Compression modes in nuclei: microscopic models with Skyrme interactions

The isoscalar giant monopole resonances (ISGMR) and giant dipole resonances (ISGDR) in medium-heavy nuclei are investigated in the framework of HF+RPA and HF-BCS+QRPA with Skyrme effective interactions. It is found that pairing has little effect on these modes. It is also found that the coupling of the RPA states to 2p-2h configurations results in about (or less than) 1 MeV shifts of the resonance energies and at the same time gives the correct total widths. For the ISGMR, comparison with recent data leads to a value of nuclear matter compression modulus close to 215 MeV. However, a discrepancy between calculated and measured energies of the ISGDR in $^{208}$Pb is found and remains an open problem.Comment: To appear in: ``RIKEN Symposium and Workshop on Selected Topics in Nuclear Collective Excitations'', proceedings of the meeting, RIKEN, Wako city (Japan), March 20--24, 199

On local scale symmetry in Riemann, Weyl and Riemann-Cartan geometry based gravitational theories and the role of the Noether current

In this paper, we delve into the significance of local scale symmetry and the role of the associated Noether current, within Riemann, Weyl and Riemann-Cartan geometry based gravitational theories. Our primary emphasis lies in conformal coupling scalar gravitational theories and pure quadratic curvature theories, wherein we examine the circumstances under which these can exhibit a local scale symmetry. We show that local scale symmetry is associated with vanishing Noether current whenever there are not new propagating (gravitational) degrees of freedom beyond the two polarizations of the massless graviton. In contrast, in local scale invariant theories where there are more than two propagating gravitational degrees of freedom, local scale symmetry is associated with nonvanishing Noether current.Comment: 15 page

Autonomous detection and ascent of a step for an electric wheelchair

With the number of individuals using a wheelchair on the rise, the issue of removing architectural barriers, or at least overcoming them, has to be faced to improve independence, inclusiveness, and participation of wheelchair users. Some electric wheelchairs can climb and descend stairs and obstacles, however, the actual operations required to do so safely may be complex and may require an experienced or trained user. To overcome this issue, a method to first detect and classify a step and then autonomously climb it safely is proposed here. The same method is then applied and tested on an actual stair-climbing wheelchair prototype to prove its reliability in different conditions

The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single particle levels of a potential well (mean field) and interacting through a pairing force. The associated solutions of the Richardson's equations are classified in terms of a number $v_l$, which reduces to the seniority $v$ in the limit of large values of the pairing strength $G$ and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the $G\to\infty$ limit. We express analytically, through the moments of the single particle levels distribution, the collective mode energy and the two critical values $G_{\rm cr}^{+}$ and $G_{\rm cr}^{-}$ of the coupling which can exist on a single particle level with no pair degeneracy. Notably $G_{\rm cr}^{+}$ and $G_{\rm cr}^{-}$ merge when the number of single particle levels goes to infinity, where they coincide with the $G_{\rm cr}$ (when it exists) of a one pair system, not envisioned by the Richardson theory. In correspondence of $G_{\rm cr}$ the system undergoes a transition from a mean field to a pairing dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes finding out that the former, for $G>G_{\rm cr}^{-}$, come close to the BCS predictions, whereas the latter display a divergence at $G_{\rm cr}$, signaling the onset of a long range off-diagonal order in the system.Comment: 35 pages, 6 figures, 2 tables, to be published in EPJ