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From page 22.2 of the 2005 ARRL Handbook

"CONDUCTOR SIZE"

"The impedance of the antenna also depends on the diameter of the
conductor in relation to the wavelength. If the diameter of the
conductor is increased, the capacitance per unit length increases
and
the inductance per unit length decreases. Since the radiation
resistance is affected relatively little, the decreased L/C ratio
causes the Q of the antenna to decrease so that the resonance curve
becomes less sharp with change in frequency. This effect is greater
as
the diameter is increased, and is a property of some importance at
the
very high frequencies where the wavelength is small."

Lots of interesting graphs and charts in the ARRL Antenna Handbook
as
well.
======================================
A nice summary.

But to be more precise, it is the ratio of conductor diameter over
length which matters.

Inductance and capacitance change very slowly with diameter/length.
The changes are hardly noticeable.

L = 0.2 * Length * ( Ln( 4 * Length / Dia ) -1 ) microhenrys.

C = 55.55 * Length / ( Ln( 4 * Length / Dia ) -1 ) picofarads.

Zo = Sqrt( L / C ) = 60 * Ln( 4 * Length / Dia ) -1 ) ohms.

Antenna Q = 2 * Pi * Freq * L / (Distributed Radiation Resistance).

For a half-wave dipole the distributed radiation resistance is 146
ohms, or twice the feedpoint resistance.
----
Reg.