[Richard777 (OP)]

A “bound electron” orbits the atomic nucleus. It may be “paired” with a proton also “bound” within the nucleus. A “bound pair” (electron-proton) are assumed to form an electric dipole.

The quantized magnitude of “electric dipole moment” with undefined direction may be estimated. The moment contains a “quantum number” for electric dipole which has similar value to the quantum number (m_s) for magnetic dipole.

The Periodic Table of Elements has 18 “groups” and 7 “periods”. Evidence for the existence of magnetic and electric dipoles are hinted at by the arrangement of groups and periods within the Periodic Table. Evidence for an electric dipole within the atom is hinted at by “period pairs”. Evidence for a magnetic dipole within the atom is represented by “group sets”.

If the quantum number for electric dipole is included, then six quantum numbers may be arranged as a “quantum matrix”. The top row is associated with motion (radial, orbital, spin).

Is there some basis for experimental investigation of electric dipoles within the atom?
See reference attached.

[alancalverd]

Whilst the spin vectors of unpaired protons and electrons produce effective magnetic dipoles, atoms are electrically neutral and isolated atoms are effectively spherically symmetric, so do not present electric poles.

[Bored chemist]

The dipole in which Alan fervently doesn't believe are a contributor to this well documented effect.
https://en.wikipedia.org/wiki/London_dispersion_force

It depends on the timescale you look at.
On average an atom has no dipole.
At any given instant, it has.

[alancalverd]

Careful readers will note that I said "isolated atoms are spherically symmetric". The London dispersion  force is a

type of force acting between atoms and molecules that are normally electrically symmetric

, i.e. not a phenomenon associated with an isolated atom.
 

[Bored chemist]

Very careful readers will notice that the London forces are only displayed with 2 or more atoms, but that the dipoles exist anyway, even for a single atom.

Very Very careful readers will also note that Alan claims to have solved the problem for a perfectly spherical horse in a vacuum, rather than anything to do with the real universe.

The OP asks for experimental evidence.
Well, you can't do any experiment with an isolated atom. At the very least, you also need an experimenter.

[evan_au]

A “bound electron” ... may be “paired” with a proton also “bound” within the nucleus.

I assume you are referring to the Beta decay process: neutron → proton + electron + neutrino?
or the electron capture process: proton + electron → neutron + neutrino?

The proton is made up of 3 quarks: two up quarks of charge +2/3e and one down quark of charge −1/3e
- The neutron is made up of 3 quarks: one up quark of charge +2/3e and two down quarks of charge −1/3e
- Although the neutron has no overall charge, it does have a magnetic moment of −0.97×10⁻²⁶ J·T⁻¹ (compared to the proton's larger and opposite moment of 1.4×10⁻²⁶ J⋅T⁻¹)
- But there is no distinct electron within the neutron
- You could describe these decay reactions as changing a down quark to an up quark (or vice-versa)

See: https://en.wikipedia.org/wiki/Neutron#Structure_and_geometry_of_charge_distribution