Paradoxically, in beta decay, for instance, the final-state Coulomb forces pulling the electron inwards accelerate the emission. Quantum mechanics (q. m. ) makes the rate proportional to
α
≡
ρ
0
/
ρ
∞
;
ρ
0, ∞
(and
v
0, ∞
) are the particle densities (and speeds) at
r
= 0 and far upstream in the scattering state which describes the electron. Hence, as regards the effects of finalstate interactions, one must base one’s physical intuition on this ratio
α
. It is shown that according to (non-relativistic) classical mechanics, if the origin is accessible, then any central potential
U(r)
where
v
0
< ∞ (i. e. where
U
(0) > -∞) gives in 1, 2 and 3 dimensions,
α
1
=
v
∞
/
v
0
,
α
2
= 1,
α
3
=
v
0
/
v
∞
; the remaining course of
U(r)
is irrelevant to
α
. The same results hold also in q. m. in the semiclassical regime, i. e. in the W. K. B. approximation which for such potentials becomes valid at high wavenumbers; in 2D it needs rather careful formulation, and in 3D one must avoid the Langer modification. (The W. K. B. results apply even if d
U
/ d
r
diverges at
r
= 0, provided
U
(0) remains finite; these cases are covered by a simple extension of the argument. ) The square-well and exponential potentials are discussed as examples. Potentials which diverge at the origin are treated in the following paper.