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4. Decomposition of degenerate Gromov–Witten invariants

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   Abramovich, Dan; Chen, Qile; Gross, Mark; Siebert, Bernd (October 2020, Compositio Mathematica)

   null (Ed.)

   We prove a decomposition formula of logarithmic Gromov–Witten invariants in a degeneration setting. A one-parameter log smooth family $$X \longrightarrow B$$ with singular fibre over $$b_0\in B$$ yields a family $$\mathscr {M}(X/B,\beta ) \longrightarrow B$$ of moduli stacks of stable logarithmic maps. We give a virtual decomposition of the fibre of this family over $$b_0$$ in terms of rigid tropical maps to the tropicalization of $X/B$ . This generalizes one aspect of known results in the case that the fibre $$X_{b_0}$$ is a normal crossings union of two divisors. We exhibit our formulas in explicit examples. 

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5. Capture rates of highly degenerate neutrons

   https://doi.org/10.1088/1361-6471/ad616f  

   Knight, B.; Caballero, O_L; Schatz, H. (July 2024, Journal of Physics G: Nuclear and Particle Physics)

   Abstract At the low temperature and high density conditions of a neutron star crust neutrons are degenerate. In this work, we study the effect of this degeneracy on the capture rates of neutrons on neutron rich nuclei in accreted crusts. We use a statistical Hauser–Feshbach model to calculate neutron capture rates and find that neutron degeneracy can increase rates significantly. Changes increase from a factor of a few to many orders of magnitude near the neutron drip line. We also quantify uncertainties due to model inputs for masses,γ-strength functions, and level densities. We find that uncertainties increase dramatically away from stability and that degeneracy tends to increase these uncertainties further, except for cases near the neutron drip line where degeneracy leads to more robustness. As in the case of capture of classically distributed neutrons, variations in the mass model have the strongest impact. Corresponding variations in the reaction rates can be as high as 3–4 orders of magnitude, and be more than 5 times larger than under classical conditions. To ease the incorporation of neutron degeneracy in nucleosynthesis networks, we provide tabulated results of capture rates as well as analytical expressions as function of temperature and neutron chemical potential, for proton numbers between 3 ≤Z≤ 85, derived from fits to our numerical results. Fits are based on a new parametrization that complements previously employed power law approximations with additional Lorentzian terms that account for low energy resonances, significantly improving accuracy. 

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