Weak interaction, fusion, and tunneling

[ephedyn]

I have 2 questions...

I was told that the transmutation of Li-7 to Be-8 by proton collisions at energies below the classical barrier verifies the QM description of the weak interaction cross section. Firstly, I found the leap in logic very confusing - does the weak force have a role in tunneling and fusion at all?

I only knew that the weak interaction is at work in the deuteron formation step in the proton-proton chain and beta decay.

I've been studying the subject only from Enge's Introduction to Nuclear Physics, which doesn't seem to help with my task. I need to figure what exactly is "the quantum mechanical description of reaction cross sections" for certain 1~2 MeV collisions... It seems to me that most introductory texts only briefly mention tunneling for collisions, and use a semi-classical description involving surmounting a Coulomb barrier, which you can say is the opposite of what I'm looking for. So, secondly, are there any texts one would recommend which are more relevant? And if the weak force is indeed implicated here, where can I start an understanding of the quantum description of the weak force?

Thanks in advance!

 

[bcrowell]

I was told that the transmutation of Li-7 to Be-8 by proton collisions at energies below the classical barrier verifies the QM description of the weak interaction cross section. Firstly, I found the leap in logic very confusing - does the weak force have a role in tunneling and fusion at all?

8Be is unstable with respect to breakup into two alpha particles. This is a strong-force decay, so its decay time is very short (less than a femtosecond). In the WP article on nucleosynthesis, for example, they list the reaction as 7Li+p -> 4He+4He, since the intermediate 8Be state is just a resonance, not a bound state.

I don't know if there's some small probability of 7Li+p -> 8Li or 7Li+p -> 8B. If so, then that would be an example of a weak-interaction process.

I need to figure what exactly is "the quantum mechanical description of reaction cross sections" for certain 1~2 MeV collisions... It seems to me that most introductory texts only briefly mention tunneling for collisions, and use a semi-classical description involving surmounting a Coulomb barrier, which you can say is the opposite of what I'm looking for.

I don't think there are two ways of looking at it, one semiclassical and one involving tunneling. For a given process, it's either classically forbidden or its not. If the energy is below the Coulomb barrier, then it's classically forbidden, and you have to use tunneling to get the cross-section. If the energy is above the Coulomb barrier, then there can be quantum-mechanical corrections, but basically the total cross-section for nuclear reactions is pretty close to what you expect classically.

 

[sir-pinski]

Firstly, it is important to understand that the weak interaction is one of the four fundamental forces in nature, along with gravity, electromagnetism, and the strong interaction. It is responsible for processes such as beta decay and neutrino interactions. However, it is also involved in other processes such as fusion and tunneling, although to a lesser extent compared to the strong and electromagnetic forces.

In the case of fusion, the weak interaction plays a role in the formation of the deuteron, which is the first step in the proton-proton chain. This is because the weak interaction allows for the conversion of a proton into a neutron, which is necessary for the formation of the deuteron. Without this conversion, fusion reactions would not be possible.

In the case of tunneling, the weak interaction is involved in the transmutation of Li-7 to Be-8 by proton collisions at energies below the classical barrier. This is because the weak interaction allows for the exchange of a proton and a neutron, leading to the formation of Be-8. Without the weak interaction, this process would not be possible.

As for your second question, there are many texts that discuss the quantum mechanical description of reaction cross sections for collisions. Some recommended texts include "Introduction to Nuclear Reactions" by Enrico Fermi and "Nuclear Reactions for Astrophysics" by Iliadis et al. These texts will provide a more in-depth understanding of the quantum description of reactions, including the role of the weak interaction.

To understand the quantum description of the weak force, it is important to study the Standard Model of particle physics. This theory describes the fundamental particles and their interactions, including the weak force. Additionally, studying quantum field theory will also provide insights into the quantum description of the weak force.

Overall, the weak interaction does play a role in tunneling and fusion reactions, and understanding its quantum description is crucial in understanding these processes. I hope this helps clarify your questions.