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Isotopes

A fact that mystified early chemists was that a few elements such as chlorine had atomic masses that were very far from unity.  Even allowing for experimental error the mystery remained.  Chlorine had an atomic mass of 35.45.  The answer became obvious when it was discovered that the atomic nucleus contained two types of sub-units - not only were there positively charged protons but there were also neutral sub-particles which were named neutrons.  The reason for the observed atomic mass of chlorine was that it was a mixture of two types of chlorine with different atomic masses - the term applied to the different types was that they were ISOTOPES of one another. The bulk of the mass of an atom is made up of the combined effects of the protons and the neutrons in the nucleus with a very small contribution from the electrons.  We now know that the electrons play by far and away the major role in determining the chemical properties of an atom (only very slight differences are due to the different masses of the isotopic forms).  

The Periodic Table

  01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18
Period 1 01 H                                 02 He
Period 2 03 Li 04 Be                     05  B 06 C 07 N 08 0 09 F 10 Ne
Period 3 11 Na 12 Mg                     13 Al 14 Si 15 P 16 S 17 Cl 18 Ar
Period 4 19 K 13 Ca 21 Sc 22 Ti 23 V 24 Cr 25 Mn 26 Fe 27 Co 28 Ni 29 Cu 30 Zn 31 Ga 32 Ge 33 As 34 Se 35 Br 36 Kr
Period 5 37 Rb 38 Sr 39 Y 40 Zr 41 Nb 42 Mo 43 Tc 44 Ru 45 Rh 46 Pd 47 Ag 48 Cd 49 In 50 Sn 51 Sb 52 Te 53 I 54 Xe
Period 6 55 Cs 56 Ba 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn
Period 7 87 Fr 88 Ra 103Lr 104Rf 105Db 106Sg 107Bh 108Hs 109Mt 110Ds 111 112 113 114 115 116 117 118

Due to the limitations of screen width the elements 57-70 and the elements 88-102 are shown in the supplementary table below

Elements 57-70 are called the Lanthanides or Rare Earths   Elements 89-102 are called the actinides

Period  6 57 La 58 Ce 59 Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb
Period  7 89 Ac 90 Th 91 Pa 92 U 93 Np 94 Pu 95 Am 96 Cm 97 Bk 98 Cf 99 Fm 100 Es 101 Md 102 No

Elements shown in green are the main elements found in living organisms .  A few others such as fluorine, copper, zinc and iodine are used in trace amounts by many organisms.  A particularly striking example is the use of copper instead of iron in oxygen transport in some animals such as the cephalopods  (the squid and the octopus)

Elements shown in red have no completely stable isotopes.  Note that despite their relative low mass compared to the other radioactive elements there are no stable isotopes of Technetium and Promethium.  Isotopes of both elements have been artificially produced and isotopes of technetium have been detected in certain types of stars.

The study of isotopes has been of enormous use in many fields of science. Isotopes can be classified into five groups

1) Completely stable isotopes

2) Radioactive Isotopes with very long half life periods of many millions or even billions of years  Examples are potassium-40, rubidium-87,uranium -238

3) Radioactive isotopes of long half life periods such as plutonium-244 and aluminium-27

4) Radioactive isotopes of fairly short half life periods such as carbon-14

5) Radioactive isotopes with half life periods of a few days or hours.

6) Radioactive isotopes of extremely short half life periods such as beryllium-8

The majority of isotopes listed as unstable belong to the latter two groups and are mostly of little interest. However that is not to say that they are always unimportant as we have already seen when we discussed the Triple Alpha Reaction and Beryllium - 8 and excited Carbon -12.

The data for all the tables shown below is taken from 75th edition of CRC Press Handbook of chemistry and Physics Editor David R Lide  Pub in Boca Raton, Ann Arbor, London and Tokyo.  CRC is the Chemical Rubber Co and the book is often referred to as 'The rubber Book'  With the exception of the stable isotopes and long lived radioactive isotopes , most of the isotopes have very short half lives.

Table of the Isotopes Hydrogen (H) to Neon (Ne)

Name of Isotope Symbol Atomic Number Natural Abundance Stable Unstable Total Comments
Hydrogen-1 1H 1 98.985 2 forms 1 form 3 forms Hydrogen is the only element where it's isotopes are sometimes given different symbols
Hydrogen-2 2H or D   0.015       Deuterium differs a tiny but significant amount from ordinary hydrogen and is often given the symbol D
Hydrogen-3 3H or T 2         Tritium is very radioactive and has a half-life period of only 12.23 years
Helium-3 3He   1.37 X 10-8 2 forms 5 forms 7 forms  
Helium-4 4He   Almost 100%        
Lithium-6 6Li 3 7.5        
Lithium-7 7Li   92.5        
Beryllium-8 8Be 4         Half-life only about 7X 10-17seconds   Important in Triple Alpha Reaction Series in Carbon Nucleosynthesis from Helium-4
Beryllium-9 9Be   100% 1 form 7 forms 8 forms  
Boron-10 10B 5 19.9 2 forms 9 forms 11 forms  
Boron-11 11B   80.1        
Carbon-12 12C 6 98.90 2 forms 11 forms 13 forms Carbon isotope ratios play an important role in biology in particular as well as in astronomy, geology and climate studies.
Carbon-13 13C   1.10        
Carbon-14 14C   Traces       Traces of 14C produced in upper atmosphere . Half life  5,715 years.  Used in carbon dating
Nitrogen-14 14N 7 99.63 2 forms 9 forms 11 forms  
Nitrogen-15 15N   0.37        
Oxygen-16 16O 8 99.76 3 forms 10 forms 13 forms Oxygen isotope ratios play an important role in biology, climate studies. Temperature studies in ice cores. Geology and astronomy
Oxygen-17 17O   0.04        
Oxygen-18 18O   0.40        
Fluorine-19 19F 9 100% 1 form 13 forms 14 forms  
Neon-20 20Ne 10 90.48 3 forms 10 forms 13 forms  
Neon-21 21Ne   0.27        
Neon-22 22Ne   9.25        

All the abundances apply to our planet the Earth.  Significant differences may occur on other planets, in star photospheres and in interstellar space.

We shall consider important isotopes from the above table

Isotopes of hydrogen

Hyrogen-1  is the only atomic nucleus which consists of only one particle - the proton and the only one without a neutron

Hydrogen-2 is the only stable isotope of hydrogen and is dignified by being given a separate name.  Deuterium behaves in a very similar way to ordinary hydrogen and is the only isotope which is chemically sufficiently different to be given a special name.  Thus D2) is heavy water a substance which boils at 101.4 degrees Celsius and freezes at 3.82 degrees.  It played a prominent role during the war when Nazis were trying to make an atomic bomb and forms the subject of the film of 'The Heroes of Telemark' the Norwegian resistance fighters who sabotaged the heavy water plant.

From the point of view of astronomy it is also interest in several ways.  Many authorities think that the very high ratio of deuterium to ordinary hydrogen is the atmosphere of Venus is evidence that in its earliest years Venus like the Earth was covered by seas and may be oceans.  One current theory is that about 3 to 3.5 billion years ago the temperature of the oceans of Venus reached a tipping point of 27 degrees which initiated a run-away greenhouse effect.

Another matter of importance is the deuterium can undergo thermonuclear reaction with protons at the 'low temperature of half a million degrees Celsius and that it burns in brown dwarfs as well of course as fully fledged stars.

Tritium is a fairly short live isotope of hydrogen and has been the possible source of nuclear fusion experiments .

The isotopes of Helium

On the  face of it helium-4 is the most important isotope.  Highly energetic helium nuclei are known as alpha  particles and play an important role in nucleosynthesis.  Helium-3 however is also of interest  .It is a stable isotope and has been suggested as a much better candidate for nuclear fusion since unlike tritium it is not radioactive and does not produce high concentrations of neutrons when it undergoes fusion with deuterium.

The isotopes of Carbon

The two stable isotopes of carbon are carbon - 12 and carbon -13.   Because of the way in which they are synthesized in stars the highest production rate by far is in carbon - 12.  Of particular interest is in biology and by implication astrobiology.  Living organisms show a slight preference for the 'lighter isotope.   This could be of particular interest on Mars where the presence of methane in the atmosphere  could arise biogenically of from volcanic activity.   Biogenic methane should be ever so slightly richer in the 'lighter' isotope.

The same general rule applies to hydrogen, nitrogen, oxygen sulphur but not of course to phosphorus which only has one stable isotope.

This must not get confused with the radioactive carbon - 14 and carbon dating where different rules apply.

Carbon 14 is formed in the upper atmosphere by radiation from the Sun creating secondary radiation in the form of energetic neutrons.  Reactions occur in which nitrogen-14 is converted to carbon - 14.  Carbon -14 undergoes radioactive decay back to nitrogen -14 with a half life period of 5,730 years.  The short half-life of carbon-14 means its cannot be used to date extremely old fossils. Levels of carbon-14 become difficult to measure and compare after about 50,000 years.

Carbon-14 becomes incorporated into plants via 14C labeled CO2.  Carbon-14 in the bodies of animals and plants is constantly decaying. However, the decaying carbon-14 is constantly being replaced as the plant or animal consumes more carbon-14 from the air or through its food. At any given moment all living plants and animals have approximately the same percentage of carbon-14 in their bodies.  When a plant or animal dies it stops bringing in new carbon-14.  However, the carbon-14 already in the organism's body continues to decay at a constant rate. Therefore, the amount of carbon-14 in an artifact decreases at a predictable rate while the amount of carbon-12 remains constant. By comparing the ratio of carbon-14 to carbon-12 in an artifact to the ratio of carbon-14 to carbon-12 in living organisms scientists can determine the age of an artifact.

The isotopes of nitrogen.

Apart from its biological interest it is of noteworthy that the ratio of 14N to 15N is different of Mars to that of the Earth.

The isotopes of Oxygen

The ratio of the two rare stable forms of oxygen to the major oxygen-16 are widely used in studying ice cores from the Antarctic and from Greenland and in biological work.  It is as a result of biological activity that the study of the ice cores has enabled scientists to follow the changes in temperature over the last million years.

Table of Isotopes Sodium (Na) to Potassium (K)

Name of Isotope Symbol Atomic Number Natural Abundance Stable Unstable Total Comments
Sodium-23 23Na 11 100% 1 18 18  
Magnesium-24 24Mg 12 78.99 3 12 15  
Magnesium-25 25Mg   10.00        
Magnesium-26 26Mg   11.01        
Aluminium-26 26Al   Radioactive       Half-life 710,000 (7.1 x105) Decays to 26Mg. Mineralogical .  'fossil' evidence found in meteorites. (see asteroids in the web-site)
Aluminium-27 27Al 13 100% 1 16 17  
Silicon-28 28Si 14 92.23 3 18 21  
Silicon-29 29Si   4.67        
Silicon-30 30Si   3.10        
Silicon-32 32Si   Radioactive       Half life only 160 years
Phosphorus-31 31P 15 100% 1 16 17  
Sulphur-32 32S 16 95.02 4 12 16  
Sulphur-33 33S   0.75        
Sulphur-34 34S   4.21        
Sulphur-36 36S   0.02        
Chlorine-35 35Cl 17 75.77 2 15 17  
Chlorine-36 36Cl   Radioactive       Half-life period 301,000 years (3.01 X105)
Chlorine-37 37Cl   24.26        
Argon-36 36Ar 18 0.337 3 14 17  
Argon-38 38Ar   0.063        
Argon-40 40Ar   99.60        
Potassium-39 39K 19 93.2581 2 22 24  
Potassium-40 40K   0.0117 Radioactive       Half-life period 1.26 billion years(1.26 X 109). Naturally occurring used in potassium/argon dating in rocks and in meteorites
Potassium-41 41K   6.7302        

The data for all the tables is taken from 75th edition of CRC Press Handbook of chemistry and Physics Editor David R Lide  Pub in Boca Raton, Ann Arbor, London and Tokyo.  CRC is the Chemical Rubber Co and the book is often referred to as 'The rubber Book'  With the exception of the long lived radioactive isotopes , most of the isotopes have very short half lives.  The radio-isotope of aluminium  (26Al) is of particular interest since it was present after the formation of the Solar system as evidenced by the presence of distortion of 26Mg in meteorites.  The radioactive isotope of potassium (40K) is of particular interest since it decays to 40Ar and is used in the dating of the time of the melting of rocks in meteorites and on the Earth and doubtless other planets such as Mars, Venus and the Asteroids.  It is referred to as potassium/argon dating.  The element chlorine is of particular interest in that its mean atomic mass is 34.45.  Like hydrogen, nitrogen, carbon and oxygen analysis of the ratio of sulphur isotopes in living organisms compared to the ratios in inorganic situations is of interest to biologists and future astrobiologists!

Isotopes of Calcium (Ca)

Name of Isotope Symbol Atomic number Natural Abundance Stable Unstable Total Comments
Calcium-40 40Ca 20 96.94 6 forms 20 26  
Calcium-42 42Ca   0.647        
Calcium-43 43Ca   0.135        
Calcium-44 44Ca   2.086        
Calcium-48 48Ca   0.004        
Calcium-49 49Ca   0.187        

Calcium forms six stable isotopes of which by far the commonest occurring is calcium-40.  Calcium is important in the formation of bones and muscles

Isotopes of Transition Metals Scandium (Sc) to Zinc (Zn)

Name of Isotope Symbol Atomic number Natural Abundance Stable Unstable Total Comments
Scandium-45 45Sc 21 100% 1 15 16  
Titanium-46 46Ti 22 8.0 5 9 14  
Titanium-47 47Ti   7.3        
Titanium-48 48Ti   73.8        
Titanium-49 49Ti   5.5        
Titanium-50 50Ti   5.4        
Vanadium-50 50V 23 0.250 Radioactive       Very long half-life Beta emitter.  Half-life approx 1.4 X 1017
Vanadium-51 51V   99.75 1 15 16  
Chromium-50 50Cr 24 4.345 4 15 19  
Chromium-52 52Cr   83.79        
Chromium-53 53Cr   9.50        
Chromium-54 54Cr   2.365        
Manganese-52 52Mn 25 100% 1 22 23  
Manganese-53 53Mn           Radioactive  Half-life 3.7 million years (3.7 x 106)
Iron-54 54Fe 26 5.9 4 19 23  
Iron-56 56Fe   91,72        
Iron-57 57Fe   2.1        
Iron-58 58Fe   0.28        
Iron-60 60Fe   Radioactive       Half-life 1.5 million years  (1,5 x 106)
Cobalt-56 56Co           Half-life 77.3 days Important in following gamma radiation in supernova.  See web-site 'The Magic Furnace'
Cobalt-59 59Co 27 100% 1 25 26  
Nickel-56 56Ni           Half-life 6.10 days Important in following gamma radiation in supernova.  See web-site 'The Magic Furnace'
Nickel-58 58Ni 28 68.077 5 19 24  
Nickel-60 60Ni   26.223        
Nickel-61 61Ni   1.140        
Nickel-62 62Ni   3.634        
Nickel-64 64Ni   0.926        
Copper-63 63Cu 29 69.17 2 23 25  
Copper-65 65Cu   30.83        
Zinc-64 64Zn 30 48.6 5 19 24  
Zinc-66 66Zn   27.9        
Zinc-67 67Zn   4.1        
Zinc-68 68Zn   18.8        
Zinc-70 70Zn   0.6        

The transition metals form a group of chemical elements.  As with the earlier elements shown on the tables above they all have a large number of isotopes.  However most of them are very short lived radioactive forms.  Two of these are of great importance to astrophysics because they play a major role in supernova studies namely 56Co and 56Ni which undergo rapid decay to 56Fe as discussed in the previous chapter 'The Magic Furnace'.   Like potassium , naturally occurring vanadium contains small quantities of the radioactive isotope 50V.   It has such a long half life however that the radioactivity is quite hard to detect.

The last table in this discussion will deal with a number of elements with higher atomic numbers than those already dealt with of special interest to geologists and astronomers.

Isotopes of Selected Elements

Name of Isotope Symbol Atomic number Natural Abundance Stable Unstable* Total Comments
Rubidium-85 85Rb 37 72.17 1 32 33  
Rubidium-87 87Rb   27.83 radioactive       The half-life period 4.88 x 1010. 87Rb is a beta emitter which changes to 87Sr.  It is therefore very weakly radioactive
Strontium-84 84Sr 38 0.56        
Strontium-86 86Sr   8.86        
Strontium-87 87Sr   7.00       The rubidium-strontium dating method is a technique used by geologists to determine the age of rocks.
Strontium-88 88Sr   82.58        
Technecium-97 97Tc 43 Radioactive       There are no stable forms  Half-life 2.6 x106.
Technecium-98 98Tc   Radioactive       Technecium is not found on the Erath 4.2 x106
Technecium-99 99Tc   Radioactive       Technecium has been detected in some stars 2.13 x 105
Iodine-127 127I 53 100%        
Iodine -129 129I           Half-life is  1.7 x 107
Promethium-145 145Pm 61 None in nature None 35 35 The isotope with the longest half-life is 145Pm. No isotopes found in nature of course
Samarium-147 147Sm 62 15.0     Radioactive 1 26 27 Half-life 1.03 x 108        Radioactivity in all forms found in nature very weak indeed
Samarium-148 148Sm   11.3     Radioactive       Half-life 1.06 x 1011
Samarium-149 149Sm   13.8     Radioactive       Half-life 7 x 1015
Samarium-150 150Sm   7.4       Radioactive       Half-life 1016
Samarium-152 152Sm   26.7     stable        
Bismuth-209 209Bi 83 100% 1 29 30 The last element to have a stable isotope*
Polonium-210 210Po 84   0 28 28 All isotopes are radioactive
Radon-222   86 Detectable amounts emitted fro rocks.  Steady state 0 25 25 Half-life 3.8 days,.  Radon is a natural radioactive gas. .  It presents a minor but detectable health hazard.
Radium-226 226Ra 88   0 16 16 Half-life 1,620 years produced by decay of Uranium
Thorium-232 232Th 90 100% 0 24 24 Half-life approx 1.4 x 1010 (over ten billion years)
Uranium--234 234U 92 0.0055 0 15 15 Half-life 2.45 x105
Uranium--235 235U   0.720 0     Half-life 7.04 x 108
Uranium--238 238U   33.2745 0     Half-life 4.4 x 10
Plutonium-238 238Pu 94 Not found on Earth 0 15 15 Half-life 87.74 years widely used in radioactive thermoelectric generators (RTGs) in space probes including Voyager and Cassini-Huygens
Plutonium-239 239Pu 94 Not found on Earth 0     Half-life 2.411 x 104  fissile weapons grade
Plutonium-241 242Pu   Not found on Earth 0     Half-life3.76 x 105 fissile weapons grade
Plutonium-244 244Pu   Not found on Earth 0     Half-life8.2 x 10Existed in early solar system

 

*Unstable  -  does not include unstable excited states (these are called nuclear isomers).  Details are given in the CRC (Rubber) Book

 According to David Arnett radioactivity from Bismuth-209 can not be detected.  Theory postulates it is an alpha emitter with a half-life of over 2 x 1018 which is a hundred million times the estimated age of the Universe!

POLONIUM was discovered in Uranium ore and named after Marie Curie's native country.  Notably, the murder of Alexander Litvinenko, a Russian dissident, in 2006 was announced as due to 210Po poisoning.   Generally, 210Po is most lethal when it is ingested.  According to Nick Priest, a radiation expert speaking on Sky News on 2 December 2006 Litvinenko was probably the first person ever to die of the  α-radiation effects of 210Po deliberately administered..

 Ironically, Irène Joliot-Curie, the daughter of Marie Curie who first isolated polonium, died because of it but her exposure was accidental. It happened when a sealed capsule of polonium exploded in her laboratory bench many years earlier. It was this which finally led to her death from leukemia in 1956 although the accident had occurred a decade earlier..

RADON

Radon is a natural radioactive gas. You cannot see, hear, feel or taste it. It comes from the minute amounts of uranium that occur naturally in all rocks and soils.

It is present in all parts of the UK, although the gas disperses outdoors so levels are generally very low.

We all breathe it in throughout our lives - for most UK residents, radon accounts for half of their total annual radiation dosage.

However, geological conditions in certain areas can lead to higher than average levels. Some of the highest radon levels have been found in the southwest, but levels well above average have been found in some other parts of the UK. Exposure to particularly high levels of radon may increase the risk of developing lung cancer.  An excellent American web-site published by Accustar Laboratories gives extensive details of radon.  The illustration is from their web-site

http://www.accustarlabs.com/shop_homeowner.php

THORIUM is a naturally-occurring, slightly radioactive metal discovered in 1828 by the Swedish chemist Jons Jakob Berzelius, who named it after Thor, the Norse god of thunder. It is found in small amounts in most rocks and soils, where it is about three times more abundant than uranium. Soil commonly contains an average of around 6 parts per million (ppm) of thorium.

URANIUM is a well known mineral in rocks.  Its main ore is Pitchblende a French physicist, Henri Becquerel, discovered that minerals containing uranium gave off rays. Marie Sklodowska Curie decided to investigate the uranium rays.

 Maria Sklodowska was born on at birth was born on November 7, 1867, in Warsaw.  After her emigration to Paris she married Professor Pierre Curie.  In 1897, following the discovery of Becquerel,  There was so little work on them for her to read about that she could begin experiments at once.
Trying out various chemicals, Marie found that substances which contained an uncommon element, thorium, also gave off rays. To describe the behavior of these two elements, Marie made up the term “radioactivity.”

She found that, the mineral pitchblende, rich in uranium, gave off more radioactivity than could be accounted for by the uranium in it (and there was no thorium). She figured the pitchblende must contain another element, fiercely radioactive, and never seen before. The promise of a strange new element was so exciting that her husband Pierre put aside his work on crystals to help speed up the discovery. They worked as a team, each responsible for a specific task..

The Uranium was decaying via  a number of other radio-isotopes to finally form lead.  Among the decay products were polonium, radium and radon.

After the tragic loss of her husband Pierre in a road accident with a horse carriage, Marie continued her work.  She was awarded TWO Nobel Prizes and herself died of radiation sickness in 1934.

Uranium is the last element of the periodic table to be found in nature and is used in the dating of rocks.
 

PLUTONIUM is the most important of the artificial elements following Uranium.  Four of its isotopes are of particular interest. Pltonium-238 is used in RTGs and was used in the Cassini-Huygens project.  The heat provided keeps the instruments in the space vessels warm.  At the distance from the Sun it is too distant from the Sun to rely on solar power.

Plutonium has one long-lived isotope ,plutonium 244.   'Fossil' mineralogical evidence for its existence during the earliest years of the solar system is found in meteorites.

Of the 92 elements up to Uranium, Technecium, Promethium, Astatine, Francium are not found at all in the Earth. and Polonium, Radon, Radium, Actinium and Protactinium are only found as a result of the radioactive decay of Uranium and Thorium.  This presents an interesting case of a 'steady state'.  For example, the amount of Radon given off by a rock will remain almost constant since the Radon that rapidly decays is replaced by the same amount of Radon due to the decay of Uranium (via Radium).

 

The Half-life Period

The time taken for half the amount of a radioactive isotope to decay into the 'daughter isotope' is called the half life period.  The graph shown below is true of all radioactive isotopes and credit for the diagram is given to the web-site of Accustar Laboratories

 

The Valley of stability

In the earlier elements the number of protons is the same or only slightly lower than the number of neutrons. As the nuclear mass increases there is a growing tendency for the number of neutrons to increase compared to protons.   The stable and radioactive nuclei of very long life lie on a so called valley of stability.  Nuclei outside this range become increasingly unstable.

Credit for the illustration.     Exotic nuclei: why and how to make them?  by  Mittig, P.Roussel-Chomaz and A.C.C.Villari 
GANIL, B.P. 5027,14076 Caen-Cedex 5 
Europhysics News (2004) Vol. 35 No. 4

Chart of the nuclides representing the nuclei according to their number of protons Z and of neutrons N. The clear outline shows the limit of the nuclei observed experimentally, and the outline of the brown zone indicates the theoretical limit of nuclear cohesion. The horizontal and vertical red lines represent the magic numbers (2,8,20,28,50,82,126).  These so called magic numbers represent the most stable arrangements of protons and neutrons

 

This illustration of 'The Valley of Stability' is taken from a paper entitled

Quest for superheavy nuclei

Authors

P.H. Heenen1 and W. Nazarewicz2-4
1Service de Physique Nucléaire Théorique, U.L.B.-C.P.229, B-1050 Brussels, Belgium
2Department of Physics, University of Tennessee, Knoxville, Tennessee 37996
3Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
4Institute of Theoretical Physics, University of Warsaw, ul. Ho\.za 69, PL-00-681 Warsaw, Poland

Europhysics News (2002) Vol. 33 No. 1

web-site  http://www.europhysicsnews.com/full/13/article2/article2.html

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