High precision analytical description of the allowed β spectrum shape

Abstract

A fully analytical description of the allowed β spectrum shape is given in view of ongoing and planned measurements. Its study forms an invaluable tool in the search for physics beyond the standard electroweak model and the weak magnetism recoil term. Contributions stemming from finite size corrections, mass effects, and radiative corrections are reviewed. A particular focus is placed on atomic and chemical effects, where the existing description is extended and analytically provided. The effects of QCD-induced recoil terms are discussed, and cross-checks were performed for different theoretical formalisms. Special attention was given to a comparison of the treatment of nuclear structure effects in different formalisms. Corrections were derived for both Fermi and Gamow-Teller transitions, and methods of analytical evaluation thoroughly discussed. In its integrated form, calculated f values were in agreement with the most precise numerical results within the aimed for precision. We stress the need for an accurate evaluation of weak magnetism contributions, and note the possible significance of the oft-neglected induced pseudoscalar interaction. Together with improved atomic corrections, we then present an analytical description of the allowed β spectrum shape accurate to a few parts in 10 −4 down to 1 keV for low to medium Z nuclei, thereby extending the work by previous authors by nearly an order of magnitude.

First-forbidden transitions in the reactor anomaly

“…with W = E kin /m e c 2 + 1 the total electron energy in units of its rest mass, W 0 the spectral endpoint, p = √ W 2 − 1 the electron momentum in units of m e c, Z the atomic number of the final state, F (Z, W ) the wellknown Fermi function, C(Z, W ) the so-called shape factor and K(Z, W ) higher-order correction terms [21]. All nuclear structure information resides in the shape factor, C, which depends primarily on the degree of forbiddenness of the decay.…”

Relativistic Theory and Ab Initio Simulations of Electroweak Decay Spectra in Medium‐Heavy Nuclei and of Atomic and Molecular Electronic Structure

“…[18], where the reader may find further details on this topic. In particular, for the former discussion we refer to ref.…”

“…Finally, for later purposes, Equation (18) can be posted in the following form: The δ function enforces the energy conservation.…”

“…If one neglects the recoil of the daughter nucleus, the conserva-tion of energy leads to Q = T C + T ν , where T C = W C − c 2 is the kinetic energy of the emitted electron and T ν = W ν = c · q ν is the kinetic energy of the antineutrino. Finally, for later purposes, Equation (18) can be posted in the following form:…”

Decay microscope for trapped neon isotopes

“…On the other hand, there is a strong potential for improvement for the GT case, and it is the focus of several new betaspectrum campaigns utilizing nuclear [55][56][57][58][59][60][61], and neutron [62][63][64] decays, and aiming at σ(b GT ) 10 −3 (see table II). Correspondingly, theoretical corrections to the beta-spectrum shape are now at the level of a few 10 −4 [65].…”