Noncausal chains

The equivalence of the Feynman rules for gauge fields and the usual Feynman rules is demonstrated, by explicit calculation, for the special case of a scalar field with self-coupling. The result may be applicable to more general cases, such as the quantum theory of gravity.     

Measurement of absolute cross sections for excitation of the 3s(2)3p(5) 2P(o)(3/2)- 3s(2)3p(5) 2P(o)(1/2) fine-structure transition in Fe9+

Experimental cross sections are reported for the 3s(2)3p(5) 2P(o)(3/2)- 3s(2)3p(5) 2P(o)(1/2) transition in Fe9+ located at 1.945 eV. The center-of-mass interaction energies are in the range of 1.72 eV (below threshold) through threshold, to 5.6 eV (2.9 x threshold). Data are compared with results of a 49-state Breit-Pauli R-matrix theory. The experiment detects structures at 3.5 and 4.6 eV corresponding to enhancement of the direct excitation via many narrow, closely spaced resonances about these energies calculated by the theory. Iron is present in practically every astrophysical object, as well as being an impurity in fusion plasmas. Present data are the first electron-energy-loss measurements on a highly charged iron ion.