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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
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