The existence of a system of short-lived, discrete, volume-localized, electronic, quantum levels in positively charged fullerenes is shown theoretically and numerically for the example of the fullerenes C60. The results of three-dimensional calculations performed using the QuantumEspresso package are presented. The structures of the quantum levels in charged fullerenes were calculated numerically in a wide range of transitions from 4 eV for the fullerene C60+1$$ {C}_{60}^{+ 1} $$ to 40 eV for the fullerene C60+1$$ {C}_{60}^{+ 1} $$. The results confirm previous theoretical work on the possible existence of single-particle excited electronic states localized in the volume of positively charged fullerene C60. Thus, the electrons captured in these discrete levels of fullerene form a kind of short-lived superheavy pseudoatom in which the electrons are localized inside a positively charged spherical nucleus with atomic mass 240 a.u. for C20 and 720 a.u. for C60. In conclusion, the possibility of generating coherent radiation on these transitions is discussed.

中文翻译：

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带电富勒烯中的体积局域化量子能级

以富勒烯 C60 为例，在理论上和数值上显示了在带正电荷的富勒烯中存在短寿命、离散、体积局部化、电子、量子能级系统。展示了使用 QuantumEspresso 软件包执行的三维计算结果。在从富勒烯 C60 的 4 eV+1$$ {C}_{60}^{+ 1} $$ 到富勒烯 C60 的 40 eV 的广泛跃迁范围内，对带电富勒烯中的量子能级结构进行了数值计算+1$$ {C}_{60}^{+ 1} $$。结果证实了先前关于可能存在位于带正电的富勒烯 C60 体积中的单粒子激发电子态的理论工作。因此，在富勒烯的这些离散水平中捕获的电子形成一种短寿命的超重假原子，其中电子位于带正电的球形核内，C20 的原子质量为 240 au，C60 的原子质量为 720 au。总之，讨论了在这些跃迁上产生相干辐射的可能性。