发表机构
Baku State University（巴库国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究具有双环形角势垒的非中心Schiöberg型双曲势在克莱因 - 戈登方程中的奇异相互作用机制，通过格林 - 奥尔德里奇近似求解，得到波函数和量子化条件，与实验对比发现低能相符但近解离有偏差。
AI 中文摘要
奇异相互作用可通过改变允许的波函数域来重塑量子光谱。本研究在具有双环形角势垒的非中心Schiöberg型双曲势的克莱因 - 戈登方程中研究此机制。等标量和矢量耦合分离了径向和角向动力学。精确求解角向方程并用格林 - 奥尔德里奇近似处理径向方程，得到雅可比多项式波函数和隐式相对论量子化条件。赤道平方反比奇点将构型空间分成具有相同角谱的反射相关扇区。在一个扇区内将势垒降至零仅保留奇宇称态，与常规全域问题不同，常规问题会恢复奇偶宇称。非相对论极限恢复薛定谔光谱。对于NaH和Na₂，低振动能量与实验合理相符，而近解离偏差揭示了渐近局限性。
英文摘要
Singular interactions can reshape quantum spectra by changing admissible wavefunction domains. In this study, we investigate this mechanism in the Klein--Gordon equation for a non-central Schiöberg-type hyperbolic potential with double ring-shaped angular barriers. Equal scalar and vector couplings separate the radial and angular dynamics. We solve the angular equation exactly on each hemisphere with principal boundary conditions and treat the radial equation with the Greene--Aldrich approximation, obtaining Jacobi-polynomial wavefunctions and an implicit relativistic quantization condition. With this boundary realization, the equatorial inverse-square singularity splits configuration space into reflection-related sectors with identical angular spectra. Reducing the barrier to zero while retaining the equatorial wall selects the odd-reflection spectral branch of the regular full-domain problem; a single hemisphere has no intrinsic parity. The nonrelativistic limit recovers the corresponding Schr{ö}dinger formulation. State-resolved nonrelativistic and relativistic benchmarks quantify the centrifugal error. In a dimensionless relativistic example, the relative error in the remaining binding exceeds unity near threshold although the absolute energy error decreases. For NaH and Na$_2$, low-lying central-radial vibrational energies agree reasonably with spectroscopic reference values, whereas the global radial shape limits near-dissociation accuracy and gives an incorrect NaH bound-state count.
Comments12 pages, 4 figures
