# PHYSICS 24 LECTURE NOTES

SUMMARY

## I. Introduction

Primordial Nucleosynthesis (aka Big Bang Nucleosynthesis) is the study of the formation of atomic nuclei in the early universe. The formation and relatives amounts of the nuclei are predicted by the Big Bang theory, and their calculations provide justification for it.

BBN also explains how and why the lighter elements were created in the early universe, and why the heavier elements were not created until the first stars formed.

## II. Background Physics on Energy

Kinetic energy is the energy of motion. It is directly related to temperature and the square of the velocity of an object.

 definition of kinetic energy KE = (1/2) mv2 average kinetic energy for a collection of particles in thermal equilibrium KE = (3/2) kT

Potential energy is the energy inherent to an object. During nucleosynthesis, the most important role of potential energy is the "potential barrier" that the heavier elements must penetrate in order to reach the "potential well" where nuclear bonding takes place. The threshold between these two is about 10-15 m, which is much smaller than the 10-10 m radii of small atoms.

Conservation of Energy: Together, potential and kinetic energy are related by the First Law of Thermodynamics, where energy is conserves as thus...

 Total Energy = Potential Energy + Kinetic Energy + Thermal Energy = a constant

Therefore, there is a trade-off between kinetic energy and potential energy, assuming that the excess thermal energy lost is negligible. As one increases, the other decreases.

Also, given an expanding universe, the density of the universe decreases as time goes on. Since the change in energy is proportional to the negative of the pressure times the change in volume, and given that pressure is positive, the increase in the change in volume of the expanding universe leads to a decrease in the change in total energy. As the amount of energy decreases, so does temperature (T) also decrease. Thus: temperature has dropped since the beginning of the universe, which means the early universe was much hotter than it is now. This decrease in temperature in the very early universe also made the formation of the lightest elements, such as Deuterium, possible.

## II. How Nuclei Are Formed

In the beginning, the universe was very hot, with temperatures much higher than 1010 Kelvin. The building blocks of nuclei, protons and neutrons, moved around along with other particles. However, they did not form many nuclei due to the high temperatures involved, which favored weak processes like n + n -> p + e-. After a second or so of cooling down, lighter elements such as Deuterium, Helium-3, Hydrogen-3, and Helium-4 began to form. By the time of 5 minutes, much small amounts of Deuterium, Helium-3, and some Lithium-7 formed. The first to form in the very beginning are the building blocks of nuclei: protons and neutrons. Protons by themselves cannot stick together, and therefore stable nuclei with more than one proton also needs neutrons to bind them all together.

The Formation of Deuterium (2H)

 proton + neutron => Helium-2 + photon

This process requires the emission of a photon of ~2.2 MeV in order to conserve/lose energy. It can also occur at temperatures much smaller than 2.2 MeV. Thus, it does not require high temperatures. On the contrary, this process requires lower temperatures to a degree, as higher temperatures would reverse the process.

The Formation of Helium

 2 protons + 2 neutrons => Helium-4 + photon

There is more repulsion between the two Helium ions; thus, this process requires higher temperatures to take place, though not high enough to reverse it. This increase in energy going into the process is needed to overcome the Coulomb repulsion between the Helium nuclei. After the nuclei penetrates the potential barrier at ~10-15 m, nuclear attraction takes over in the potential well, and the two atoms bond. Here, a photon of ~2.8 MeV is released in the process. The abundance of He-4 in the universe and the high temperatures required for them to take place thus supports the theory of a hot Big Bang.

The heavier elements, though, could not form during this time because of the higher Coulomb/potential barriers of heavier elements, the fast decay rates of neutrons, and the decreasing density of the expanding universe. This limit occurred about 5 minutes after the Big Bang. It was known as the "Big Freeze Out" - when temperature and density became too low to support any more large-scale nucleosynthesis. Thus, the elements in the early universe remained so until the first stars provided the conditions necessary to form the heavier elements through stellar fusion.

## III. What This Means

The relative amounts of the elements Hydrogen, Helium, and Lithium were fairly successfully predicted by the Big Bang Theory.

According to the theory, the first element to be created was Hydrogen, which remains the most abundant element in the universe today. After some period of cooling down (about a second or so, to about 1010 Kelvin), protons and neutrons were able to collide to form heavier atoms like Helium and Lithium. That extreme temperature, however, was not enough to create elements heavier than Lithium. The remaining elements were later created during stellar fusion. This fusion did not create much Deuterium or Lithium, and these elements which exist today are mostly still remainders from the early universe.

Also, the abundance of the lighter elements depends on the current density of baryonic matter (matter made out of protons and neutrons); specifically, the baryon/photon ratio.

Big Bang Nucleosynthesis
A site on the topic by one of Berkeley's own professors

Initial Conditions and Primordial Nucleosynthesis
Notes from Physics-320 class at the University of Shefield, UK

Big Bang Nucleosynthesis
A collection of reviews and papers by Subir Sarkar at Oxford University

Big Bang Nucleosynthesis
A collection of works by K. Jedamzik and J.B. Rehm at the Max-Planck-Institut für Astrophysik

Big Bang Java Calculator v1.1
An online applet that creates graphs of the predictions and relative amounts of elementary particles in the early universe; from the University of Washington