Helium-4 as a Boson: Exploring an Atom's Quantum Nature

In summary, the Wikipedia article on Bose-Einstein condensates states that helium-4 can be considered a boson when in a condensate due to its integer spin. However, this statement is only approximately correct and applies to low densities of helium-4. The commutation relations for operators of creation and annihilation of helium-4 atoms are derived from the anticommutation relations for protons, neutrons, and electrons, and this can result in a different definition of bosons for composite particles. This can have implications for the behavior of composite bosons, such as in Bose-Einstein condensation.
  • #1
Iamu
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The wikipedia article on Bose-Einstein condensates mentions that helium-4 is, or can be, a boson. It says that a condensate is made by putting many bosons, such as helium-4, into the lowest energy state.

How can an atom be a boson? I figured that an atom, composed of fermions, would have to be a fermion as well. How do the electrons and protons of helium-4 occupy the same space?
 
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  • #2
Add the spins of all the particles in the nucleus.
He-4 2 has protons and 2 neutrons -> 4*1/2 =2 ->Integer spin meaning it is a boson
He-3 2 has protons and 1 neutron -> 3*1/2 =2 ->half-integer spin meaning it is a fermion
 
  • #3
Boson is not defined as occupying the same space.
The wave function of two identical bosons is unchanged if the two are interchanged,
while the WF of two fermions changes sign.
If two He atoms are interchanged , the WF has four sign changes, which results in no overall sign change.
 
  • #4
wow, I made an almost identical post to this and I thought this was mine. haha sorry for posting you can delete this if you want. Thanks for the answer the meir.
 
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  • #5
I am afraid the situation is not so simple. The statement "Helium-4 is a boson" is just approximately correct (i.e. only correct for relatively low density of Helium-4, when wave functions of the fermions in the Helium-4 atoms essentially do not overlap). The commutation relations for operators of creation/annihilation of Helium-4 atoms are derived from the anticommutation relations for the operators of creation/annihilation of protons, neutrons, and electrons that are parts of Helium-4 atoms, and those commutation relations approximately coincide with the commutation relations for boson creation/annihilation operators in the limit of low density. See the details (for the example of deuterons) in the book by Lipkin called Quantum Mechanics, or something of the kind. So Iamu actually asked a good question.
 
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  • #6
akhmeteli said:
I am afraid the situation is not so simple. The statement "Helium-4 is a boson" is just approximately correct (i.e. only correct for relatively low density of Helium-4, when wave functions of the fermions in the Helium-4 atoms essentially do not overlap). The commutation relations for operators of creation/annihilation of Helium-4 atoms are derived from the anticommutation relations for the operators of creation/annihilation of protons, neutrons, and electrons that are parts of Helium-4 atoms, and those commutation relations approximately coincide with the commutation relations for boson creation/annihilation operators in the limit of low density. See the details (for the example of deuterons) in the book by Lipkin called Quantum Mechanics, or something of the kind. So Iamu actually asked a good question.
I think you (and Lipkin?) are describing a dynamical complication for composite bosons, but they still satisfy the usual definition of "boson".
 
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  • #7
I agree, if you use the definition of bosons as particles with integer spin. However, e.g., Dirac in his book "The principles of quantum mechanics" defines bosons as particles for which only symmetric states exist in nature (my quote may be a bit imprecise as my book is a translation from English). If the usual Bose commutation relationships are not satisfied, as is the case for composite particles, the particles are not bosons under this definition. On the one hand, arguing about choice of definitions does not make much sense, on the other hand, the usual conclusions about Bose-Einstein condensation and so on are not exactly correct for composite integer spin particles. For example, one cannot have too many Helium-4 atoms with limited energy within limited space, because they do consist of fermions. This important fact is not widely appreciated, and it seemed highly relevant to the question raised by the original poster. That's why I mentioned it.
 
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What is Helium-4 as a Boson?

Helium-4 is a type of isotope of the element Helium that has 4 neutrons in its nucleus. A boson is a type of particle that follows the rules of quantum mechanics and has integer spin. Helium-4, due to its unique atomic structure, exhibits bosonic behavior.

How does Helium-4 exhibit its bosonic nature?

Helium-4 atoms, unlike other elements, can occupy the same quantum state without any repulsion. This behavior is known as Bose-Einstein condensation and is a result of Helium-4's bosonic nature. This phenomenon allows for the formation of superfluidity, a state of matter with zero viscosity.

What is the significance of studying Helium-4 as a boson?

Studying Helium-4 as a boson allows us to understand the fundamental principles of quantum mechanics and the behavior of matter at a microscopic level. It also has practical applications in fields such as superconductivity and superfluidity, which have potential uses in technology and industry.

Can Helium-4 be used to create new materials or technologies?

Yes, the unique properties of Helium-4 as a boson have led to the development of new materials and technologies such as superconducting magnets and cryogenics. Its use in these applications is due to its ability to exhibit superfluidity and remain in a liquid state at very low temperatures.

Are there any other elements or atoms that exhibit bosonic behavior?

Yes, other elements such as lithium-7 and sodium-23 also exhibit bosonic behavior. Additionally, particles such as photons, which have zero mass, are also considered bosons. However, Helium-4 is the only element that can exhibit Bose-Einstein condensation at temperatures achievable in a laboratory setting.

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