English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider nuclei composed of nucleons which interact via two-bodypotentials decreasing exponentially at infinity. Protons and neutrons are notdistinguished in order to simplify notations. The basic result is the rigorousmathematical proof that the bound eigenstates of the nuclei belong to thesubspace $P \mathscr{H}$ spanned by the states of a single hole in the groundstate $\psi_{0}$ of the parent nucleus with an extra nucleon, as in theuncorrelated models. This follows from the exponential decay of $\psi_{0}$ whena nucleon is very far apart from the residual nucleus. We prove that the realdifference from the uncorrelated models is that $P \mathscr{H}$ has an infinitedimension and contains generalized single hole states, distinguishable from theusual ones by the fact that one cannot assign a wave function to the hole. Thebound eigenstates of the nuclei are just states of this kind. Some physicalconsequences are discussed, in particular the unexpected fact that thedynamical part of the single-hole Hamiltonian, although nonnull, does notaffect the single-hole overlaps with the bound eigenstates. The decay of$\psi_{0}$ provides the asymptotic behaviours of many single-hole quantities,in particular the nuclear density matrix. Thus a by product of this paper isthe rigorous proof of the method developed by Van Neck, Waroquier and Heyde tocalculate overlaps and separation energies.

Asymptotics of the nucleus ground-state and single-hole nature of the bound states of the nuclei