Abstract
A trapezoidal approximation to the Fermi-Dirac distribution function is used in order to obtain a simple description of semi-degenerate bound-states of fermions. The model coincides with the exact result up to the first correction in the low-temperature expansion while leading to finite equilibrium configurations; thus, it represents an alternative to the use of confining cells or of energy-or density-cutoffs. The atom and the self-gravitating cluster are worked out as explicit examples.
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