Nucleosynthesis Of The Light Elements

Although we can't directly observe the first 400 millennia of the universe, we can still deduce indirectly various properties of the natural world at those earlier times. For instance, we know that in the early universe, neutral hydrogen atoms couldn't exist because some of the cosmic background photons had energies larger than the hydrogen ionization energy, which is % = 13.6eV. An electron volt (eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. This is a very small amount of energy by usual standards, 1.6 x 10-19/. Just as there was a time when protons and electrons combined to form neutral hydrogen atoms (at t ~ 400,000 years), there must have been an earlier time when protons and neutrons combined to form atomic nuclei. This time is known as the era of Big Bang nucleosynthesis.

Consider, for simplicity, a deuterium (D) nucleus. This is the simplest of all compound nuclei; it consists of one proton and one neutron, bound together with a binding energy of B = 2.22MeV. A gamma-ray photon with energy e > B can split deuterium, in

Helium Isotopes and the Early Universe

Elements in the periodic table are distinguished by the number of protons in the nucleus, since this determines the total charge of the nucleus, and hence the number of electrons in an electrically neutral version of the atom, which in turn mostly determines the chemical bonding properties of the atom. Natural helium is a mixture of two stable isotopes, helium-3 and helium-4. In natural helium, about one atom in 10 million is helium-3. The unstable isotopes helium-5, helium-6, and helium-8 have been synthesized. The alpha particles emitted from certain radioactive substances are identical to helium-4 nuclei (two protons and two neutrons).

It is reasonable to expect that there existed a time when bound atomic nuclei could not exist, because the cosmic background photons had energies larger than the nuclear binding energy, so as soon as the nuclei bound, they would break apart again. Prior to about one second after the Big Bang, matter—in the form of free neutrons and protons—was very hot and dense. As the universe expanded, the temperature fell and some of these nucleons were synthesized into the light elements: deuterium, helium-3, and helium-4.

a process known as photodissociation, and pictured in the schematic diagram

The Equation 6.3 can also run in the opposite direction; a proton and neutron can fuse to form a deuterium nucleus, with a gamma-ray photon carrying off the excess energy:

The process of deuterium synthesis (Equation 6.4) has obvious analogies to the radiative recombination of hydrogen, depicted in Equation 6.2. In each case, two particles are bound together, with a photon carrying away the extra energy. The main difference is the energies involved. The photodissociation energy of deuterium is B = 2.22MeV = 1.6 x 105x.

Since the energy released when deuterium is formed is 160,000 times the energy released when a neutral hydrogen atom is formed, we expect the temperature at the time of nucleosynthesis to be 160,000 times larger than the temperature at the time of last scattering, when the universe became transparent:

In the most widely accepted current model for the early universe, the universe had temperature equal to Tnuc when its age was about 7 minutes. A basic prediction of Big Bang nucleosynthesis is that helium contributed 25% of the mass density in baryons, even before the first generation of stars started to "pollute" the universe with heavier elements. The helium mass fraction in the Sun is about Y = 0.28, but the Sun contains helium formed in earlier generations of stars. When we look at astronomical objects of different sorts, the minimum value found for the helium fraction is

Y = 0.24, which agrees more closely with the predictions of Big Bang nucleosynthesis.

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