标题： 簇物理中的折叠势 - 弥散势和库仑势与瑞斯分数阶积分的比较 显示英文标题

标题： Folded potentials in cluster physics - a comparison of Yukawa and Coulomb potentials with Riesz fractional integrals

摘要： 在簇物理中，为了计算集体构型总能量的微观部分，需要一个单粒子势。 在本文中，我们研究了Riesz分数阶积分的性质，并将其性质与通常使用的标准库仑和尤卡夫势进行了比较。 结果表明，Riesz势可以作为标准势的一种有前景的扩展，并可根据分数参数$\alpha$被视为从库仑到尤卡夫类似势的平滑过渡。 对于总能量的宏观部分，Riesz势从广义的角度处理库仑、对称性和配对贡献，因为它们被证明是在不同$\alpha$值下的相同分数积分的不同实现。 显示英文摘要

摘要： In cluster physics a single particle potential to determine the microscopic part of the total energy of a collective configuration is necessary to calculate the shell- and pairing effects. In this paper we investigate the properties of the Riesz fractional integrals and compare their properties with the standard Coulomb and Yukawa potentials commonly used. It is demonstrated, that Riesz potentials may serve as a promising extension of standard potentials and may be reckoned as a smooth transition from Coulomb to Yukawa like potentials, depending of the fractional parameter $\alpha$. For the macroscopic part of the total energy the Riesz potentials treat the Coulomb-, symmetry- and pairing-contributions from a generalized point of view, since they turn out to be similar realizations of the same fractional integral at distinct $\alpha$ values.