Muon production of ^92,94Nb in the Earth's crust

Abstract

ACTIVITIES due to long-lived ⁹²Nb (t_1/2 ≃ 1.7×10⁸ yr) and to ⁹⁴Nb (t_1/2 = 2.03×10⁴ yr) in a refined bar of terrestrial niobium were discovered by Apt et al.¹. They speculated that the ⁹²Nb activity could have applications to chronologies of nucleosynthesis and to cosmogony. As an example, they calculated that their observed activity level would result if the isotopic ratio 4.7×10⁹ yr ago were ⁹²Nb/⁹³Nb = 10⁻³ and if the halflife were 1.58×10⁸ yr. More definite conclusions were difficult because the concentration expected today depends so strongly on the poorly known halflife, which they estimated to be 1.7×10⁸ yr from a reactor irradiation. This sensitivity can be illustrated by noting that a 5% error in halflife corresponds after 4.7×10⁹ yr to an error of a factor 2.74 in the anticipated activity. Quantitative calculations from galactic nucleosynthesis must therefore await a more precise measurement of the halflife. Implications of primordial ⁹²Nb have recently been enlarged with the proposal² to use enrichments δ(⁹²Zr) in the isotopic composition of Zr due to extinct ⁹²Nb to measure absolute time differences in the formation of meteorites and planets. If an initial ⁹²Zr/⁹⁴Zr ratio for each body can be obtained, differences between those initial values could be translated into time differences in the formation of the respective objects. We argue here that both projects are probably doomed to disappointment. It seems to us unlikely that the near equality in the two measured activities is a coincidence. They are respectively 0.058±0.035 d.p.m. per kg (Nb) for ⁹²Nb and 0.32±0.03 d.p.m. per kg (Nb) for ⁹⁴Nb. Such a result would be expected, for example, if both nuclei were created terrestrially over geologic time in the ratio of their activities, in this case in a production ratio p(⁹²Nb)/p(⁹⁴Nb) = 0.18±0.11. We suggest that nuclear reactions following the capture of stopped cosmic-ray muons is the likely source, and we will show that both the magnitude of the activities and their relative strengths are consistent with this idea. Similar ideas have been developed by others, most notably to explain Xe anomalies in Te ores³.