The N7/5 Law for Charged Bosons
Non-relativistic bosons interacting with Coulomb forces are unstable, as Dyson showed 20 years ago, in the sense that the ground state energy satisfies E 0 ≦ −AN 7/5 We prove that 7/5 is the correct power by proving that E o ≧ −BN 7/5. For the non-relativistic bosonic, one-component jellium problem, Foldy and Girardeau showed that E 0 ≦ − CN p 1/4 This 1/4 law is also validated here by showing that E 0 ≧ −DN p 1/4. These bounds prove that the Bogoliubov type paired wave function correctly predicts the order of magnitude of the energy.
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