Evaluate the effect of Coulomb-dressed forbidden-state projections in other charged-pair calculations

Evaluate the size of the Coulomb-dressing effect on calculated observables in other cluster or halo calculations that remove deep forbidden states of charged pairs by projection or by a supersymmetric transformation.

Background

The paper argues that, when a Coulomb force is included, Pauli-forbidden states should be projected as eigenstates of the nuclear-plus-Coulomb pair Hamiltonian rather than as undressed nuclear states or oscillator approximations. In the systems studied, replacing Coulomb-dressed forbidden states can shift three-body energies by amounts ranging from approximately 20 keV in alpha-nucleon channels to more than 1 MeV in the three-alpha system.

The authors note that the same issue may arise in other cluster and halo calculations, including methods based on projection or supersymmetric transformations, but state that its magnitude has not yet been determined in those settings.

References

The same distinction may apply to other cluster or halo calculations which remove deep forbidden states of charged pairs, by projection or by a supersymmetric transformation such as that of Ref.; its size has not been evaluated there, and in the systems of this paper it ranges from about $20$~keV, as estimated for the $\alpha N$ pairs in Sec.~\ref{sec:conv3b}, to the $3\alpha$ value of Table~\ref{tab:dressedtest}.

— The Fock representation of the Coulomb interaction. II. Three-body bound states  (2610.08520 - Nishonov, 6 Oct 2026) in Section 6, 'Summary and outlook' (section label sec:summary)