The "He-d" Reaction Activated Complex
Introduction
This is the chapter that bridges the gap between the chemical and the nuclear energy scales. This gap has always been assumed to be unbridgeable for practical applications. We will show ~quantitatively how this transition occurs in the palladium deuteride crystal; calculating the deuteron wave function in the tetrahedral position and from this, calculating the helium wave function as it channels thorough the crystal . We will then show how the wave function, of the colliding helium-deuterium “activated complex”, leads to the formation of the linear momentum state bond. We will show how the linear momentum state wave functions derive directly from the standard “free electron” states.
There are two angular momentum states (l=1 & 2) of the colliding nuclear pair (He & d), shown to be available during the formation of the “He-d bond”. This leads to three different states of the “He-d2” molecule (l=1,1-1,2 - 2,2). The angular momentum of the “activated complex” derives from the transverse wave function of the otherwise “free particle” wave function of the channeled helium. In the next chapter, we will show how only two of these states participate in the chain reaction. The third state (odd l) has a much higher energy than the two odd states and will emitt a low energy x-ray photon and drop to an even state wave function. We will set up the equations to calculate the probabilities of the 3 “intermediate” molecules that lead to the eventual fusion reactions. The solution to these equations will be put off until the chapter on macroscopic behavior.
“He-d2” and the Sun
As motivation for studying the activated complex in some detail, it is interesting to contrast the sun's core density and temperature to the He-d2 molecule, and calculate the reaction time of the deuterium fusion reaction in “He-d2”, if it were allowed. The energy of the deuterons in the “He-d2” molecule is on the order of 100,000eV. This translates into ~1.1x109 degrees Celsius, compared to the sun's core temperature of only 1.36x107. The core density of the sun is 150 gr/cc. This compares to the “He-d2” density of ~108 gr/cc. The “He-d2” molecule is about one million times the density and 100 times the temperature of the sun’s core, where nuclear fusion takes place. At this temperature and density (in “He-d2”), the deuterium would react in about 10-16 seconds. We will see in this chapter how the “He-d2“ molecule can only form in an angular momentum state, which prevents the evolution of the d+d reaction channel.
Activated Complex
The activated complex of the He-d molecule forms after the helium nuclei slows to ~200-500eV kinetic energy, and becomes trapped (channeled) by the palladium deuteride crystal structure as shown in figure 4-1. The probability of the helium being channeled as a function of energy, is a critical factor in the chain reaction dynamics, and will be addressed later. The “activated complex” forms as the helium approaches deuterium in a tetrahedral site of the palladium lattice at an “acceptable” energy. We will see how the “acceptable” energy is defined by angular momentum constraints on the “He-d” molecule. As mentioned before, there are basically five particles involved with the collision;
1) helium nucleus (alpha particle)
2) Deuterium nucleus(deuteron)
3) 2 angular momentum state electrons (1s state) from helium
4) ~1 electron charge worth of every free electron in the crystal; all free electron wave functions contribute to charge on deuterium
As before, we will mostly ignore the two “1s” electrons from helium except for their affect on forcing the charge on deuterium into an approximate ~“2p” configuration. Again, we say charge distribution because the electron probability around deuterium is made up of the crystal’s free electrons, not a localized electron.
The transition from the “activated state” of the three main particles, to the localized linear momentum state molecule, “He-d”, requires that the wave functions of the two states substantially overlap physically. We will see that there are two angular momentum states of the “He-d” wave function with substantial overlap; with the first two angular momentum quantum numbers of l =1 & 2. We will show how the angular momentum arises from the helium wave function caught in the channel of the crystal.