The S-matrix approach to the treatment of photon splitting in a magnetized vacuum, with the electron propagators expressed in the Landau representation, is discussed critically. Although the analytic results of Mentzel, Berg and Wunner are confirmed, we propose that their available numerical results may be subject to two previously unidentified sources of error associated with the sum over principal quantum number n, leading to spurious contributions to the amplitude, and the extremely slow convergence of the sum for weak fields. It is shown how the sums may be rearranged to avoid the spurious contributions. If the Euler-Maclaurin summation formula is used to evaluate the infinite sums over n, the S-matrix approach then reproduces results derived by the effective Lagrangian and proper-time techniques in the weak-field, low-frequency limit. This method gives reliable results, for Bտ0.01 and Շ0.1, that reproduce those obtained by proper-time techniques. The S-matrix approach simplifies in the strong-field limit, Bӷ1, where the sum over n converges rapidly. Our results show that the branching ratio for the splittings Ќ→ЌЌ and Ќ→ʈʈ decreases from its known value ϳ3.4 for BӶ1 towards zero for Bӷ1. For weak fields the S-matrix approach is unnecessarily cumbersome, and future numerical work should be based on the alternative approaches. ͓S0556-2821͑98͒04809-7͔ PACS number͑s͒: 12.20.Ds, 95.30.Cq, 97.60.Jd, 98.70.Rz *
Relativistic effects on dispersion in a degenerate electron gas are discussed by comparing known response functions derived relativistically (by Jancovici) and nonrelativistically (by Lindhard). The main distinguishing feature is one-photon pair creation, which leads to logarithmic singularities in the response functions. Dispersion curves for longitudinal waves have a similar tongue-like appearance in the relativistic and nonrelativistic case, with the main relativistic effects being on the Fermi speed and the cutoff frequency. For transverse waves the nonrelativistic treatment has a nonphysical feature near the cutoff frequency for large Fermi momenta, and this is attributed to an incorrect treatment of the electron spin. We find (with two important provisos) that one-photon pair creation is allowed in superdense plasmas, implying relatively strong coupling between transverse waves and pair creation
Potential energy curves for different states of XO + (X = Ar, Kr, Xe) have been determined by experimental and theoretical methods. Elastic scattering cross sections obtained from the scattering of O+(2P, *D, 4S) on Ar, Kr and Xe were used to determine the corresponding potential curves. The curve for the _y4Z-state of ArO + calculated including correlation effects is in very good ~ agreement with the experimental curve. The lower excited states of ArO + which correlate with Ar+(~P) and O(sP) are calculated, including correlation effects.
It is shown how the fully relativistic quantum expression for the response of an arbitrary magnetized electron (plus positron) gas reproduces its nonquantum counterpart. In the relativistic quantum case the dispersion is due to both gyromagnetic absorption and one-photon pair creation. Although one-photon pair creation has no classical counterpart, somewhat surprisingly it needs to be retained to reproduce the nonquantum limit correctly. For unpolarized electrons it is shown that the first quantum correction (order ℏ) to the nonquantum limit for the dispersion vanishes when one sums over all excited states, as for an unmagnetized electron gas. However, in the magnetized case there is a contribution of order ℏ from the ground state, which is the only state with a specific spin.
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