# Fermion Index

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## Fermion Index

### Definition

The Fermion Index calculated for each species is the sum of all fermion atomic isotopes in the mineral species' empirical formula. This calculation assumes the following:
1. The overall contribution for each isotope in each mineral matches the natural abundance (no isotopic fractionation) of that element.
2. Each unit cell is electrically neutral.
3. Lattice effects on the position of each element are ignored.

## Calculation of Fermion Index

The calculation of the fermion index is fairly straightforward, each element in the periodic table is generally composed of a mixture of isotopes. Each neutral isotope is either a fermion atom or a boson atom.

•  Fermion Atom - Sum of all neutrons, protons, and electrons is an odd number.
• Has an odd half integer spin (i.e. 1/2, 3/2, 5/2, etc.).
• Obeys Fermi-Dirac quantum mechanical statistics.
•  Boson Atom - Sum of all neutrons, protons, and electrons is an even number.
• Has an even net spin (i.e. 1, 2, 3, etc.).
• Obeys Bose-Einstein quantum mechanical statistics.

For each element, the fermion index is the sum of all fermion atomic isotopes times the natural abundance. See Example for:

 Isotope Protons Neutrons Electrons Fermion/Boson % Natural Abundance Fermion Index 11Na23 11 12 11 (11+12+11=34) Boson 100.00 % 0.0 Fermion Index for Naturally Occurring Sodium 0.0

 Isotope Protons Neutrons Electrons Fermion/Boson % Natural Abundance Fermion Index 56Ba130 56 74 56 (56+74+56=186) Boson 0.1060 % 0.0 56Ba132 56 76 56 (56+76+56=188) Boson 0.1010 % 0.0 56Ba134 56 78 56 (56+78+56=190) Boson 2.4170% 0.0 56Ba135 56 79 56 (56+79+56=191) Fermion 6.5920% 0.06592 56Ba137 56 81 56 (56+81+56=193) Fermion 11.2300% 0.11230 56Ba138 56 82 56 (56+82+56=194) Boson 71.7000% 0.0 Fermion Index for Naturally Occurring Barium 0.17822

For each mineral, the fermion index for each element is summed from the mineral's empirical formula and is presented in the Calculated Property section on the Mineral Species page. The boson index for each mineral is simply calculated as (1 - fermion index).

## Table of Fermion Index Values for each Element

 Element Symbol Fermion Index Boson Index Element Symbol Fermion Index Boson Index Actinium Ac 0.0000 1.0000 Manganese Mn 0.0000 1.0000 Silver Ag 0.0000 1.0000 Molybdenum Mo 0.2547 0.7453 Aluminum Al 0.0000 1.0000 Nitrogen N 0.9963 0.0037 Americium Am 0.0000 1.0000 Sodium Na 0.0000 1.0000 Argon Ar 0.0000 1.0000 Niobium Nb 0.0000 1.0000 Arsenic As 0.0000 1.0000 Neodymium Nd 0.2048 0.7952 Astatine At 0.5290 0.4710 Neon Ne 0.0027 0.9973 Gold Au 0.0000 1.0000 Nickel Ni 0.0113 0.9887 Boron B 0.1990 0.8010 Nobelium No 0.0000 1.0000 Barium Ba 0.1782 0.8218 Neptunium Np 0.0000 1.0000 Beryllium Be 1.0000 0.0000 Oxygen O 0.0005 0.9995 Bismuth Bi 0.0000 1.0000 Osmium Os 0.1770 0.8230 Berkelium Bk 0.0000 1.0000 Phosphorus P 0.0000 1.0000 Bromine Br 0.0000 1.0000 Protactinium Pa 0.0000 1.0000 Carbon C 0.0110 0.9890 Lead Pb 0.2210 0.7790 Calcium Ca 0.0014 0.9987 Palladium Pd 0.2233 0.7767 Cadmium Cd 0.2503 0.7497 Promethium Pm 0.0000 1.0000 Cerium Ce 0.0000 1.0000 Polonium Po 0.0000 1.0000 Calfornium Cf 0.0000 1.0000 Praeseodymium Pr 0.0000 1.0000 Chlorine Cl 0.0000 1.0000 Platinum Pt 0.3380 0.6620 Curium Cm 0.0000 1.0000 Plutonium Pu 0.0000 1.0000 Cobalt Co 0.0000 1.0000 Radium Ra 0.0000 1.0000 Chromium Cr 0.0950 0.9050 Rubidium Rb 0.0000 1.0000 Cesium Cs 0.0000 1.0000 Rhenium Re 0.0000 1.0000 Copper Cu 0.0000 1.0000 Rare Earth Elements REE 0.1861 0.8139 Dysprosium Dy 0.4380 0.5620 Rhodium Rh 0.0000 1.0000 Erbium Er 0.2295 0.7705 Radon Rn 0.0000 1.0000 Einsteinium Es 0.0000 1.0000 Ruthenium Ru 0.2980 0.7020 Europium Eu 0.0000 1.0000 Sulfur S 0.0075 0.9925 Fluorine F 0.0000 1.0000 Antimony Sb 0.0000 1.0000 Iron Fe 0.0212 0.9788 Scandium Sc 0.0000 1.0000 Fermium Fm 0.0000 1.0000 Selenium Se 0.0760 0.9240 Francium Fr 0.0000 1.0000 Silicon Si 0.0467 0.9533 Gallium Ga 0.0000 1.0000 Samarium Sm 0.2880 0.7120 Gadolinium Gd 0.6935 0.3065 Tin Sn 0.1662 0.8338 Germanium Ge 0.0780 0.9220 Strontium Sr 0.0700 0.9300 Hydrogen H 0.0002 0.9999 Tantalum Ta 0.0001 0.9999 Helium He 0.0000 1.0000 Terbium Tb 0.0000 1.0000 Hafnium Hf 0.3223 0.6777 Technetium Tc 0.0000 1.0000 Mercury Hg 0.3020 0.6980 Tellurium Te 0.0799 0.9201 Holmium Ho 0.0000 1.0000 Thorium Th 0.0000 1.0000 Iodine I 0.0000 1.0000 Titanium Ti 0.1293 0.8707 Indium In 0.0000 1.0000 Thallium Tl 0.0000 1.0000 Iridium Ir 0.0000 1.0000 Thulium Tm 0.0000 1.0000 Potassium K 0.0001 0.9999 Uranium U 0.0072 0.9928 Krypton Kr 0.1185 0.8815 Vanadium V 0.0025 0.9975 Lanthanum La 0.0009 0.9991 Tungsten W 0.1428 0.8572 Lithium Li 0.0750 0.9250 Xenon Xe 0.4760 0.5240 Lawrencium Lr 0.0000 1.0000 Yttrium Y 0.0000 1.0000 Lutetium Lu 0.0259 0.9741 Ytterbium Yb 0.3050 0.6950 Mendelevium Md 0.0000 1.0000 Zinc Zn 0.0410 0.9590 Magnesium Mg 0.1000 0.9000 Zirconium Zr 0.1122 0.8878

### Other References to Fermion Index

#### There are additional references to the Fermion Index. Caution: Some of these references are based on pseudo-scientific principles.

ORMUS (orbitally rearranged monatomic elements)
Fermion Atoms or Fermi Condensate

Boson Atoms or Bose Condensate

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