Fermi theory of nuclearβdecay and heavy neutrino searches

Abstract

We examine the data analysis of nuclear 1 3 decay of 3~, 14C, 3 5~, and 6 3~i , using a relativistic Fermi function for a Hulthen screened field. This Fermi function does not differ much from that used by Hime, Jelley, and Simpson in the cases of light nuclei, but in the cases of sulfur and nickel reduces significantly the claimed spectral excess and, hence, the mixing of the heavy neutrino. We also discuss radiative corrections to 35S data. PACS numberk): 23.40. Bw, 12.15.Ff, 23.40.Hc, 29.30.Dn Recent controversy regarding the existence of a heavy neutrino in nuclear p decay has attracted much attention [I-71. A t issue is the reported spectral excess in P decay which is interpreted by authors of Refs. [1,3,4] as the evidence of a 17-keV neutrino with a 0.8% to 1.6% mixing. Since the claimed mixing is of the order 1% and since many factors are involved in the data analysis, corrections of the same order ( > 0.1%) should be addressed and fully investigated.The dimensionless Fermi function is an important factor affecting p decay. It plays an important role in the decay process, and its screening is important especially in the case of heavy nuclei or low energies [8]. In this note we examine the effect of an alternative Fermi function on different decay processes in the energy regions of interest relevant to the reported heavy-neutrino signal [9]. In particular, we use a relativistic Fermi function obtained by Durand [8] based on an exact solution to the KleinGordon equation with a Hulthen potential for the screened field and compare it to the screened Fermi functions employed by Hime, Jelley, and Simpson [1,3,4]. It is found that while the two different approaches do not differ significantly in the cases of 3~ and 14c, our results reduce the spectral excess by about 0.3% and 1% for 3 5~ and 6 3~i , respectively. This undoubtedly calls for further investigation regarding theoretical uncertainties which are larger than 0.1% in order to fully understand the issue of heavy-neutrino mixing. The correction in this Rapid Communication makes the excess signal in the 6 3~i data of Ref.[4] totally vanish.The screened Fermi function was first studied by Rose [lo] using the W K B method. Further calculations have been done since then, based both on exactly solvable models [8,11] and on approximation methods [12,13]. In allowed nuclear / 3 decay, one can write the decay spectra, assuming only a zero mass neutrino, as where p, E, T, and Q are the electron momentum, total energy, kinetic energy, and its maximum allowed kinetic energy, and Z is the atomic number for the daughter nucleus. The function R (E) is for radiative corrections which we will briefly discuss toward the end. The shape correction C (E) is usually not large [14]. P, is the probability for a final state n with energy E,. For the purpose of this paper we take n = 1, P, =1, and E, -0. We shall concentrate on F ( Z , E). It affects the data analysis in the Kuri plot, and the shape function defined as If the neutrino is truly massless, the Kurie plot should be...

Integral Equations in Neutrino Mass Searches from Beta Decay

“…The theory of beta decay with all possible corrections, from which theoretical beta spectra are derived, can be given only to a finite accuracy, which is a limiting factor for neutrino mass searches in beta decay, regardless of the method used [24].…”

“…The relative uncertainty is negligible for the principal eigenvalue and between 1-2% for the minor eigenvalues. When comparing experimental and theoretical β spectra, small smooth discrepancies were observed, which increase with decreasing kinetic energy [24]. They can be corrected for with a shape-correction factor , which is assumed to be a parabola with an argument .…”

“…There exist established formalisms for calculating allowed and superallowed beta spectra, which differ in some approaches [6,24,25]. For the purpose of this work, we define the beta-energy spectrum as follows:…”

“…Factor is defined as follows: , 2 where is relativistic momentum, is total (relativistic) energy, is a non-relativistic Fermi function, is a relativistic correction to the Fermi function [26], and is a radiative correction [24]. is a shape correction [24], which corrects for small smooth discrepancies between the theoretical and measured spectra at low energies, is assumed to be a parabola with an argument of . Also, a screening correction [27,28] is applied to .…”