AI 中文总结
本文利用WKB作用积分计算p-p聚变反应的天体物理S因子，通过逆势方法构建核势，避免裸库仑势，得到的S(0)值比现有结果低一个数量级。
AI 中文摘要
当前弱pp相互作用的S因子计算涉及使用裸库仑Gamow因子确定低能穿透概率，这使得实际相互作用的性质和形状变得不重要。在本工作中，天体物理S因子通过利用WKB作用积分获得，该积分在pp相互作用的S波逆散射势上评估，其中不涉及裸库仑相互作用。通过相位函数法，使用由三个平滑组合的Morse函数组成的参考势构建np和pp逆势，其模型参数通过遗传算法优化，以最小化获得的和预期的散射相移之间的均方误差。在高达0.0001 MeV的不同能量下评估了束缚态氘核与pp S波散射态之间的重叠积分，并确定了相应的聚变截面。WKB作用积分在所有能量下无近似计算。最后，计算了不同能量下的S因子，并使用监督神经网络获得了S(0)。使用我们的方法（涉及无近似的完整WKB作用积分评估）获得的S(0)值为$(0.1678\pm 0.0058)\times10^{-25}$，这比目前使用各种方法接受的值低大约一个数量级。使用参考势方法构建的逆势不涉及核和库仑相互作用的显式考虑，导致pp相互作用具有有限范围，成功地提供了依赖于实际势的性质和形状的天体物理S因子的新估计。
英文摘要
The current S-factor calculations for weak pp interaction involve the determination of low-energy penetration probability using the bare Coulomb Gamow factor, which renders the nature and shape of actual interaction to be insignificant. In this work, the astrophysical S-factor is obtained utilizing the WKB action integral evaluated over the inverse scattering potential for the S-wave of pp-interaction, which does not involve bare Coulomb interaction in it. The np and pp inverse potentials are constructed using the phase function method by providing a reference potential consisting of three smoothly combined Morse functions, whose model parameters are optimized using a genetic algorithm to minimize the mean-squared error between the obtained and expected scattering phase shifts. The overlap integral between the bound-state deuteron and the scattering state of pp S-wave has been evaluated at different energies all the way up to 0.0001 MeV, and corresponding fusion cross-sections are determined. The WKB action integral has been computed at all energies without any approximations. Finally, the S-factor at various energies are calculated, and S(0) has been obtained using a supervised neural network. The value of S(0) obtained using our methodology involving complete evaluation of WKB action integral without approximations is $(0.1261\pm 0.0043)\times10^{-25}$, which is almost one order of magnitude lower than the currently accepted values using various methods. The inverse potentials constructed using the reference potential approach, which does not involve explicit consideration of nuclear $\&$ Coulomb interaction, resulting in a finite range of pp-interaction, have been successful in providing a new estimate for the astrophysical s-factor that depends on the nature and shape of the actual potentials.
Comments22 pages, 8 figures, 6 tables
