تقرير
Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. III. Spin-quartet state of the Lithium sequence
| العنوان: | Ultra-Compact accurate wave functions for He-like and Li-like iso-electronic sequences and variational calculus. III. Spin-quartet state of the Lithium sequence |
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| المؤلفون: | Nader, D. J., del Valle, J. C., Vieyra, J. C. Lopez, Turbiner, A. V. |
| المصدر: | Int Journal of Quantum Chemistry 123 (8) (2022) qua.26952 |
| سنة النشر: | 2022 |
| مصطلحات موضوعية: | Physics - Atomic Physics |
| الوصف: | As a continuation of Part I, dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges $Z \leq 20$, and Part II, dedicated to two excited states of He-like sequence, two ultra-compact wave functions in the form of generalized Guevara-Harris-Turbiner functions are constructed for Li-like sequence. They describe accurately the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC) for energies (2-3 significant digits (s.d.)) of the spin-quartet state $1^40^+$ of Li-like ions (in static approximation with point-like, infinitely heavy nuclei). Variational parameters are fitted in $Z$ by 2nd degree polynomials. The most accurate ultra-compact function leads to the absolute accuracy $\sim 10^{-3}$\,a.u. for energy, and $\sim 10^{-4}$ for the normalized electron-nuclear cusp parameter for $Z \leq 20$. Critical charge $Z=Z_B$, where the ultra-compact trial function for the $1^40^+$ state looses its square-integrability, is estimated, $Z_B(1^4\,0^+) \sim 1.26 - 1.30$. As a complement to Part I, square integrability for the compact functions constructed for the {\it ground, spin-doublet state} $1^2\,0^+$ of the Li-like sequence is discussed. The critical charge, for which these functions stop to be normalizable, is estimated as $Z_B( 1^2\,0^+) = 1.62 - 1.65$. It implies that at $Z=2$ - the negative helium ion He${}^-$ - both states $1^2\,0^+$ and $1^4\,0^+$ exist as states embedded to continuum. Comment: 29 pages, 5 figures, 2 tables |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1002/qua.26952 |
| URL الوصول: | http://arxiv.org/abs/2202.05774 |
| رقم الأكسشن: | edsarx.2202.05774 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1002/qua.26952 |
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