Helium-like ions in d-dimensions: analyticity and generalized ground state Majorana solutions
نویسندگان
چکیده
Abstract Non-relativistic Helium-like ions (−e, −e, Ze) with static nucleus in a d−dimensional space (d > 1) are considered. Assuming r−1Coulomb interactions, 2-parametric correlated Hylleraas-type trial function is used to calculate the ground state energy of system domain Z ≤ 10. For odd d = 3, 5, variational given by rational algebraic parameters whilst for even 2, 4 it shown first time that corresponds more complicated non-algebraic expression. This twofold analyticity will hold any d. It allows us construct reasonably accurate approximate solutions E0(Z, d) form compact analytical expressions. We call them generalized Majorana solutions. They reproduce leading terms celebrated 1Z expansion, and serve as generating functions certain correlation-dependent properties. The (first) critical charge Zc vs Shannon entropy S(d)r also calculated within present approach. In light these results, physically important case 3 general 3-parametric compute finite mass effects solution three-body Coulomb arbitrary charges masses. admits straightforward generalization well. Concrete results systems e− e+, H+2 H− indicated explicitly. Our excellent agreement exact numerical values reported literature.
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ژورنال
عنوان ژورنال: Journal of Physics B
سال: 2021
ISSN: ['0953-4075', '1361-6455']
DOI: https://doi.org/10.1088/1361-6455/ac3fbf