What is the meaning of Directivity and Reflection coefficient for a RX antenna?
There's a long discussion in comments. Here's some echoes.
You use the common series equivalent circuit for the  antenna. It's the Thevenin equivalent. If we assume that the equivalent circuit is valid then the radiation resistance can be shown to exist also when an antenna receives and it should re-radiate (=scatter) 50% of the catched power if nothing is dissipated in resistive losses and the load (=line+receiver) are exactly matched to the antenna. More re-radiation can be got by having mismatched load and that extra can be calculated with the reflection factor you asked. An open or shorted receiver end of the antenna reflects everything back and that is radiated to the space if nothing is dissipated in resistive losses.
The said automatic 50% minimum re-radiation power in lossless case can be found in numerous antenna theory writings including Wikipedia and the book of Balanis which is referenced in comments. The book is freely readable here https://archive.org/details/Antenna.Theory.Analysis.and.Design3rd.Edition/page/n97/mode/1up
The 50% re-radiation is presented in page 85 (by the original page numbering, not the web reader numbering).
Not everyone accept the idea that well matched lossless antennas should re-radiate 50% of the catched RF power. But it must happen if we accept that an antenna should have the same simplistically deduced Thevenin equivalent circuit, no matter is it connected to a passive load or to a device which maybe also transmits something.
How to present Thevenin (or Norton) equivalent of receiving antenna without that obscure automatic re-radiation? Some people seem to want that the receiver should see an equivalent circuit which outputs what's really captured. Some scientific papers are published of the problem. Here's links to 2 of them. The first one is free (or pirated), but full of cryptic math: https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205.6066&amp;rep=rep1&amp;type=pdf
I unfortunately haven't good enough math skills to judge the calculations and how well it succeeds to get over the automatic 50% re-radiation. Maybe someone with the needed skills could give a comprehensive explanation for practical electricians.
The text has in its end a long list of references to earlier  texts of the same problem.
The second one must be purchased (I do not have it): https://ieeexplore.ieee.org/document/1203128
Directivity is connected with the effective catching area of the antenna. For the radiation which comes from the most sensitive direction of the antenna the effective catching area Ae = G((wavelength)^2 )/(4Pi) where G=the gain. The catched power is the wave intensity (watts/square meter) multiplied by Ae.