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首页> 外文期刊>Physical Review, A. Atomic, molecular, and optical physics >Convergence of the hyperspherical-harmonics expansion with increasing number of particles for bosonic systems. II. Inclusion of the three-body force
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Convergence of the hyperspherical-harmonics expansion with increasing number of particles for bosonic systems. II. Inclusion of the three-body force

机译：随着超音波系统中粒子数量的增加，超球谐谐波的收敛性。二。包含三体力

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This paper presents a numerical convergence study of a hyperspherical-harmonics expansion for binding energies of a system of 4 <= N <= 728 helium atoms using a phenomenological soft attractive two-body He-He potential and a repulsive three-body force aimed at compensating for the absence of the two-body repulsive core. Earlier calculations with such a potential have shown an improved convergence when N increases from four to six. The present study reveals that the improved convergence occurs only for a limited range of N determined by the range of the three-body repulsion. For a soft repulsive three-body force, the convergence is fast for N <= 20, while for a short-range three-body repulsion it deteriorates at N >= 10. The reasons for this deterioration are discussed. The range of the three-body force also determines the binding energy behavior with N, and it is also responsible for binding the excited states. The long-range force binds all first excited 0(+) states but strongly underbinds the systems of N helium atoms at large N. The short-range force does not bind the first 0(+) states for A <= 7 but gives better predictions of binding energies as compared to the calculations of other authors though overestimating them. Some options to improve both the description of the binding energies and the convergence of the hyperspherical-harmonics expansion using phenomenological forces are discussed. It is pointed out that a fast convergence is very much needed for the reliable predictions of states with nonzero angular momentum, examples of which are also given.
机译：本文利用现象学的软吸引力两体He-He势和以排斥力为三体的力，对超球形调和展开对4 <= N <= 728个氦原子系统的结合能进行了数值收敛研究。补偿缺少两体排斥核心。当N从4增加到6时，具有这种潜力的早期计算显示出改善的收敛性。本研究表明，改进的收敛性仅在由三体排斥力范围决定的有限N范围内发生。对于软排斥的三体力，当N <= 20时，收敛速度很快，而对于短距离的三体斥力，在N> = 10时会恶化。讨论了这种恶化的原因。三体力的范围还决定了与N的结合能行为，并且还负责结合激发态。远距离力束缚所有最初的激发0（+）状态，但在大N时强烈地束缚了N个氦原子系统。短距离力不束缚A <= 7的前0（+）状态，但能提供更好的结合力与其他作者的计算相比，结合能的预测虽然被高估了。讨论了一些使用现象学力来改善结合能的描述和超球谐谐波展开的收敛性的选项。要指出的是，对于具有非零角动量的状态的可靠预测，非常需要快速收敛，并给出了示例。

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