A model for orientation effects in electron‐transfer reactions

A method for solving the single‐particle Schrödinger equation with an oblate spheroidal potential of finite depth is presented. The wave functions are then used to calculate the matrix element T_BA which appears in theories of nonadiabatic electron transfer. The results illustrate the effects of mutual orientation and separation of the two centers on TBA. Trends in these results are discussed in terms of geometrical and nodal structure effects. Analytical expressions related to T_BA for states of spherical wells are presented and used to analyze the nodal structure effects for T_BA for the spheroidal wells

Approximating parabolas as natural bounds of Heisenberg spectra: Reply on the comment of O. Waldmann

O. Waldmann has shown that some spin systems, which fulfill the condition of a weakly homogeneous coupling matrix, have a spectrum whose minimal or maximal energies are rather poorly approximated by a quadratic dependence on the total spin quantum number. We comment on this observation and provide the new argument that, under certain conditions, the approximating parabolas appear as natural bounds of the spectrum generated by spin coherent states.Comment: 2 pages, accepted for Europhysics Letter

Comment on "Bounding and approximating parabolas for the spectrum of Heisenberg spin systems" by Schmidt, Schnack and Luban

Recently, Schmidt et al. proved that the energy spectrum of a Heisenberg spin system (HSS) is bounded by two parabolas, i.e. lines which depend on the total spin quantum number S as S(S+1). The prove holds for homonuclear HSSs which fulfill a weak homogenity condition. Moreover, the extremal values of the exact spectrum of various HSS which were studied numerically were found to lie on approximate parabolas, named rotational bands, which could be obtained by a shift of the boundary parabolas. In view of this, it has been claimed that the rotational band structure (RBS) of the energy spectrum is a general behavior of HSSs. Furthermore, since the approximate parabolas are very close to the true boundaries of the spectrum for the examples discussed, it has been claimed that the methods allow to predict the detailed shape of the spectrum and related properties for a general HSS. In this comment I will show by means of examples that the RBS hypothesis is not valid for general HSSs. In particular, weak homogenity is neither a necessary nor a sufficient condition for a HSS to exhibit a spectrum with RBS.Comment: Comments on the work of Schmidt et al, Europhys. Lett. 55, 105 (2001), cond-mat/0101228 (for the reply see cond-mat/0111581). To be published in Europhys. Let

IPCS implications for future supersonic transport aircraft

The Integrated Propulsion Control System (IPCS) demonstrates control of an entire supersonic propulsion module - inlet, engine afterburner, and nozzle - with an HDC 601 digital computer. The program encompasses the design, build, qualification, and flight testing of control modes, software, and hardware. The flight test vehicle is an F-111E airplane. The L.H. inlet and engine will be operated under control of a digital computer mounted in the weapons bay. A general description and the current status of the IPCS program are given

Renormalization group study of the four-body problem

We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length is infinite and all energies are at the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of Platter et al. and von Stecher et al. that the four-body problem is universal, now also from a renormalization group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound state spectrum and comment on the influence of effective range corrections.Comment: 11 pages, 6 figures; v2: revised and published versio