Dave Shrader wrote:
"The effective aperture is the effective aperture is the effective
aperture...."

And by any other name it would likely smell as sweet.

Terman has a definitionin of sorts in his 1955 edition on page 899:
Directive gain=(4 pi)(effective aperture)(k) divided by lambda squared.

Arnold B. Bailey is much more descriptive in "TV and Other Receiving
Antennas", starting around page 298. I`ve tried to condense and number
his points:
1. The radio field is expressed in volts per meter or in watts per
square meter.
2. Our standard dipole will have a capture area within the radio field,
broadside to the field, with the rod positioned in the direction of the
electric vector. (not cross-polarized)
3. Our 1/2-wave dipole has a capture area extending the 1/2-wavelength
of the rod, and 1/8-wavelength either side of the center of the rod.
4. The area thus calculates as lambda squared over 8.
5. This effective area representation is a simplification but it works
for most purposes.
6. If we can modify our 1/2-wave antenna to capture more signal than
normal, we say the antenna has gain.
7. "Capture area" is pure fiction but it gives the right answers.
8. Zero-dB gain antennas all have the same "capture area", and are
assumed to be resonant which is an essential requirement enabling full
performance.
9. Shape, size, power transfer capability, and directional response are
the four main factors which determine an antenna`s utility. (Bailey has
great elaboration on each of these four factors.)
10. Some antenna shapes operate well over a wide frequency bandwidth,
others don`t.
11. Fat antennas tend to be broadband and are shorter than a free-space
wavelength, indicating a reduced signal velocity along their lengths.
12. All parts of the receiving antenna rod intercept the radio wave.
13. Induced current is reflected by open-circuit ends of the antenna
rod.
14. Impedance at the center of the rod is the result of incident and
reflected waves interacting.
15. Resonance is a result of interaction of incident and reflected
signal components in the rod.
16. The antenna rod has a characteristic resistance independent of the
reflected signal, and this resistance is determined by the ratio of
voltage on the rod to current.. (This is found on page 306.)
17. From the size of an antenna rod we can determiner its capacitance
per unit length. This factor determines its characteristic resistance.
(voltage to current ratio)
18. Reflection coefficient at the ends of the rod depends on
configuration. Thicker antennas have smaller reflections at their ends.
19. Conical rods which are thicker toward their extremities produce weak
reflections, and tend to have broadband responses.
20. On thin dipoles at first resonance, there is substantial reflection
from its ends and the reflection is 180-degrees out of phase with the
incident signal.
21. 1/4-wave back from the open-circuit ends of the antenna, the voltage
is low and the current is high, so the impedance (a resistance) is low.
The resistance 1/4-wavelencth back from the open-circuit ends is much
lower than the characteristic resistance of the rod to the signal
traveling in either direction alonng the antenna rod.
22. With reflection----
R = Vincident - Vreflected / Iincident + Ireflected
(Whereas, the Ro = V/I
23. Fat antennas are less directional than thin antennas and keep their
broadside lobe together better at harmonic frequencies.

Don`t know what the particular value of effective aperture is. Terman
found it useful in describing the directional characteristics of a
matress antenna. Since effective aperture is related to directive gain
by constants, why not just stick with directive gain? Bailey, a leading
Bell Labs antenna researcher, said capture area is pure fiction anyway
as the grip on radiated energy does not start and stop abrubtly at the
imaginary boundaries used to describe it.

Obviously, effective aperture has enjoyed some popularity among some who
found it useful. The effective area of an antenna has a dictionary
definition: The square of the wavelength multiplied by the power gain in
a particular direction, divided by 4 pi. The "capture area" is defined
as: The area of the antenna elements that intercept radio signals.
I may have confused the definitions.

Best regards, Richard Harrison, KB5WZI