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

Abstract

Explicit relations between the effective-range expansion and the nuclear vertex constant or asymptotic normalization coefficient (ANC) for the virtual decay B → 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, α + t, and α + 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 than 5 MeV.

Determination of the3He+α→7Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of theTursunmahatov1, Yarmukhamedov2 2012Phys. Rev. CSelf Cite182161View full textAdd to dashboardCite

“…Therefore, the self-consistent result obtained in Ref. [45] between the fundamental characteristics of the bound (α + 3 He) state of the nuclear 7 Be in the form of the ANCs, the effective-range expansion parameters, and the low-energy phase shifts for α-3 He scattering, confirms the reliability of the ANC values recommended in the present work. Therefore, at present the ANC values recommended in this work can be considered as straightforward "best indirectly determined" values of the ANCs (NVCs) by means of the analysis of the modern precisely measured astrophysical S factors [9][10][11][12][13][14], and they are the most important result of this work.…”

“…[45], the ANC values recommended in the present work have already been applied to the analysis of low-energy experimental phase shifts for α-3 He scattering within the effective-range expansions restricted to terms up to k 4 , and the "indirectly determined" values of the effective-range expansion parameters were obtained, which reproduce fairly well the corresponding experimental phase shifts up to energies E of about 5 MeV. Therefore, the self-consistent result obtained in Ref.…”

Combiningab initiocalculations and low-energy effective field theory for halo nuclear systems: The case of7Li+n→8Li+γ

“…We note that similar connections between ANCs and effective-range parameters have previously been obtained without the use of EFT, e.g. in deriving S-factor parameterizations of radiative-capture cross sections [67,68].…”

Low-energy bound states, resonances, and scattering of light ions

“…Theoretical approaches can roughly be divided into two kinds, taking either the ions as degrees of freedom or starting from individual nucleons. The former approach includes a variety of models [2][3][4][5], effective range expansions [6][7][8][9][10][11][12], and effective field theories (EFTs) [13][14][15][16][17][18]; the microscopic approach ranges from simpler models [19] to ab initio computations [20][21][22][23]. Unfortunately, there are still significant uncertainties [1], and data tables for relevant quantities such as asymptotic normalization coefficients (ANCs) or astrophysical S factors may [24] or may not [25,26] contain theoretical uncertainties.…”