费米子在原子阱和原子核中的配对
Pairing of fermions in atomic traps and nuclei
摘要：
在谐振子阱中的费米子原子的配对间隙的计算范围广泛的相互作用强度和粒子数，并在核配对相比。特别是对能隙超过能级间距但小于壳层分裂$\hbarω$的系统进行了研究，这适用于大多数囚禁费米原子系统以及有限核。当求解具有这种多能级配对的大陷阱的能隙方程时，人们发现附近谐振子能级和准粒子能量之间的矩阵元导致能隙的双对数，以及在幻数处的明显壳结构。有人认为，在核中的中子和质子配对属于类的多级配对，他们的壳层结构自然遵循和差距规模为$\sim A^{-1/3}$ -所有在定性协议与奇偶交错的核结合能。大系统中的配对与大系统中的配对有关。对于大核，中子和质子超流能隙接近无限核物质中的渐近值：$Δ\simeq 1.1$ MeV。
英文摘要：
Pairing gaps for fermionic atoms in harmonic oscillator traps are calculated for a wide range of interaction strengths and particle number, and compared to pairing in nuclei. Especially systems, where the pairing gap exceeds the level spacing but is smaller than the shell splitting $\hbarω$, are studied which applies to most trapped Fermi atomic systems as well as to finite nuclei. When solving the gap equation for a large trap with such multi-level pairing, one finds that the matrix elements between nearby harmonic oscillator levels and the quasi-particle energies lead to a double logarithm of the gap, and a pronounced shell structure at magic numbers. It is argued that neutron and proton pairing in nuclei belongs to the class of multi-level pairing, that their shell structure follows naturally and that the gaps scale as $\sim A^{-1/3}$ - all in qualitative agreement with odd-even staggering of nuclear binding energies. Pairing in large systems are related to that in the bulk limit. For large nuclei the neutron and proton superfluid gaps approach the asymptotic value in infinite nuclear matter: $Δ\simeq 1.1$ MeV.
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