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We study the evolution of $K^{\pi}=6^{+}$ and $8^{-}$ two-quasiparticle (q.p.) configurations in the isotopic and isotonic chains of even-even deformed nuclei around $^{178}$Hf and their ability to describe series of observed $K$-isomer excitations within the framework of a Skyrme Hartree--Fock--BCS (SHFBCS) approach using SIII interaction and seniority pairing strengths with self-consistent blocking. We apply the approach along the prescription in [Phys. Rev. C {\bf 105}, 044329 (2022)] used to describe $K$-isomers in the actinide and transfermium mass regions. The calculations allow us to identify the regions where proton or neutron configurations or their mixture may be responsible for the $K$-isomer formation. The obtained results provide a detailed test for the Skyrme SIII interaction used and outline the limits of applicability of the overall SHFBCS approach in the regions of well deformed nuclei. The study suggests that similar systematic analysis can be implemented in the heavier mass regions whenever enough data are available., Comment: 10 pages, 4 figures, 2 tables

We discuss a test of a recently proposed approach to determine average pairing matrix elements within a given interval of single-particle states (sp) around the Fermi level $\lambda$ as obtained in the so-called uniform gap method (UGM). It takes stock of the crucial role played by the averaged sp level density $\tilde{\rho}(e)$. These matrix elements are deduced within the UGM approach, from microscopically calculated $\tilde{\rho}(e)$ and gaps obtained from analytical formulae of a semi-classical nature. Two effects generally ignored in similar fits have been taken care of. They are: (a) the correction for a systematic bias in choosing to fit pairing gaps corresponding to equilibrium deformation solutions as discussed by M\"{o}ller and Nix [Nucl. Phys. A 476, 1 (1992)] and (b) the correction for a systematic spurious enhancement of $\tilde{\rho}(e)$ for protons in the vicinity of $\lambda$, because of the local Slater approximation used for the treatment of the Coulomb exchange terms in most calculations (see e.g. [Phys. Rev C 84, 014310 (2011)]). This approach has been deemed to be very efficient upon performing Hartree-Fock + BCS (with seniority force and self-consistent blocking when dealing with odd nuclei) calculations of a large sample of well and rigidly deformed even-even rare-earth nuclei. The reproduction of their experimental moments of inertia has been found to be at least of the same quality as what has been obtained in a direct fit of these data [Phys. Rev C 99, 064306 (2019)]. We extend here the test of our approach to the reproduction, in the same region, of three-point odd-even mass differences centered on odd-$N$ or odd-$Z$ nuclei. The agreement with the data is again roughly of the same quality as what has been obtained in a direct fit, as performed in [Phys. Rev C 99, 064306 (2019)]., Comment: 3 tables, submitted to Chinese Physics C

We explore the effects on nuclear bulk properties of using regularization cutoffs larger than the nucleon mass within the chiral effective field theory with a power counting that ensures order-by-order renormalization in the two-nucleon system. To do so we calculate ground-state properties of the $^{16}$O nucleus in the Hartree--Fock approach in a basis made up of plane waves confined in a cube. We find that regularization cutoff effects manifest themselves in two distinct ways: a strong sensitivity to the the counter-terms in attractive singular partial waves (related to the sign of the corresponding low-energy constant) and to the correction for spurious deeply bound states (for high enough cutoffs). In fact the latter happens to deprive the Hartree--Fock approximation of yielding bound solutions in nuclei. We conclude that, when using a leading-order chiral potential in the Nogga--Timmermans--van Kolck's power counting (with a regularization cutoff higher than the nucleon mass), one cannot produce a selfconsistent mean field free of spurious bound-state effects that can serve as a reference state for beyond-mean-field methods. For high regularization cutoffs which yield an attractive $^3S_1$ contact potential, one can at best incorporate in the mean-field solution a partial correction for spurious bound states. Then the remaining correction has to be added to the residual interaction in a treatment beyond the Hartree--Fock approximation. In fact a ``full'' correction in the $^3D_2$ channel, with energy shifts of the order of or somewhat larger than those recommended in Phys. Rev. C 103, 054304 (2021), is possible., Comment: Resubmitted to Physical Review C. Thoroughly revised version

Two fits of the pairing residual interaction in the rare-earth region are independently performed. One is made on the odd-even staggering of masses by comparing measured and explicitly calculated three-point binding-energy differences centered on odd-even nuclei. Another deals with the moments of inertia of the first 2+ states of well deformed even-even nuclei upon comparing experimental data with the results of Inglis-Belyaev moments (supplemented by a crude estimate of the so-called Thouless-Valatin corrections). The sample includes 24 even-even and 31 odd-mass nuclei selected according to two criteria: they should have good rotor properties and should not correspond to low pairing-correlation regimes in their ground states. Calculations are performed in the self-consistent Hartree-Fock plus BCS framework (implementing a self-consistent blocking in the case of odd-mass nuclei). The Skyrme SIII parametrization is used in the particle-hole channel and the fitted quantities are the strengths of |Tz|=1 proton and neutron seniority residual interactions. As a result, the two fits yield sets of strengths in excellent agreement: about 0.1% for the neutron parameters and 0.2% for protons. In contrast when one performs such a fit on odd-even staggering from quantities deduced from BCS gaps or minimal quasiparticle energies in even-even nuclei, as is traditional, one obtains results significantly different from those obtained in the same nuclei by a fit of moments of inertia. As a conclusion, beyond providing a phenomenological tool for microscopic calculations in this region, we have illustrated the proposition made in the seminal paper of Bohr, Mottelson and Pines that moments of inertia and odd-even staggering in selected nuclei were excellent measuring sticks of nuclear pairing correlations., Comment: Accepted for publication in Physical Review C

Background: Fission barriers of actinide nuclei have been mostly and for long been microscopi- cally calculated for even-even fissioning systems. Calculations in the case of odd nuclei have been performed merely within a so-called equal-filling approximation (EFA) as opposed to an approach taking explicitly into account the time reversal breaking properties at the mean field level- and for only one single-particle configuration. Purpose: We study the dependence of the fission barriers on various relevant configurations (e.g. to evaluate the so-called specialization energy). Besides, we want to assess the relevance as a func- tion of the deformation of the EFA approach which has been already found out at ground state deformation. Methods: Calculations within the Hartree-Fock plus BCS with self-consistent particle blocking have been performed using the SkM* Skyrme effective interaction in the particle-hole channel and a seniority force in the particle-particle channel. Axial symmetry has been imposed throughout the whole fission path while the intrinsic parity symmetry has been allowed to be broken in the outer fission barrier region. Results: Potential energy curves have been determined for six different configurations in U-235 and four in Pu-239. Inner and outer fission barriers have been calculated along with some spectroscopic properties in the fission isomeric well. These results have been compared with available data. The influence of time-reversal breaking mean fields on the solutions has been investigated. Conclusions: A sizeable configuration dependence of the fission barrier (width and height) has been demonstrated. A reasonable agreement with available systematic evaluations of fission barrier heights has been found. The EFA approach has been validated at the large elongations occurring at the outer barrier region., Comment: 25 pages, 11 figures, accepted for publication in PRC

Two systematic sources of error in most current microscopic evaluations of fission-barrier heights are studied. They are concerned with an approximate treatment of the Coulomb exchange terms (known as the Slater approximation) in the self-consistent mean fields and the projection on good parity states (e.g., of positive parity for the spontaneous fission of an even-even nucleus) of left-right reflection asymmetric intrinsic solutions (e.g., around the second barrier). Approximate or unprojected solutions are shown to lead each to an underestimation of the barrier heights by a few hundred keV.

The restoration of the parity symmetry has been performed in the framework of the Highly Truncated Diagonalization Approach suited to treat correlations in an explicitly particle-number conserving microscopic approach. To do so we have assumed axial symmetry and used a generalized Wick's theorem due to L\"owdin in a projection-after-variation scheme. We have chosen the Skyrme SkM$^*$ energy-density functional for the particle-hole channel and a density-independent delta force for the residual interaction. We have applied this approach in the region of the outer fission barrier of the $^{240}$Pu nucleus. As a result, we have shown that the $K^{\pi} = 0^+$ fission isomeric state is statically unstable against intrinsic-parity breaking modes, while the projection does not affect the energy at the top of the intrinsic outer fission barrier. Altogether, this leads to an increase of the height of the outer fission barrier--with respect to the fission isomeric state--by about 350 keV, affecting thus significantly the fission-decay lifetime of the considered fission isomer.

Due to the non-linearity of Hertzian contacts, the speed of sound in granular matter increases with pressure. Under gravity, the non-linear elastic description predicts that acoustic propagation is only possible through surface modes, called Rayleigh-Hertz modes and guided by the index gradient. Here we directly evidence these modes in a controlled laboratory experiment and use them to probe the elastic properties of a granular packing under vanishing confining pressure. The shape and the dispersion relation of both transverse and sagittal modes are compared to the prediction of non-linear elasticity that includes finite size effects. This allows to test the existence of a shear stiffness anomaly close to the jamming transition., Comment: 4 pages 4 figures

We show here that the standard physical model used by Vriend et al. to analyse seismograph data, namely a non-dispersive bulk propagation, does not apply to the surface layer of sand dunes. According to several experimental, theoretical and field results, the only possible propagation of sound waves in a dry sand bed under gravity is through an infinite, yet discrete, number of dispersive surface modes. Besides, we present a series of evidences, most of which have already been published in the literature, that the frequency of booming avalanches is not controlled by any resonance as argued in this article. In particular, plotting the data provided by Vriend et al. as a table, it turns out that they do not present any correlation between the booming frequency and their estimate of the resonant frequency., Comment: 7 pages, 8 figures, 2 Tables see also the movie: http://www.pmmh.espci.fr/fr/morphodynamique/Booming.mov

We calculate the isospin-mixing parameter for several Tz=-1, Tz=0 and Tz=1 nuclei from Mg to Sn in the particle-number conserving Higher Tamm-Dancoff approach taking into account the pairing correlations. In particular we investigate the role of the Coulomb interaction and the |Tz|=1 pairing correlations. To do so the HTDA approach is implemented with the SIII Skyrme effective nucleon-nucleon interaction in the mean-field channel and a delta interaction in the pairing channel. We conclude from this investigation that the pairing correlations bring a large contribution to isospin-symmetry breaking, whereas the Coulomb interaction turns out to play a less important role. Moreover we find that the isospin-mixing parameters for Tz=-1 and Tz=1 nuclei are comparable while they are about twice as large for Tz=0 nuclei (between 3% and 6%, including doubly magic nuclei)., Comment: 13 pages, 7 figures, 3 tables; submitted to Physical Review C

We calculate the ground-state properties of well deformed, even-even N=Z nuclei in the region between Ni-56 and Sn-100 within two different approaches, focusing on the binding energy and deformation and pairing properties. First, we employ the Hartree-Fock-BCS (HFBCS) approximation with the Skyrme effective nucleon-nucleon interaction and discuss how the results depend on the parameterization of the interaction and on the pairing force parameters adjusted in various schemes to reproduce the experimental odd-even mass differences. Then, within the Higher Tamm-Dancoff Approximation (HTDA), which explicitly conserves the particle number, we calculate the same properties starting from the HFBCS solutions. The HTDA treatment of the ground-state correlations is converged within a n-particle-n-hole expansion using up to n=4 particle-hole excitations of the pair type (in the sense of Cooper pairs). We compare the ground-state properties calculated in these two descriptions of pairing correlations and deduce the importance of the particle-number conservation in weak pairing regimes. Finally, we extend the HTDA calculations so as to include the proton-neutron residual interaction and investigate the role of proton-neutron pairing on the above ground-state properties., Comment: 12 pages, 3 figures, 11 tables, submitted to Physical Review C

A static microscopic study of potential-energy surfaces within the Skyrme-Hartree-Fock-plus-BCS model is carried out for the 256Fm and 258Fm isotopes with the goal of deducing some properties of spontaneous fission. The calculated fission modes are found to be in agreement with the experimentaly observed asymmetric-to-symmetric transition in the fragment-mass distributions and with the high- and low-total-kinetic-energy modes experimentally observed in 258Fm. Most of the results are similar to those obtained in macroscopic-microscopic models as well as in recent Hartree-Fock-Bogolyubov calculations with the Gogny interaction, with a few differences in their interpretations. In particular an alternative explanation is proposed for the low-energy fission mode of 258Fm., Comment: 14 pages, 11 figures, 3 tables, submitted to Phys. Rev. C

Due to the non-linearity of Hertzian contacts, the speed of sound $c$ in granular matter is expected to increase with pressure as $P^{1/6}$. A static layer of grains under gravity is thus stratified so that bulk waves are refracted toward the surface. We investigate wave propagation in the framework of an elastic description taking into account the main features of granular matter: non-linearity between stress and strain and existence of a yielding transition. We show in this context the existence of waves localised at the free surface --~like Rayleigh waves~-- but with a wave guide effect related to the non-linear Hertz contact. The dispersion relationship shows a discrete number of modes which correspond to modes localized in the sagittal plane but also to transverse modes. The propagation speed of these waves is finally compared to recent measurements performed in the field, at the surface of a sand dune., Comment: 9 pages and 8 figures submitted to Phys. Rev.E