用真实对势变分计算~ 4 He四聚体基态和激发态
Variational calculation of 4He tetramer ground and excited states using a realistic pair potential
摘要：
用我们的高斯展开方法（GEM）对4 He三聚体和四聚体的基态和激发态进行了计算.该方法已广泛用于核物理和奇异原子/分子物理中的各种三体、四体和五体系统。三聚体（四聚体）波函数展开的对称三（四）体高斯基函数，从非常紧凑的非常扩散，没有假设任何对关联函数。对三聚体基态和激发态的计算结果与文献值符合得很好。四聚体基态和激发态的结合能分别为558.98 mK和127.33 mK（比三聚体基态低0.93 mK）。在三聚体和四聚体的基态和激发态中，二聚体中的短程关联的形状完全相同（r_ij < 4 π）。通过分析这些激发态的渐近波函数（精确到1000 μ m），我们提出了一个模型，该模型仅用二聚体结合能B_2就预言了从4个He_{N-1}基态测得的4He_N的第一激发态结合能为N/2（N-1）xB_2，在N=3和4时拟合得很好。
英文摘要：
We calculated the 4He trimer and tetramer ground and excited states with the LM2M2 potential using our Gaussian expansion method (GEM) for ab initio variational calculations of few-body systems. The method has extensively been used for a variety of three-, four- and five-body systems in nuclear physics and exotic atomic/molecular physics. The trimer (tetramer) wave function is expanded in terms of symmetric three-(four-)body Gaussian basis functions, ranging from very compact to very diffuse, without assuming any pair correlation function. Calculated results of the trimer ground and excited states are in excellent agreement with the literature. Binding energies of the tetramer ground and excited states are obtained to be 558.98 mK and 127.33 mK (0.93 mK below the trimer ground state), respectively. Precisely the same shape of the short-range correlation (r_ij < 4 Å) in the dimer appear in the ground and excited states of the trimer and tetramer. Analyzing the asymptotic wave functions (accurate up to 1000 Å) of those excited states, we propose a model which predicts the binding energy of the first excited state of 4He_N measured from the 4He_{N-1} ground state to be N/2(N-1)xB_2 using dimer binding energy B_2 only; fit in N=3 and 4 is excellent.
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