From bcc to fcc: interplay between oscillating long-range and repulsive short-range forces

This paper supplements and partly extends an earlier publication, Phys. Rev. Lett. 95, 265501 (2005). In $d$-dimensional continuous space we describe the infinite volume ground state configurations (GSCs) of pair interactions \vfi and \vfi+\psi, where \vfi is the inverse Fourier transform of a nonnegative function vanishing outside the sphere of radius $K_0$, and $\psi$ is any nonnegative finite-range interaction of range $r_0\leq\gamma_d/K_0$, where $\gamma_3=\sqrt{6}\pi$. In three dimensions the decay of \vfi can be as slow as $\sim r^{-2}$, and an interaction of asymptotic form $\sim\cos(K_0r+\pi/2)/r^3$ is among the examples. At a dimension-dependent density $\rho_d$ the ground state of \vfi is a unique Bravais lattice, and for higher densities it is continuously degenerate: any union of Bravais lattices whose reciprocal lattice vectors are not shorter than $K_0$ is a GSC. Adding $\psi$ decreases the ground state degeneracy which, nonetheless, remains continuous in the open interval $(\rho_d,\rho_d')$, where $\rho_d'$ is the close-packing density of hard balls of diameter $r_0$. The ground state is unique at both ends of the interval. In three dimensions this unique GSC is the bcc lattice at $\rho_3$ and the fcc lattice at $\rho_3'=\sqrt{2}/r_0^3$.Comment: Published versio

Ground state at high density

Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and Likos et al. (2007). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state configurations of the penetrable sphere model particles are superposed on the sites of a close-packed lattice.Comment: Note adde

Peer-provided psychological intervention for Syrian refugees: results of a randomised controlled trial on the effectiveness of Problem Management Plus

Background: The mental health burden among refugees in high-income countries (HICs) is high, whereas access to mental healthcare can be limited. Objective: To examine the effectiveness of a peer-provided psychological intervention (Problem Management Plus; PM+) in reducing symptoms of common mental disorders (CMDs) among Syrian refugees in the Netherlands. Methods: We conducted a single-blind, randomised controlled trial among adult Syrian refugees recruited in March 2019-December 2021 (No. NTR7552). Individuals with psychological distress (Kessler Psychological Distress Scale (K10) >15) and functional impairment (WHO Disability Assessment Schedule (WHODAS 2.0) >16) were allocated to PM+ in addition to care as usual (PM+/CAU) or CAU only. Participants were reassessed at 1-week and 3-month follow-up. Primary outcome was depression/anxiety combined (Hopkins Symptom Checklist; HSCL-25) at 3-month follow-up. Secondary outcomes included depression (HSCL-25), anxiety (HSCL-25), post-traumatic stress disorder (PTSD) symptoms (PTSD Checklist for Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition; PCL-5), impairment (WHODAS 2.0) and self-identified problems (PSYCHLOPS; Psychological Outcomes Profiles). Primary analysis was intention-to-treat. Findings: Participants (n=206; mean age=37 years, 62% men) were randomised into PM+/CAU (n=103) or CAU (n=103). At 3-month follow-up, PM+/CAU had greater reductions on depression/anxiety relative to CAU (mean difference -0.25; 95% CI -0.385 to -0.122; p=0.0001, Cohen's d=0.41). PM+/CAU also showed greater reductions on depression (p=0.0002, Cohen's d=0.42), anxiety (p=0.001, Cohen's d=0.27), PTSD symptoms (p=0.0005, Cohen's d=0.39) and self-identified problems (p=0.03, Cohen's d=0.26), but not on impairment (p=0.084, Cohen's d=0.21). Conclusions: PM+ effectively reduces symptoms of CMDs among Syrian refugees. A strength was high retention at follow-up. Generalisability is limited by predominantly including refugees with a resident permit. Clinical implications: Peer-provided psychological interventions should be considered for scale-up in HICs