We propose an importance-truncation scheme for the large-scale nuclear shell model that extends its range of applicability to larger valence spaces and mid-shell nuclei. It is based on a perturbative measure for the importance of individual basis states that acts as an additional truncation for the many-body model space in which the eigenvalue problem of the Hamiltonian is solved numerically. Through a posteriori extrapolations of all observables to vanishing importance threshold, the full shell-model results can be recovered. In addition to simple threshold extrapolations, we explore extrapolations based on the energy variance. We apply the importancetruncated shell model for the study of 56 Ni in the p f valence space and of 60 Zn and 64 Ge in the p f g9 /2 space. We demonstrate the efficiency and accuracy of the approach, which pave the way for future shell-model calculations in larger valence spaces with valence-space interactions derived in ab initio approaches.PACS numbers: 21.60. Cs, 27.50.+e Introduction. The nuclear valence-space shell model is one of the work horses in nuclear structure theory. It is very successful for the description of spectra and spectroscopic observables over a large range of nuclei and plays an important role in guiding and interpreting experiments from stable to exotic nuclei [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Two critical aspects in the application of the shell model (SM) are the construction of the effective valence-space interaction as well as corresponding effective operators and the solution of the eigenvalue problem in the model space of the valence nucleons.

Given recent advances in information technology and artificial intelligence, web-based education systems have became complementary and, in some cases, viable alternatives to traditional classroom teaching. The popularity of these systems stems from their ability to make education available to a large demographics (see MOOCs). However, existing systems do not take advantage of the personalization which becomes possible when web-based education is offered: they continue to be one-size-fits-all. In this paper, we aim to provide a first systematic method for designing a personalized web-based education system. Personalizing education is challenging: (i) students need to be provided personalized teaching and training depending on their contexts (e.g. classes already taken, methods of learning preferred, etc.), (ii) for each specific context, the best teaching and training method (e.g type and order of teaching materials to be shown) must be learned, (iii) teaching and training should be adapted online, based on the scores/feedback (e.g. tests, quizzes, final exam, likes/dislikes etc.) of the students. Our personalized online system, e-Tutor, is able to address these challenges by learning how to adapt the teaching methodology (in this case what sequence of teaching material to present to a student) to maximize her performance in the final exam, while minimizing the time spent by the students to learn the course (and possibly dropouts). We illustrate the efficiency of the proposed method on a real-world eTutor platform which is used for remedial training for a Digital Signal Processing (DSP) course.

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We compute the electric form factors of one-neutron halo nuclei with shallow D-wave states up to nextto-leading order and the E2 transition from the S-wave to the D-wave state up to leading order in Halo Effective Field Theory (Halo EFT). The relevant degrees of freedom are the core and the halo neutron. The EFT expansion is carried out in powers of R core /R halo , where R core and R halo denote the length scales of the core and the halo, respectively. We propose a power counting scenario for weakly-bound states in one-neutron Halo EFT and discuss its implications for higher partial waves in terms of universality. The scenario is applied to the 5 2 + first excited state and the 1 2 + ground state of 15 C. We obtain several universal correlations between electric observables and use data for the E2 transition 5 2 + → 1 2 + together with ab initio results from the No-Core Shell Model to predict the quadrupole moment.

We exploit the separation of scales in weakly-bound nuclei to compute E2 transitions and electric form factors in a Halo EFT framework. The relevant degrees of freedom are the core and the halo neutron. The EFT expansion is carried out in powers of R core /R halo , where R core and R halo denote the length scales of the core and halo, respectively. We include the strong s-wave and d-wave interactions by introducing dimer fields. The dimer propagators are regulated by employing the power divergence subtraction scheme and matched to the effective range expansion in the respective channel. Electromagnetic interactions are included via minimal substitution in the Lagrangian. We demonstrate that, depending on the observable and respective partial wave, additional local gauge-invariant operators contribute in LO, NLO and higher orders. * This work has been supported by Deutsche Forschungsgemeinschaft (SFB 1245).