Fermi heap and Fermi hole

Fermi heap and Fermi hole refer to two closely related quantum phenomena that occur in many-electron atoms. They arise due to the Pauli exclusion principle, according to which no two electrons can be in the same quantum state in a system (which, accounting for electrons' spin, means that there can be up to two electrons in the same orbital). Due to indistinguishability of elementary particles, the probability of a measurement yielding a certain eigenvalue must be invariant when electrons are exchanged, which means that the probability amplitude must either remain the same or change sign. For instance, consider an excited state of the helium atom in which electron 1 is in the 1s orbital and electron 2 has been excited to the 2s orbital. It is not possible, even in principle, to distinguish electron 1 from electron 2. In other words, electron 2 might be in the 1s orbital with electron 1 in the 2s orbital. As they are fermions, electrons must be described by an anti-symmetric wavefunction which must change sign under electron exchange, resulting in either a Fermi hole (having a lower probability of being found close to each other) or a Fermi heap (having a higher probability of being found close to each other). Since electrons repel one another electrically, Fermi holes and Fermi heaps have drastic effects on the energy of many-electron atoms, although the effect can be illustrated in the case of the helium atom.