Understanding Fermions in 4He & 3He - Why Different Behaviors?

[yxgao]

Why does 4He act like a boson but 3He doesn't? What accounts for their different behavior at low temperatures? Why does 4He act as a Bose Condensate, but 3He doesn't?

I read somewhere that because 4He has an even number of fermions (2 protons, 2 neutrons, 2 electrons), it behaves as a boson. What is the physical origins of this statement?


Can someone please help?
Thanks!
YG

 

[Gokul43201]

The quick answer is as follows : Each nucleon has a spin of $\frac{\hbar}{2}$. A Boson is a particle whose spin is an integer multiple of $\hbar$. So, it takes an even number of nucleons to make a boson.

 

[misogynisticfeminist]

As a sidenote, He 3 behaves as a superfluid at much lower temperatures than He-4, forming a fermionic condensate.

 

[ZapperZ]

Why does 4He act like a boson but 3He doesn't? What accounts for their different behavior at low temperatures? Why does 4He act as a Bose Condensate, but 3He doesn't?

I read somewhere that because 4He has an even number of fermions (2 protons, 2 neutrons, 2 electrons), it behaves as a boson. What is the physical origins of this statement?


Can someone please help?
Thanks!
YG

I have to make some guesses on what you are exactly asking for, since I am not exactly sure what you wanted to know here...

He4 is your "typical" helium : 2 protons, 2 neutrons, and certainly 2 electrons to preserve neutrality.

He3 is an isotope of He: 2 protons (of course, because if this number is different, it's a different element), 1 neutron, and 2 electrons.

So there is a difference in the number of neutrons. Now, each proton, neutron, and electron has a quantum spin of 1/2. So for He4, it is possible for the the protons, neutrons, and electrons to allign themselves with respect to each other to make the whole atom to have a net spin of ZERO (note that this only occurs at very low temperatures). When this happens, the He atom now is a boson.

Now look at He3. Because of the odd number of neutron, you can never get the whole atom to be in a net spin of an integer. This means the whole atom cannot become a boson. However, He3 can still form a BE condensate by pairing up with another He3 atom and together they form a composite boson (very much like the Cooper pairs in superconductors). Only then do they condense into a BE condensate.

Zz.