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arXiv 1408.0072nucl-th
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Yb偶同位素唯象模型与IBM-1模型的对应

A Correspondence between Phenomenological and IBM-1 Models of Even Isotopes of Yb

Abdurahim Okhunov, Fadhil I. Sharrad, Anwer A. Al-Sammarea

摘要:

研究了弱条件文法的非终结符复杂性,证明了每一种递归可枚举语言都可以由不超过\textit{seven}非终结符的弱条件文法生成。此外,它表明,在弱条件文法的非终结符的数量没有擦除规则导致一个无限的层次的弱条件文法生成的语言的家庭。用唯象模型($PhM$)和相互作用玻色子模型($IBM-1$)计算了质子数$Z=70$和中子数在100 ~ 106之间的镱同位素的$E2$ --跃迁能级和约化几率。预测的低位水平(能量,自旋和宇称)和减少概率$E2$ -过渡结果是合理的与现有的实验数据相一致。对于所有感兴趣的核,在$PhM$中产生的预测的低水平($gr$ --,$β_1$ --和$γ_1$ --带)与$IBM-1$的实验数据比较,符合得很好。此外,唯象模型成功地预测了$β_2$ --、$β_3$ --、$β_4$ --、$γ_2$ --和$1^+$ --带,而对$IBM-1$则是失败的。此外,$3^+$ -带由$^{172}Yb$和$^{174}Yb$核的$IBM-1$模型预测。所有的计算与现有的实验数据进行了比较。

英文摘要:

This paper studies the nonterminal complexity of weakly conditional grammars, and it proves that every recursively enumerable language can be generated by a weak conditional grammar with no more than \textit{seven} nonterminals. Moreover, it is shown that the number of nonterminals in weakly conditional grammars without erasing rules leads to an infinite hierarchy of families of languages generated by weakly conditional grammars. Energy levels and the reduced probability of $E2$-- transitions for Ytterbium isotopes with proton number $Z=70$ and neutron numbers between 100 and 106 have been calculated through phenomenological ($PhM$) and interacting boson ($IBM-1$) models. The predicted low-lying levels (energies, spins and parities) and the reduced probability for $E2$-- transitions results are reasonably consistent with the available experimental data. The predicted low-lying levels ($gr$--, $β_1$-- and $γ_1$-- band) by produced in the $PhM$ are in good agreement with the experimental data comparison with those by $IBM-1$ for all nuclei of interest. In addition, the phenomenological model was successful in predicted the $β_2$--, $β_3$--, $β_4$--, $γ_2$-- and $1^+$-- band while it was a failure with $IBM-1$. Also, the $3^+$-- band is predicted by the $IBM-1$ model for $^{172}Yb$ and $^{174}Yb$ nuclei. All calculations are compared with the available experimental data.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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