Phenomenological wave functions for the massA=14 system and a consistent description of beta decay observables

Abstract

A set of phenomenological wave functions has been derived to describe the 14N ground state and the isospin triplet consisting of the 14C ground state, the first excited state of 14N at 2.313 MeV and the 140 ground state. Elastic and inelastic electron scattering form factors, the magnetic moment of the 14N ground state and the shape factors in the /~ -+ decay have been employed in a multiparameter fitting procedure to determine the amplitudes of the wave functions in L-S coupling. The inclusion of the beta decay observables in the fit has become possible for the first time since exact formulas for the shape factor in higher order do exist. The set of wave functions deduced exhibit predominately an L = 0 contribution for the 0 +; 1 states and L --1 and 2 contributions of nearly equal weight for the 1 § 0 state. It was observed that the inclusion of the shape factors allowed a more stringent determination of the amplitudes compared to previous attempts reported in the literature and led in the case of the 0 +; 1 states to wave functions that show a small but noticeable difference within the isospin triplet. Besides the observables used for the fit, the radiative width Fy (M1) of the 2.313 MeV state in 14N can be described quite well with the derived wave functions, and in addition it has become possible to predict the pathological large ft-value of the 14C decay and the ft + value of the 140 decay precisely. The wave functions are also applied to calculate the 14N (y, g +) cross section.

Search for the electron decay mode e→γ + ν with the prototype of the BOREXINO detector

“…The 14 C spectrum shape factor can be parametrized as C(E) = 1 + αE. In the experiments [46,47] the parameter α was measured to be α −1.0 ± 0.04 MeV −1 in good agreement with theoretical predictions of [48]. But in experiment [49] a value α −0.45 ± 0.04 MeV −1 was obtained, which is consistent with other theoretical calculations [50,51].…”

Comparison of 14C liquid scintillation counting at NIST and NRC Canada

“…As we discovered, the 14 C beta spectrum is known to deviate from a purely allowed shape, with several discrepant shape factors reported in the literature based on experiment and calculation (Sonntag et al, 1970; Genz et al, 1991; García and Brown, 1995; Alimonti et al, 1998; Kuzminov and Osetrova, 2000). We reanalyzed our data with six different sets of shape factor coefficients (including allowed) from the literature, input into MICELLE2 for efficiency calculations.…”

Gamow-Teller Strengths in theA=14Multiplet: A Challenge to the Shell Model

“…and the 3.95 MeV state of 14 N were characterized by angular momentum transfers L 2 and 0, respectively [6]. This idea was also investigated extensively by Genz et al [7], who extracted phenomenological wave functions which were capable of describing many (but not all) features of the A 14 multiplet simultaneously. García and Brown [8] found that by mixing the two lowest 1 states and adding 2@!…”