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W. Prochazka, F. Bensch:
"Geometriefaktoren endlicher Anordnungen in der Feldphysik";
Report for AIAU 74203, Atominstitut der Österreichischen Hochschulen, Wien, Austria; 1974.

The geometric factors in problems of field physics (radiation fields and also gravitational fields and electromagnetic fields) are investigated for finite arrangements. Although in theoretical considerations field source and probe (test object) are usually assumed to be point-like, realistic measuring arrangements do not justify this assumption. In many cases the assumption is justified that the deviation of the properties of the "real" from the idealized arrangement is caused solely by geometric factors. Based on this assumption we derive and discuss correction formulae for finite sizes of several geometric arrangements. The proposed correction formulae result from second order approximations and are quite accurate. The correction problem of field sources and probes not idealized as points and located arbitrarily is investigated for the first time. The examples of application are taken mainly from neutron physics (for example activation detectors), from radiation physics (for example the calculation of effective solid angles) and from electrostatics. Two main problems are considered: Firstly, for a source and/or a probe of general shape we derive the expected measured quantity from the known field distribution of point-like sources. Secondly, we relate measured quantities to values obtained from fields of point-like sources and probes. Furthermore, we demonstrate that the proposed correction formulae are closely related to an expansion of the corresponding functions in "generalized" static multipoles. The investigation of the asymptotic behaviour of the measurable quantities for distances between source and probe converging to infinity reveals unexpected results in certain cases.

Keywords: activation detectors, asymptotic solutions, corrections, diffusion length, electric fields, field equations, flux density, geometry, gravitational fields, magnetic fields, multipoles, neutron age, neutron detection, neutron flux, neutron sources, probes, series expansion, size, spatial distributions