• Oscar Basuyaux

The Beautiful Process of Nucleosynthesis

Why is the universe made of this stuff and not that stuff? Perhaps this question has crossed your mind during existential ponderings in the shower, or even when helping your children or little siblings with their science homework.

The “stuff” we are talking about is the elements, like the ones you’ve probably seen on your science class’ colorful periodic table [1]. Our universe is made up of multitudes of different combinations of elements but is primarily composed of hydrogen and helium (by mass, ~75%, and ~25% respectively). But thinking back to that periodic table, you must recall that there were a lot more than just these elements. Hmm. But why?

The production of certain “light” elements, such as hydrogen and helium, took place right at the beginning of time, following the Big Bang. Despite the abundance of hydrogen, there are a lot more elements, some “heavy”, which are crucial to understanding the universe’s evolution. These heavy elements are not produced here on Earth, but far out into space, which makes them all the more difficult to detect and study.

Heavy elements are produced by nucleosynthesis, which is a process where elements heavier than hydrogen are formed from pre-existing nucleons and nuclei. Now don’t let these impressive, fancy terms scare you, because you will come to realize they’re not that fancy or impressive after all – they’re not effective either when trying to flirt at a party – but they are quite important to understand our central question: Why is the universe composed of the specific materials we see around us?

Hydrogen is the first, lightest, and most basic element. One proton and one electron – doesn’t get simpler than this. Hydrogen served as the first “building block” as it led to the production of increasingly heavier elements through nuclear fusion, where two atoms of different (or the same) elements are fused to form a new element. Nuclear fusion is a viable production method up until Iron (Fe), which is the element with an atomic mass number of 56. In nuclear physics, elements up to iron are considered “light”; it follows that elements beyond iron are then called “heavy” [2].


“Why iron?” you might ask. Well, this has to do with a concept called binding energy and the binding energy curve [3]. Binding energy is the total energy required to completely separate the nucleons bound in a nucleus and is given by the famous E = mcˆ2 equation, where E is energy, m is mass defect (total mass of individual nucleons - mass of nucleus) and c is the speed of light. It turns out that when protons and neutrons bind together to form a nucleus, some of their mass is converted to energy. Hence "binding energy."





This graph shows the average binding energy per nucleon plotted against the nucleon number (atomic mass number). As you can see, the maximum of this curve is iron, which makes this element particularly stable (because it’s the one that requires the most energy, on average, to be taken apart). Furthermore, it is suggested by the curve that it is more energetically favorable for light elements to undergo fusion reactions and heavy elements to undergo fission reactions (a process in which a heavy nucleus splits into lighter nuclei). This is likewise why all elements beyond iron are called “heavy” and those below are considered “light”. Finally, this explains why nuclear fusion is only so useful in the production of new elements as it stops at iron.


In contrast, heavier elements are produced by a process called neutron capture, where, shockingly enough, a nucleus captures neutrons. Yes, I know… *mind blown*. I’ll delve into this later, but first, let’s talk about a recent study on the subject!



Scientists from the US Department of Energy’s Argonne National Laboratory led an experiment in the endeavor to study the nature and origin of heavy elements in the universe. This study was conducted at CERN, a facility in Switzerland that specializes in nuclear research and that is the largest physics laboratory in the world. Specifically, the team focused on elements with more than 126 neutrons and fewer protons than Lead (Pb), which has an atomic number of 82.

Now, this team was interested in these heavy elements because their production may offer valuable information that may help improve our models of the early universe. The production of heavy elements is thought to take place during neutron star formation and supernovae. I will discuss this experiment in depth later on, so before we get into the core (pun intended) of nucleosynthesis, let’s define some things!


Hubble Image: Crab Nebula

A type II supernova (seen left) is produced when a massive red supergiant star explodes. This explosion is caused because the core of the star is very hot, giving nearby photons (particles of light) enough energy to penetrate and split nuclei apart in about 1 second, thereby undoing millions of years of nuclear fusion. These nuclei are ripped to individual protons and neutrons, and shortly after, the star is composed of free electrons, photons, neutrons, and protons. Finally, the high densities force electrons into protons, turning them into neutrons and releasing neutrinos (chargeless, ultra-light, energy-carrying particles). The core then contracts rapidly and is now made almost entirely of neutrons.


Image Courtesy: ESO/L. Calçada

The neutrons then start to get close to each other so fast that they exceed limits set by what’s called neutron degeneracy, causing pressure to develop. This pressure makes the core rebound to a larger equilibrium size which in turn creates a shockwave traveling outwards, ripping the outer layers of the star apart and causing the supernova explosion. The core that is left behind – assuming it has a mass between the Chandrasekhar and Volkoff-Oppenheimer limits; i.e. between 1.4 to 2-3 solar masses – will become a neutron star! (seen right) This star – big reveal – is an extremely dense, hot star made up entirely of neutrons.

Neutron stars are of interest to many scientists in part due to their display of neutron degeneracy, which is explained by the Pauli exclusion principle. We’re now getting into quantum physics [4], so strap your seat belts. Neutron degeneracy is a stellar application of the Pauli exclusion principle. It is similar to electron degeneracy, given that the reason why pressure develops is that no two particles (electrons or neutrons) can simultaneously have the same quantum configuration.

In the case of neutron stars, however, there is enough energy from gravitational collapse, given that the Chandrasekhar limit is exceeded, to overcome electron degeneracy pressure. Electron degeneracy pressure primarily bears effects on the formation of white dwarfs during type 1a supernovae, but it works the same way as neutron degeneracy pressure.

The Pauli exclusion principle applies to all fermions, which is a class of particles that all have half-integral spin [5] and follow the Fermi-Dirac statistics [6]. It states that no two fermions can have identical quantum numbers. To explain this, suppose electrons 1 and 2 are in states “a” and “b” respectively as shown in the following representation of an atom.



The wavefunction [7] for this system would thus be:


This equation represents the probability amplitude that electron 1 is in state “a” AND electron 2 is in state “b”. Psi-1(a) represents the probability amplitude that electron 1 is in state “a”. Psi-2(b) represents the probability amplitude that electron 2 is in state “b”.


This equation is analogous to the probability of one coin landing on heads, and another on tails, which is simply 0.5 x 0.5. In other words, it is the probability that a single coin (or electron) lands on heads/tails (or state “a”/”b”) multiplied by the probability that another coin (or a second electron) lands on the opposite side (or state) of where the first coin (or electron) landed. The above equation therefore gives the overall probability of each electron being in different states (or coins landing on different sides).

However, this wavefunction isn’t acceptable because the electrons are identical and indistinguishable. In other words, the separation of their “orbits” is small compared to their de Broglie wavelength [8]. To account for this problem, we must use a linear combination of the two possibilities, because it is not feasible to determine which electron is in which state using the above equation. Hence, we use the following equation which gives the probability amplitude that both states “a” and “b” are occupied by electrons 1 and 2, in either order.


This is a sort of probability “trick” that allows us to determine whether or not each state is occupied by a different electron, regardless of the order. The minus sign forces the wavefunction to collapse or vanish if both states are either “a” or “b”, implying that it is impossible for both electrons to occupy the same state. Therefore, to follow the Pauli exclusion principle, all particles of half-integer spin (e.g. electrons or neutrons) must have asymmetric wave functions so that their respective wavefunctions don’t cancel each other out.

Alternatively, we say that two fermions cannot have the same quantum numbers, because three out of four of those numbers are the solutions for the Schrödinger wavefunction; the fourth number is the value of spin. This means that if the particles have the same quantum configuration (given that they already have the same spin because they’re fermions), the aforementioned wavefunction of the system cancels out and collapses. The three quantum numbers we’re talking about are represented by spherical coordinates - denoted by r, theta, and psi - called the principal quantum number, orbital quantum number and magnetic quantum number, respectively. The wavefunction of a particle is then calculated like so:

These coordinates can be represented on this diagram of a simple hydrogen atom:




To make this all a little less confusing and easier to conceptualize, suppose that there are two men in a room. These men have defined hair color, their arms and legs may be in many different positions, and they may stand in any of the four corners of the room. All of these characteristics are analogous to spin, principal quantum number, orbital quantum number, and magnetic quantum number.


Now suppose that both of these men are in the back left corner of the room, with their arms crossed and legs standing straight. Also, both have brown hair. Well, according to the Pauli exclusion principle, this cannot be the case because these men have identical physical configurations, much like if two fermions have identical quantum configurations. Thus, pressure starts to develop between the two men, preventing them from getting too close to each other, similar to electron/neutron degeneracy pressure. This pressure is what keeps the neutrons from getting too close to each other and prevents the neutron star core to collapse completely under its own weight.

**Quantum mechanics interlude is over** (pheww…)

Circling back to nucleosynthesis – yes, I also forgot that’s what I was discussing – heavy elements are formed through a process called neutron capture, which takes place when a nucleus absorbs a neutron and becomes an isotope [9] of the original nucleus (as it now has a different number of neutrons). This isotope is usually unstable and will decay (the action of emitting a particle and energy from a nucleus), but it may or may not absorb another neutron before it has enough time to decay. Hence, this means there are two types of processes – the s-process (s for slow) and r-process (r for rapid).

Fundamentally, the s-process is when the isotope has enough time to decay before absorbing another neutron, since there’s a small number of neutrons laying around. The isotope will undergo a series of decays, including a type of decay called beta-minus decay, where a neutron turns into a proton, thereby emitting an electron and antineutrino. This has the effect of increasing the atomic number of the nucleus and leaving the atomic mass unchanged.


i.e. [10]:



The s-process accounts for the production of about half of the nuclei above iron and ends with the production of Bismuth-209. The r-process, on the other hand, occurs in the presence of a very large number of neutrons, for example in a type II supernova. In fact, the process is thought to require densities of 10ˆ24 neutrons per cm cubed and at least 100 captures per second. This means that the nuclei do not have enough time to decay before capturing another neutron, thereby forming heavy isotopes.


These isotopes are then hurled out into space by the explosion, where they will undergo beta minus decay and experience an increase in atomic number (as the neutron turns into a proton). Also, given that there is a massive number of neutrinos released into space by the supernova, the following reaction may occur, which is also a method of increasing proton number, aside from beta minus decay. A neutron may absorb a neutrino and turn into a proton like so: .

Now let’s talk about this in the context of the aforementioned experiment conducted at CERN by the team from Argonne National Laboratory. These scientists chose to experiment with nuclei of mass numbers exceeding 126 because, along with mass numbers of 8, 20, 28, or 50, nuclei of these masses are known to have higher average binding energies per nucleon and thus increased stability. Accordingly, these are considered “magic numbers” in the field of nuclear physics [11]. More stability means that the nucleus is less likely to undergo decay and therefore more likely to absorb a new neutron before decaying – i.e. the r-process!

This study focused on the mercury isotope Hg-207, which may “shed light on properties of its close neighbors” [12], as all of these nuclei are in one way or another involved in the r-process. The central challenge was re-creating supernova conditions to be able to observe how reactions unfold, as Earth’s environments do not allow such processes to occur naturally.

You may wonder how on Earth (pun intended) this experiment was conducted? Well CERN has amazing facilities with tons of groundbreaking technologies and equipment. One of them is called the HIE-ISOLDE (High Intensity and Energy Isotope mass Separator On-Line) facility. If this sounds complicated, that’s because it is.


The HIE-ISOLDE is a source of high-energy beams of radioactive [13] nuclides [14]; it can accelerate the nuclei up to 10 MeV/nucleon [15]. The experiment used a high-energy beam of protons which was fired at a molten lead target; this resulted in the production of hundreds of exotic, radioactive isotopes.


The scientists then separated all the Hg-206 nuclei and used the HIE-ISOLDE accelerator to create a beam of this nuclide which they aimed at a deuterium [16] target inside the ISOLDE Solenoidal Spectrometer (ISS). And before you say anything, let me explain what the ISS is.

“The ISS is a newly developed magnetic spectrometer” [17] that is used to detect Hg-206 nuclei that are in the process of capturing a neutron to turn into Hg-207. Given that “ISS” stands for ISOLDE Solenoidal Spectrometer, it follows that this is a magnetic spectrometer because a solenoid is a type of electromagnet. But before getting into the magnetic aspect, let’s define what a spectrometer is.


A spectrometer is an instrument that is used to analyze light, specifically the spectrum of wavelengths of light emitted by an atom. As you may know, an atom is composed of different energy levels where electrons can excite to and relax from; this is illustrated in the following diagram.





In this instance, when electron “a” is excited from energy level 2 (n=2) to energy level 3 (n=3), it absorbs a photon of a certain wavelength (which corresponds to the energy difference between the levels). Likewise, when electron “b” relaxes from energy level 2 to energy level 1, it emits a photon of a wavelength corresponding to the energy difference between the two levels. The ensemble of wavelengths of all the photons that are emitted/absorbed as a result of electrons relaxing/exciting between all possible energy levels is called the emission/absorption spectrum.


The spectrometer in the experiment was used to observe “the spectrum of the excited states in Hg-207 for the first time” [18], in part because of the ISS’ outstanding resolving power. Resolution is an important concept in optics; it is the ability to distinctly see multiple lines in a spectrum that each corresponds to a wavelength of an emitted/absorbed photon. Because the wavelengths are relatively close to each other, high resolving power is required to distinguish each line of the spectrum and effectively determine the wavelengths of the excited states of mercury.



The emission spectrum of Mercury [19] is shown above. As you can see, the lines which represent emissions at specific wavelengths are close together and are on the order of nanometers (i.e. 10ˆ-9 m). This is why having a high resolving power is important, to be able to properly distinguish the different lines of mercury’s emission spectrum.


Finally, the last part of the ISS is its electromagnet, which is a “recycled 4-Tesla superconducting MRI magnet” [20] from an Australian hospital. This isn’t too important to understand but just know that the purpose of the magnet is to redirect charged particles to detectors in the ISS which then record the energy and position of these particles.


Specifically, when the mercury beam is directed at the deuterium target and absorbs its neutron, a proton is left behind which recoils and is directed to sensors in the ISS by the solenoid electromagnet; the magnet also allows the spectrum to be “uncompressed” as the protons travel in a spiral towards a detector. This unfolds the spectrum compression [21] thanks to a mathematical “trick” in the kinematics of this experiment. Being able to measure the position and energy of the recoiling protons “yield key information on the structure of the nucleus and how it is bound together” [22].


Energy and position are rather important properties to know because of their impact on the r-process and “the results can inform important calculations in models of nuclear astrophysics” [23]. Ultimately, the ISS inside of the HIE-ISOLDE facility not only measured the spectrum of excited states of mercury, but also measured the position and energies of the particles involved in the reaction (including the recoiling proton), thereby having a twofold function.

Overall, this experiment offered valuable insights into the workings of the r-process and provides a framework to study other nuclei in the region of Hg-207. Finally, the data gathered from the CERN study confirms theoretical predictions of our current models, bringing us one step closer to understanding the complex evolution of our universe.

“Why do we care?” you might ask. That’s a valid question, one that I’ve asked myself multiple times, especially on the eve of an important physics exam or when taking notes in class.

Well, first of all, it’s hella interesting and you can’t tell me it isn’t cool to be able to understand and explain how the universe formed and evolved. Additionally, these elements are the very reason why you and I are alive today! Carbon, which is an element produced by fusion in the cores of stars, is a major component of many molecules that make up your cells and ultimately, yourselves. These elements also constitute the food and drinks you ingest every day, notably water whose chemical composition is H2O.


So technically, you and I are the products of supernovae and we subsist on other products of supernovae and other stellar events and processes.

But beyond satisfying our curiosity, beyond the “cool” factor, and beyond the intrinsic value of this knowledge lies the instrumental value which affects each and every one of us. Being able to study the universe, harness processes of nucleosynthesis for energy production, apply findings to quantum computing, etc. makes everyone better off!

This is likewise why I want to pursue a STEM major in college and be able to contribute to the betterment of lives across the globe, and the advancement of human knowledge and human-made technology. And MOST importantly, you’ll finally be able to answer the questions you’ve been pondering over in the shower for all those years!

Honestly, you’re welcome…


Footnotes:


[1] Chem 101: When reading a period table: atomic mass is the sum of protons and neutrons; the atomic number is the number of protons; the term ‘nucleon’ refers to either protons or neutrons. [2] **Confusing terminology** Alternatively, in astrophysics specifically, any element heavier than hydrogen or helium is considered “heavy” because of a stellar property called metallicity. This property refers to an abundance of elements in a star other than hydrogen or helium and has nothing to do with actual metal; it is simply a way to refer to elements heavier than hydrogen and helium. This may be confusing considering the definition of heavy elements in nuclear physics. [3] Tsokos, K. A. (2016). Physics for the Ib Diploma. Cambridge: Cambridge University Press. [4] Physics 101: Quantum physics is simply the study of the properties of nature on an atomic scale, the nature of the particles that make up matter and their interactions with the fundamental forces, which are electromagnetic, strong, weak, and gravitational. [5] Chem 101: Spin is the amount of angular momentum that a subatomic particle/nucleus has. Angular momentum is the product of mass, velocity, and radius of the circular path followed, i.e. L = mvr. It is measured as a multiple of h-bar which is equal to Planck’s constant divided by 2π ; all fermions have a half-integer spin, which means the multiple can be 0.5, 1.5, 2.5, etc. [6] Quantum Physics 101: Simply put, Fermi-Dirac statistics are a description of the distribution of particles over energy states in systems consisting of many identical particles that obey the Pauli exclusion principle. These particles all have half-integer spin and are the counterpart to a class of particles called bosons. [7] Quantum Physics 101: A wavefunction is a probability function that aims to calculate where an electron, or other particle, may be found within a defined volume, from a given position, at a precise time – i.e. it is a calculation of the quantum “state”. This theory, developed by Schrödinger, assumes that there is a wave associated with the particle (see next footnote) which is called the wavefunction, and is a function of position and time. This isn’t too important to understand nucleosynthesis, but essential to explaining the Pauli exclusion principle. [8] Quantum Physics 101: The DeBroglie wavelength comes from a hypothesis that all matter can behave as both a particle and wave, but not simultaneously. This suggests that every particle, including electrons, has a wavelength that is measurable. This hypothesis was proved by a diffraction experiment involving double-slits and yielded the same results as if light had been shone through the slits – a pattern on the screen behind the slits called a double-slit interference pattern. [9] Chem 101: The term isotope refers to different forms of the same element, differing in the number of neutrons, but not protons and conserving the same chemical properties. [10] ‘X’ represents the nucleus that undergoes the decay, ‘Y’ represents the resultant nucleus, AKA “daughter nucleus”, “e” is an electron and “v” (with the bar above) is the antineutrino. [11] Physicists weigh in on the origin of heavy elements (2020, March 31) retrieved 16 April 2020 from https://phys.org/news/2020-03-physicists-heavy-elements.html. [12] Physicists weigh in on the origin of heavy elements (2020, March 31). [13] Physics 101: Radioactivity simply refers to the phenomenon in which nuclei emit particles and energy randomly and spontaneously. [14] Chem 101: This term is used to refer to a distinct kind of nucleus or atom with a specific number of neutrons and protons. [15] Physics 101: MeV is a unit of energy; it is pronounced “Mega Electron Volts”. Mega is a metric multiplier of value 10ˆ6. An electron volt is a standardized unit of energy and is the energy required for one electron to move through an electric potential difference of one volt. It is quite useful when dealing with energies of small magnitudes. 10 MeV is approximately 1.6 * 10ˆ-12 Joules (which is the standardized SI unit of energy); to put this into context, the average human, per day, eats and drinks around 8,700,000 Joules (or 8700 kJ) worth of energy. [16] Chem 101: Deuterium is a rare and heavy isotope of hydrogen which consists of one proton and one neutron. [17] Physicists weigh in on the origin of heavy elements (2020, March 31). [18] Physicists weigh in on the origin of heavy elements (2020, March 31). [19] Science Photo Library. (2020). H-He-Hg emission spectra - Stock Image - C017/7260. Retrieved April 28, 2020, from https://www.sciencephoto.com/media/540572/view/h-he-hg-emission-spectra. [20] Physicists weigh in on the origin of heavy elements (2020, March 31). [21] Nuclear Physics 101: The reason why the spectrum is compressed is because of the changing kinematics when a heavy beam is aimed at a light target (Hg-207 vs. H-2). In other words, the physics of the collision between the mercury nuclei and the deuterium target becomes distorted and more difficult to examine and analyze. This is why the ISS electromagnet is an important component to the HIE-ISOLDE facility. [22] Physicists weigh in on the origin of heavy elements (2020, March 31). [23] Physicists weigh in on the origin of heavy elements (2020, March 31).


Works Cited

CERN. (2017, October 16). CERN ISOLDE and HIE-ISOLDE. Retrieved April 28, 2020, from https://home.cern/science/experiments/isolde.

CERN. (2020). CERN ISOLDE Seloinodal Spectrometer. Retrieved April 28, 2020, from https://isolde.web.cern.ch/experiments/isolde-solenoidal-spectrometer-iss.

Nave, C. R. (2016). Neutron Star. Retrieved April 28, 2020, from http://hyperphysics.phy-astr.gsu.edu/hbase/Astro/pulsar.html.

Nave, C. R. (2016). The Pauli Exclusion Principle. Retrieved April 28, 2020, from http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html#c1.

Nave, C. R. (2016). The Distribution of Energy. Retrieved April 28, 2020, from http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/disene.html#c3.

Nave, C. R. (2016). Geometry of Hydrogen Atom Solution. Retrieved April 28, 2020, from http://hyperphysics.phy-astr.gsu.edu/hbase/qunoh.html#c2.

Physicists weigh in on the origin of heavy elements (2020, March 31) retrieved 16 April 2020 from https://phys.org/news/2020-03-physicists-heavy-elements.html.

Science Photo Library. (2020). H-He-Hg emission spectra - Stock Image - C017/7260. Retrieved April 28, 2020, from https://www.sciencephoto.com/media/540572/view/h-he-hg-emission-spectra.

Sorlin, O., & Porquet, M.-G. (2008, May 27). Nuclear magic numbers: New features far from stability. Retrieved April 28, 2020, from https://www.sciencedirect.com/science/article/abs/pii/S0146641008000380.

The Editors of Encyclopaedia Britannica. (2010, October 12). Fermi-Dirac statistics. Retrieved April 28, 2020, from https://www.britannica.com/science/Fermi-Dirac-statistics.

The Editors of Encyclopaedia Britannica. (2018, January 9). Spin. Retrieved April 27, 2020, from https://www.britannica.com/science/spin-atomic-physics.

T. L. Tang et al, First Exploration of Neutron Shell Structure below Lead and beyond N=126, Physical Review Letters (2020). DOI: 10.1103/PhysRevLett.124.062502.

Tsokos, K. A. (2016). Physics for the Ib Diploma. Cambridge: Cambridge University Press.

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