Evaluation of fusion suppression factors for 6Li and 7Li using multilayer perceptron neural networks

Abstract

Recent advancements have enhanced the measurement of complete fusion cross-sections, particularly for reactions involving weakly bound projectiles. It is well-established that the complete fusion cross-section for these nuclei is suppressed at above-barrier energies due to breakup effects. This study utilized feedforward Artificial Neural Networks (ANNs) with a Multilayer Perceptron architecture to estimate the complete fusion suppression factor for reactions involving ⁶Li and ⁷Li projectiles. By comparing ANN-predicted reduced fusion functions $F\left(x\right)$ with the Universal Fusion Function $F_0\left(x\right)$, average suppression factors of 0.68 and 0.74 were determined for ⁶Li and ⁷Li, respectively. The Normalized Mean Squared Error (NMSE) for ⁶Li was 1.85% (training) and 1.92% (testing), while for ⁷Li it was 3.73% and 6.48%. Comparisons with Support Vector Regression, Random Forest Regression, and Gaussian Process Regression showed that ANNs provided superior accuracy, suggesting their viability for estimating fusion suppression factors. The study is further extended to ${}^8\mathrm{Li}$, ${}^7\mathrm{Be}$, ${}^9\mathrm{Be}$, ${}^{10}B$, ${}^{11}B$, ${}^{12}C$, and ${}^{13}C$ projectiles, revealing that fusion suppression is strongly influenced by the breakup threshold energy, with direct breakup dominating at sub-barrier energies.