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1. Exploring Jahn-Teller distortions: a local vibrational mode perspective

   https://doi.org/10.1007/s00894-024-05882-8  

   Quintano, Mateus ; Moura, Renaldo T ; Kraka, Elfi ( April 2024 , Journal of Molecular Modeling)

   The characterization of normal mode (CNM) procedure coupled with an adiabatic connection scheme (ACS) between local and normal vibrational modes, both being a part of the Local Vibrational Mode theory developed in our group, can identify spectral changes as structural fingerprints that monitor symmetry alterations, such as those caused by Jahn-Teller (JT) distortions. Employing the PBE0/Def2-TZVP level of theory, we investigated in this proof-of-concept study the hexaaquachromium cation case,$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$/$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$, as a commonly known example for a JT distortion, followed by the more difficult ferrous and ferric hexacyanide anion case,$$\mathrm {[Fe{(CN)}_6]^{4-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$/$$\mathrm {[Fe{(CN)}_6]^{3-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$. We found that in both cases CNM of the characteristic normal vibrational modes reflects delocalization consistent with high symmetry and ACS confirms symmetry breaking, as evidenced by the separation of axial and equatorial group frequencies. As underlined by the Cremer-Kraka criterion for covalent bonding, from$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$to$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$there is an increase in axial covalency whereas the equatorial bonds shift toward electrostatic character. From$$\mathrm {[Fe{(CN)}_6]^{4-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$to$$\mathrm {[Fe{(CN)}_6]^{3-}}$$${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$we observed an increase in covalency without altering the bond nature. Distinct$$\pi $$$\pi$back-donation disparity could be confirmed by comparison with the isolated CN$$^-$$${}^{-}$system. In summary, our study positions the CNM/ACS protocol as a robust tool for investigating less-explored JT distortions, paving the way for future applications.

   The adiabatic connection scheme relates local to normal modes, with symmetry breaking giving rise to axial and equatorial group local frequencies

    

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2. Photo-response of the $$N=Z$$ nucleus $$^{24}$$Mg

   https://doi.org/10.1140/epja/s10050-023-01111-7  

   Deary, J ; Scheck, M ; Schwengner, R ; O’Donnell, D ; Bemmerer, D ; Beyer, R ; Hensel, Th ; Junghans, A R ; Kögler, T ; Müller, S E ; et al ( September 2023 , The European Physical Journal A)

   The electricE1 and magneticM1 dipole responses of the$$N=Z$$$N=Z$nucleus$$^{24}$$${}^{24}$Mg were investigated in an inelastic photon scattering experiment. The 13.0 MeV electrons, which were used to produce the unpolarised bremsstrahlung in the entrance channel of the$$^{24}$$${}^{24}$Mg($$\gamma ,\gamma ^{\prime }$$$\gamma ,{\gamma }^{\prime }$) reaction, were delivered by the ELBE accelerator of the Helmholtz-Zentrum Dresden-Rossendorf. The collimated bremsstrahlung photons excited one$$J^{\pi }=1^-$$$J^{\pi }=1^{-}$, four$$J^{\pi }=1^+$$$J^{\pi }=1^{+}$, and six$$J^{\pi }=2^+$$$J^{\pi }=2^{+}$states in$$^{24}$$${}^{24}$Mg. De-excitation$$\gamma $$$\gamma$rays were detected using the four high-purity germanium detectors of the$$\gamma $$$\gamma$ELBE setup, which is dedicated to nuclear resonance fluorescence experiments. In the energy region up to 13.0 MeV a total$$B(M1)\uparrow = 2.7(3)~\mu _N^2$$$B\left(M1\right)\uparrow =2.7\left(3\right){\mu }_N^2$is observed, but this$$N=Z$$$N=Z$nucleus exhibits only marginalE1 strength of less than$$\sum B(E1)\uparrow \le 0.61 \times 10^{-3}$$$\sum B\left(E1\right)\uparrow \le 0.61\times {10}^{-3}$ e$$^2 \, $$${}^2$fm$$^2$$${}^2$. The$$B(\varPi 1, 1^{\pi }_i \rightarrow 2^+_1)/B(\varPi 1, 1^{\pi }_i \rightarrow 0^+_{gs})$$$B(\Pi 1,1_i^{\pi }\to 2_1^{+})/B(\Pi 1,1_i^{\pi }\to 0_{\mathrm{gs}}^{+})$branching ratios in combination with the expected results from the Alaga rules demonstrate thatKis a good approximative quantum number for$$^{24}$$${}^{24}$Mg. The use of the known$$\rho ^2(E0, 0^+_2 \rightarrow 0^+_{gs})$$${\rho }^2(E0,0_2^{+}\to 0_{\mathrm{gs}}^{+})$strength and the measured$$B(M1, 1^+ \rightarrow 0^+_2)/B(M1, 1^+ \rightarrow 0^+_{gs})$$$B(M1,1^{+}\to 0_2^{+})/B(M1,1^{+}\to 0_{\mathrm{gs}}^{+})$branching ratio of the 10.712 MeV$$1^+$$$1^{+}$level allows, in a two-state mixing model, an extraction of the difference$$\varDelta \beta _2^2$$$\Delta {\beta }_2^2$between the prolate ground-state structure and shape-coexisting superdeformed structure built upon the 6432-keV$$0^+_2$$$0_2^{+}$level.

    

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3. Torsion phenomena for zero-cycles on a product of curves over a number field

   https://doi.org/10.1007/s40993-024-00519-4  

   Gazaki, Evangelia ; Love, Jonathan ( March 2024 , Research in Number Theory)

   For a smooth projective varietyXover an algebraic number fieldka conjecture of Bloch and Beilinson predicts that the kernel of the Albanese map ofXis a torsion group. In this article we consider a product$$X=C_1\times \cdots \times C_d$$$X=C_1\times \cdots \times C_d$of smooth projective curves and show that if the conjecture is true for any subproduct of two curves, then it is true forX. For a product$$X=C_1\times C_2$$$X=C_1\times C_2$of two curves over$$\mathbb {Q} $$$Q$with positive genus we construct many nontrivial examples that satisfy the weaker property that the image of the natural map$$J_1(\mathbb {Q})\otimes J_2(\mathbb {Q})\xrightarrow {\varepsilon }{{\,\textrm{CH}\,}}_0(C_1\times C_2)$$$J_1\left(Q\right)\otimes J_2\left(Q\right)\stackrel{\epsilon }{\to }{\text{CH}}_0(C_1\times C_2)$is finite, where$$J_i$$$J_i$is the Jacobian variety of$$C_i$$$C_i$. Our constructions include many new examples of non-isogenous pairs of elliptic curves$$E_1, E_2$$$E_1,E_2$with positive rank, including the first known examples of rank greater than 1. Combining these constructions with our previous result, we obtain infinitely many nontrivial products$$X=C_1\times \cdots \times C_d$$$X=C_1\times \cdots \times C_d$for which the analogous map$$\varepsilon $$$\epsilon$has finite image.

    

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4. 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)

   We 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.

    

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5. Searching for a dark matter particle with anti-protonic atoms

   https://doi.org/10.1140/epjc/s10052-023-12319-8  

   Doser, Michael ; Farrar, Glennys ; Kornakov, Georgy ( December 2023 , The European Physical Journal C)

   A wide range of dark matter candidates have been proposed and are actively being searched for in a large number of experiments, both at high (TeV) and low (sub meV) energies. One dark matter candidate, a deeply bounduuddsssexaquark,$$S$$$S$, with mass$$\sim 2$$$\sim 2$GeV (having the same quark content as the hypothesized H-dibaryon, but long lived) is particularly difficult to explore experimentally. In this paper, we propose a scheme in which such a state could be produced at rest through the formation of$$\bar{p}$$$\overline{p}$–$$^3$$$_{}^3$He antiprotonic atoms and their annihilation into$$S$$$S$+$$K^+K^+\pi ^-$$$K^{+}{K}^{+}{\pi }^{-}$, identified both through the unique tag of a$$S=+2, Q=+1$$$S=+2,Q=+1$final state, as well as through full kinematic reconstruction of the final state recoiling against it.

    

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