Connection between effective-range expansion and nuclear vertex constant or asymptotic normalization coefficient

TL;DR

This paper derives explicit relations linking the effective-range expansion with the nuclear vertex constant or ANC, enabling improved parameter determination for nuclear scattering and bound states, validated with experimental data for specific nuclear collisions.

Contribution

It introduces general relations between effective-range expansion and ANC for arbitrary orbital momentum, applicable to both charged and neutral cases, and demonstrates their practical use in nuclear physics.

Findings

Effective-range expansions valid up to 5 MeV for specific nuclear collisions.

Reduced free parameters in effective-range analysis when ANC is known.

Consistent determination of scattering parameters from experimental ANCs.

Abstract

Explicit relations between the effective-range expansion and the nuclear vertex constant or asymptotic normalization coefficient (ANC) for the virtual decay $B\to A+a$ are derived for an arbitrary orbital momentum together with the corresponding location condition for the ($A+a$) bound-state energy. They are valid both for the charged case and for the neutral case. Combining these relations with the standard effective-range function up to order six makes it possible to reduce to two the number of free effective-range parameters if an ANC value is known from experiment. Values for the scattering length, effective range, and form parameter are determined in this way for the $^{16}$O+$p$, $\alpha+t$ and $\alpha+^3$He collisions in partial waves where a bound state exists by using available ANCs deduced from experiments. The resulting effective-range expansions for these collisions are valid up to energies larger 5 MeV.