Renormalizability of the nuclear many-body problem with the Skyrme interaction beyond mean field

Phenomenological effective interactions like Skyrme forces are currently used in mean--field calculations in nuclear physics. Mean--field models have strong analogies with the first order of the perturbative many--body problem and the currently used effective interactions are adjusted at the mean--field level. In this work, we analyze the renormalizability of the nuclear many--body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters could renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. For achieving renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.Comment: Revised versio

Second--order equation of state with the Skyrme interaction. Cutoff and dimensional regularization with the inclusion of rearrangement terms

We evaluate the second--order (beyond--mean--field) contribution to the equation of state of nuclear matter with the effective Skyrme force and use cutoff and dimensional regularizations to treat the ultraviolet divergence produced by the zero--range character of this interaction. An adjustment of the force parameters is then performed in both cases to remove any double counting generated by the explicit computation of beyond--mean--field corrections with the Skyrme force. In addition, we include at second order the rearrangement terms associated to the density--dependent part of the Skyrme force and discuss their effect. Sets of parameters are proposed to define new effective forces which are specially designed for second--order calculations in nuclear matter.Comment: 29 figures, 9 table

Evaluation of the effectiveness of a tailored mobile application in increasing the duration of wear of thermoplastic retainers: a randomized controlled trial.

This article has been accepted for publication in European Journal of Orthodontics Published by Oxford University PressBACKGROUND: The 'My Retainers' mobile application is a patient-informed intervention designed to enhance removable retainer wear and associated patient experiences during the retention phase. OBJECTIVES: To evaluate the effect of receiving the 'My Retainers' application on objectively assessed thermoplastic retainer (TPR) wear time, stability, periodontal outcomes, patient experiences, and knowledge related to retainers. MATERIALS AND METHODS: Eighty-four participants planned for removable retention with TPRs were assigned either to receive the 'My Retainers' application or to control not receiving electronic reminders during the 3-month period. Randomization was based on computer-generated random numbers and allocation was concealed using opaque, sealed envelopes. The primary outcome was objectively assessed retainer wear recorded using an embedded TheraMon® micro-electronic sensor. Secondary outcomes, including irregularity of the maxillary and mandibular incisors, plaque levels, bleeding on probing and probing depth, were assessed at baseline and 3-month follow-up; and analysed using a series of mixed models. Experiences and knowledge related to orthodontic retainers were recorded using questionnaires. The outcome assessor was blinded when possible. RESULTS: Receipt of the mobile application resulted in slightly higher median wear time (0.91 hours/day); however, this difference was not statistically significant (P = 0.56; 95% confidence interval [CI]: -2.19, 4.01). No significant differences were found between the treatment groups in terms of stability (P = 0.92; 95% CI: -0.03, 0.04), plaque levels (P = 0.44; 95% CI: -0.07, 0.03), bleeding on probing (P = 0.61; 95% CI: -0.05, 0.03) and probing depth (P = 0.79; 95% CI: -0.09, 0.07). Furthermore, similar levels of patient experiences (P = 0.94) and knowledge related to retainers (P = 0.26) were found. However, marginally better levels of knowledge were identified in the intervention group. No harms were observed. LIMITATIONS: A relatively short follow-up period with the study confined to a single-center in a university-based hospital. CONCLUSIONS: Provision of the bespoke 'My Retainers' application did not lead to an improvement in adherence with TPR wear over a 3-month follow-up period. Further refinement and research are required to develop and investigate means of enhancing adherence levels. CLINICAL REGISTRATION: NCT03224481.This work was supported by funding from the European Orthodontic Society. DA’s PhD is funded by the Saudi Arabian Cultural Bureau

Beyond mean-field calculations with the Skyrme interaction

International audienc

A beyond-mean-field example with zero–range effective interactions in infinite nuclear matter

Zero–range effective interactions are commonly used in nuclear physics to describe a many-body system in the mean-field framework. If they are employed in beyond-mean-field models, an artificial ultraviolet divergence is generated by the zero-range of the interaction. We analyze this problem in symmetric nuclear matter with the t0 – t3 Skyrme model. In this case, the second-order energy correction diverges linearly with the momentum cutoff Λ. After that, we extend the work to the case of nuclear matter with the full Skyrme interaction. A strong divergence (∼ Λ5) related to the velocity-dependent terms of the interaction is obtained. Moreover, a global fit can be simultaneously performed for both symmetric and nuclear matter with different neutron-to-proton ratios. These results pave the way for applications to finite nuclei in the framework of beyond mean-field theories

Beyond Mean-Field Theories with Zero-Range Effective Interactions: A Way to Handle the Ultraviolet Divergence

Zero-range effective interactions are commonly used in nuclear physics and in other domains to describe many-body systems within the mean-field model. If they are used within a beyond-mean-field framework, contributions to the total energy that display an ultraviolet divergence are found. We propose a general strategy to regularize this divergence and we illustrate it in the case of the second-order corrections to the equation of state (EOS) of uniform symmetric matter. By setting a momentum cutoff Λ, we show that for every (physically meaningful) value of Λ it is possible to determine a new interaction such that the EOS with the second-order corrections reproduces the empirical EOS, with a fit of the same quality as that obtained at the mean-field level

Microscopic theory of particle-vibration coupling

International audienceSome recent microscopic implementations of the particle-vibration coupling (PVC) theory for atomic nuclei are briefly reviewed. Within the nonrelativistic framework, the results seem to point to the necessity of fitting new effective interactions that can work beyond mean field. In keeping with this, the divergences which arise must be cured. A method is proposed, and the future perspectives that are opened are addressed