Basic Concepts

Nautilus provides support for data identifiers that represent a variety of related concepts that are useful in nuclear and atomic computational tools. This page discusses some of these concepts and the terminology that Nautilus uses, to help provide clarity in understanding the capabilities of Nautilus.

Atomic Nuclei

An atomic nucleus consists of protons and neutrons, which are generically referred to as nucleons.

• The number of protons (\(Z\)) is called the atomic number.

• The number of neutrons (\(N\)) is called the neutron number.

• The number of nucleons (\(A = Z + N\)) is called the atomic mass number.

Nuclei with the same atomic number are the same element. Nuclei with the same atomic number but different neutron numbers are different isotopes of the same element.

However, two nuclei that are the same isotope can still differ in their excitation state. The ground state is the lowest-energy state of a given nuclide, while all other states are called excited states. The ground state is often, but not always, the longest-lived state of a given isotope.

There are special excited states called metastable states. Unfortunately, there is not a standard definition of metastable states, but the various definitions typically focus on the “long-lived” states. For example, Wikipedia presents two different definitions of metastable states:

• Metastable states have a half-life of 1ns or longer, “100 to 1000 times longer than the half-lives of the excited nuclear states that decay with a ‘prompt’ half-live (ordinarily on the order of 1e-12 seconds).

• Metastable states have a half-life of 5ns or longer, “to distinguish the metastable half-life from the normal ‘prompt’ gamma-emission half-life.”

Nuclei of the same isotope but different excited states are referred to as isomers (although sometimes this term refers only to the metastable states and not to “short-lived” excited states).

The term nuclide refers to a specific nucleus: the same atomic number, the same atomic mass number, and the same excited state. If any of these differs, then you are considering different nuclides.

To summarize some terminology, when comparing two nuclei:

• If the atomic number differs, they are different elements.

• If the atomic number is the same but the neutron number differs, then they are different isotopes of the same element.

• If the atomic number and neutron number are the same but the excitation state differs, then they are different isomers of the same isotope of the same element.

• If the atomic number, neutron number, and excitation state are all the same, then they are the same nuclide.

Nautilus is focused primarily on nuclear applications, and thus does not provide any indication of the ionization state of an atomic nucleus.

Elementals vs. Nuclides

For a given element, we can speak of specific nuclides or we can speak of distributions with a mixture of different isotopes. Following a convention used in various data libraries, Nautilus also can indicate elementals, which are distributions of different isotopes of a single element. The distribution is defined by the data library, but is typically the natural abundance distribution of that element.

Element Names and Symbols

The official names and symbols for elements are defined by the International Union of Pure and Applied Chemistry (IUPAC). However, because many elements have been known since ancient times, there are regional and linguistic variations in the names of some elements. Nautilus focuses only on the English names, but that still leaves four distinct variants:

• IUPAC standard

• American English

• British English

• Canadian English

Some references use “Commonwealth English” instead of “British English”, to indicate the wide geographic usage of that particular variety of English. Nautilus has opted for “British English” because the spelling variations discussed here differ between England and Canada, despite Canada being part of the Commonwealth of Nations. For nations in the Commonwealth but outside of North America, either “British English” or the IUPAC standard is likely to be the correct regional spelling.

Fortunately, the distinctions between these regional variations is only in the spelling of a few elements. By default, Nautilus will use the IUPAC standard spelling. Some features of Nautilus provide the option to specifically request the spelling according to one of the regional standards.

IUPAC also defines the “systematic name” for elements that do not yet have an official IUPAC name. As of the time of writing, it appears that all elements that have been observed in nature or confirmed in experiment have official names. Therefore Nautilus does not currently support the systematic name.

The atomic symbol for each element is, thankfully, fully standardized according to the rules set out by IUPAC with no regional variations.

Particles

In addition to atomic nuclei, Nautilus can also indicate particles. Before presenting the list of available particles, we first present some basic particle physics terminology.

Classes of Particles

This will be a very brief, incomplete, and approximate sketch of the standard model of particle physics, with an eye towards defining some terms useful in further discussion of particles.

The standard model identifies four classes of elementary particles:

• quarks: up, down, charm, strange, top, bottom

• leptons: electron, muon, tau; each with its own corresponding neutrino

• gauge bosons: gluons, photon, Z boson, W bosons

• scalar bosons: Higgs boson

Each of these particles also has an antiparticle with the same mass and opposite charge, with the exception of the neutral bosons, which are their own antiparticle.

The quarks and leptons are organized into generations (first, second, and third) and subtypes (down-type or up-type for quarks, charged or neutral for leptons). Nautilus does not include any quarks, but they are useful for classifying composite particles.

Composite particles are called hadrons and are described as a combination of two or more “valence” quarks. If the particle has two valence quarks, it is called a meson. If the particle has three valence quarks, it is called a baryon. Further combinations (tetraquarks, pentaquarks, and so on) are sometimes referred to as “exotic” hadrons, and are currently not included in Nautilus.

Particle Names and Symbols

The standard name for particles is defined by the Particle Data Group (PDG). Unlike with elements, there are no regional variations of the particle names. However, there is an alternate standard used by some authors (see, for example, Claude Amsler’s 2015 book “Nuclear and Particle Physics”), which can cause some confusion due to the sometimes subtle differences between the two standards. We will refer to this alternate standard as the “textbook” standard due to its use in several common textbooks.

The difference between the two standards is the naming of antibaryons. In the PDG standard, the name of a particle includes its own charge, regardless of whether that particle is ordinary matter or antimatter. However, in the textbook standard, antibaryons are named for the charge of their corresponding ordinary matter particle. Consider, for example, the positive sigma baryon (valence quarks: \(uus\)), which is paired with an antiparticle of the same mass but opposite charge (valence quarks: \(\overline{u}\overline{u}\overline{s}\)). In the PDG standard, that antiparticle is called the negative sigma antibaryon because it has a negative charge. However, in the textbook standard, that antiparticle is called the antiparticle of the positive sigma baryon or the positive sigma antibaryon. The confusion gets worse if you consider that there is a negative sigma baryon (valence quarks: \(dds\)) and its corresponding antiparticle, which is called either the positive sigma antibaryon (PDG standard) or the antiparticle of the negative sigma baryon or the negative sigma antibaryon (textbook standard).

The symbols, if drawn carefully, can help to disambiguate. Using our example above with the sigma (anti)baryons, the PDG standard gives \(\Sigma^+\) and its antiparticle \(\overline{\Sigma}^-\), along with \(\Sigma^-\) and its antiparticle \(\overline{\Sigma}^+\). The textbook standard gives \(\Sigma^+\) and its antiparticle \(\overline{\Sigma^+}\) along with \(\Sigma^-\) and its antiparticle \(\overline{\Sigma^-}\). However, the distinction is subtle, being simply whether or not the overline continues over the sign.

Nautilus defaults to the PDG standard, but some parts of Nautilus provide the option to work with the textbook standard.

Particles Available in Nautilus

The particles that Nautilus currently supports are listed below, along with some annotations regarding the classification and standard symbol for each particle.

particle	class	generation / subtype or valence quarks	PDG symbol
photon	gauge boson		\(\gamma\)
electron (a.k.a., negative beta)	lepton	first generation / charged	\(e^-\)
positron (a.k.a., positive beta)	lepton	first generation / charged	\(e^+\)
electron neutrino	lepton	first generation / neutral	\(\nu_e\)
electron antineutrino	lepton	first generation / neutral	\(\overline{\nu}_e\)
muon	lepton	second generation / charged	\(\mu^-\)
antimuon	lepton	second generation / charged	\(\mu^+\)
muon neutrino	lepton	second generation / neutral	\(\nu_\mu\)
muon antineutrino	lepton	second generation / neutral	\(\overline{\nu}_\mu\)
neutral pion	meson	\(\frac{u\overline{u}-d\overline{d}}{\sqrt{2}}\)	\(\pi^0\)
positive pion	meson	\(u\overline{d}\)	\(\pi^+\)
negative pion	meson	\(d\overline{u}\)	\(\pi^-\)
short kaon	meson	\(\frac{d\overline{s}-s\overline{d}}{\sqrt{2}}\)	\(K^0_S\)
long kaon	meson	\(\frac{d\overline{s}+s\overline{d}}{\sqrt{2}}\)	\(K^0_L\)
positive kaon	meson	\(u\overline{s}\)	\(K^+\)
negative kaon	meson	\(s\overline{u}\)	\(K^-\)
neutron	baryon	\(udd\)	\(n\)
antineutron	baryon	\(\overline{u}\overline{d}\overline{d}\)	\(\overline{n}\)
proton	baryon	\(uud\)	\(p\)
antiproton	baryon	\(\overline{u}\overline{u}\overline{d}\)	\(\overline{p}\)
neutral lambda baryon	baryon	\(uds\)	\(\Lambda^0\)
neutral lambda antibaryon	baryon	\(\overline{u}\overline{d}\overline{s}\)	\(\overline{\Lambda}^0\)
positive sigma baryon	baryon	\(uus\)	\(\Sigma^+\)
negative sigma antibaryon	baryon	\(\overline{u}\overline{u}\overline{s}\)	\(\overline{\Sigma}^-\)
negative sigma baryon	baryon	\(dds\)	\(\Sigma^-\)
positive sigma antibaryon	baryon	\(\overline{d}\overline{d}\overline{s}\)	\(\overline{\Sigma}^+\)
neutral xi baryon	baryon	\(uss\)	\(\Xi^0\)
neutral xi antibaryon	baryon	\(\overline{u}\overline{s}\overline{s}\)	\(\overline{\Xi}^0\)
negative xi baryon	baryon	\(dss\)	\(\Xi^-\)
positive xi antibaryon	baryon	\(\overline{d}\overline{s}\overline{s}\)	\(\overline{\Xi}^+\)
negative omega baryon	baryon	\(sss\)	\(\Omega^-\)
positive omega antibaryon	baryon	\(\overline{s}\overline{s}\overline{s}\)	\(\overline{\Omega}^+\)

An ionized hydrogen-1 nucleus is just a bare proton, so there is some ambiguity between a proton (particle) and hydrogen-1 (isotope) in Nautilus. Nautilus addresses this in different ways depending on the context, so this will be discussed in more detail in each context.

In some contexts, a few light atomic nuclei are treated as particles and given special names for this usage. While Nautilus does not encode them as particles (other than the hydrogen-1 vs proton question as noted above), it is worth being aware of the “particle” names that are sometimes used for these light nuclei:

• hydrogen-1 is also known as protium, and as a particle is called a proton

• hydrogen-2 is also known as deuterium, and as a particle is called a deuteron

• hydrogen-3 is also known as tritium, and as a particle is called a triton

• helium-3 as a particle is called a helion

• helium-4 as a particle is called an alpha