Identificación de figuras geométricas en fotografías de objetos reales: un estudio con maestros en formación

En este trabajo se analizan (cuantitativa y cualitativamente) las respuestas de 173 estudiantes de Magisterio ante una tarea en la que debían identificar figuras geométricas presentes en 4 fotografías de objetos reales

Análisis histórico sobre la enseñanza de la razón y la proporción

En este trabajo se realiza un análisis del tratamiento recibido por los conceptos de razón y proporción en textos escolares españoles de los últimos 160 años. Fruto de dicho análisis se presentan algunas alternativas a la enseñanza actual que pretenden mejorar el modo en que los alumnos de secundaria adquieren y manejan dichos conceptos

Nuclear matter from the ladder resummation in terms of the experimental nucleon-nucleon scattering amplitudes

Infinite nuclear matter is studied by resuming the series of ladder diagrams based on the results developed by us [Ann. Phys. (NY) 437, 168741 (2022)]. The master formula for the energy density is explicitly solved for the case of contact interactions, within a pionless description of the nucleon-nucleon interactions. Renormalized results are obtained which are directly expressed in terms of the nucleon-nucleon phase shifts and mixing angles in partial-wave amplitudes up to and including G waves, with convergence reached under the inclusion of higher partial waves. The energy per particle, density, and sound velocity resulting from the ladder series are given for symmetric and neutron matter. This resummation of the ladder diagrams provides a rigorous result that may be used as low-density reference for other parametrizations of ¯¯¯E for higher densities.Agencia Estatal de InvestigaciónEuropean Commissio

Ultracold spin-balanced fermionic quantum liquids with renormalized P-wave interactions

We consider a spin-balanced degenerate gas of spin-1/2 fermions whose dynamics is governed by low-energy P-wave interactions characterized by the scattering volume a1 and effective momentum r1. The energy per particle ¯¯¯E in the many-body system is calculated by resumming the ladder diagrams comprising both particle-particle and hole-hole intermediate states, following the novel advances recently developed by us in Ann. Phys. (NY) 437, 168741 (2022). This allows us to obtain a renormalized result for ¯¯¯E within generic cutoff regularization schemes, with ¯¯¯E directly expressed in terms of the scattering parameters a1 and r1, once the cutoff is sent to infinity. The whole set of possible values of a1 and r1 is explored, looking for minima in the energy per particle with ¯¯¯E given as described. They are actually found, but a further inspection reveals that the associated scattering parameters give rise to resonance poles in the complex momentum plane with positive imaginary part, which is at odds with the Hermiticity of the Hamiltonian. We also determine that these conflictive poles, with a pole-position momentum that is smaller in absolute value than the Fermi momentum of the system, clearly impact the calculation of ¯¯¯E. As a result, we conclude that unpolarized spin-1/2 fermionic normal matter interacting in P-wave is not stable. We also study three universal parameters around the unitary limit. Finally, the whole set of values for the parameters a1, r1 is characterized according to whether they give rise to unallowed poles and, if so, by attending to their pole positions relative to the Fermi momentum of the system explored.Agencia Estatal de Investigació

Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content

We resum the ladder diagrams for the calculation of the en ergy density E of a spin 1/2 fermion many-body system in terms of arbitrary vacuum two-body scattering amplitudes. The partial-wave decomposition of the in-medium two-body scatter ing amplitudes is developed, and the expression for calculating E in a partial-wave amplitude expansion is also given. The case of contact interactions is completely solved for any con tent in partial waves and it is shown to provide renormalized results, expressed directly in terms of scattering data parameters, within cutoff regularization in a wide class of schemes. The S- and P-wave interactions are considered up to including the first three-terms in the effective-range expansion, paying special attention to the parametric region around the unitary limitAgencia Estatal de InvestigaciónEuropean Commissio

Strangeness changing scalar form factors

We derive expressions for strangeness-changing scalar form factors, which incorporate known theoretical constraints both at low and high energies. Their leading behaviour in the limit of a large number of colours is calculated from the resonance chiral Lagrangian, and a set of short-distance constraints on the scalar resonance couplings is obtained, imposing the form factors to vanish at infinite momentum transfer. The important effects of meson rescattering are taken into account by exploiting unitarity and analyticity. Making use of previous results on S-wave Kpi scattering [1], and a coupled-channel dispersion-relation analysis, the Kpi, Keta and Keta' scalar form factors are calculated up to 2 GeV These scalar form factors are a key ingredient in the determination of the corresponding scalar spectral function which is important in the extraction of the mass of the strange quark from QCD sum rules as well as hadronic tau decays