The stability and instability of relativistic matter
The stability and instability of relativistic matter
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相对论物质的稳定性和不稳定性
DOI：
10.1007/3-540-27056-6_34
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发表时间：
1988
影响因子：
2.4
通讯作者：
H. Yau
中科院分区：
文献类型：
--
作者：
E. Lieb;H. Yau
我们考虑了电子和固定核通过库仑力相互作用的量子力学多体问题，但在动能的相对论形式下，(P_2C_2+M_2C_4)1/2−_mC_2代替了2/2M。电子被允许有q个自旋态(q=2)。对于一个电子和一个核，如果z为α>；2/π，则发生不稳定性，其中z为核电荷，α为精细结构常数。我们证明了在多体情况下，如果α≦2/π和α<；1/(47q)是稳定的。对于Smallza，也给出了在α上更好的界。在另一个方向，我们证明了存在一个临界αc(不大于12 8/15π)，使得如果α>；α，当原子核数目足够大时，对于所有正的z(不一定是积分的)，总是发生不稳定性。文中还给出了其他几个技术性质的结果，如相对论动能的局域化估计和界限。
We consider the quantum mechanical many-body problem of electrons and fixed nuclei interacting via Coulomb forces, but with a relativistic form for the kinetic energy, namelyp2/2mis replaced by (p2c2+m2c4)1/2−mc2. The electrons are allowed to haveqspin states (q= 2 in nature). For one electron and one nucleus instability occurs ifzα > 2/πwherezis the nuclear charge and α is the fine structure constant. We prove that stability occurs in the many-body case ifzα≦ 2/π and α < 1/(47q). For smallza better bound onαis also given. In the other direction we show that there is a critical αc(no greater than 128/15π) such that if α > αcthen instability always occurs forallpositivez(not necessarily integral) when the number of nuclei is large enough. Several other results of a technical nature are also given such as localization estimates and bounds for the relativistic kinetic energy.