arXiv 1702.059282017-02-20nucl-th

程函近似修正的研究

Study of corrections to the eikonal approximation

Chloë Hebborn, Pierre Capel

备注：: 7 pages, 2 figures, contribution to 55th International Winter Meeting on Nuclear Physics (January 2017, Bormio, Italy)

摘要：

在过去的几十年里，多个国际设施已经开发了放射性离子束（RIB）来测量包括奇异核在内的反应过程。这些测量加上精确的反应理论模型，使我们能够推断出这些原子核的结构信息。分波展开提供了一个精确的描述两体碰撞，但有一个大的计算成本。为了解决这个问题，程函近似是一个强大的工具，因为它减少了计算时间，仍然描述了反应中观察到的量子效应。然而，它的有效性范围是有限的高能量和前向散射角。在这项工作中，我们分析了扩展的程函近似，以较低的能量和较大的角度，通过实施两个修正。这些旨在改善程函模型内的核和库仑相互作用的处理。第一个校正是基于扩展的$T$ -矩阵，而第二个依赖于一个半经典的方法。它们允许更好地解释在标准程函模型中被忽略的由目标引起的射弹偏转。通过分析用标准程函模型计算的角截面、其修正和分波展开，评估了每个修正的精度增益。这些分析已经进行了紧密结合的弹丸（$^{10}\mathrm{Be}$）从中间能量（67兆电子伏/核子）到未来的RIB设施，如HIE-ISOLDE和ReA 12在MSU（10兆电子伏/核子）的利益的能量。

英文摘要：

For the last decades, multiple international facilities have developed Radioactive-Ion Beams (RIB) to measure reaction processes including exotic nuclei. These measurements coupled with an accurate theoretical model of the reaction enable us to infer information about the structure of these nuclei. The partial-wave expansion provides a precise description of two-body collisions but has a large computational cost. To cope with this issue, the eikonal approximation is a powerful tool as it reduces the computational time and still describes the quantum effects observed in reaction observables. However, its range of validity is restricted to high energy and to forward scattering angles. In this work, we analyse the extension of the eikonal approximation to lower energies and larger angles through the implementation of two corrections. These aim to improve the treatment of the nuclear and Coulomb interactions within the eikonal model. The first correction is based on an expansion of the $T$-matrix while the second relies on a semi-classical approach. They permit to better account for the deflection of the projectile by the target, which is neglected in the standard eikonal model. The gain in accuracy of each correction is evaluated through the analyses of angular cross sections computed with the standard eikonal model, its corrections and the partial-wave expansion. These analyses have been performed for tightly bound projectiles ($^{10}\mathrm{Be}$) from intermediate energies (67 MeV/nucleon) down to energies of interest of future RIB facilities such as HIE-ISOLDE and ReA12 at MSU (10 MeV/nucleon).

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