On the interactions between nucleons in the valence shells of trans-²⁰⁸Pb nuclei

Summary

A lot of information concerning the interaction laws between nucleons in the valence shells of trans-²⁰⁸Pb nuclei can be obtained from experimental mass tables. The proton-neutron interaction energy can be expressed by$E_{np} = N_p N_n \varepsilon '_{np}$, whereN _p N _n is the number of n-p couples in the valence shells, and$\varepsilon '_{np}$ a weak, nearly constant interaction energy per n-p couple. Two methods are proposed for the calculation ofE _np. In even-even nuclei, the integral 2p-2p interaction energy is given by$E_{2p - 2p} = - \mathcal{N}_p (\mathcal{N}_p - 1)\varepsilon _{2p - 2p} /2$, where$\mathcal{N}_p$ is the number of proton pairs, and$\varepsilon _{2p - 2p}$ a weak, nearly constant interaction energy per 2p-2p couple. A similar relation holds for valence neutron pairs. The energy binding all the valence proton pairs to the²⁰⁸Pb core is$\mathcal{N}_p \bar \sigma _{2p}$, where$\bar \sigma _{2p}$ is calculable in a simple way fromZ=84 toZ=92; its value is independent of the number of pairs of nucleons of the other kind in the valence shells. A similar relation holds for valence neutron pairs. Similar laws hold in odd nuclei. The weakness of all these valence shell interaction energies, and the fact that the energy binding an unpaired proton to the²⁰⁸Pb core of odd-Z nuclei decreases rapidly as$\mathcal{N}_p$ increases, explain several properties, which are briefly discussed, of trans-²⁰⁸Pb nuclei: repulsion between valence neutrons, feasibility of Oganessian reactions, shell internal energy, and reactivity of the valence nucleons.