Proposal of a directly measurable parameter quantifying the halo nature of one-neutron nuclei

We propose a measurable parameter H quantifying the halo nature of one-neutron halo nuclei (a) and investigate the properties of H, assuming the core + neutron (c+n) model for a. The parameter H is defined by H=[σabs(a)-σabs(c)]/σabs(n) with directly measurable absorption cross sections σabs of a, c, and n scattering at the same incident energy per nucleon. It varies with the one-neutron separation energy Sn in a range of 0≤H≤1, and the halo structure is most developed when H=1. This situation is realized only for s-wave halo nuclei in the Sn=0 limit. We consider Be11 and C15,19 as s-wave halo nuclei, Ne31 and Mg37 as p-wave halo nuclei, and C17 as an example of d-wave nonhalo nuclei. For each of halo nuclei, the value of H is deduced at a measured Sn from measured total reaction cross sections for c, n, and a scattering at intermediate and high incident energies where projectile breakup effects are negligible. The location of the resulting (Sn,H) is plotted in the Sn-H plane. The empirical values of H at the measured Sn are extrapolated to small Sn with model calculations based on the eikonal + adiabatic approximation. In the Sn-H plane, the model lines are well separated into three groups of s-wave halo, p-wave halo, and d-wave nonhalo particularly in the vicinity of Sn=0, and the s-wave halo lines are always above the other lines, since only the s-wave halo lines can reach a point (Sn,H)=(0,1) independently of the concrete form of the interaction between c and n. The relation among the three kinds of lines may be universal for any halo nucleus with small Sn. The point (Sn,H)=(0,1) can be regarded as a scale-invariant point in the sense that the z-integrated neutron density characterizing halo structure is invariant under the scale transformation there.