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arXiv 1406.2264nucl-thnucl-ex
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中能核散射Eikonal近似的修正

Corrections to Eikonal Approximation for Nuclear Scattering at Medium Energies

Micah Buuck, Gerald A. Miller

摘要:

密歇根州立大学国家超导回旋加速器实验室(NSCL)即将建立的稀有同位素束(FRIB)设施再次强调了低能核-核散射精确建模的重要性。用程函近似简化了这种计算。然而,作为一个高能量近似,它的准确性受到当前实验感兴趣的中能量束。由Wallace \cite{Wallace:1971zz,Wallace:1973iu}开发的处方获得了散射传播子作为程函传播子周围的扩展(Glauber方法),有可能将近似的有效范围扩展到较低的能量。在这里,我们研究这种扩展的属性,并计算一阶,二阶和三阶修正的无自旋粒子散射的${}^{40}$钙核,并为核分裂反应涉及${}^{11}$ Be。我们发现,包括这些修正扩展的有效性范围的下限的能量为40兆电子伏。在该能量下,校正对某些过程提供多达15%的校正。

英文摘要:

The upcoming Facility for Rare Isotope Beams (FRIB) at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University has reemphasized the importance of accurate modeling of low energy nucleus-nucleus scattering. Such calculations have been simplified by using the eikonal approximation. As a high energy approximation, however, its accuracy suffers for the medium energy beams that are of current experimental interest. A prescription developed by Wallace \cite{Wallace:1971zz,Wallace:1973iu} that obtains the scattering propagator as an expansion around the eikonal propagator (Glauber approach) has the potential to extend the range of validity of the approximation to lower energies. Here we examine the properties of this expansion, and calculate the first-, second-, and third-order corrections for the scattering of a spinless particle off of a ${}^{40}$Ca nucleus, and for nuclear breakup reactions involving ${}^{11}$Be. We find that, including these corrections extends the lower bound of the range of validity of the down to energies of 40 MeV. At that energy the corrections provide as much as a 15\% correction to certain processes.

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