Description of nuclear systems with a self-consistent configuration-mixing approach. I: Theory, algorithm, and application to the 12^{12}C test nucleus

Although self-consistent multi-configuration methods have been used for decades to address the description of atomic and molecular many-body systems, only a few trials have been made in the context of nuclear structure. This work aims at the development of such an approach to describe in a unified way various types of correlations in nuclei, in a self-consistent manner where the mean-field is improved as correlations are introduced. The goal is to reconcile the usually set apart Shell-Model and Self-Consistent Mean-Field methods. This approach is referred as "variational multiparticle-multihole configuration mixing method". It is based on a double variational principle which yields a set of two coupled equations that determine at the same time the expansion coefficients of the many-body wave function and the single particle states. The formalism is derived and discussed in a general context, starting from a three-body Hamiltonian. Links to existing many-body techniques such as the formalism of Green's functions are established. First applications are done using the two-body D1S Gogny effective force. The numerical procedure is tested on the $^{12}$C nucleus in order to study the convergence features of the algorithm in different contexts. Ground state properties as well as single-particle quantities are analyzed, and the description of the first $2^+$ state is examined. This study allows to validate our numerical algorithm and leads to encouraging results. In order to test the method further, we will realize in the second article of this series, a systematic description of more nuclei and observables obtained by applying the newly-developed numerical procedure with the same Gogny force. As raised in the present work, applications of the variational multiparticle-multihole configuration mixing method will however ultimately require the use of an extended and more constrained Gogny force.Comment: 22 pages, 18 figures, accepted for publication in Phys. Rev. C. v2: minor corrections and references adde

Upscaling A Challenge-Based And Modular Education Concept (CMODE-UP)

In 2019, a course at a Dutch University of Technology was redesigned towards challenge-based and modular education. The course was received positively by students and their learning outcomes (grades and engagement) increased compared to previous years. This redesign was quite intensive, and case-specific. It did not deliver a specific set of design principles that can easily be used to redesign other courses within the university or even other universities. Therefore, a follow-up project was started, that aims to deliver a framework to scale-up the course redesign tested in the previous study (CMODE; Challenge-based Modular On-demand Digital Education). This framework will be designed using practical principles and will be evidence-informed. The project consists of three stages: (1) informal interviews with key actors at our university, experienced in studying and/or designing modular instruction, a systematic literature review on challenge-based education and modular instruction; (2) a test of the design principles that were developed using the interviews and literature review; and (3) a test of the CMODE-up framework that was built on the results from the second stage, using think-out-loud protocols. In the current study we specifically focus on the first stage. A first look at the already existing literature around challenge-based education and modular instruction shows us that both concepts have been around for a long time in higher engineering education. Since education has become more and more digitized (and the development of MOOCs), it appears that the concepts have taken a quick increase in relevance. However, both concepts have only been studied minimally in relation to each other. We deem it thus highly relevant to first build a clear and proper view on both concepts, the strengths and weaknesses, and where both (can) meet. So that anyone who has intentions like ours - to implement both in higher education - can do this in an evidence-informed manner.</p