Abstract

In a previous paper (ref 3, AP4.7), a self-consistent theory called Model 1 was developed to answer ten major connected questions in astrophysics. The most important of these questions are:

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• Where do the extremely high-energy cosmic rays that occur beyond the GZK cutoff come from?

Model 1 appears to successfully answer these questions. The unique features of this model are:

• There are two spaces in the universe, particle space and quantum vacuum space. A potential barrier separates them. One space contains visible matter, and the other space contains dark matter.

• There is a cycling of mass-energy between these spaces through the black holes that connect them. Particles pass from our space through black holes where they are converted into super particles that operate with unified force. They then pass into the high-energy vacuum space where they become dark matter operating behind the potential barrier.

• Dark matter particles interact with each other and form a slowly moving halo centered on a galaxy. The halos of dark matter are connected to each other by corridors of dark matter forming a cosmic web, which guides the development of new galaxies.

• There, behind a potential barrier, the dark matter particles gain energy, build up in number and eventually exceed the ability of the barrier to contain them. They then explode back into particle space as a big bang. This process repeats to make a series of new universes.

• After the big bang exhausts itself, super particles continue to tunnel through the barrier into particle space. The super particles are unstable and break down into particles with extreme kinetic energy. In doing so, they give up potential energy into particle space. The potential energy gradually builds up to become the dark energy that we observe as the cause of our accelerating, expanding universe. The extreme energy protons are observed as cosmic rays with energy between the energy of force unification and the Planck energy, which is beyond the GZK cutoff.  

In this paper, the details of the interaction rate of dark with visible matter will be explored. It will be shown that it might be possible to detect dark matter particles directly, and that an experiment to do so was under way. Preliminary results from the experiment agree with the calculations based on Model 1 shown here.

 

The Problem

Here, we explore the characteristics of super particles to see if they can be observed in particle space- i.e. are they too dark to observe? First, super particles covered by a potential shell do not show charges associated with the electromagnetic, weak, and strong forces. They are combined into one super charge and hidden behind the barrier potential. The super particle spin, if any, could show beyond the barrier, however, but it is not certain. Particles in particle space will scatter off the potential barrier surrounding the super particle, however, so it is necessary to calculate this scattering cross section. This scattering cross section is like the scattering of a neutron off a proton, but with different energies. This n-p scattering cross-section has been calculated for high energy and low energy collisions. (Halliday, 47). With appropriate alterations for mass and energy, it has been possible to calculate the scattering cross section of a super particle off of a proton.

            σ = 4 π ћ²/M  [ 1/(Vo + E)]

            Where:

            M = m_s m_p/ (m_{s +} m_p)

            m_p = mass of particle space baryons = 1 GeV.

            m_s = mass of super baryons = 10¹⁷ GeV.

            V_o = potential of super baryons = 10¹⁹ GeV

            E = kinetic energy of the particle space baryons = 1 GeV or less.

            Then:  

             σ = 10 ^-62 cm²  (Note-this is for S scattering.)

This calculation is for high-energy scattering (S scattering), i.e. scattering of particles with kinetic energy that is of the order of the potential energy of the target particles (super particles with barrier shells). Halliday notes the possibility that there may be other scattering contributions due to the spin of the particles involved (Halliday, 48). Under these conditions,

             σ = 4 π ћ²/M  [ 1/(Vo + E)] + K π ћ²/M  [ 1/(Wo + E)]

             Where:

             Wo is unknown and associated with the spin interaction.

             K is to be determined by experiment.

If the Wo is low and of the order of the potential energy of normal spin particle potential energy (10⁴ to 10⁵ ev), rather than super particle potential energy (~10¹⁹ GeV) the cross section would be higher. Here, the total cross section would be:

             σ ~ 10 ^-45 cm² 

It is not unreasonable to expect a spin contribution to scattering for super particles, since they are formed from particles, and the internal states certainly have spin.

Clearly, a particle with either of these scattering cross sections would be difficult to detect. So matter is dark or difficult to detect in particle space. Also, the collision cross section of the dark matter particles in visible matter is low enough that in colliding galaxies, the dark matter particles would pass right through visible matter, while the visible matter would interact with itself and coalesce. This behavior has been observed by observing the bending of light from far galaxies by colliding galaxies that are nearer.

It is desirable to detect this particle shell directly, however, in order to measure its parameters directly. Indeed it would be significant to determine if the super particle has observable spin. In this paper, we will investigate the feasibility of detecting dark matter particles directly.

 

The Solution

There is a possibility for this direction if the larger cross section applies. The dark matter is believed to rotate very slowly around the galactic center because it diffuses out from the central black hole rather than falling in from the outside as visible matter does. Now the visible matter is known to rotate around the galactic center at a speed of ~100 km/s (Peebles, 47) (earth rotation speed around sun is ~ 30 km/sec, so galactic speed dominates). Thus there is a relative interaction speed between particles of ~100 km/s. We may be able to take advantage of this interaction to detect scattering.

First, we must define the concept of a cross section (see Halliday, 13). Consider a thin slab of material of thickness x and area A. We assume a collimated beam of single energy particles strikes A at rate R_o. The beam consists of dark matter (fixed) moving through the slab of material at the speed of the earth rotating with the sun around the galactic center. The velocity of the earth rotating around the sun is less. We will call the rate of interaction of these particles with the material in the slab R

Option 1.

We could try a bubble chamber with liquid nitrogen as the detector. It can be tested with neutron collisions for efficacy. Nitrogen will be used for our calculations. The rate R is

            R = R_onσ x

Where:

            n = number of baryons in the slab.

               =  (14x6x10²³ baryons/14 gm of N) (0.8 gm/cc) (10⁸ cc)

               ~ 10³² baryons.

            σ = cross-section (cm²); try ~10^-45 cm²

            R_o =vNA= rate at which the interaction occurs (events/sec).

v = average velocity of our star around the galactic center~100 km/s (Peebles, 47) (earth rotation speed around sun is ~ 30 km/sec, so galactic speed dominates)

            N = density of dark matter = 5 x density of visible matter

                = 5 x 5 x10^-8 x (0.5)² ~ 10^-7 super particles/cc (Peebles, 123)

Now a reasonable experiment needs at least one event per year to be measurable with any degree of accuracy. So, we choose a detector, which is large enough:

            A = 10² cm x 10³ cm

            R_o = vNA = 10⁷ (cm/s) x 10^-7 (s part/cm³) x 10⁵(cm²) = 10⁵ (s part/s)

            x =  10³ cm

So, for a 1x10x1 m³ volume of liquid nitrogen, the rate R is:

            R = 10^-5  (events/s) = 100 (event/yr)

The detector is not perfect in turning an event into a recognizable detection rate, S. Assume an efficiency of E ~ 0.1. Then,

            S = 10 (detections/yr)

Thus we need a volume of liquid nitrogen ~ 10² (m³), to get a reasonable detection rate.

Option 2.

Now, perhaps a more efficient detector might be a crystal such as silicon or germanium (E ~ 0.7). A dark matter, visible matter collision will ring the crystal, and give an electronic signal. Very large, near perfect crystals will be required. Large crystals of Germanium are probably cheaper; so we will do the calculation with Germanium parameters.

                n = (72 baryons x 10²³ /72 gm of Ge) x (5.4 gm/cc) x (10⁷ cc) = 5.4 x 10³⁰ baryons

                 σ = 10^-45 cm² (see above)

            R_o = vNA = 10⁴ (part/s)

            A = 10² cm x 10² cm

            x = 10³ cm

So for a 1x1x10 m³ volume of germanium, the rate R is:

            R = 5 x 10^-8  (events/s) = 1.6 (events/yr)

For a Germanium detector of efficiency ~ 0.7, we get a detection rate of:

            S = 1.1 (detections/yr)

The above calculations only show that there appears to be a signal to find if we look for it. The signal will be faint, and mixed with a lot of noise and clutter. The details of equipment design and what one must do to suppress the noise and clutter and enhance the signal are beyond the scope of this paper and so are left to a later paper.

So, it may be feasible to detect a super particle with its barrier shell directly, but only if spin effects can be observed through the barrier.

 

Summary and Conclusions

A model (Model 1) has been developed in AP4.7 (ref 3) that predicts dark matter, dark energy and extremely high-energy cosmic rays, which are observed between the energy of unification and the Planck energy, which is beyond the GZK cutoff, and describes where they come from.

In this paper, a calculation was pursued that estimates the rate of production and detection of interactions between dark matter and visible matter. This calculation is for S scattering. A second calculation was pursued, which included the effects of spin. While working on this paper, it was found that an experiment was already underway using Germanium as the detector. The experiment is not complete, but initial results agree with the calculated rates, but only if spin effects are significant. After the data from the current experiment are published, it would be useful to consider scattering from spin and the higher angular momentum components.   

 

References

1. D. Halliday, Introductory Nuclear Physics, John Wiley and Sons, New York, 1955.
2. P. J. E. Peebles, Principles of Physical Cosmology, Princeton, New Jersey, Princeton University Press.
3. L. H. Wald, “AP4.7 DARK MATTER AND ENERGY-FUNDAMENTAL PROBLEMS IN ASTROPHYSICS” www.Aquater2050.com/2015/11/
4. L. H. Wald, “AP4.7A SUPER PARTICLE CHARACTERISTICS” www.Aquater2050.com/2015/11/
5. L. H. Wald, “AP4.7B SHAPING THE DARK MATTER CLOUD” www.Aquater2050.com/2015/11/
6. L. H. Wald, “AP4.7C DARK MATTER RATE EQUATIONS” www.Aquater2050.com/2015/11/