Forbidden mechanism

Tiny bits of matter can hold onto light. Usually, they let light go very fast. But sometimes, they hold it for a long time. This can take minutes or even hours.

This happens because of special rules. These rules make it hard for the light to leave. It is like a door that is hard to open.

Some things stay excited for a very long time. They can last for billions of years!

This slow light helps us see things in space. It lets us see cold gas far away.

It is a slow and steady way to shine.

Tiny bits of matter, like atoms, can hold onto light. Most of the time, they let light go very fast. But sometimes, they follow special rules called selection rules. These rules make it hard for light to leave. We call these slow steps forbidden transitions.

In a forbidden transition, the matter stays in an excited state for a long time. This state is called a meta-stable state. It can last for seconds or even years. Some states last for billions of years! This happens because the matter must change its spin to let the light out. Spin is a type of movement in an atom. If the change is too big, the light is let out very slowly.

These slow steps are very helpful. They help us make strong lasers. They also help us make very accurate atomic clocks. In space, gas is very thin. Because the gas is thin, atoms do not bump into each other much. This lets them use forbidden transitions to shine. This light helps us see cold gas in deep space.

Tiny bits of matter, like atoms, have special rules for how they behave. These rules are called selection rules. They decide how atoms or nuclei can release energy by emitting light, which we call photons. Usually, an atom lets go of its extra energy very quickly. However, some transitions do not follow the easiest path. Scientists call these forbidden transitions. They are not truly impossible, but they are very unlikely to happen quickly. This happens when a transition does not follow the usual rules for light.

How does a forbidden transition work? It all depends on a property called spin or angular momentum. In many cases, an atom wants to move from a high-energy state to a lower one. To do this, it must change its spin by a specific amount. For example, a photon in gamma decay usually carries away one unit of spin. If the atom needs to change its spin by two or more units, the process is much harder. This creates a slow way for the energy to escape. The atom enters a meta-stable state, which is a state that lasts a long time.

Scientists have studied these rules for a long time to understand the universe. They found that each extra unit of spin change makes the process much slower. Each degree of forbiddenness can slow the decay by about five orders of magnitude. This means the process becomes thousands of times slower for every extra step. In some special cases, like the decay of Ta-180m, the spin change is eight units. This makes the decay incredibly slow. Instead of lasting a tiny fraction of a second, it lasts more than 10^23 seconds. That is at least 3 x 10^15 years!

There are many different types of these transitions in nature. In beta decay, some transitions are called super-allowed because they happen very fast. This happens when the electron and neutrino carry away zero total angular momentum. Other beta decays are ranked by how forbidden they are based on their spin and parity. We also see forbidden transitions in the way atoms act in solids. For example, rare earth atoms like neodymium are used in high-power lasers. These atoms are held in a matrix so they do not bump into other things. This allows them to stay in an excited state for a long time.

Forbidden transitions help us see things that would otherwise be invisible. In the deep reaches of space, the gas is very thin. There are only a few atoms in every cubic centimeter. Because the gas is so thin, atoms rarely bump into each other. This means they do not lose their energy through collisions. Instead, they wait and eventually release light through forbidden transitions. This light helps astronomers see cold hydrogen gas or bright planetary nebulae. We also use these transitions to build very accurate atomic and quantum clocks.

In the field of spectroscopy, scientists study how matter interacts with light. They often encounter a phenomenon known as a forbidden mechanism. This refers to a spectral line created when an atom, molecule, or nucleus undergoes a transition. This transition is not permitted by a specific set of rules called selection rules. These rules are based on certain mathematical approximations, such as the electric dipole approximation. While these processes are nominally forbidden, they are not impossible. They can occur if a higher level of approximation is used, such as magnetic dipole or electric quadrupole transitions. These higher-level processes happen, but they occur at a very low rate.

To understand how this works, we must look at the relationship between energy and probability. When an entity is in an excited state, it wants to return to a lower energy state. Usually, it follows a permitted path that happens almost instantly. A forbidden transition occurs when the path is restricted by physical laws, such as the conservation of angular momentum. If a permitted path is available, the entity will almost certainly take it first. However, if only a forbidden path exists, the entity enters what is called a meta-stable state. In these states, the entity stays excited for a much longer time. For example, permitted transitions might last less than a microsecond. In contrast, meta-stable states can last from milliseconds to many seconds.

There are different types of forbidden transitions depending on the system. In phosphorescent materials, atoms absorb light and enter an excited state. To decay, the atom must undergo a spin flip. This specific change is forbidden by electric dipole transitions. Because of this, the material emits light very slowly, sometimes over minutes or hours. In radioactive decay, the mechanism involves the change in nuclear angular momentum. Most gamma decays are most common when the spin changes by exactly one quantum unit. This is because a gamma-ray photon carries a spin of one unit. If the change in angular momentum is two, three, or four units, the transition is considered forbidden.

Nuclear physics provides some of the most extreme examples of these mechanisms. Each additional unit of spin change increases the level of forbiddenness. Each degree of forbiddenness can inhibit the decay rate by about five orders of magnitude. This means the process becomes much slower with every extra unit of spin. One incredible example is the decay of Ta-180m. This isotope requires a spin change of eight units. This massive change suppresses its decay by a factor of 10^35 compared to a one-unit change. While a normal gamma decay might last 10^-12 seconds, Ta-180m has a half-life of more than 10^23 seconds. This is at least 3 x 10^15 years, meaning its decay has not even been observed.

Beta decay follows its own set of rules regarding angular momentum and parity. Some beta decays are classified as super-allowed, such as the Fermi transition. This happens when a nucleus moves from a spin-zero state to another spin-zero state. It is possible because the emitted electron and neutrino can have opposing spins. This results in a total radiation angular momentum of zero. The next type is the Gamow-Teller transition, where the emitted radiation has a combined spin of one. This changes the nuclear spin by one unit to compensate. Other decays are ranked by their degree of forbiddenness based on higher angular momentum. These transitions are also slowed by factors of four to five orders of magnitude for each level.

Forbidden transitions also play a vital role in solid-state physics and technology. Rare earth atoms, such as neodymium and erbium, are used as dopants in lasers. In these materials, the atoms are held in a matrix. This matrix prevents them from losing energy through collisions with other atoms. Because their excited states have long half-lives, they are easy to pump with light. Neodymium-doped glass is especially useful for high-power solid-state lasers. The unique color of this glass comes from forbidden f-f transitions within the neodymium atom. Additionally, symmetry in bulk semiconductors can cause forbidden transitions, which changes how they absorb light.

Finally, these mechanisms are essential for understanding the universe through astrophysics. In the extremely low-density gases of outer space, atoms rarely collide. Because collisions are rare, excited atoms are likely to decay via forbidden transitions. This produces specific light that astronomers use to study the cosmos. For instance, the 21-cm hydrogen line is vital for radio astronomy. It allows scientists to see very cold, neutral hydrogen gas. We also see forbidden lines from nitrogen, sulfur, and oxygen in planetary nebulae. These lines help scientists calculate the energy balance of these massive space structures. Scientists also use forbidden transitions in laboratory settings to stabilize highly accurate atomic and quantum clocks.