Dynamic spin-orbit interaction of heavy ions in semiclassical calculations of elastic scattering

Experimental results of the 1st rank analyzing power for elastic scattering of⁶Li and⁷Li could be only understood when including coupling to inelastic channels in the calculations. This finding — established for some time — yet presents some open questions regarding the energy dependence of the spin and polarization effects. Semiclassical calculations presented here might clarify the relevant physical background of the earlier quantummechanically exact results.     

In Situ Topochemical Transformation of ZnIn2S4 for Efficient Photocatalytic Oxidation of 5-Hydroxymethylfurfural to 2,5-Diformylfuran

Photocatalytic selective oxidation of 5-hydroxymethylfurfural (HMF) coupled H₂ production offers a promising approach to producing valuable chemicals. Herein, an efficient in situ topological transformation tactic is developed for producing porous O-doped ZnIn₂S₄ nanosheets for HMF oxidation cooperative with H₂ evolution. Aberration-corrected high-angle annular dark-field scanning TEM images show that the hierarchical porous O-ZIS-120 possesses abundant atomic scale edge steps and lattice defects, which is beneficial for electron accumulation and molecule adsorption. The optimal catalyst (O-ZIS-120) exhibits remarkable performance with 2,5-diformylfuran (DFF) yields of 1624 µmol h⁻¹ g⁻¹ and the selectivity of >97%, simultaneously with the H₂ evolution rate of 1522 µmol h⁻¹ g⁻¹. Mechanistic investigations through theoretical calculations show that O in the O-ZIS-120 lattice can reduce the oxidation energy barrier of hydroxyl groups of HMF. In situ attenuated total reflection surface-enhanced infrared absorption spectroscopy (ATR-SEIRAS) results reveal that DFF^* (C₄H₂(CHO)₂O^*) intermediate has a weak interaction with O-ZIS-120 and desorb as the final product. This study elucidates the topotactic structural transitions of 2D materials simultaneously with electronic structure modulation for efficient photocatalytic DFF production.     

Scavenging of “Dead Sulfur” and “Dead Lithium” Revealed by Integrated–Heterogeneous Catalysis for Advanced Lithium–Sulfur Batteries

The simultaneous engineering of sulfur cathode and Li anode is critical for electrolyte-starved high energy density Li–S batteries, in which slow electrochemical conversions and side chemical reactions of dead sulfur are found to be the determining factors in limiting the sulfur utilization, corresponding to the poor reversible capacity of Li–S batteries. Herein, this work challenges the conventional wisdom of heterogeneous and homogeneous catalyses in Li–S batteries and proposes the concept of integrated–heterogeneous catalysis to simultaneously scavenge the dead sulfur and dead lithium to compensate the active materials sulfur and lithium loss simply through adding a small amount of ZnI₂ into conventional electrolyte of Li–S cells. Regulated by integrated–heterogeneous catalysis, over 1300 h of cycling is realized in Li||Li symmetric cells, revealing superb compatibility of the ZnI₂-incorporated electrolyte with lithium metal. Meanwhile, the ZnI₂ shows good prospects in promoting the reutilization of dead sulfur in both theoretical calculation and experimental tests. Practically, a high initial capacity of 1170 mAh g⁻¹ with decent cycling stability is achieved in electrolyte-starved and high-loading pouch cells (5.0 µL mg⁻¹ and 5.2 mg cm⁻²).     

Air-Stable Li2S Cathode for Quasi-Solid-State Anode-Free Batteries with High Volumetric Energy

Anode-free batteries can maximize the energy density but their development is hindered by a lack of Li-rich cathodes for compensating the irreversible Li loss. Li₂S cathode is particularly appealing to this desire due to 2.6–4.7 folds more Li content and 4.2–6.8 times higher capacity than conventional intercalation cathodes. But its practical application is hindered by poor stability against moisture attacking in the air. Herein, a facile expendable polymer sheathing strategy toward air-stable Li₂S cathodes with high capacities for developing high-performance quasi-solid-state anode-free batteries without risk of cell leakage is reported. Tight protection by dense polymer barrier dramatically prolongs the lifetime of Li₂S cathode by 2,000 times at least in the air. Such air-stable Li₂S cathode allows for high compatibility of anode-free battery production with commercial schemes. More attractively, the polymer protective layer can in situ transform to multifunctional gel polymer electrolyte for releasing ionic pathways and enhancing cell performance by inhibiting LiPS loss and smoothing Li plating. With air-stable Li₂S cathode, the quasi-solid-state anode-free cells are assembled in ambient environment to deliver superb volumetric energy density of 1093 Wh L⁻¹. This study may shed new light to push the commercialization of high-energy and reliable anode-free batteries forward.     

Mo-Modified ZnIn2S4@NiTiO3 S-Scheme Heterojunction with Enhanced Interfacial Electric Field for Efficient Visible-Light-Driven Hydrogen Evolution

Designing and developing visible-light-responsive materials for solar to chemical energy is an efficient and promising approach to green and sustainable carbon-neutral energy systems. Herein, a facile in situ growth hydrothermal strategy using Mo-modified ZnIn₂S₄ (Mo-ZIS) nanosheets coupled with NiTiO₃ (NTO) microrods to synthesize multifunctional Mo-modified ZIS wrapped NTO microrods (Mo-ZIS@NTO) photocatalyst with enhanced interfacial electric field (IEF) effect and typical S-scheme heterojunction is reported. Mo-ZIS@NTO catalyst possesses wide-spectrum light absorption properties, excellent visible light-to-thermal energy effect, electron mobility, charges transfer, and strong IEF and exhibits excellent solar-to-chemical energy conversion for efficient visible-light-driven photocatalytic hydrogen evolution. Notably, the engineered Mo_1.4-ZIS@NTO catalyst exhibits superior performance with H₂ evolution rate of up to 14.06 mmol g⁻¹ h^{− 1} and the apparent quantum efficiency of 44.1% at 420 nm. The scientific explorations provide an in-depth understanding of microstructure, S-scheme heterojunction, enhanced IEF, Mo-dopant facilitation effect. Moreover, the theoretical simulations verify the critical role of Mo element in promoting the adsorption and activation of H₂O molecules, modulating the H adsorption behavior on active S sites, and thus accelerating the overall catalytic efficiency. The photocatalytic hydrogen evolution mechanism via S-scheme heterojunction with adjustable IEF regulation over Mo_1.4-ZIS@NTO is also demonstrated.     

Path integrals on finite sets

We construct an analogue of the Feynman path integral for the case of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0YaaS% aaaeaacaaIXaaabaGaamyAaaaadaWcaaqaaiabgkGi2cqaaiabgkGi% 2kaadshaaaqeduuDJXwAKbYu51MyVXgaiuaacqWFvpGAcaWG0bGaey% ypa0JaamisamaaBaaaleaacaGGOaaabeaakmaaBaaaleaacaGGPaaa% beaakiab-v9aQjaadshaaaa!4A8D!\[ - \frac{1}{i}\frac{\partial }{{\partial t}}\varphi t = H_( _) \varphi t\] in which H ₍₎ is a self-adjoint operator in the space L ²(M)= % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSOaHmkaaa!3744!\[\mathbb{C}\], where _M is a finite set, the paths being functions of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeSyhHekaaa!375D!\[\mathbb{R}\] with values in M. The path integral is a family of measures F _t,t with values in the operators on L ²(M), or equivalently, a family of complex measures corresponding to matrix coefficients.It is shown that these measures on path space are in some sense dominated by the measure of a Markov process. This implies that F _t,t is concentrated on the set of step functions S[t,t].This allows one to make sense of, and prove, the analogue of Feynman's formula for the propagator of the Hamiltonian H=H ₀+V, where V is a potential, namely the formula: % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyzamaaCa% aaleqabaGaeyOeI0IaamyAaiaacIcacaWG0bGaai4jaiabgkHiTiaa% dshacaGGPaGaamisaaaakiabg2da9maapebabaGaaeyzamaaCaaale% qabaGaeyOeI0IaamyAamaapedabaGaamOvaiaacIcatCvAUfKttLea% ryqr1ngBPrgaiuGacqWF4baEcaGGOaGaam4CaiaacMcacaGGPaGaae% izaiaabohaaWqaaiaadshaaeaacaWG0bGaai4jaaGdcqGHRiI8aaaa% kiaadAeadaWgaaWcbaGaamiDaiaacEcacaGGSaGaamiDaaqabaGcca% GGOaGaaeizaiab-Hha4jaacMcaaSqaaiaadofacaGGBbGaamiDaiaa% cYcacaWG0bGaai4jaiaac2faaeqaniabgUIiYdaaaa!6410!\[{\text{e}}^{ - i(t' - t)H} = \int_{S[t,t']} {{\text{e}}^{ - i\int_t^{t'} {V(x(s)){\text{ds}}} } F_{t',t} ({\text{d}}x)} \]and the corresponding formulas for the matrix coefficients, in which the integral extends over the paths beginning and ending in the appropriate points. We show that the measures F _t,t are completely determined by these equations and by a certain multiplicative property.The path integral corresponding to a two-particle system without interaction is the direct product of the corresponding path integrals. The propagator for a two-particle system with interaction can be obtained by repeated integration.Finally, we show that the above integral formula can be generalized to the case where the potential is time dependent.     

Fermionic stochastic differential equations and the index of Fredholm operators

The index of a Fredholm operator associated to a-summable Fredholm module is expressed in terms of the vacuum expectation value of a unitary operator-valued stochastic process which satisfies a stochastic differential equation with unbounded coefficients driven by fermion noise.     

Absorption and refraction phenomena in proton- and antiproton-nucleus scattering

The experimental data on the 180 MeV proton and 50, 180 MeV antiproton scattering by the nuclei¹²C,⁴⁰Ca and²⁰⁸Pb have been analysed on the basis of the phenomenological diffraction theory. The optical properties of the nuclei with regards to the incident protons and antiprotons are investigated. Various limiting cases of the proton- and antiproton-nucleus scattering are considered. The contribution of the Coulomb and the spin-orbit interactions to the differential cross sections of these processes has been also analysed.The authors are indebted to D.M. Skrypnik for assistance in preparing the English version of this paper.     

Cyclic actions on some Klein bottle bundles over S1

Leth be a cyclic action of periodn onM, whereM is eitherS ¹×K, K is the Klein bottle or on , the twisted Klein bottle bundle overS ¹, such that there is a fiberingq:MS ¹ with fiber a Klein bottleK or a torusT with respect to which the action is fiber preserving. We classify all such actions and show that they might be distinguished by their fixed points or by their orbit spaces.