Abstract This paper studies full vibrational spectra {$E_\upsilon $} and molecular dissociation energies $D_{\rm e}$ by using conventional least-squares (LS) fitting and an algebraic method (AM) proposed recently for 10 diatomic electronic states of ${ }^7$Li$_2 $, Na$_2$, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [$E_\upsilon ^{\exp t} $] respectively. Studies show that: (1) although both the full AM spectrum {$E_\upsilon ^{\rm AM} $} and the LS spectrum {$E_\upsilon ^{\rm LS} $} can reproduce the known experimental energies in [$E_\upsilon ^{\exp t} $], the {$E_\upsilon ^{\rm AM} $} is superior to the {$E_\upsilon ^{\rm LS} $} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {$E_\upsilon ^{\rm LS} $}, and so is the AM dissociation energy $D_{\rm e}^{\rm AM} $; (2) the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.
Received: 13 September 2007
Revised: 18 October 2007
Accepted manuscript online:
Fund: Project supported by the National
Natural Science Foundation of China (Grant No 10774105) and the
Science Foundation of the Chinese Educational Ministry.
Cite this article:
Liu Xiu-Ying(刘秀英), Sun Wei-Guo(孙卫国), and Fan Qun-Chao(樊群超) Accurate studies of dissociation energies and vibrational energies on alkali metals 2008 Chin. Phys. B 17 2048
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