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Superconducting sensors doped with rare isotopes have recently demonstrated powerful sensing performance for sub-keV radiation from nuclear decay. Here, we report the first high-resolution recoil spectroscopy of a single, selected nuclear state using superconducting tunnel junction (STJ) sensors. The STJ sensors were used to measure the eV-scale nuclear recoils produced in $^7$Be electron capture decay in coincidence with a 478 keV $\gamma$-ray emitted in decays to the lowest-lying excited nuclear state in $^7$Li. Details of the Doppler broadened recoil spectrum depend on the slow-down dynamics of the recoil ion. The measured spectral broadening is compared to empirical stopping power models as well as modern molecular dynamics simulations at low energy. The results have implications in several areas from nuclear structure and stopping powers at eV-scale energies to direct searches for dark matter, neutrino mass measurements, and other physics beyond the standard model.

The BeEST experiment is a precision laboratory search for physics beyond the standard model that measures the electron capture decay of $^7$Be implanted into superconducting tunnel junction (STJ) detectors. For Phase-III of the experiment, we constructed a continuously sampling data acquisition system to extract pulse shape and timing information from 16 STJ pixels offline. Four additional pixels are read out with a fast list-mode digitizer, and one with a nuclear MCA already used in the earlier limit-setting phases of the experiment. We present the performance of the data acquisition system and discuss the relative advantages of the different digitizers., Comment: 8 pages, 4 figures, proceedings for The 20th International Conference on Low Temperature Detectors

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy. In the proposed experiment, the $\mu$p atom is excited by a laser pulse from the singlet to the triplet hyperfine sub-levels, and is quenched back to the singlet state by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after this cycle modifies the $\mu$p atom diffusion in the hydrogen gas and the arrival time of the $\mu$p atoms at the target walls. This laser-induced modification of the arrival times is used to expose the atomic transition. In this paper we present the simulation of the $\mu$p diffusion in the H$_2$ gas which is at the core of the experimental scheme. These simulations have been implemented with the Geant4 framework by introducing various low-energy processes including the motion of the H$_2$ molecules, i.e. the effects related with the hydrogen target temperature. The simulations have been used to optimize the hydrogen target parameters (pressure, temperatures and thickness) and to estimate signal and background rates. These rates allow to estimate the maximum time needed to find the resonance and the statistical accuracy of the spectroscopy experiment., Comment: Submission to SciPost

Ongoing experimental efforts to measure with unprecedented precision electron-capture probabilities challenges the current theoretical models. The short range of the weak interaction necessitates an accurate description of the atomic structure down to the nucleus region. A recent electron-capture modeling has been modified in order to test the influence of three different atomic descriptions on the decay and shaking probabilities. To this end, a specific atomic modeling was developed in the framework of the relativistic density-functional theory, exploring several exchange-correlation functionals and self-interaction-corrected models. It was found that the probabilities of total shaking, tested on both photoionization and electron-capture processes, depend strongly on the accuracy of the atomic modeling. Predictions of capture probabilities have been compared with experimental values evaluated from available published data for different radionuclides from $^{7}$Be to $^{138}$La. New high-precision measurements are strongly encouraged because the accuracy of the current experimental values is insufficient to test the models beyond the inner shells., Comment: 36 pages, 7 figures and 3 tables

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with $2\times10^{-4}$ relative accuracy. In the proposed experiment, the $\mu$p atom undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, {then} is quenched back to the singlet state by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after the collisional deexcitation is used as a signature of a successful laser transition between hyperfine states. In this paper, we calculate the combined probability that a $\mu$p atom initially in the singlet hyperfine state undergoes a laser excitation to the triplet state followed by a collisional-induced deexcitation back to the singlet state. This combined probability has been computed using the optical Bloch equations including the inelastic and elastic collisions. Omitting the decoherence effects caused by {the laser bandwidth and }collisions would overestimate the transition probability by more than a factor of two in the experimental conditions. Moreover, we also account for Doppler effects and provide the matrix element, the saturation fluence, the elastic and inelastic collision rates for the singlet and triplet states, and the resonance linewidth. This calculation thus quantifies one of the key unknowns of the HFS experiment, leading to a precise definition of the requirements for the laser system and to an optimization of the hydrogen gas target where $\mu$p is formed and the laser spectroscopy will occur., Comment: 21 pages, 4 figures

The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to foresee, if possible, the future evolution, or, at least, the challenges identified in the scope of advanced research works. This paper gives a vision about the directions for further research as well as some open problems of FC. A number of topics in mathematics, numerical algorithms and physics are analyzed, giving a systematic perspective for future research., Comment: 3 figures

In this article we propose a shooting algorithm for partially-affine optimal control problems, this is, systems in which the controls appear both linearly and nonlinearly in the dynamics. Since the shooting system generally has more equations than unknowns, the algorithm relies on the Gauss-Newton method. As a consequence, the convergence is locally quadratic provided that the derivative of the shooting function is injective and Lipschitz continuous at the optimal solution. We provide a proof of the convergence for the proposed algorithm using recently developed second order sufficient conditions for weak optimality of partially-affine problems. We illustrate the applicability of the algorithm by solving an optimal treatment-vaccination epidemiological problem.

The evolution of the traditional nuclear magic numbers away from the valley of stability is an active field of research. Experimental efforts focus on providing key spectroscopic information that will shed light into the structure of exotic nuclei and understanding the driving mechanism behind the shell evolution. In this work, we investigate the Z = 6 spin-orbit shell gap towards the neutron dripline. To do so, we employed $^{A}$N(p,2p)$^{A-1}$C quasi-free scattering reactions to measure the proton component of the 2$^+_1$ state of $^{16,18,20}$C. The experimental findings support the notion of a moderate reduction of the proton 1p$_{1/2}$-1p$_{3/2}$ spin-orbit splitting, at variance to recent claims for a prevalent Z = 6 magic number towards the neutron dripline., Comment: 27 pages, 5 figures, 2 tables. Submitted to Physics Letter B

In this paper, we deal with the global exact controllability to the trajectories of the Boussinesq system. We consider 2D and 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier slip-with-friction boundary condition and a Robin boundary condition is imposed to the temperature. We assume that one can act on the velocity and the temperature on an arbitrary small part of the boundary. The proof relies on three main arguments. First, we transform the problem into a distributed controllability problem by using a domain extension procedure. Then, we prove a global approximate controllability result by following the strategy of Coron et al [J. Eur. Math. Soc., 22 (2020), pp. 1625-1673], which deals with the Navier-Stokes equations. This part relies on the controllability of the inviscid Boussinesq system and asymptotic boundary layer expansions. Finally, we conclude with a local controllability result that we establish with the help of a linearization argument and appropriate Carleman estimates., Comment: 48 pages

Phenomena such as state-swap, quadrature squeezing, entanglement and violation of entanglement inequalities are frequently reported to occur in quantum systems only. It is shown here that these effects can also occur in cholesteric liquid crystals in the presence of an applied magnetic field. The nature of these effects as well as the conditions for their observation are analysed., Comment: Correction: due to a sign error, the potential in the previous version was minimised around a maximum instead of a minimum. This is corrected in the current version. To be able to observe the same effects, cholesteric liquid crystals were considered instead of plain nematics. Figures depicting the potential and the effects of squeezing were added. 17 pages, 4 figures

We consider an electromechanical system where a microwave cavity is coupled to a mechanical resonator, with a mechanical frequency twice the microwave frequency. In this regime, the effective photon-phonon interaction is equivalent to that of a degenerate parametric amplifier, instead of the typical radiation pressure interaction. If the mechanical resonator is strongly driven, it undergoes a phase transition to a state where the energy pumped into the mechanical mode is entirely converted to the photonic mode. Quantum fluctuations smear this phase transition. We describe these effects with a steady-state Fokker-Planck equation in the complex P-representation, and compute the photonic field intensity and quadrature variances, as well as the mechanical amplitude. This Fokker-Planck method performs better than the standard linearization results, when compared to numerical simulations., Comment: 8 pages, 8 figures

Precision spectroscopy of light muonic atoms provides unique information about the atomic and nuclear structure of these systems and thus represents a way to access fundamental interactions, properties and constants. One application comprises the determination of absolute nuclear charge radii with unprecedented accuracy from measurements of the 2S$\,$-$\,$2P Lamb shift. Here, we review recent results of nuclear charge radii extracted from muonic hydrogen and helium spectroscopy and present experiment proposals to access light muonic atoms with $Z \geq 3$. In addition, our approaches towards a precise measurement of the Zemach radii in muonic hydrogen ($\mu$p) and helium ($\mu$$^{3}$He$^{+}$) are discussed. These results will provide new tests of bound-state quantum-electrodynamics in hydrogen-like systems and can be used as benchmarks for nuclear structure theories., Comment: 17 pages, 8 figures

We analyze quantum effects occurring in optomechanical systems where the coupling between an optical mode and a mechanical mode is quadratic in displacement (membrane-in-the-middle geometry). We show that it is possible to observe quantum effects in these systems without achieving the single-photon strong coupling regime. We find that zero-point energy causes a mechanical frequency shift, and we propose an experimental way to measure it. Further, we show that it is possible to determine the phonon statistics from the cavity transmission, and propose a way to infer the resonator's temperature based on this feature. For completeness, we revisit the case of an isolated system and show that different types of mechanical quantum states can be created, depending on the initial cavity state. In this situation, mechanical motion undergoes collapse and revivals, and we compute the collapse and revival times, as well as the degree of squeezing., Comment: 7 pages, 6 figures, 2nd version

Sideband asymmetry in cavity optomechanics has been explained by particle creation and annihilation processes, which bestow an amplitude proportional to 'n+1' and 'n' excitations to each of the respective sidebands. We discuss the issues with this as well as other interpretations, such as quantum backaction and noise interference, and show that the asymmetry is due to the optomechanical damping caused by the probe and the cooling lasers instead., Comment: difference from previous version: small edits from the review process

The emission of neutron pairs from the neutron-rich $N\!=\!12$ isotones $^{18}$C and $^{20}$O has been studied by high-energy nucleon knockout from $^{19}$N and $^{21}$O secondary beams, populating unbound states of the two isotones up to 15~MeV above their two-neutron emission thresholds. The analysis of triple fragment-$n$-$n$ correlations shows that the decay $^{19}$N$(-1p)^{18}$C$^*\!\rightarrow^{16}$C+$n$+$n$ is clearly dominated by direct pair emission. The two-neutron correlation strength, the largest ever observed, suggests the predominance of a $^{14}$C core surrounded by four valence neutrons arranged in strongly correlated pairs. On the other hand, a significant competition of a sequential branch is found in the decay $^{21}$O$(-1n)^{20}$O$^*\!\rightarrow^{18}$O+$n$+$n$, attributed to its formation through the knockout of a deeply-bound neutron that breaks the $^{16}$O core and reduces the number of pairs., Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev. Lett

We performed a reference-free measurement of the transition energies of the $1s 2p\,^1P\_1\to 1s^2 \,^1S\_0$ line in He-like argon, and of the $1s 2s^2 2p\,^1P\_1\to 1s^2 2s^2\,^1S\_0$ line in Be-like argon ions. The highly-charged ions were produced in the plasma of an Electron-Cyclotron Resonance Ion Source. Both energy measurements were performed with an accuracy better than 3 parts in $10^6$, using a double flat-crystal spectrometer, without reference to any theoretical or experimental energy. The $1s 2s^2 2p\,^1P\_1\to 1s^2 2s^2\,^1S\_0$ transition measurement is the first reference-free measurement for this core-excited transition. The $1s 2p\,^1P\_1\to 1s^2 \,^1S\_0$ transition measurement confirms recent measurement performed at the Heidelberg Electron-Beam Ion Trap (EBIT). The width measurement in the He-like transition provides test of a purely radiative decay calculations. In the case of the Be-like argon transition, the width results from the sum of a radiative channel and three main Auger channels. We also performed Multiconfiguration Dirac-Fock (MCDF) calculations of transition energies and rates and have done an extensive comparison with theory and other experimental data. For both measurements reported here, we find agreement with the most recent theoretical calculations within the combined theoretical and experimental uncertainties.

Background: Odd-odd nuclei, around doubly closed shells, have been extensively used to study proton-neutron interactions. However, the evolution of these interactions as a function of the binding energy, ultimately when nuclei become unbound, is poorly known. The $^{26}$F nucleus, composed of a deeply bound $\pi0d\_{5/2}$ proton and an unbound $\nu0d\_{3/2}$ neutron on top of an $^{24}$O core, is particularly adapted for this purpose. The coupling of this proton and neutron results in a $J^{\pi} = 1^{+}\_1 - 4^{+}\_1$ multiplet, whose energies must be determined to study the influence of the proximity of the continuum on the corresponding proton-neutron interaction. The $J^{\pi} = 1^{+}\_1, 2^{+}\_1,4^{+}\_1$ bound states have been determined, and only a clear identification of the $J^{\pi} =3^{+}\_1$ is missing.Purpose: We wish to complete the study of the $J^{\pi} = 1^{+}\_1 - 4^{+}\_1$ multiplet in $^{26}$F, by studying the energy and width of the $J^{\pi} =3^{+}\_1$ unbound state. The method was firstly validated by the study of unbound states in $^{25}$F, for which resonances were already observed in a previous experiment.Method: Radioactive beams of $^{26}$Ne and $^{27}$Ne, produced at about $440A$\,MeV by the FRagment Separator at the GSI facility, were used to populate unbound states in $^{25}$F and $^{26}$F via one-proton knockout reactions on a CH$\_2$ target, located at the object focal point of the R$^3$B/LAND setup. The detection of emitted $\gamma$-rays and neutrons, added to the reconstruction of the momentum vector of the $A-1$ nuclei, allowed the determination of the energy of three unbound states in $^{25}$F and two in $^{26}$F. Results: Based on its width and decay properties, the first unbound state in $^{25}$F is proposed to be a $J^{\pi} = 1/2^-$ arising from a $p\_{1/2}$ proton-hole state. In $^{26}$F, the first resonance at 323(33)~keV is proposed to be the $J^{\pi} =3^{+}\_1$ member of the $J^{\pi} = 1^{+}\_1 - 4^{+}\_1$ multiplet. Energies of observed states in $^{25,26}$F have been compared to calculations using the independent-particle shell model, a phenomenological shell-model, and the ab initio valence-space in-medium similarity renormalization group method.Conclusions: The deduced effective proton-neutron interaction is weakened by about 30-40\% in comparison to the models, pointing to the need of implementing the role of the continuum in theoretical descriptions, or to a wrong determination of the atomic mass of $^{26}$F., Comment: 14 pages, 7 figures, 3 tables, submitted to PRC

Plastic scintillators detectors (PSDs) have been studied as dosimeters, since they provide a cost-effective alternative to conventional ionization chambers. Measurement and analysis of energy dependency were performed on a Siemens Mammomat tomograph for two different peak kilovoltages: 26 kV and 35 kV. Both PSD displayed good linearity for each energy considered and almost no energy dependence., Comment: 5 pages, 3 figures, 1 table