries to analyze changes in the allocation of time decided by mothers and how their characteristics influence that allocation across the period 1981-1997 in the United States. Data reveals that there exists an increase on the quantity and quality of time devoted to children by some types of mothers. Shift-share analysis shows that behind the increase there is a change in maternal behaviour. Then, it seems reasonable to model the decisions of the mothers and try to explain which are the determinants. Estimations suggest that working time is a substitute of quantity, but not quality, of time with children. Being single reduces not only time but also its quality. Mother’s earnings and level of education have changed their influence on time with children across time.Time-use, quantity and quality of time with children, family economics, simultaneous equation system, and three-stage least squares.

Educational System, Altruism and Inequality in the Distribution of Income

This paper studies the impact of public provision of education on the distribution of income in a framework where parents are altruistic toward children. Any child receives two transfers, one as a non-human transfer and the other as a human capital transfer. Under different education regimes, non-human transfers offset the low realization of innate ability, which despite the human capital transfer implies a low level of earnings. Then the questions that will arise are, first, to what extent skill-compensating investments are important as ex-ante income inequality reduction mechanisms in the private provision system, and secondly, how public education can affect this reduction mechanism. I show that tax policy may have unexpected effects on the compensatory effect, that is, on the income gap. The result is that the distribution of income induced by the public provision system is not more equally distributed. Moreover, the fraction of population that does not improve is just at the bottom of the income distribution. I also explore some possibilities to avoid this negative effect and preserve public education as an essential public service.Altruism, human capital and non-human capital transfers, systems of education, inequality

Changes in quantity and quality of time for children: United States, 1981-1997

This paper tries to analyze changes in the allocation of time decided by mothers and how different characteristics of them, such us marital status, employment status, etc., influences that allocation across the period 1981-1997 in the United States. Data reveals that there exists an increase on the quantity and quality of time devoted to children by some types of mothers and children. It is shown that the behavioral component of this change is larger than the structural component. Then, the determinants of direct and indirect time, quality versus quantity, are analyzed in a simultaneous equation framework. Estimations suggest that if a mother works, children's time is reduced. However working time is a substitutes of quantity of time with children, but not quality. Being single reduces not only time but its quality. Mother's earnings and level of education have changed their influence on the allocation of time across time.Time-use, quantity and quality of time with children, family ecomics, simultaneous equation system, three-stage least squares