Nuclear reactions inside stars synthesized the majority of the chemical elements, including carbon, oxygen and other star-stuff found on Earth.  Optical telescopes are unable to peer into stellar cores to observe nucleosynthesis directly. Instead, measurement of star light emitted from the stellar surface provides an indirect observational technique to infer the conditions in the stellar interior. To achieve this, astronomers use a technique called spectroscopy to analyze the light emitted by stars. Many properties of stars are measured using this data such as stellar rotation, red-shift, mass, temperature and chemical composition. Chemical elements present in stellar atmospheres are identified by the strength of absorption lines in the stellar spectra. Relative abundances of each element are then found by comparing those line strengths. 
Finding an abundance of any given heavy element on a stellar surface may, however, only reflect the relative chemical abundances of the gas cloud from which the star materialized. For example, an ordinary star such as the Sun cannot build up elements much heavier than 4He in its stellar core via fusion (though cosmic ray spallation and other forms of naturally occurring nuclear fission can produce heavier elements such as lithium in the solar atmosphere). ) As a result, sodium, carbon, oxygen and many other heavy elements present in the solar spectrum must have existed long before nuclear fusion occurred in the solar protostar as remnants of an earlier stellar generation.  In order to observe the characteristic absorption lines of synthesized elements in stellar spectra, a mechanism must also exist to dredge-up or convect such matter from the stellar core up to the stellar atmosphere.  Such processes, including helium shell flashes, occur in the later stages of stellar evolution when convective mixing acts in pulses on a timescale comparable to nuclear burning of heavy elements.  Models of stellar evolution, convection, and nuclear reaction networks are often required to evaluate such processes of stellar nucleosynthesis.  To illustrate these mechanisms, a brief history of the first observations of the unstable element technetium in stars are reviewed. Estimates of the relevant stellar and nuclear burning timescales are presented that suggest such stars continuously synthesize technetium via slow neutron capture and beta decay.
Technetium was first identified in molybdenum scrap metal parts from a Berkeley cyclotron in 1937.  The scrap metal had been bombarded with deuterons in the cyclotron such that radioactive isotopes of technetium were produced in sufficient quantities for chemical identification. But, even with the largest cyclotrons, the amount of technetium produced was still relatively small. Isolation of milligram quantities of technetium from fission products of uranium in nuclear reactors, however, did provide sufficient quantities for detailed chemical analysis and spectrographic measurements.  Before 1937, technetium had not been found in nature leaving a gap between molybdenum and ruthenium in early forms of the periodic table. Liquid drop and shell models of the atomic nucleus both predict that isotopes of technetium are unstable to beta decay. Experiments have also not found any completely stable isotopes of technetium; the most stable isotopes having a half-life of about one million years. Based on this evidence, any technetium formed in the early solar system would have gone through many thousand half-life periods and effectively decayed long ago. [10,11]
In 1952, absorption lines of technetium were observed in the stellar spectra of several red giant stars, especially of long-period variables with relatively strong lines of other heavy metals such as zirconium and barium.  The discovery of an unstable element in the stars suggested that either an unknown stable isotope exists, that the stars formed only a short time ago, or that such stars generate technetium in the course of stellar evolution. At the time, the resolution of spectral measurements was not sufficient to distinguish between or determine which isotopes of technetium were observed in the stars.  Theoretical models of the atomic nucleus did not predict the existence of a stable isotope in agreement with the experimental evidence for the known isotopes. The relatively rapid decay rates of technetium isotopes when compared to both universal and geologic records may be better appreciated by a simple calculation.
Radioactive decay for a collection of particles follows a binomial distribution so that the probability that at least one of those original technetium atoms still exist and have not yet decayed is given by P = [1 - (1 - 0.5k)N] where k is the number of half-life periods that have elapsed and N is the original number of atoms. Let us assume, for the sake of argument, that one solar mass of technetium was present in the giant molecular cloud that collapsed to form the solar system. Such a cloud would consist of about N=1.2 x 1055 atoms of technetium, which we assume are the most stable isotopes with half-life periods of about one million years. Estimates for the age of the Sun exceed 1 billion years, which is characteristic of technetium-rich red-giant stars, so that at least k = 103 half-life periods have since passed.  For these numbers, the probability that a single atom of technetium has not yet decayed is then approximately P = 10-245. Such a low probability and a comparatively large number of technetium-rich stars suggests that primordial technetium has effectively decayed without a trace. For this calculation, a half-life for the most stable technetium isotopes was used, but such measurements are made at low temperatures. In fact, the half-life of technetium is substantially reduced at temperatures sufficiently high to excite the lowest nuclear energy levels populated by the Boltzmann distribution. For example, the half-life of an average 99Tc nucleus is reduced from 2 x 105 years at low temperatures to about 12 years at temperatures near 3.5 x 108 °K, characteristic of ignition temperatures for helium fusion and helium flashes, which transport material from the stellar interior to the atmosphere on a dynamical timescale that typically lasts several minutes. [14,15]. Technetium is apparently able to survive the hot environments of helium flashes and slow neutron capture sites and not significantly decay before being dredged up to the stellar surface.  Given these lower and upper bounds for stellar and radioactive decay timescales, stars whose spectra show technetium absorption lines appear to have recently synthesized technetium via nuclear reactions.
© Curtis W. Hamman. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
 E. M. Burbidge et al., "Synthesis of Elements in Stars," Rev. Mod. Phys. 29, 547 (1957).
 J. B. Hearnshaw, The Analysis of Starlight (Cambridge University Press,1986).
 M. Chaussidon and F. Robert, "Lithium Nucleosynthesis in the Sun Inferred from the solar-wind 7Li/6Li ratio," Nature 402, 270 (1999).
 H.A. Bethe, "Energy Production in Stars," Phys. Rev. 55, 434 (1939).
 S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Oxford University Press, 1961).
 G. Wallerstein et al., "Synthesis of the Elements in Stars: Forty Years of Progress," Rev. Mod. Phys. 69, 547 (1997).
 T. A. Weaver, G. B. Zimmerman and S. E. Woosley, "Presupernova Evolution of Massive Stars," Astrophys. J. 225, 1021 (1978).
 C. Perrier and E. Segrè, "Technetium: The Element of Atomic Number 43," Nature 159, 24 (1947).
 W. F. Meggers, "The Spectrochemistry of Technetium and Promethium," Spectrochim. Acta 4, 317 (1951).
 G. R. Choppin, J. Liljenzin and J. Rydber, Radiochemistry and Nuclear Chemistry (Butterworth-Heinemann, 2002).
 F. de Jonge and E. Pauwels, "Technetium, the Missing Element," Eur. J. Nucl. Med. 23, 336 (1996).
 P.W. Merrill, "Technetium in the Stars," Science 115, 484 (1952).
 R.L. Kurucz, "Atomic Data for Interpreting Stellar Spectra: Isotopic and Hyperfine Data," Physica Scripta T47, 110 (1993).
 G. Wallerstein, "Spectroscopy of Heavy Elements in Stars," J. Opt. Soc. Am. 1, 307 (1984).
 R. G. Deupree and R.K. Wallace, "The Core Helium Flash and Surface Abundance Anomalies," Astrophys. J. 317, 724 (1987).
 K. Takahashi, G. J. Mathews and S. D. Bloom, "Shell-Model Calculation of 99Tc Beta Decay in Astrophysical Environments," Phys. Rev. C 33, 296 (1985).