Element lighter than hydrogen

[Subduction Zone]

Okay, I was tempted to use scare quotes. But it is all about the clicks baby!

At any rate Muonium is an exotic atom made up of an antimuon and an electron. Chemically it would be almost identical to hydrogen, except that it is slightly radioactive. They have been made in the lab, they just don't hang around for very long. But they do hang around long enough to do at least some spectroscopic analysis of them and that is how this atom may be useful in physics.

Muonium - Wikipedia

"Although muonium is short-lived, physical chemists study it using muon spin spectroscopy (μSR),[5] a magnetic resonance technique analogous to nuclear magnetic resonance (NMR) or electron spin resonance (ESR) spectroscopy. Like ESR, μSR is useful for the analysis of chemical transformations and the structure of compounds with novel or potentially valuable electronic properties. Muonium is usually studied by muon spin rotation, in which the Mu atom's spin precesses in a magnetic field applied transverse to the muon spin direction (since muons are typically produced in a spin-polarized state from the decay of pions), and by avoided level crossing (ALC), which is also called level crossing resonance (LCR).[5] The latter employs a magnetic field applied longitudinally to the polarization direction, and monitors the relaxation of muon spins caused by "flip/flop" transitions with other magnetic nuclei.

Because the muon is a lepton, the atomic energy levels of muonium can be calculated with great precision from quantum electrodynamics (QED), unlike in the case of hydrogen, where the precision is limited by uncertainties related to the internal structure of the proton. For this reason, muonium is an ideal system for studying bound-state QED and also for searching for physics beyond the Standard Model.[6][7]"

And it even has a chemical symbol Mu.

There is of course also antimuonium. It is a regular muon with a positron orbiting it. If the analysis of the two is different it may tell us more about the universe that we live in. Physicists are hoping to see some rule breaking.

 

[exchemist]

Okay, I was tempted to use scare quotes. But it is all about the clicks baby!

At any rate Muonium is an exotic atom made up of an antimuon and an electron. Chemically it would be almost identical to hydrogen, except that it is slightly radioactive. They have been made in the lab, they just don't hang around for very long. But they do hang around long enough to do at least some spectroscopic analysis of them and that is how this atom may be useful in physics.

Muonium - Wikipedia

"Although muonium is short-lived, physical chemists study it using muon spin spectroscopy (μSR),[5] a magnetic resonance technique analogous to nuclear magnetic resonance (NMR) or electron spin resonance (ESR) spectroscopy. Like ESR, μSR is useful for the analysis of chemical transformations and the structure of compounds with novel or potentially valuable electronic properties. Muonium is usually studied by muon spin rotation, in which the Mu atom's spin precesses in a magnetic field applied transverse to the muon spin direction (since muons are typically produced in a spin-polarized state from the decay of pions), and by avoided level crossing (ALC), which is also called level crossing resonance (LCR).[5] The latter employs a magnetic field applied longitudinally to the polarization direction, and monitors the relaxation of muon spins caused by "flip/flop" transitions with other magnetic nuclei.

Because the muon is a lepton, the atomic energy levels of muonium can be calculated with great precision from quantum electrodynamics (QED), unlike in the case of hydrogen, where the precision is limited by uncertainties related to the internal structure of the proton. For this reason, muonium is an ideal system for studying bound-state QED and also for searching for physics beyond the Standard Model.[6][7]"

And it even has a chemical symbol Mu.

There is of course also antimuonium. It is a regular muon with a positron orbiting it. If the analysis of the two is different it may tell us more about the universe that we live in. Physicists are hoping to see some rule breaking.

Ha! By coincidence I was just looking at ESR, or rather EPR, as we seem to call it nowadays, for a discussion on another forum.

I had not heard of muonium, but it makes sense. However it should be pointed out that its chemistry is distinctly limited, as it has a half life of 1.5μs! So "slightly radioactive" is a bit of an understatement.

 

[Twilight Hue]

Okay, I was tempted to use scare quotes. But it is all about the clicks baby!

At any rate Muonium is an exotic atom made up of an antimuon and an electron. Chemically it would be almost identical to hydrogen, except that it is slightly radioactive. They have been made in the lab, they just don't hang around for very long. But they do hang around long enough to do at least some spectroscopic analysis of them and that is how this atom may be useful in physics.

Muonium - Wikipedia

"Although muonium is short-lived, physical chemists study it using muon spin spectroscopy (μSR),[5] a magnetic resonance technique analogous to nuclear magnetic resonance (NMR) or electron spin resonance (ESR) spectroscopy. Like ESR, μSR is useful for the analysis of chemical transformations and the structure of compounds with novel or potentially valuable electronic properties. Muonium is usually studied by muon spin rotation, in which the Mu atom's spin precesses in a magnetic field applied transverse to the muon spin direction (since muons are typically produced in a spin-polarized state from the decay of pions), and by avoided level crossing (ALC), which is also called level crossing resonance (LCR).[5] The latter employs a magnetic field applied longitudinally to the polarization direction, and monitors the relaxation of muon spins caused by "flip/flop" transitions with other magnetic nuclei.

Because the muon is a lepton, the atomic energy levels of muonium can be calculated with great precision from quantum electrodynamics (QED), unlike in the case of hydrogen, where the precision is limited by uncertainties related to the internal structure of the proton. For this reason, muonium is an ideal system for studying bound-state QED and also for searching for physics beyond the Standard Model.[6][7]"

And it even has a chemical symbol Mu.

There is of course also antimuonium. It is a regular muon with a positron orbiting it. If the analysis of the two is different it may tell us more about the universe that we live in. Physicists are hoping to see some rule breaking.

I wonder if Nottingham University has info. The home of my favorite video professor!

 

[Subduction Zone]

Ha! By coincidence I was just looking at ESR, or rather EPR, as we seem to call it nowadays, for a discussion on another forum.

I had not heard of muonium, but it makes sense. However it should be pointed out that its chemistry is distinctly limited, as it has a half life of 1.5μs! So "slightly radioactive" is a bit of an understatement.

Well maybe just a teeny tiny understatement. I remember how muons confirmed Einstein's special relativity. It of course was not the only "proof" of his theory. I am sure that it was not even the first confirmation of his theory. Many of the muons that are observed are from cosmic rays. The problem is that they were formed by collisions with cosmic rays at the top of our atmosphere and that is too far away for almost any to survive the trip to the surface. But not only are they formed at the top of the atmosphere, They are also formed with a very high velocity. Relativity kicks in. They can form and take a trip at subliminal speeds and make it to the Earth due to the "clock" of the muon being slower:

Muon Experiment in Relativity

https://hal.science/hal-02531926/document#:~:text=Muons are created in the,at rest T0 ~ 2.2 µs.

 

[exchemist]

Well maybe just a teeny tiny understatement. I remember how muons confirmed Einstein's special relativity. It of course was not the only "proof" of his theory. I am sure that it was not even the first confirmation of his theory. Many of the muons that are observed are from cosmic rays. The problem is that they were formed by collisions with cosmic rays at the top of our atmosphere and that is too far away for almost any to survive the trip to the surface. But not only are they formed at the top of the atmosphere, They are also formed with a very high velocity. Relativity kicks in. They can form and take a trip at subliminal speeds and make it to the Earth due to the "clock" of the muon being slower:

Muon Experiment in Relativity

https://hal.science/hal-02531926/document#:~:text=Muons are created in the,at rest T0 ~ 2.2 µs.

You'd struggle to get any chemistry at all out of muons moving at relativistic velocities, though. You certainly couldn't put them into an EPR machine and get a reading from their microwave absorption.

 

[John53]

Hydrogen lite? Half the calories but the same flavour?

 

[Subduction Zone]

You'd struggle to get any chemistry at all out of muons moving at relativistic velocities, though. You certainly couldn't put them into an EPR machine and get a reading from their microwave absorption.

Yes, I wonder how they plan to detect the muon spin resonance. I remember from a course many many years ago how variations of the Earth's magnetic field was detected by hydrogen spin resonance. I am probably wrong after forty years, but I do believe that our detector used an electrically generated magnetic field and then it was shut off and then the decay of that field in a container of hydrogen, whether as a gas or as water, was observed. The rate of decay could be used to calculate local field strength. Let's see what the internet says.

EDIT: Close, but not quite right. Nuclear magnetic resonance. The induced field causes hydrogen nuclei to become aligned. Once the field is cut the nuclei undergo precession. The frequency of the precession gives us the strength of the field:


Magnetometer - Wikipedia

You have to scroll down to Scalar magnetometers.

 

[Twilight Hue]

Hydrogen lite? Half the calories but the same flavour?

Does that mean hydrogen ballons explode quieter with half the noise?

 

[Polymath257]

Muonium? That's the heavy brother of positronium!

Positronium is the combination of a positron and an electron as a single 'atom'. It forms a 'stable' system until the electron and positron annihilate each other.

The spin states of positronium are quite different, with the parallel spin version (ortho-positronium) lasting much longer (142 nano-seconds) than the anti-parallel spin version (para-positronium) which lasts only .12 nano-seconds.

Muonium is also really helpful in learning more about the different types of neutrino. Electron neutrinos are different than muon neutrinos and the decay of muonium involves both types.

One of the goals is to understand the anomalous magnetic dipole moment. For electrons, this is one of the most accurately known constants, with theoretical prediction and actual measurements agreeing to over 13 decimal places of accuracy. For muons, the presence of other neutrinos complicates both the calculations and the observations, but there *appear* to be discrepancies that point to new physics!

Also, it is possible to form 'atoms' with positive pions and electrons. At least the 'nucleus' is made of hadrons and not leptons.

 

[Brickjectivity]

What's next: Mulithium?

 

[exchemist]

Yes, I wonder how they plan to detect the muon spin resonance. I remember from a course many many years ago how variations of the Earth's magnetic field was detected by hydrogen spin resonance. I am probably wrong after forty years, but I do believe that our detector used an electrically generated magnetic field and then it was shut off and then the decay of that field in a container of hydrogen, whether as a gas or as water, was observed. The rate of decay could be used to calculate local field strength. Let's see what the internet says.

EDIT: Close, but not quite right. Nuclear magnetic resonance. The induced field causes hydrogen nuclei to become aligned. Once the field is cut the nuclei undergo precession. The frequency of the precession gives us the strength of the field:


Magnetometer - Wikipedia

You have to scroll down to Scalar magnetometers.

Interesting. I didn't know that was how they worked. I ought to revise this ESR/NMR stuff. I haven't looked at it for 40 years. Spin-echo always baffled me.

 

[PureX]

You all sound like the gun nut crowd talking about guns and ammo.

 

[exchemist]

Muonium? That's the heavy brother of positronium!

Positronium is the combination of a positron and an electron as a single 'atom'. It forms a 'stable' system until the electron and positron annihilate each other.

The spin states of positronium are quite different, with the parallel spin version (ortho-positronium) lasting much longer (142 nano-seconds) than the anti-parallel spin version (para-positronium) which lasts only .12 nano-seconds.

Muonium is also really helpful in learning more about the different types of neutrino. Electron neutrinos are different than muon neutrinos and the decay of muonium involves both types.

One of the goals is to understand the anomalous magnetic dipole moment. For electrons, this is one of the most accurately known constants, with theoretical prediction and actual measurements agreeing to over 13 decimal places of accuracy. For muons, the presence of other neutrinos complicates both the calculations and the observations, but there *appear* to be discrepancies that point to new physics!

Also, it is possible to form 'atoms' with positive pions and electrons. At least the 'nucleus' is made of hadrons and not leptons.

Does the triplet positronium last longer because the 2 particles are on average further apart, or something?

 

[Polymath257]

Does the triplet positronium last longer because the 2 particles are on average further apart, or something?

In a broad sense. There are two things going on: a selection rule that forces the parallel spin version to decay into 3 photons, while the anti-parallel version can decay into 2. This already makes the anti-parallel version decay faster.

But, the rate of this conversion is determined by the overlap of a couple of wave functions at the origin. But the anti-spin version is spin 0, which corresponds to an S state and the parallel version is a spin 1, which corresponds to the P state. The S state has more probability at the origin, so has a faster decay rate. This does *roughly* correspond to being closer together, but quantum effects dominate.

 

[Polymath257]

I should also point out that there are 'muonic atoms' where muons replace electrons.

So, there is a heavier version of hydrogen with one proton in the nucleus and one muon in 'orbit'. Because the muon is so massive, this atom has a much smaller reduced mass, and so a very different energy spectrum from ordinary hydrogen (but still a version of Balmer, etc series).

This is also a very good way to study lepton/hadron interactions.

 

[exchemist]

In a broad sense. There are two things going on: a selection rule that forces the parallel spin version to decay into 3 photons, while the anti-parallel version can decay into 2. This already makes the anti-parallel version decay faster.

But, the rate of this conversion is determined by the overlap of a couple of wave functions at the origin. But the anti-spin version is spin 0, which corresponds to an S state and the parallel version is a spin 1, which corresponds to the P state. The S state has more probability at the origin, so has a faster decay rate. This does *roughly* correspond to being closer together, but quantum effects dominate.

How does that work, though? Surely the p state implies orbital angular momentum, not just a particular spin orientation?

 

[exchemist]

In a broad sense. There are two things going on: a selection rule that forces the parallel spin version to decay into 3 photons, while the anti-parallel version can decay into 2. This already makes the anti-parallel version decay faster.

But, the rate of this conversion is determined by the overlap of a couple of wave functions at the origin. But the anti-spin version is spin 0, which corresponds to an S state and the parallel version is a spin 1, which corresponds to the P state. The S state has more probability at the origin, so has a faster decay rate. This does *roughly* correspond to being closer together, but quantum effects dominate.

How does that work, though? Surely the p state implies orbital angular momentum, not just a particular spin orientation? Can't you have an S state with parallel spins, like ortho hydrogen?

 

[Polymath257]

How does that work, though? Surely the p state implies orbital angular momentum, not just a particular spin orientation? Can't you have an S state with parallel spins, like ortho hydrogen?

My bad. It should have been singlet (not S state) and triplet (not P state). It is the total spin angular momentum that is relevant here. In both cases, we are in an orbital L=0 state. I was also misreading my QFT book (it considered higher orbital states).

In a hydrogen molecule, the protons must have a total wave function that is anti-symmetric. This wave function consists of a spin factor and an orbital factor. If the spins are parallel, the spin factor is symmetric, so the orbital factor is forced to be anti-symmetric (and so a singlet state for angular momentum).

But the anti-symmetry is forced because the two protons are identical particles and are fermions. Electrons and positrons are not identical, so the anti-symmetry is no longer required. In particular both the spin singlet and spin triplet states are consistent with an orbital singlet state, the 1S orbital.

In any case, the singlet spin state decays into 2 photons (or an even number) and the triplet state into 3 (or an odd number more than 1). The fact that 3 photons is required in the decay is largely why the triplet state is more stable.

Now, it *is* possible to have positronium in a 2S orbital state and it has a *much* longer lifetime.

Positronium - Wikipedia

As an aside, the analog of the hydrogen *molecule*, di-positronium, has been formed.

Di-positronium - Wikipedia

 

[exchemist]

My bad. It should have been singlet (not S state) and triplet (not P state). It is the total spin angular momentum that is relevant here. In both cases, we are in an orbital L=0 state. I was also misreading my QFT book (it considered higher orbital states).

In a hydrogen molecule, the protons must have a total wave function that is anti-symmetric. This wave function consists of a spin factor and an orbital factor. If the spins are parallel, the spin factor is symmetric, so the orbital factor is forced to be anti-symmetric (and so a singlet state for angular momentum).

But the anti-symmetry is forced because the two protons are identical particles and are fermions. Electrons and positrons are not identical, so the anti-symmetry is no longer required. In particular both the spin singlet and spin triplet states are consistent with an orbital singlet state, the 1S orbital.

In any case, the singlet spin state decays into 2 photons (or an even number) and the triplet state into 3 (or an odd number more than 1). The fact that 3 photons is required in the decay is largely why the triplet state is more stable.

Now, it *is* possible to have positronium in a 2S orbital state and it has a *much* longer lifetime.

Positronium - Wikipedia

As an aside, the analog of the hydrogen *molecule*, di-positronium, has been formed.

Di-positronium - Wikipedia

I must admit I find it hard to envisage a p orbital, given that there are, I suppose, two equal masses circulating around their common centre of mass, rather than a light electron circulating around a much heavier and essentially "fixed" - per Born-Oppenheimer approximation - nucleus. One is tempted to say a p state should have a long lifetime as there is a node at the nucleus so the 2 particles should not encounter one another, but I have no confidence such a picture works in the case of positronium.

But I suppose this is all off-topic: we don't @PureX to keep comparing us to tattooed gun nuts with reversed MAGA baseball caps.

 

[Subduction Zone]

I should also point out that there are 'muonic atoms' where muons replace electrons.

So, there is a heavier version of hydrogen with one proton in the nucleus and one muon in 'orbit'. Because the muon is so massive, this atom has a much smaller reduced mass, and so a very different energy spectrum from ordinary hydrogen (but still a version of Balmer, etc series).

This is also a very good way to study lepton/hadron interactions.

I know the "orbits" are not classical at all, but do the orbits in any way affect the decay rates? In other words is there a relativistic effect at all in prolong the life of a muon to an outside observer as the high velocity of a muon created by a cosmic ray that makes it to the Earth's surface long after it "should" have decayed if one uses classical physics?