What is the potential field of an ion near the Bohr radius?

[Ganesh Ujwal]

I figure that at large enough distances, the potential field of an ion is just the Coulomb potential for its net charge. But what happens at scales comparable to the ion's Bohr radius? Could there be, for example, some sort of screening effect from the electron shell that changes the potential? (depending on what the test charge is, like if you dropped a single electron near an ion)

I'm a bit rusty on quantum mechanics, but I do remember that the math for atoms that aren't hydrogen gets complicated. Is there a known good way to approximate this potential? Or is my best bet to go download some quantum chemistry software?

 

[ShayanJ]

Study about multipole expansion of electric potential!

 

[DrClaude]

I figure that at large enough distances, the potential field of an ion is just the Coulomb potential for its net charge. But what happens at scales comparable to the ion's Bohr radius? Could there be, for example, some sort of screening effect from the electron shell that changes the potential? (depending on what the test charge is, like if you dropped a single electron near an ion)

I'm a bit rusty on quantum mechanics, but I do remember that the math for atoms that aren't hydrogen gets complicated. Is there a known good way to approximate this potential? Or is my best bet to go download some quantum chemistry software?

Not only is there a screening effect, but you have to include electron-electron interactions also. For simple calculations, you use the Central Field Approximation, but to get anything reliable, I guess that numerical calculations are the way to go.

 

[DrClaude]

Study about multipole expansion of electric potential!

That won't work at the short distances the OP is considering.