Question on Baryons and Specific Decays

[olv]

1) We know in case of beta decay if there is excess of protons or neutrons in the nucleus beta decay take place.
Force involved - weak interaction
Reason involved - to stabilize, to obtain proton neuton 1:1 ratio in the nucleus.
E. g., Beta minus - Carbon 14 transforms into Nitrogen 14

2) Case of Lambda & Sigma baryons -

Force involved - weak
Reason involved - ?

Does anyone know the reason why Lambda Λ0 (uds - quark composition) decays into,
p+ + π−
or
n0 + π0

Also why Sigma Σ+(uss - quark composition) decays into,
p+ + π0
or
n0 + π+

What mechanism make them go decay into proton or neutron( ignore the π0 & π+) ? What is the reason involved ?

 

[malawi_glenn]

Beta decay of nuclei occur when the daughter nuclei has lower mass than the parent nuclei.
You have to specify what "stabilize" means. Here it means minimizing the mass.

Decays occur whenever it is possible. If something is possible in quantum physics, there is a non zero probability for it to happen.

 

[topsquark]

1) We know in case of beta decay if there is excess of protons or neutrons in the nucleus beta decay take place.
Force involved - weak interaction
Reason involved - to stabilize, to obtain proton neuton 1:1 ratio in the nucleus.
E. g., Beta minus - Carbon 14 transforms into Nitrogen 14

2) Case of Lambda & Sigma baryons -

Force involved - weak
Reason involved - ?

Does anyone know the reason why Lambda Λ0 (uds - quark composition) decays into,
p+ + π−
or
n0 + π0

Also why Sigma Σ+(uss - quark composition) decays into,
p+ + π0
or
n0 + π+

What mechanism make them go decay into proton or neutron( ignore the π0 & π+) ? What is the reason involved ?

The short answer is the answer to the question "Why does any particle decay?" It's always the same answer: because the decay products are more stable than the particle that is decaying.

The reason $C^{14}$ decays into $N^{14}$ is because $N^{14}$ has a more stable nucleus than $C^{14}$ does, not that we need the number of protons to equal the number of neutrons. (That reasoning only works for the smaller atomic numbers.)

Also, note that the $\Lambda ^0$ has two decay modes:
$\Lambda ^0 \rightarrow p^+ + \pi ^-$

and
$\Lambda ^0 \rightarrow p^+ + e^- + \overline{ \nu }_e$

When it comes to subatomic particles it is almost always true that the higher the mass, the quicker it decays. So (generally, not always) the reason for the decay is to reduce the mass of the constituent particles.

-Dan

 

[Meir Achuz]

"More stable" has nothing to do with why particles decay.
Particles decay if the sum of the masses of the decay products is less than the mass of the decaying particle.

 

[topsquark]

"More stable" has nothing to do with why particles decay.
Particles decay if the sum of the masses of the decay products is less than the mass of the decaying particle.

That's more or less the content of the lifetime amplitude. But wouldn't that define the measure of the stability of a particle? That's the way I've always looked at it, anyway. Is there a more exact definition of stability?

-Dan

 

[Meir Achuz]

I usually consider the lifetime to be a measure of stability, with the shorter the lifetime, the less stable.

 

[malawi_glenn]

Particles decay if the sum of the masses of the decay products is less than the mass of the decaying particle.

And if the conservation laws are fulfilled, like electric charge etc

 

[Meir Achuz]

And if the conservation laws are fulfilled, like electric charge etc

Of course.

 

[mfb]

That's more or less the content of the lifetime amplitude. But wouldn't that define the measure of the stability of a particle? That's the way I've always looked at it, anyway. Is there a more exact definition of stability?

Uranium-238 with a half life of 4.5 billion years decays to thorium-234 with a half life of 24 days (which then decays to ^234mPa with a half life of just 1 minute). I see no way how the thorium isotope could be called "more stable" than its parent.

$\Lambda$ with a lifetime of 2.6*10^-10 seconds has a 1/3 chance to decay to a neutron plus $\pi^0$, the latter has a lifetime of just 8*10^-17 seconds.

 

[topsquark]

Uranium-238 with a half life of 4.5 billion years decays to thorium-234 with a half life of 24 days (which then decays to ^234mPa with a half life of just 1 minute). I see no way how the thorium isotope could be called "more stable" than its parent.

$\Lambda$ with a lifetime of 2.6*10^-10 seconds has a 1/3 chance to decay to a neutron plus $\pi^0$, the latter has a lifetime of just 8*10^-17 seconds.

A very good point. Even though the problem started with a nucleus, I hadn't really thought that one through. (I usually ignore anything bigger than a proton. :) )

Thanks for the catch!

-Dan