A recent work devoted to the longitudinal optical forces exerted by circularly symmetric Bessel beams on point-like particles in the Rayleigh regime of the generalized Lorenz–Mie theory (GLMT) confirmed the existence of nonstandard forces (named axicon forces in the context of Bessel beams) that seemingly cannot be expressed in terms of scattering and gradient forces traditionally discussed in the framework of the dipole theory of forces. These results lead to this question: Do the Rayleigh limit of the GLMT and the dipole theory of forces actually agree, or are they in disagreement? If so, the Rayleigh limit of the generalized Lorenz–Mie theory would have to be preferred because it provides a highly accurate formulation. To find a definitive answer to the question, numerical comparisons done between optical forces exerted in both frameworks demonstrated an extremely accurate agreement up to 1000 decimal places. This leads to the conjecture that the Rayleigh limit of GLMT might indeed exactly identify with the usual dipole theory of forces.

中文翻译：

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广义Lorenz-Mie理论中的纵向辐射压力横截面及其与力偶极子理论的数值关系

最近的研究致力于在广义Lorenz-Mie理论（GLMT）的Rayleigh态下，圆形对称贝塞尔光束在点状粒子上施加的纵向光学力证实了存在非标准力（在贝塞尔光束的情况下称为轴锥力） ）似乎无法用偶极力理论框架中传统讨论的散射力和梯度力来表达。这些结果引出了一个问题：GLMT的Rayleigh极限和力的偶极理论实际上是一致的，还是不一致？如果是这样，则必须首选广义Lorenz-Mie理论的Rayleigh极限，因为它提供了高度准确的表述。要找到该问题的明确答案，在两个框架中施加的光学力之间进行的数值比较表明，精确度最高可达1000个小数位。这导致了这样一个猜想，即GLMT的Rayleigh极限可能确实与惯常的偶极力理论完全吻合。