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1. A multiple-timing analysis of temporal ratcheting

   https://doi.org/10.1140/epje/s10189-024-00421-y  

   Hashemi, Aref; Gilman, Edward T; Khair, Aditya S (April 2024, The European Physical Journal E)

   AbstractWe develop a two-timing perturbation analysis to provide quantitative insights on the existence of temporal ratchets in an exemplary system of a particle moving in a tank of fluid in response to an external vibration of the tank. We consider two-mode vibrations with angular frequencies$$\omega $$ $\omega$ and$$\alpha \omega $$ $\alpha \omega$ , where$$\alpha $$ $\alpha$ is a rational number. If$$\alpha $$ $\alpha$ is a ratio of odd and even integers (e.g.,$$\tfrac{2}{1},\,\tfrac{3}{2},\,\tfrac{4}{3}$$ $\frac{2}{1},\frac{3}{2},\frac{4}{3}$ ), the system yields a net response: here, a nonzero time-average particle velocity. Our first-order perturbation solution predicts the existence of temporal ratchets for$$\alpha =2$$ $\alpha =2$ . Furthermore, we demonstrate, for a reduced model, that the temporal ratcheting effect for$$\alpha =\tfrac{3}{2}$$ $\alpha =\frac{3}{2}$ and$$\tfrac{4}{3}$$ $\frac{4}{3}$ appears at the third-order perturbation solution. More importantly, we find closed-form formulas for the magnitude and direction of the induced net velocities for these$$\alpha $$ $\alpha$ values. On a broader scale, our methodology offers a new mathematical approach to study the complicated nature of temporal ratchets in physical systems. Graphic abstract 

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2. Lieb–Thirring Inequality for the 2D Pauli Operator

   https://doi.org/10.1007/s00220-024-05177-2  

   Frank, Rupert L; Kovařík, Hynek (February 2025, Communications in Mathematical Physics)

   Abstract By the Aharonov–Casher theorem, the Pauli operatorPhas no zero eigenvalue when the normalized magnetic flux$$\alpha $$ $\alpha$ satisfies$$|\alpha |<1$$ $\left|\alpha \right|<1$ , but it does have a zero energy resonance. We prove that in this case a Lieb–Thirring inequality for the$$\gamma $$ $\gamma$ -th moment of the eigenvalues of$$P+V$$ $P+V$ is valid under the optimal restrictions$$\gamma \ge |\alpha |$$ $\gamma \ge \left|\alpha \right|$ and$$\gamma >0$$ $\gamma >0$ . Besides the usual semiclassical integral, the right side of our inequality involves an integral where the zero energy resonance state appears explicitly. Our inequality improves earlier works that were restricted to moments of order$$\gamma \ge 1$$ $\gamma \ge 1$ . 

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3. Spectroscopic investigation of $$^{54}$$Cr via $$\alpha $$-transfer reaction

   https://doi.org/10.1140/epja/s10050-025-01619-0  

   Das, Biswajit; Kundu, A; Palit, R; Dey, P; Malik, Vishal; Garg, U; Negi, D; Laskar, S R; Santra, Rajkumar; Jadhav, S K; et al (June 2025, The European Physical Journal A)

   Abstract Low-lying states in$$^{54}$$ $_{}^{54}$ Cr have been investigated via the$$\alpha $$ $\alpha$ -transfer reaction$$^{50}$$ $_{}^{50}$ Ti($$^{7}$$ $_{}^7$ Li,t) at a bombarding energy of 20 MeV. The exclusive$$\alpha $$ $\alpha$ -transfer channel is separated from other reaction channels through the appropriate energy gate on the complementary particle, triton. Levels of$$^{54}$$ $_{}^{54}$ Cr populated exclusively by the$$\alpha $$ $\alpha$ -transfer process could be identified up to$$\approx $$ $\approx$ 5 MeV excitation energy and angular momentum up to$$(8)^{+}$$ ${\left(8\right)}^{+}$ , by identifying the corresponding known$$\gamma $$ $\gamma$ -rays. These include multiple low-lying non-yrast 2$$^+$$ $_{}^{+}$ and 4$$^+$$ $_{}^{+}$ states, which would otherwise be unfavorable via fusion evaporation reactions. The feeding-subtracted$$\gamma $$ $\gamma$ -ray yields have been extracted to estimate the population of various excited states through the transfer process. The measured integrated transfer cross sections for all the observed yrast and non-yrast states are compared with Coupled Channels calculations usingfrescoto extract the$$\alpha $$ $\alpha$ +$$^{50}$$ $_{}^{50}$ Ti core spectroscopic factors. For the yrast states, a higher$$\alpha $$ $\alpha$ +core overlap is seen for the$$2^+$$ $2^{+}$ and$$4^+$$ $4^{+}$ states, while it is seen to be less favorable for the$$6^+$$ $6^{+}$ and$$(8)^+$$ ${\left(8\right)}^{+}$ states when$$\alpha $$ $\alpha$ -transfer is considered to occur predominantly as a direct one-step process to the$$^{50}$$ $_{}^{50}$ Ti core ground state. The yrast$$2^+$$ $2^{+}$ , and$$4^+$$ $4^{+}$ states are predominantly populated by single-step transfer, while for the states with spin$$\ge $$ $\ge$ 5, the possibility of core excitation followed by$$\alpha $$ $\alpha$ -transfer shows a larger$$\alpha $$ $\alpha$ -core overlap. For the non-yrast$$0^+$$ $0^{+}$ ,$$2^+$$ $2^{+}$ , and$$4^+$$ $4^{+}$ states, single-step transfer shows moderate to small$$\alpha $$ $\alpha$ -core overlap. No higher spin non-yrast states are observed. 

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4. Simulation of the background from ¹³C(α,n)¹⁶O reaction in the JUNO scintillator

   https://doi.org/10.1140/epjc/s10052-025-14333-4  

   Adam, Thomas; Adamowicz, Kai; Ahmad, Shakeel; Ahmed, Rizwan; Aiello, Sebastiano; An, Fengpeng; Andreopoulos, Costas; Andronico, Giuseppe; Anfimov, Nikolay; Antonelli, Vito; et al (September 2025, The European Physical Journal C)

   Abstract Large-scale organic liquid scintillator detectors are highly efficient in the detection of MeV-scale electron antineutrinos. These signal events can be detected through inverse beta decay on protons, which produce a positron accompanied by a neutron. A noteworthy background for antineutrinos coming from nuclear power reactors and from the depths of the Earth (geoneutrinos) is generated by ($$\alpha ,\,n$$ $\alpha ,n$ ) reactions. In organic liquid scintillator detectors,$$\alpha $$ $\alpha$ particles emitted from intrinsic contaminants such as$$^{238}$$ $_{}^{238}$ U,$$^{232}$$ $_{}^{232}$ Th, and$$^{210}$$ $_{}^{210}$ Pb/$$^{210}$$ $_{}^{210}$ Po, can be captured on$$^{13}$$ $_{}^{13}$ C nuclei, followed by the emission of a MeV-scale neutron. Three distinct interaction mechanisms can produce prompt energy depositions preceding the delayed neutron capture, leading to a pair of events correlated in space and time within the detector. Thus, ($$\alpha ,\,n$$ $\alpha ,n$ ) reactions represent an indistinguishable background in liquid scintillator-based antineutrino detectors, where their expected rate and energy spectrum are typically evaluated via Monte Carlo simulations. This work presents results from the open-source SaG4n software, used to calculate the expected energy depositions from the neutron and any associated de-excitation products. Also simulated is a detailed detector response to these interactions, using a dedicated Geant4-based simulation software from the JUNO experiment. An expected measurable$$^{13}$$ $_{}^{13}$ C$$(\alpha ,\,n)^{16}$$ ${(\alpha ,n)}^{16}$ O event rate and reconstructed prompt energy spectrum with associated uncertainties, are presented in the context of JUNO, however, the methods and results are applicable and relevant to other organic liquid scintillator neutrino detectors. 

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5. The $$^{12}$$C$$(\alpha ,\gamma )^{16}$$O reaction, in the laboratory and in the stars

   https://doi.org/10.1140/epja/s10050-025-01537-1  

   de_Boer, R J; Best, A; Brune, C R; Chieffi, A; Hebborn, C; Imbriani, G; Liu, W P; Shen, Y P; Timmes, F X; Wiescher, M (April 2025, The European Physical Journal A)

   Abstract The evolutionary path of massive stars begins at helium burning. Energy production for this phase of stellar evolution is dominated by the reaction path 3$$\alpha \rightarrow ^{12}$$ $\alpha {\to }^{12}$ C$$(\alpha ,\gamma )^{16}$$ ${(\alpha ,\gamma )}^{16}$ O and also determines the ratio of$$^{12}$$ $_{}^{12}$ C/$$^{16}$$ $_{}^{16}$ O in the stellar core. This ratio then sets the evolutionary trajectory as the star evolves towards a white dwarf, neutron star or black hole. Although the reaction rate of the 3$$\alpha $$ $\alpha$ process is relatively well known, since it proceeds mainly through a single narrow resonance in$$^{12}$$ $_{}^{12}$ C, that of the$$^{12}$$ $_{}^{12}$ C$$(\alpha ,\gamma )^{16}$$ ${(\alpha ,\gamma )}^{16}$ O reaction remains uncertain since it is the result of a more difficult to pin down, slowly-varying, portion of the cross section over a strong interference region between the high-energy tails of subthreshold resonances, the low-energy tails of higher-energy broad resonances and direct capture. Experimental measurements of this cross section require herculean efforts, since even at higher energies the cross section remains small and large background sources are often present that require the use of very sensitive experimental methods. Since the$$^{12}$$ $_{}^{12}$ C$$(\alpha ,\gamma )^{16}$$ ${(\alpha ,\gamma )}^{16}$ O reaction has such a strong influence on many different stellar objects, it is also interesting to try to back calculate the required rate needed to match astrophysical observations. This has become increasingly tempting, as the accuracy and precision of observational data has been steadily improving. Yet, the pitfall to this approach lies in the intermediary steps of modeling, where other uncertainties needed to model a star’s internal behavior remain highly uncertain. 

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