|MadSci Network: Physics|
First of all, excellent question. Not many students your age have read enough about nuclear reactions or given them enough detailed thought to ask such a question. It turns out that this is one of the reactions I started studying in graduate school, a project that was taken over by one of my best friends. It's difficult to measure the D + D -> 4He + gamma reaction near stellar energies. A 24 MeV gamma-ray is a very high-energy photon, so it's easy to pick it out from other photons, but the huge flux of neutrons swamps the large Sodium Iodide (NaI) scintillation spectrometers we use to measure it. You can google search any terms above for further information, or refer to the textbook "Radiation Detection and Measurement" by Knoll. Yes, generally nature favors the more energetically stable solution. Given that simple fact, one would indeed expect the reaction to proceed to the most stable situation, 4He + gamma. However, the details of the reaction are governed by quantum mechanics. In a full calculation of the reaction rates, there are four "exit channels." One is 3He + n, one which you neglected above is 3H + p (3H is tritium, which as you probably know is a radioactive isotope of hydrogen commonly used in biological research and hydrogen bombs), and a third is 4He + gamma. The fourth "exit channel" is actually by far the most common at low enegires, simple scattering (d + d -> d + d). In a quantum mechanical calculation, the probability of the reaction ending in one of these four situations (assuming the collision energy is low enough that the production of high-energy particles like mesons and such is impossible) must sum to 1. The incident particles are described by wave functions, their interaction by a potential function, and the outgoing particles and photons are described by different sets of wave functions. The potential function will create a mathematical operator (here we slide into quantum mechanics) which describes the interaction between the incoming and outgoing particles for each of the four situations. An integral (called an overlap integral) over the two wave functions with the mathematical operator between them determines the probability of the incoming particles ending up in one of the four outgoing states. When one actually does the math, the probability of particle emission vs. gamma-ray emission (which is described by classical electromagnetic potential operators rather than strong nuclear force potential operators) is generally around 10,000 to 1. That's just an order of magnitude guesstimate, every reaction is different. The difference comes largely from the relative strengths of the strong nuclear force to the electromagnetic force at that range when construction the reaction's mathematical operator. In the case of d + d -> 4He + gamma, however, we have a special situation. Normally, simple electric dipole radiation dominates many reactions. But it's quantum mechanically disallowed by angular momentum conservation-like rules, so the system is forced to radiate by electric quadrupole radiation instead. This radiation is much weaker than dipole radiation. When electromagnetic radiation is broken up into multipole components, the lowest orders (dipole, quadrupole, octupole) dominate. That's something you'll learn about in advanced E&M classes in college. So in this case, the gamma-emission is even more suppressed than usual and the probability of proton or neutron emission is staggeringly high relative to the gamma emission. Some questions you might have: What is a wave function? A particle is also a wave, in quantum mechanics. It travels and diffracts and reacts just like a wave. The shape of that wave can be described by a mathematical function. How do we do that? That's an entire first month's worth of quantum mechanics courses. The potentials and operators and details of how the reactions proceed are further details best saved for a formal course on quantum mechanics, though David Griffiths wrote and excellent text on the subject from which you could pretty much teach yourself (it's called, creatively enough, "Quantum Mechanics" and has a picture of a live cat on the front and a dead one on the back). The same author wrote a good E&M textbook for undergraduates which explains electromagnetic multipoles. There's a lot of information here, and a lot of roads for you to follow to a complete answer to your question. And there are some strange mysteries in this reaction, not usually talked about. For example: p-wave capture strength at low energies, meaning with just one unit of angular momentum in the incoming particles, is observed in the angular spread of the outgoing radiation when polarized deuterons are used...but this incoming wave's reaction probability is supposedly disallowed by simple quantum mechanical rules. We don't know the exact form of the strong nuclear force yet, one of the last great frontiers of nuclear physics. A complete answer would take you all the way through my friend Konstantin's doctoral dissertation (published just last year, but the paper isn't out yet), so don't expect to learn it all overnight. Good luck!
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