Submitted by:
Thomas Brunner
General area of research:
Nuclear physics
McGill courses:
Nuclear
Why you chose to feature this researcher:
Maria Goeppert Mayer did such an extensive work in theoretical physics. There are so many research areas that she is mentioned in. For example, Donna Strickland mentioned her during her talk on photonics because of Goeppert Mayer's work on two-photon transitions in the atom. In nuclear physics, she proposed the nuclear shell model but also proposed two-gamma decays and double beta decays. I am always impressed by the breath of her work and the impact she has on several fields.
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Introduction slide / General speaker notes:
Synopsis of work:
Maria Goeppert Mayer was a theoretical physicist and Nobel Laureate who developed the mathematical model for the structure of nuclear shells, which she published in 1950. She explained why certain numbers (called “magic numbers” by Eugene Wigner) of nucleons appear in the most stable configurations in atomic nuclei. She first theorized two-photon absorption by atoms in her doctoral thesis, work which was mentioned by Donna Strickland in her 2008 Nobel lecture on photonics. Goeppert Mayer also proposed double beta decay in 1935, which was experimentally observed over 50 years later by Micheal More.
Researcher's background:
Goeppert Mayer (1906-1972) was a German-born American physicist who graduated from the University of Göttingen, and she was awarded her doctorate in 1930. Due to anti-nepotism rules, she was not permitted to take on a faculty position at Johns Hopkins University where her husband was an associate professor, but she was given a job as an assistant. During this time, she published a paper on double beta decay, and took an unpaid position at Columbia University two years later. She worked for the Manhattan project on isotope separation and developed the hydrogen bomb with Edward Teller at the Los Alamos Laboratory. Following World War II she became a voluntary associate professor of Physics at the University of Chicago. She developed the mathematical model for the structure of nuclear shells while working as a senior physicist at the Argonne National Laboratory. After publishing her theory, she found that Hans Jensen and his colleagues had simultaneously discovered the same model. She was the second woman (following Marie Curie) to be awarded a Nobel Prize in Physics, which she shared with Hans Jensen and Eugene Wigner in 1963. In 1960, at the age of 58, she finally became a full professor of physics at the University of California.
Societal relevance:
Goeppert Mayer used her background in quantum mechanics to revolutionize chemical and nuclear physics at a time when quantum mechanics was only beginning to have an effect on the field of chemistry. She made advances in the study of the structure of organic compounds using her background in mathematics, publishing a milestone paper on the spectrum of benzene with A. L. Sklar. She was the first person to determine the atomic properties of the newly discovered elements: neptunium and plutonium. Her discovery of the mathematical model of nuclear shell structure is one of the foundations of modern nuclear physics and would later influence the quark model. She was the first to predict double beta decay, leading to the search for neutrinoless double beta decays which cannot be explained by the Standard Model of elementary particles and could lead to new physics.
Goepert Mayer’s legacy includes several awards and honours in her name, including the Maria Goeppert Mayer Award created by the American Physical Society to honour young female physicists who hold Ph.D.s, an award by the Argonne National Laboratory for young female scientists or engineers, and the University of California, San Diego’s annual Maria Goeppert Mayer symposium which features science discussions by female researchers.
General citations and resources:
https://en.wikipedia.org/wiki/Maria_Goeppert_Mayer
https://en.wikipedia.org/wiki/Double_beta_decay
https://www.nobelprize.org/womenwhochangedscience/stories/maria-goeppert-mayer
https://www.mediatheque.lindau-nobel.org/research-profile/laureate-goeppert-mayer
Slide 1: Nuclear shell structure: “magic numbers”
Science details:
In 1946, Goeppert Mayer began working with Edward Teller to determine the origin of the elements by creating a list of isotope (elements with the same number of protons and different numbers of neutrons) abundances. This work led her to discover a pattern: certain nuclei were especially stable, namely those with 2, 8, 20, 28, or 50 protons or neutrons. These numbers were later termed “magic numbers” by Eugene Wigner. She suggested that the shell structure for nuclei was a better candidate than the widely accepted model of the time (the liquid drop model of nuclei). This is analogous to the electron shell structure in atoms. In this model, fixed numbers of nucleons (protons or neutrons) inhabit shells with specific energies determined by their quantum properties (like orbital angular momentum, spin-orbit coupling). It is energetically favorable to have nuclei with completely filled outer shells, making these nuclei the most stable.
Citations and resources:
https://www.aps.org/publications/apsnews/200808/physicshistory.cfm
http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/shell.html#c1
Figures:
Chart of binding energy above Weizsaecker formula (in MeV) for isotopes of calcium (calcium-40 to calcium-48). Calcium-40, calcium-47, and calcium-48 have binding energies greater than those calculated by the Weizsaecker formula, with values exceeding 1 MeV in calcium-40 and calcium-48. Calcium is “doubly magic”, as it has two isotopes with magic neutron numbers: 20 and 28, respectively. http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/shell.html#c1
Slide 2: Nuclear shell structure: energy levels
Science details:
In the shell structure for nuclei, each nucleon moves in a central potential well created by other nucleons, and the orbits form a series of shells of increasing energy. Nuclei with completely filled outer shells are the most stable. After collecting evidence for the nuclear shell model, Goeppert Mayer was unable to explain the pattern of “magic numbers” using quantum mechanics and a simple central potential alone. She then factored in spin-orbit coupling, which allowed her to predict the sequence of magic numbers and calculate nuclear energy levels.
The “Woods-Saxon” potential describes the strong interaction between a nucleon moving in a potential well created by the rest of the nucleus. The nucleon is a distance r from the center, the constant V₀ represents the depth of the potential well, the length a represents the surface thickness of the nucleus, and the length R is the nuclear radius relating to the atomic number. A nucleon near the surface of the nucleus is subject to large strong forces from the other nucleons. The strong force is short-ranged, so the potential approaches zero outside the boundaries of the nucleus. This potential leads to orbital angular momentum effects, which gives the quantum energy states labelled by principal quantum number n and orbital angular momentum quantum number l (which has symbols s, p, d, f, ... corresponding to l=0, 1, 2, 3, …). These energy levels alone do not predict the magic numbers: there is further splitting due to spin-orbit coupling.
Spin-orbit coupling acts like a perturbative term to the Woods-Saxon potential. It describes the interaction between orbital angular momentum (L) and spin angular momentum (S) inside a potential. The subscripts on the orbital angular momentum quantum numbers give the total angular momentum (quantum number j=1/2, 3/2, 5/2, …). These give the “multiplicity states” (number of states with a unique set of quantum numbers for a given total angular momentum), indicating the maximum number of nucleons a closed shell can accommodate. The magic numbers correspond to complete shells of protons or neutrons, explaining the stability of nuclei with magic proton and/or neutron numbers.
Citations and resources:
https://www.aps.org/publications/apsnews/200808/physicshistory.cfm
http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/shell.html#c1
https://en.wikipedia.org/wiki/Woods%E2%80%93Saxon_potential
Figures:
Low-lying energy levels in a single-particle shell model. With an oscillator potential and without spin-orbit coupling (left, blue band), the energy levels are given by principal quantum numbers and orbital angular momentum quantum numbers. When spin-orbit coupling is included (right, green band), the energy levels are split and further denoted by total angular momentum quantum numbers. These give the multiplicity of states (red band), which add as energy increases to filled shells with magic numbers of protons/neutrons (purple band). https://en.wikipedia.org/wiki/File:Shells.png
Slide 3: Two-photon absorption: analogy
Science details:
The photo-electric effect is the emission of electrons from a material due to light hitting it. The incident photon must have a minimum frequency to cause the emission, rather than a minimum intensity. For example, a red light (lowest frequency photons), green light (intermediate frequency photons), and violet light (highest frequency photons) are each shone on a particular material. The red photons will not cause any electron emissions, green photons will cause electron emissions but at a slow speed, and violet light will cause the emissions at the highest speed. The total energy of a light pulse is given by the energy of one photon times the total number of photons. Donna Strickland gives an analogy of this phenomena using basketball players in her Nobel Lecture in 2018:
When a ball is dropped from a given height it picks up speed as it falls. In the analogy, the photons can be thought of as basketball players of different heights carrying basketballs (photons) and the speed of the ball as it falls through a net will act as the speed of the electron as it is emitted from the material due to the photoelectric effect. A red photon has the longest wavelength (lowest frequency) therefore the smallest energy, analogous to the shortest basketball player. They are shorter than the height of the net, so no balls will pass through meaning no electrons will be emitted from the material. A green photon has an intermediate wavelength, so the basketball player has an intermediate height and is just able to drop the ball into the net, meaning the electron is emitted from the material but at a low speed. Finally, a violet photon is analogous to the tallest basketball player who drops the ball from the largest height allowing it to pick up speed, meaning the electron is emitted from the material at a high speed.
The analogy of two-photon absorption comes from imagining two short basketball players working together to drop the ball into the net: their combined heights mean the ball can be dropped from the same height as the tallest basketball player, so two red photons can cause an electron emission of the same speed as one violet photon. In her 1931 PhD thesis, Goeppert Mayer predicted two-photon absorption. It took 30 years, with the invention of the laser, for this to ever be observed! A laser is able to emit light in a single color and focuses all the photons in the same direction. Lasers are tightly packed enough that multiple photons can interact with a single atom, which allows for measurements of two-photon absorption.
Citations and resources:
https://en.wikipedia.org/wiki/Photoelectric_effect
Figures:
Left: short (red, left), intermediate (green, middle), and tall (right, violet) basketball players holding their respective colored basketballs.
Right: two red basketball players stand on top of each other, the upper one is holding a violet basketball.
https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.91.030502
Slide 4: Two-photon absorption: fluorescence
Science details:
In her 1931 PhD thesis, Goeppart Mayer predicted two-photon absorption. It took 30 years, with the invention of the laser, for the phenomenon to be observed.
Molecules have discrete energy levels, and absorb or emit quantized energy to transition between levels. Two-photon absorption (TPA) is the simultaneous absorption of two photons of identical or differing frequencies to excite a molecule from one energy state (ground) to a higher energy state.
TPA of a fluorescent molecule leads to two-photon excited fluorescence, where the excited state decays by spontaneous emission of a photon.
Citations and resources:
https://en.wikipedia.org/wiki/Two-photon_absorption
Figures:
Left: Schematic of energy levels involved in TPA. The energy difference between the ground state and first excited state is equal to the energy of two photons. The virtual state marks the hypothetical energy level associated with one photon absorption/emission. Adapted from https://en.wikipedia.org/wiki/File:Two_photons_absorption_energy_scheme.png
Right: Schematic of energy levels involved in two-photon excited fluorescence. An electron is initially at the ground state, then is excited by a two-photon absorption where the combined photons’ energy is 2ω₁ (red arrows). The electron initially lowers its energy by a non-radiative deexcitation then further lowers energy levels by a fluorescence emission with energy ω₂ (green arrows). Finally, the electron returns to its ground state energy by another non-radiative deexcitation. The fluorescent emission energy (ω₂) is less than the combined energy of the absorbed photons (2ω₁). https://en.wikipedia.org/wiki/File:Two_photons_excited_fluorescence_energy_levels.png
Slide 5: (Neutrinoless) double beta decay
Science details:
In 1935, Goeppert Mayer predicted double beta decay. More than 50 years later, the first laboratory observation of double beta decay was made by Micheal More in 1987.
Double beta decay is a type of radioactive decay, where two neutrons transform into two protons inside an atomic nucleus and two beta particles (electrons or positrons) are produced. A single beta decay is when a neutron turns into a proton which emits a negative beta particle (electron) and an antineutrino (antiparticle of the neutrino).
Nuclear binding energy is the minimum energy needed to disassemble the protons and neutrons making up the nucleus of an atom. It is greater for stable nuclei, meaning an unstable nucleus that beta decays into a stable nucleus has lower binding energy before the decay. Beta decay also obeys conservation of lepton number: a lepton number can take the value 1,-1, or 0 for leptons, antileptons, or non-lepton particles, respectively. In the case of beta decay, the neutron and proton both have lepton number 0, the electron has lepton number 1, and the antineutrino has lepton number -1.
Neutrinoless double beta decay is yet to be observed, but is theorized if the neutrino is its own antiparticle, meaning the neutrino and antineutrino would be Majorana particles. In this process, only the electrons escape the nucleus and the neutrino/antineutrino are exchanged by the two neutrons and absorbed back into the nucleus. If this decay were to be observed then it would be evidence that conservation of lepton number is violated, which would explain the mystery of why our universe is composed of more matter than antimatter.
Citations and resources:
https://www.quantumdiaries.org/2015/09/22/majorananeutrinos-0vbb/
http://wwwkm.phys.sci.osaka-u.ac.jp/en/research/r01.html
Figures:
Depiction of double beta decay of a nucleus (left) and neutrinoless double beta decay of a nucleus (right). Protons are depicted shown red, neutrons in blue, the two neutrons that transform into protons by radiating a W boson are shown in yellow. In the case of double beta decay, the W boson decays into an electron and an antineutrino. In the case of neutrinoless double beta decay, one W boson decays into an electron and an antineutrino, the other decays into an electron and a neutrino. The antineutrino and neutrino are exchanged by the decaying neutrons (shown by the connected decay line), which is possible if neutrinos are their own antiparticles, i.e. they are Majorana particles. https://www.quantumdiaries.org/2015/09/22/majorananeutrinos-0vbb/
Slide 6: Double beta decay
Science details:
In 1935, Goeppert Mayer predicted double beta decay. More than 50 years later, the first laboratory observation of double beta decay was made by Micheal More in 1987.
Double beta decay is a type of radioactive decay, where two neutrons transform into two protons inside an atomic nucleus and two beta particles (electrons or positrons) are produced. A single beta decay is when a neutron turns into a proton which emits a negative beta particle (electron) and an antineutrino (antiparticle of the neutrino).
Nuclear binding energy is the minimum energy needed to disassemble the protons and neutrons making up the nucleus of an atom. It is greater for stable nuclei, meaning an unstable nucleus that beta decays into a stable nucleus has lower binding energy before the decay. Beta decay also obeys conservation of lepton number: a lepton number can take the value 1,-1, or 0 for leptons, antileptons, or non-lepton particles, respectively. In the case of beta decay, the neutron and proton both have lepton number 0, the electron has lepton number 1, and the antineutrino has lepton number -1.
Neutrinoless double beta decay is yet to be observed, but is theorized if the neutrino is its own antiparticle, meaning the neutrino and antineutrino would be Majorana particles. In this process, only the electrons escape the nucleus and the neutrino/antineutrino are exchanged by the two neutrons and absorbed back into the nucleus. If this decay were to be observed then it would be evidence that conservation of lepton number is violated, which would explain the mystery of why our universe is composed of more matter than antimatter.
Citations and resources:
https://www.quantumdiaries.org/2015/09/22/majorananeutrinos-0vbb/
http://wwwkm.phys.sci.osaka-u.ac.jp/en/research/r01.html
Figures:
Depiction of a double beta decay of a nucleus. A neutron (blue) transforms into a proton (yellow) by radiating a W boson (green). The W boson decays (orange) into an electron and an antineutrino. https://www.quantumdiaries.org/2015/09/22/majorananeutrinos-0vbb/
Slide 7: Double beta decay prediction
Science details:
In 1935, Goeppert Mayer predicted double beta decay. More than 50 years later, the first laboratory observation of double beta decay was made by Micheal More in 1987.
Double beta decay is a type of radioactive decay, where two neutrons transform into two protons inside an atomic nucleus and two beta particles (electrons or positrons) are produced. A single beta decay is when a neutron turns into a proton which emits a negative beta particle (electron) and an antineutrino (antiparticle of the neutrino).
Nuclear binding energy is the minimum energy needed to disassemble the protons and neutrons making up the nucleus of an atom. It is greater for stable nuclei, meaning an unstable nucleus that beta decays into a stable nucleus has lower binding energy before the decay. Beta decay also obeys conservation of lepton number: a lepton number can take the value 1,-1, or 0 for leptons, antileptons, or non-lepton particles, respectively. In the case of beta decay, the neutron and proton both have lepton number 0, the electron has lepton number 1, and the antineutrino has lepton number -1.
Neutrinoless double beta decay is yet to be observed, but is theorized if the neutrino is its own antiparticle, meaning the neutrino and antineutrino would be Majorana particles. In this process, only the electrons escape the nucleus and the neutrino/antineutrino are exchanged by the two neutrons and absorbed back into the nucleus. If this decay were to be observed then it would be evidence that conservation of lepton number is violated, which would explain the mystery of why our universe is composed of more matter than antimatter.
Citations and resources:
https://www.quantumdiaries.org/2015/09/22/majorananeutrinos-0vbb/
http://wwwkm.phys.sci.osaka-u.ac.jp/en/research/r01.html
Figures:
Title and abstract of Goeppert Mayer’s 1935 paper: Double Beta-Disintegration in the Physical Review. The abstract reads: From the Fermi theory of β-disintegration the probability of simultaneous emission of two electrons (and two neutrinos) has been calculated. The result is that this process occurs sufficiently rarely to allow a half-life of over 10⁷ years for a nucleus, even if its isobar of atomic number different by 2 were more stable by 20 times the electron mass. https://journals.aps.org/pr/abstract/10.1103/PhysRev.48.512