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In this work, I present closed-form formulas for the norm and many-body density matrices between general wave functions with exact particle numbers in pairing theory, using properties of the generalized Kronecker delta. These formulas, expressed as sums of minors and Pfaffians, apply to both even and odd particle-number systems and accommodate pair condensate as well as broken-pair configurations. This formalism directly facilitates applications in the generator coordinate method and symmetry restoration techniques, including angular momentum projection.

In this Technical Design Report (TDR) we describe the SABRE South detector to be built at the Stawell Underground Physics Laboratory (SUPL). The SABRE South detector is designed to test the long-standing DAMA/LIBRA signal of an annually modulating rate consistent with dark matter by using the same target material. SABRE South uses seven ultra-high purity NaI(Tl) crystals (with a total target mass of either 35 kg or 50 kg), hermetically sealed in copper enclosures that are suspended within a liquid scintillator active veto. High quantum efficiency and low background Hamamatsu R11065 photomultiplier tubes are directly coupled to both ends of the crystal, and enclosed with the crystal in an oxygen free high thermal conductivity copper enclosure. The active veto system consists of 11.6 kL of linear alkylbenzene (LAB) doped with a mixture of fluorophores and contained in a steel vessel, which is instrumented with at least 18 Hamamatsu R5912 photomultipliers. The active veto tags key radiogenic backgrounds intrinsic to the crystals, such as ${^{40}}$K, and is expected to suppress the total background by 27% in the 1-6 keV region of interest. In addition to the liquid scintillator veto, a muon veto is positioned above the detector shielding. This muon veto consists of eight EJ-200 scintillator modules, with Hamamatsu R13089 photomultipliers coupled to both ends. With an expected total background of 0.72 cpd/kg/keV, SABRE South can test the DAMA/LIBRA signal with 5$\sigma$ discovery or 3$\sigma$ exclusion after two years of data taking.

The persistence of the DAMA/LIBRA (DAMA) modulation over the past two decades has been a source of great contention within the dark matter community. The DAMA collaboration reports a persistent, modulating event rate within their setup of NaI(Tl) scintillating crystals at the INFN Laboratori Nazionali del Gran Sasso (LNGS) underground laboratory. A recent work alluded that this signal could have arisen due to an analysis artefact, caused by DAMA not accounting for time variation of decaying background radioisotopes in their analysis procedure. In this work, we examine in detail this 'induced modulation' effect, arguing that a number of aspects of the DAMA signal are incompatible with an induced modulation arising from decays of background isotopes over the lifetime of the experiment. Using a toy model of the DAMA/LIBRA experiment, we explore the induced modulation effect under different variations of the activities of the relevant isotopes - namely, $^3$H and $^{210}$Pb - highlighting the various inconsistencies between the resultant toy datasets and the DAMA signal. We stress the importance of the SABRE experiment, whose goal is to unambiguously test for the presence of such a modulating signal in an experiment using the same target material and comparable levels of background.

We have developed a hybrid code GMEC: Gyro-kinetic Magnetohydrodynamics (MHD) Energetic-particle Code that can numerically simulate energetic particle-driven Alfv\'en eigenmodes and energetic particle transport in tokamak plasmas. In order to resolve the Alfv\'en eigenmodes with high toroidal numbers effectively, the field-aligned coordinates and meshes are adopted. The extended MHD equations are solved with five-points finite difference method and fourth order Runge-Kutta method. The gyrokinetic equations are solved by particle-in-cell (PIC) method for the perturbed energetic particle pressures that are coupled into the MHD equations. Up to now, a simplified version of the hybrid code has been completed with several successful verifications including linear simulations of toroidal Alfv\'en eigenmodes and reversed shear Alfv\'en eigenmodes., Comment: 11 pages, 17 figures

A machine learning based surrogate model for fishbone linear instability in tokamaks is constructed. Hybrid simulations with the kinetic-magnetohydrodynamic (MHD) code M3D-K is used to generate the database of fishbone linear instability, through scanning the four key parameters which are thought to determine the fishbone physics. The four key parameters include (1) central total beta of both thermal plasma and fast ions, (2) the fast ion pressure fraction, (3) central value of safety factor $q$ and (4) the radius of $q=1$ surface. Four machine learning methods including linear regression, support vector machines (SVM) with linear kernel, SVM with nonlinear kernel and multi-layer perceptron are used to predict the fishbone instability, growth rate and real frequency, mode structure respectively. Among the four methods, SVM with nonlinear kernel performs very well to predict the linear instability with accuracy $\approx$95%, growth rate and real frequency with $R^2\approx$98%, mode structure with $R^2\approx$98%., Comment: 28 pages,19 figures

A new magnetohydrodynamics (MHD) code based on initial value approach, GMEC_I, has been developed for simulating various MHD physics in tokamak plasmas, as the MHD foundation of the gyrokinetic-MHD energetic particle simulation code (GMEC) family. GMEC_I solves multi-level reduced-MHD models that form a hierarchy of physics complexity, which provide conveniences for the cross-code verification and the identification of key physics effect in tokamak geometry. The field-aligned coordinates are used to represent mode structure efficiently. High-order finite difference methods are used for spatial discretization. The shifted metric methods are used for numerical stability. The discrete expansion forms of physics equations in the code are generated symbolically using the compile-time symbolic solver (CSS), which is specifically developed to reduce the complexity of the high-order finite difference form of the MHD equations. Advanced computational techniques have been implemented for optimizing memory access and code parallelization that show a good efficiency using both Thread Building Block (TBB) and Message Passing Interface (MPI). Benchmarks between GMEC_I and the eigenvalue code MAS are presented for ballooning modes without and with diamagnetic drift effects, and tearing modes, which show excellent agreements., Comment: 17 pages, 38 figures

An efficient numerical code FP3D has been developed to calculate particle orbits and evaluate particle confinement in 3D magnetic fields including stellarators and tokamaks with 3D fields. The magnetic field is either calculated from coils directly or obtained from equilibrium codes. FP3D has been verified with the 3D equilibrium code VMEC (S. P. Hirshman, Phys. Fluids 26, 3553 (1983)) for magnetic field calculation and with the drift-kinetic code SFINCS (M. Landreman, Physics of Plasmas 21 (4) (2014)) for neoclassical transport. The code has been applied successfully to the NCSX stellarator (B. Nelson, Fusion Engineering and design 66 (2003)) for the calculation of neoclassical transport coefficient with the 3D magnetic field obtained directly from coils. FP3D is also used to calculate ripple losses in the tokamak EAST (W. Yuanxi, Plasma Science Technology 8 (3) (2006))., Comment: 13 pages, 19 figures, submitted to Physics of Plasmas

The critical first step in the search for life on exoplanets over the next decade is to determine whether rocky planets transiting small M-dwarf stars possess atmospheres and, if so, what processes sculpt them over time. Because of its broad wavelength coverage and improved resolution compared to previous methods, spectroscopy with JWST offers a new capability to detect and characterize the atmospheres of Earth-sized, M-dwarf planets. Here we use JWST to independently validate the discovery of LHS 475b, a warm (586 K), 0.99 Earth-radius exoplanet, interior to the habitable zone, and report a precise 2.9-5.3 um transmission spectrum. With two transit observations, we rule out primordial hydrogen-dominated and cloudless pure methane atmospheres. Thus far, the featureless transmission spectrum remains consistent with a planet that has a high-altitude cloud deck (similar to Venus), a tenuous atmosphere (similar to Mars), or no appreciable atmosphere at all (akin to Mercury). There are no signs of stellar contamination due to spots or faculae. Our observations demonstrate that JWST has the requisite sensitivity to constrain the secondary atmospheres of terrestrial exoplanets with absorption features <50 ppm, and that our current atmospheric constraints speak to the nature of the planet itself, rather than instrumental limits., Comment: A co-first author paper Lustig-Yaeger and Fu et al., Nature Astronomy (2023), Comments welcome

Background: Computationally tractable models of atomic nuclei is a long-time goal of nuclear structure physics. A flexible framework which easily includes excited states and many-body correlations is the configuration-interaction shell model (SM), but the exponential growth of the basis means one needs an efficient truncation scheme, ideally one that includes both deformation and pairing correlations. Purpose: We propose an efficient truncation scheme of the SM: starting from a pair condensate variationally defined by Hartree-Fock single-particle states and the particle-number conserved Bardeen-Cooper-Schrieffer (NBCS) approximation, we carry out projection of states with good angular momentum. Methods: After generating Hartree-Fock single-particle states with Kramers degeneracy in a SM space, we optimize the pair amplitudes in the NBCS by minimizing the energy, and then use linear algebra projection (LAP) of states with good angular momentum. Both NBCS and LAP are computationally fast. Results: Our calculations yield good agreement with full configuration-interaction SM calculations for low-lying states of transitional and rotational nuclei with axially symmetric and triaxial deformation in medium- and heavy-mass regions: $^{44,46,48}$Ti, $^{48,50}$Cr, $^{52}$Fe, $^{60,62,64}$Zn, $^{66,68}$Ge, $^{68}$Se, and $^{108,110}$Xe. We predict low-lying states of $^{112-114}\textrm{Ba}$ and $^{116-120}\textrm{Ce}$, nuclei difficult to reach by large-scale SM calculations. Conclusions: Both pair correlation and the configuration mixing between different intrinsic states play a key role in reproducing collectivity and shape coexistence, demonstrating the utility of this truncation scheme of the SM to study transitional and deformed nuclei.

SABRE (Sodium iodide with Active Background REjection) is a direct detection dark matter experiment based on arrays of radio-pure NaI(Tl) crystals. The experiment aims at achieving an ultra-low background rate and its primary goal is to confirm or refute the results from the DAMA/LIBRA experiment. The SABRE Proof-of-Principle phase was carried out in 2020-2021 at the Gran Sasso National Laboratory (LNGS), in Italy. The next phase consists of two full-scale experiments: SABRE South at the Stawell Underground Physics Laboratory, in Australia, and SABRE North at LNGS. This paper focuses on SABRE South and presents a detailed simulation of the detector, which is used to characterise the background for dark matter searches including DAMA/LIBRA-like modulation. We estimate an overall background of 0.72 cpd/kg/keV$_{ee}$ in the energy range 1$-$6 keV$_{ee}$ primarily due to radioactive contamination in the crystals. Given this level of background and considering that the SABRE South has a target mass of 50 kg, we expect to exclude (confirm) DAMA/LIBRA modulation at $4~(5)\sigma$ within 2.5 years of data taking.

Elliott's SU(3) model is at the basis of the shell-model description of rotational motion in atomic nuclei. We demonstrate that SU(3) symmetry can be realized in a truncated shell-model space if constructed in terms of a sufficient number of collective $S$, $D$, $G$, $\dots$ pairs (i.e., with angular momentum zero, two, four, $\dots$) and if the structure of the pairs is optimally determined either by a conjugate-gradient minimization method or from a Hartree-Fock intrinsic state. We illustrate the procedure for 6 protons and 6 neutrons in the $pf$ ($sdg$) shell and exactly reproduce the level energies and electric quadrupole properties of the ground-state rotational band with $SDG$ ($SDGI$) pairs. The $SD$-pair approximation without significant renormalization, on the other hand, cannot describe the full SU(3) collectivity. A mapping from Elliott's fermionic SU(3) model to systems with $s$, $d$, $g$, $\dots$ bosons provides insight into the existence of a decoupled collective subspace in terms of $S$, $D$, $G$, $\dots$ pairs.

In this paper we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provides a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (denoted by $SDG$ pairs) reproduce the nuclear shape evolution in the $N=26$ isotones, $^{46}$Ca, $^{48}$Ti, $^{50}$Cr, and $^{52}$Fe, and yield good agreement with full configuration-interaction calculations of low-lying states in medium-heavy transitional and deformed nuclei: $^{44-48}$Ti, $^{48}$Cr, $^{50}$Cr, $^{52}$Fe, $^{60-64}$Zn, $^{64,66}$Ge, $^{84}$Mo, and $^{108-112}$Xe. Finally, using the $SDGI$-pair approximation we describe low-lying states of $^{112,114}$Ba, cases difficult to reach by conventional configuration-interaction methods.

The nucleon-pair approximation (NPA) can be a compact alternative to full configuration-interaction (FCI) diagonalization in nuclear shell-model spaces, but selecting good pairs is a long-standing problem. While seniority-based pairs work well for near-spherical nuclides, they do not work well for deformed nuclides with strong rotational bands. We propose an alternate approach. We show how one can write any Slater determinant for an even number of particles as a general pair condensate, from which one can project out pairs of good angular momentum. We implement this by generating unconstrained Hartree-Fock states in a shell model basis and extracting $S$, $D$, and $G$ pairs. The subsequent NPA calculations yield good agreement with FCI results using the same effective interactions., Comment: 7 pages, 4 figures

Large-scale shell-model calculations are carried out in the model space including neutron-hole orbitals $2p_{1/2}$, $1f_{5/2}$, $2p_{3/2}$, $0i_{13/2}$, $1f_{7/2}$ and $0h_{9/2}$ to study the structure and electromagnetic properties of neutron deficient Pb isotopes. An optimized effective interaction is used. Good agreement between full shell-model calculations and experimental data is obtained for the spherical states in isotopes $^{194-206}$Pb. The lighter isotopes are calculated with an importance-truncation approach constructed based on the monopole Hamiltonian. The full shell-model results also agree well with our generalized seniority and nucleon-pair-approximation truncation calculations. The deviations between theory and experiment concerning the excitation energies and electromagnetic properties of low-lying $0^+$ and $2^+$ excited states and isomeric states may provide a constraint on our understanding of nuclear deformation and intruder configuration in this region., Comment: 11 pages, to appear in PRC, supplementary materials available upon request

Remarkable progress has been made in diagnosing energetic particle instabilities on present-day machines and in establishing a theoretical framework for describing them. This overview describes the much improved diagnostics of Alfven instabilities and modelling tools developed world-wide, and discusses progress in interpreting the observed phenomena. A multi-machine comparison is presented giving information on the performance of both diagnostics and modelling tools for different plasma conditions outlining expectations for ITER based on our present knowledge., Comment: 37 pages, 20 figures

A study of the shape transition from spherical to axially deformed nuclei in the even Ce isotopes using the nucleon-pair approximation of the shell model is reported. As long as the structure of the dominant collective pairs is determined using a microscopic framework appropriate to deformed nuclei, the model is able to produce a shape transition. However, the resulting transition is too rapid, with nuclei that should be transitional being fairly well deformed, perhaps reflecting the need to maintain several pairs with each angular momentum., Comment: 7 pages, 5 figures

We investigate the correlation between integrated proton-neutron interactions obtained by using the up-to-date experimental data of binding energies and the $N_{\rm p} N_{\rm n}$, the product of valence proton number and valence neutron number with respect to the nearest doubly closed nucleus. We make corrections on a previously suggested formula for the integrated proton-neutron interaction. Our results demonstrate a nice, nearly linear, correlation between the integrated p-n interaction and $N_{\rm p} N_{\rm n}$, which provides us with a firm foundation of the applicability of the $N_{\rm p} N_{\rm n}$ scheme to nuclei far from the stability line., Comment: four pages, three figures, Physical Review C, in press

A method to probe the guiding characteristics of waveguides formed in real-time is proposed and evaluated. It is based on the analysis of the time dependent light distribution observed at the exit face of the waveguide while progressively altering its index profile and probed by a large diameter optical beam. A beam propagation method is used to model the observed dynamics. The technique is applied to retrieve the properties of soliton-induced waveguides.