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Exploring the equation of state (EoS) of isospin-asymmetric nuclear matter is essential for understanding the structure of exotic nuclei and processes in neutron-rich astrophysical environments. The symmetry energy, which encodes the isospin dependence of the EoS, is commonly characterized by its value at saturation $J$ and its slope $L$, the latter of which remains poorly constrained. In this work, we investigate the sensitivity of the total Coulomb excitation cross sections ($\sigma_C$) of neutron-rich tin isotopes $^{124-132}$Sn to the parameterization of the symmetry energy around saturation density. At relativistic beam energies above 500 MeV$/$u, $\sigma_C$ is dominated by the excitation of the Isovector Giant Dipole Resonance (IVGDR). For medium-heavy and heavy neutron-rich nuclei, $\sigma_C$ exhibits a strong correlation with dipole polarizability $\alpha_D$, which is sensitive to the isovector properties of the nuclear EoS near and below saturation density [1,2].
Although extraction of $\sigma_C$ does not require reconstruction of the full excitation-energy spectrum, detector response effects depending on the kinetic energies of the center-of-mass neutrons remain relevant. In turn, the neutron kinetic-energy distributions depend on statistical decay properties governed by nuclear level densities. We present a comparative analysis of two R3B experiments employing LAND and NeuLAND [3] neutron detectors at different beam energies. For measurements performed at $\sim$500 MeV/u with LAND, limited neutron acceptance above $\approx$3 MeV (fragment rest frame) requires generating detector response matrices using statistical decay simulations [4]. In contrast, measurements with NeuLAND at higher beam energies achieve near-complete acceptance for evaporated neutrons, enabling a direct extraction of the total Coulomb excitation cross sections above the neutron separation threshold. This removes systematic uncertainties associated with statistical decay modeling.
The extracted $\sigma_C$ values from the two experimental data sets are compared with coupled channels calculations [5] employing B(E1) and B(E2) inputs from QRPA calculations with a set of 24 relativistic and non-relativistic energy density functionals (EDFs). All models overestimate the measured cross sections and fall outside the range of experimental uncertainties for $^{124}$Sn, $^{130}$Sn and $^{132}$Sn, including interactions with the lowest predicted values of $L$. These preliminary cross sections, pending a stricter experimental uncertainty assessment, are consistent with the findings of the $\alpha_D$ measurement of $^{124}$Sn carried out at the RCNP facility [6].
[1] Horvat, A., Ph.D. thesis, Technische Universität Darmstadt, Germany (2021).
[2] Roca-Maza, X., Paar, N., & Colò, G., J. Phys. G: Nucl. Part. Phys., 42, 034003 (2015).
[3] Boretzky, K. et al., Nucl. Instrum. Methods Phys. Res. A, 1014, 165701 (2021).
[4] Rossi, D. et al., Phys. Rev. Lett., 111, 242503 (2013).
[5] C. A. Bertulani, L. F. Canto, M. S. Hussein, and A. F. R. de Toledo Piza, Phys. Rev. C \textbf{53}, 334 (1996)
[6] Bassauer, S. et al., Phys. Lett. B, 810, 135804 (2022).