Relativistic N-Boson Systems Bound by Oscillator Pair Potentials

Details Relativistic N-Boson Systems Bound by Oscillator Pair Potentials Relativistic N-Boson Systems Bound by Oscillator Pair Potentials

2001-10-11

arxiv.org/abs/math-ph/0110015v2

J.Math.Phys. 43 (2002) 1237; Erratum-ibid. 44 (2003) 2724-2725

Physics

Mathematical Physics

v2: A scale analysis of P is now included; this leads to revised energy bounds, which coalesce in the large-m limit

Scientific paper

10.1063/1.1446245

We study the lowest energy E of a relativistic system of N identical bosons bound by harmonic-oscillator pair potentials in three spatial dimensions. In natural units the system has the semirelativistic ``spinless-Salpeter'' Hamiltonian H = \sum_{i=1}^N \sqrt{m^2 + p_i^2} + \sum_{j>i=1}^N gamma |r_i - r_j|^2, gamma > 0. We derive the following energy bounds: E(N) = min_{r>0} [N (m^2 + 2 (N-1) P^2 / (N r^2))^1/2 + N (N-1) gamma r^2 / 2], N \ge 2, where P=1.376 yields a lower bound and P=3/2 yields an upper bound for all N \ge 2. A sharper lower bound is given by the function P = P(mu), where mu = m(N/(gamma(N-1)^2))^(1/3), which makes the formula for E(2) exact: with this choice of P, the bounds coincide for all N \ge 2 in the Schroedinger limit m --> infinity.

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