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Bump function

2014-01-14T14:57:55Z

195.202.243.48: /* Existence of bump functions */

A '''period 8 element''' is any one of 46 hypothetical [[chemical element]]s ([[ununennium]] through unhexquadium) belonging to an eighth [[Periodic table period|period]] of the [[extended periodic table|periodic table of the elements]]. Sometimes, elements 169 to 172 are also considered to be in period 8 as their outermost electrons fill the 8p3/2 subshells, despite behaving chemically more like the [[period 9 element]]s. They may be referred to using [[IUPAC]] [[systematic element name]]s. None of these elements have been [[synthetic element|synthesized]],<ref group="note">The heaviest element that has been synthesized to date is [[ununoctium]] with atomic number 118, which is the last [[period 7 element]].</ref> and it is possible that none have isotopes with stable enough nuclei to receive significant attention in the near future. It is also probable that, due to [[Proton drip line|drip instabilities]], only the lower period 8 elements are physically possible and the periodic table may end soon after the [[island of stability]] at [[unbihexium]] with atomic number 126.<ref name="emsley">{{cite book|last=Emsley|first=John|title=Nature's Building Blocks: An A-Z Guide to the Elements|edition=New|year=2011|publisher=Oxford University Press|location=New York, NY|isbn=978-0-19-960563-7}}</ref>{{Rp|593|date=November 2012}} The names given to these unattested elements are all [[systematic element name|IUPAC systematic names]].

If it were possible to produce sufficient quantities of sufficiently long-lived isotopes of these elements that would allow the study of their chemistry, these elements may well behave very differently from those of previous periods. This is because their [[electronic configuration]]s may be altered by [[quantum mechanics|quantum]] and [[Theory of relativity|relativistic]] effects, as the energy levels of the 5g, 6f, 7d and 8p1/2 [[atomic orbital|orbitals]] are so close to each other that they may well exchange electrons with each other.<ref>{{cite doi|10.1063/1.1672054}}</ref> This would result in a large number of elements in the [[superactinide]] series that would have extremely similar chemical properties that would be quite unrelated to elements of lower atomic number.<ref name="Fricke"/>

==History==
There are currently seven [[period (periodic table)|period]]s in the [[periodic table]] of [[chemical elements]], culminating with [[atomic number]] 118. If further elements with higher atomic numbers than this are discovered, they will be placed in additional periods, laid out (as with the existing periods) to illustrate periodically recurring trends in the properties of the elements concerned. Any additional periods are expected to contain a larger number of elements than the seventh period, as they are calculated to contain elements with filled g-[[atomic orbital|orbital]]s in their ground state. An eight-period table containing these elements was suggested by [[Glenn T. Seaborg]] in 1969.<ref name="LBNL">{{ cite web |url=http://www.lbl.gov/LBL-PID/Nobelists/Seaborg/65th-anniv/29.html |title= An Early History of LBNL |first=Glenn |last=Seaborg |date=August 26, 1996}}</ref><ref>{{cite journal | doi = 10.2307/3963006 | last1 = Frazier | first1 = K. | title = Superheavy Elements | journal = Science News | volume = 113 | issue = 15 | pages = 236–238 | year = 1978 | jstor = 3963006}}</ref> No elements in this region have been synthesized or discovered in nature. While Seaborg's version of the extended period had the heavier elements following the pattern set by lighter elements, as it did not take into account [[relativistic quantum chemistry|relativistic effects]], models that take relativistic effects into account do not. [[Pekka Pyykkö]] and B. Fricke used computer modeling to calculate the positions of elements up to ''[[Atomic number|Z]]'' = 172 (comprising periods 8 and [[period 9 element|9]]), and found that several were displaced from the Madelung rule.<ref name="Fricke">{{cite journal |last1=Fricke |first1=B. |last2=Greiner |first2=W. |last3=Waber |first3=J. T. |year=1971 |title=The continuation of the periodic table up to Z = 172. The chemistry of superheavy elements |journal=Theoretica chimica acta |volume=21 |issue=3 |pages=235–260 |publisher=Springer-Verlag |doi=10.1007/BF01172015 |url=http://link.springer.com/article/10.1007%2FBF01172015?LI=true# |accessdate=28 November 2012}}</ref><ref name="rsc.org">{{Cite web |url=http://www.rsc.org/Publishing/ChemScience/Volume/2010/11/Extended_elements.asp |title=Extended elements: new periodic table |year=2010}}</ref> Fricke predicted the structure of the extended periodic table up to ''Z'' = 172 to be:
{{Compact extended periodic table}}

==Predicted properties==

===Chemical and physical properties===

====8s elements====
<div style="float: right; margin: 1px; font-size:85%;">
:{| class="wikitable sortable"
|+ Some predicted properties of elements 119 and 120<ref name="Fricke"/><ref name="Haire"/>
! Property
! 119
! 120
|-
! [[Relative atomic mass]]
| [322]
| [325]
|-
! [[Periodic table group|Group]]
| [[alkali metal|1]]
| [[alkaline earth metal|2]]
|-
! Valence [[electron configuration]]
| 8s1
| 8s2
|-
! Stable [[oxidation state]]s
| '''1''', 3
| '''2''', 4
|-
! First [[ionization energy]]
| 437.1 [[kilojoule per mole|kJ/mol]]
| 578.9 kJ/mol
|-
! [[Metallic radius]]
| 260 pm
| 200 pm
|-
! [[Density]]
| 3 g/cm3
| 7 g/cm3
|-
! [[Melting point]]
| 0–30 [[degree Celsius|°C]]
| 680 °C
|-
! [[Boiling point]]
| 630 [[degree Celsius|°C]]
| 1700 °C
|}
</div>
The first two elements of period 8 are expected to be [[ununennium]] and [[unbinilium]], elements 119 and 120. Their electron configurations should have the 8s shell being filled. However, the 8s orbital is relativistically stabilized and contracted and thus, elements 119 and 120 should be more like [[caesium]] and [[barium]] than their immediate neighbours above, [[francium]] and [[radium]]. Another effect of the relativistic contraction of the 8s orbital is that the [[atomic radius|atomic radii]] of these two elements should be about the same of those of francium and radium. They should behave like normal [[alkali metal|alkali]] and [[alkaline earth metal]]s, normally forming +1 and +2 [[oxidation state]]s respectively, but the relativistic destabilization of the 7p3/2 subshell and the relatively low [[ionization energy|ionization energies]] of the 7p3/2 electrons should make higher oxidation states like +3 and +4 (respectively) possible as well.<ref name="Fricke"/><ref name=Haire>{{cite book| title = The Chemistry of the Actinide and Transactinide Elements| editor1-last = Morss|editor2-first = Norman M.| editor2-last = Edelstein| editor3-last = Fuger|editor3-first = Jean| last = Haire|first = Richard G.| chapter = Transactinides and the future elements| publisher = [[Springer Science+Business Media]]| year = 2006| isbn = 1-4020-3555-1| location = Dordrecht, The Netherlands| edition = 3rd| ref = CITEREFHaire2006}}</ref>

====Superactinides====
The superactinide series is expected to contain elements [[unbiunium|121]] to 155. In the superactinide series, the 7d3/2, 8p1/2, 6f5/2 and 5g7/2 shells should all fill simultaneously. The first superactinide, unbiunium (element 121), should be a [[Congener (chemistry)|congener]] of [[lanthanum]] and [[actinium]] and should have similar properties to them. In the first few superactinides, the binding energies of the added electrons are predicted to be small enough that they can lose all their valence electrons; for example, [[unbihexium]] (element 126) would usually form a +8 oxidation state, and even higher oxidation states for the next few elements may be possible. The presence of electrons in g-orbitals, which do not exist in the ground state electron configuration of any currently known element, should allow presently unknown [[orbital hybridisation|hybrid]] orbitals to form and influence the chemistry of the superactinides in new ways, although the absence of ''g'' electrons in known elements makes predicting their chemistry more difficult.<ref name=Fricke/>

In the later superactinides, the oxidation states should become lower. By element 132, the predominant most stable oxidation state will be only +6; this is further reduced to +3 and +4 by element 144, and at the end of the superactinide series it will be only +2 (and possibly even 0) because the 6f shell, which is being filled at that point, is deep inside the electron cloud and the 8s and 8p1/2 electrons are bound too strongly to be chemically active. The 5g shell should be filled at element 144 and the 6f shell at around element 154, and at this region of the superactinides the 8p1/2 electrons are bound so strongly that they are no longer active chemically, so that only a few electrons can participate in chemical reactions. Calculations by Fricke ''et al.'' predict that at element 154, the 6f shell is full and there are no d- or other electron [[wave function]]s outside the chemically inactive 8s and 8p1/2 shells. This would cause element 154 to be very [[reactivity (chemistry)|unreactive]], so that it may exhibit properties similar to those of the noble gases.<ref name=Fricke/><ref name=Haire/>

Similarly to the [[lanthanide contraction|lanthanide and actinide contractions]], there should be a superactinide contraction in the superactinide series where the [[ionic radius|ionic radii]] of the superactinides are smaller than expected. In the [[lanthanide]]s, the contraction is about 4.4 pm per element; in the [[actinide]]s, it is about 3 pm per element. The contraction is larger in the lanthanides than in the actinides due to the greater localization of the 4f wave function as compared to the 5f wave function. Comparisons with the wave functions of the outer electrons of the lanthanides, actinides, and superactinides lead to a prediction of a contraction of about 2 pm per element in the superactinides; although this is smaller than the contractions in the lanthanides and actinides, its total effect is larger due to the fact that 32 electrons are filled in the deeply buried 5g and 6f shells, instead of just 14 electrons being filled in the 4f and 5f shells in the lanthanides and actinides respectively.<ref name=Fricke/>

====Transition metals====
The transition metals in period 8 are expected to be element 156 to 164. Although the 8s and 8p1/2 electrons are bound so strongly in these elements that they should not be able to take part in any chemical reactions, the 9s and 9p1/2 levels are expected to be readily available for hybridization such that these elements will still behave chemically like their lighter [[homology (chemistry)|homologues]] in the periodic table, showing the same oxidation states as they do, in contrast to earlier predictions which predicted the period 8 transition metals to have main oxidation states two less than those of their lighter congeners.<ref name=Fricke/><ref name=Haire/>

The noble metals of this series of transition metals are not expected to be as noble as their lighter homologues, due to the absence of an outer ''s'' shell for shielding and also because the 7d shell is strongly split into two subshells due to relativistic effects. This causes the first ionization energies of the 7d transition metals to be smaller than those of their lighter congeners. Calculations predict that the 7d electrons of element 164 (unhexquadium) should participate very readily in chemical reactions, so that unhexquadium should be able to show +6 and +4 oxidation states in addition to the normal +2 state in [[aqueous solution]]s with strong [[ligand]]s. Unhexquadium should thus be able to form compounds like Uhq([[carbonyl|CO]])4, Uhq([[phosphorus trifluoride|PF3]])4 (both [[tetrahedral molecular geometry|tetrahedral]]), and {{chem|Uhq([[cyanide|CN]])|2|2-}} ([[linear molecular geometry|linear]]), which is very different behavior from that of [[lead]], which unhexquadium would be a heavier [[homology (chemistry)|homologue]] of if not for relativistic effects. Unhexquadium should be a [[hardness|soft]] metal like [[mercury (element)|mercury]], and metallic unhexquadium should have a high melting point as it is predicted to bond [[covalent bond|covalently]]. It should also have some similarities to [[ununoctium]] as well as to the other group 12 elements. The eighth period of the periodic table is expected to end here.<ref name=Fricke/><ref name=Haire/>

<div style="float: center; margin: 1px; font-size:85%;">
:{| class="wikitable sortable"
|+ Some predicted properties of the 7d transition metals. The metallic radii and densities are first approximations.<ref name="Fricke"/><ref name="Haire"/>
! Property
! 156
! 157
! 158
! 159
! 160
! 161
! 162
! 163
! 164
|-
! [[Relative atomic mass]]
| [445]
| [448]
| [452]
| [456]
| [459]
| [463]
| [466]
| [470]
| [474]
|-
! [[Periodic table group|Group]]
| [[group 4 element|4]]
| [[group 5 element|5]]
| [[group 6 element|6]]
| [[group 7 element|7]]
| [[group 8 element|8]]
| [[group 9 element|9]]
| [[group 10 element|10]]
| [[group 11 element|11]]
| [[group 12 element|12]]
|-
! Valence [[electron configuration]]
| 7d2
| 7d3
| 7d4
| 7d5
| 7d6
| 7d7
| 7d8
| 7d9
| 7d10
|-
! Stable [[oxidation state]]s
| 2, 4
| 3, 5
| 4, 6
| 1, 5, 7
| 2, 6, 8
| 3, 7
| 4, 8
| 3, 5
| 0, 2, 4, 6
|-
! First [[ionization energy]]
| 395.6 kJ/mol
| 453.5 kJ/mol
| 521.0 kJ/mol
| 337.7 kJ/mol
| 424.5 kJ/mol
| 472.8 kJ/mol
| 559.6 kJ/mol
| 617.5 kJ/mol
| 685.0 kJ/mol
|-
! [[Metallic radius]]
| 170 pm
| 163 pm
| 157 pm
| 152 pm
| 148 pm
| 148 pm
| 149 pm
| 152 pm
| 158 pm
|-
! [[Density]]
| 26 g/cm3
| 28 g/cm3
| 30 g/cm3
| 33 g/cm3
| 36 g/cm3
| 40 g/cm3
| 45 g/cm3
| 47 g/cm3
| 46 g/cm3
|}
</div>

===Nuclear properties===
The first [[island of stability]] is expected to be centered around [[unbibium]]-306 (with 122 protons and 184 neutrons),<ref name=Kratz>
{{cite conference
|last1=Kratz |first1=J. V.
|date=5 September 2011
|title=The Impact of Superheavy Elements on the Chemical and Physical Sciences
|url=http://tan11.jinr.ru/pdf/06_Sep/S_1/02_Kratz.pdf
|conference=4th International Conference on the Chemistry and Physics of the Transactinide Elements
|accessdate=27 August 2013
}}</ref> and the second is expected to be center around [[unhexquadium]]-482 (with 164 protons and 318 neutrons).<ref>http://www.eurekalert.org/pub_releases/2008-04/acs-nse031108.php</ref><ref>http://link.springer.com/article/10.1007%2FBF01406719/lookinside/000.png</ref>

==Synthesis==
The only period 8 elements that have had synthesis attempts were elements 119, 120, 122, 124, 126, and 127. So far, none of these synthesis attempts were successful.

===Ununennium===
The synthesis of ununennium was attempted in 1985 by bombarding a target of [[einsteinium]]-254 with [[calcium]]-48 ions at the superHILAC accelerator at Berkeley, California:
:<math>\,^{254}_{99}\mathrm{Es} + \,^{48}_{20}\mathrm{Ca} \to \,^{302}_{119}\mathrm{Uue} ^{*} </math>
No atoms were identified, leading to a limiting yield of 300 [[barn (unit)|nb]].<ref>{{cite journal|title=Search for superheavy elements using 48Ca + 254Esg reaction|author=R. W. Lougheed, J. H. Landrum, E. K. Hulet, J. F. Wild, R. J. Dougan, A. D. Dougan, H. Gäggeler, M. Schädel, K. J. Moody, K. E. Gregorich, and [[Glenn T. Seaborg|G. T. Seaborg]]|journal=Physical Reviews C|year=1985|pages=1760–1763|url=http://link.aps.org/abstract/PRC/v32/p1760|doi=10.1103/PhysRevC.32.1760|volume=32|issue=5|bibcode = 1985PhRvC..32.1760L }}</ref>
As of May 2012, plans are under way to attempt to synthesize the isotopes 295Uue and 296Uue by bombarding a target of [[berkelium]] with [[titanium]] at the [[GSI Helmholtz Centre for Heavy Ion Research]] in [[Darmstadt]], Germany:<ref name="economist">[http://www.economist.com/node/21554502 Modern alchemy: Turning a line], [[The Economist]]</ref><ref>http://fias.uni-frankfurt.de/kollo/Duellmann_FIAS-Kolloquium.pdf</ref>
:<math>\,^{249}_{97}\mathrm{Bk} + \,^{50}_{22}\mathrm{Ti} \to \,^{296}_{119}\mathrm{Uue} \,+3\,^{1}_{0}\mathrm{n}</math>

:<math>\,^{249}_{97}\mathrm{Bk} + \,^{50}_{22}\mathrm{Ti} \to \,^{295}_{119}\mathrm{Uue} \,+4\,^{1}_{0}\mathrm{n}</math>

====Target-projectile combinations leading to Z=119 compound nuclei====
The below table contains various combinations of targets and projectiles which could be used to form compound nuclei with an atomic number of 119.

{|class="wikitable" style="text-align:center"

!Target!!Projectile!!CN!!Attempt result
|-
!254Es
|48Ca||302Uue||{{no|Failure to date}}
|-
!249Bk
|50Ti||299Uue||{{unk|Planned reaction}}
|}

===Unbinilium===
Attempts to date to synthesize the element using fusion reactions at low excitation energy have met with failure, although there are reports that the fission of nuclei of unbinilium at very high excitation has been successfully measured, indicating a strong shell effect at Z=120.
In March–April 2007, the synthesis of unbinilium was attempted at the [[Joint Institute for Nuclear Research|Flerov Laboratory of Nuclear Reactions]] in [[Dubna]] by bombarding a [[plutonium]]-244 target with [[iron]]-58 [[ion]]s.<ref>[http://www.jinr.ru/plan/ptp-2007/e751004.htm THEME03-5-1004-94/2009]</ref> Initial analysis revealed that no atoms of element 120 were produced providing a limit of 400 [[barn (unit)|fb]] for the cross section at the energy studied.<ref>{{cite journal|journal=Phys. Rev. C|volume=79|page=024603|year=2009|title=Attempt to produce element 120 in the 244Pu+58Fe reaction|doi=10.1103/PhysRevC.79.024603|last1=Oganessian|first1=Yu. Ts.|last2=Utyonkov|first2=V.|last3=Lobanov|first3=Yu.|last4=Abdullin|first4=F.|last5=Polyakov|first5=A.|last6=Sagaidak|first6=R.|last7=Shirokovsky|first7=I.|last8=Tsyganov|first8=Yu.|last9=Voinov|first9=A.|last10=N.N.|displayauthors=9|issue=2 |bibcode = 2009PhRvC..79b4603O }}</ref>

:<math>\,^{244}_{94}\mathrm{Pu} + \,^{58}_{26}\mathrm{Fe} \to \,^{302}_{120}\mathrm{Ubn} ^{*} \to \ \mathit{fission\ only}</math>

The Russian team are planning to upgrade their facilities before attempting the reaction again.<ref name=Duellmann>>http://fias.uni-frankfurt.de/kollo/Duellmann_FIAS-Kolloquium.pdf</ref>

In April 2007, the team at [[Gesellschaft für Schwerionenforschung|GSI]] attempted to create unbinilium using [[uranium]]-238 and [[nickel]]-64:<ref name=Duellmann/>

:<math>\,^{238}_{92}\mathrm{U} + \,^{64}_{28}\mathrm{Ni} \to \,^{302}_{120}\mathrm{Ubn} ^{*} \to \ \mathit{fission\ only}</math>

No atoms were detected providing a limit of 1.6 pb on the cross section at the energy provided. The GSI repeated the experiment with higher sensitivity in three separate runs from April–May 2007, Jan–March 2008, and Sept–Oct 2008, all with negative results and providing a cross section limit of 90 fb.<ref name=Duellmann/>

In June–July 2010, scientists at the GSI attempted the fusion reaction:<ref name=Duellmann/>

:<math>\,^{248}_{96}\mathrm{Cm} + \,^{54}_{24}\mathrm{Cr} \to \,^{302}_{120}\mathrm{Ubn} ^{*} </math>

They were unable to detect any atoms but exact details are not currently available.<ref name=Duellmann/>

In August–October 2011, a different team at the GSI using the TASCA facility tried the new reaction:<ref name=Duellmann/>

:<math>\,^{249}_{98}\mathrm{Cf} + \,^{50}_{22}\mathrm{Ti} \to \,^{299}_{120}\mathrm{Ubn} ^{*} </math>

Results from this experiment are not yet available.<ref name=Duellmann/>
In 2008, the team at GANIL, France, described the results from a new technique which attempts to measure the fission [[half-life]] of a compound nucleus at high excitation energy, since the yields are significantly higher than from neutron evaporation channels. It is also a useful method for probing the effects of shell closures on the survivability of compound nuclei in the super-heavy region, which can indicate the exact position of the next proton shell (Z=114, 120, 124, or 126).
The team studied the nuclear fusion reaction between uranium ions and a target of natural nickel:

::::<math>\,^{238}_{92}\mathrm{U} + \,^{nat}_{28}\mathrm{Ni} \to \,^{296,298,299,300,302}\mathrm{Ubn} ^{*} \to \ \mathit{fission}.</math>

The results indicated that nuclei of unbinilium were produced at high (~70 MeV) excitation energy which underwent fission with measurable half-lives > 10−18 s. Although very short, the ability to measure such a process indicates a strong shell effect at Z=120. At lower excitation energy (see neutron evaporation), the effect of the shell will be enhanced and ground-state nuclei can be expected to have relatively long half-lives. This result could partially explain the relatively long half-life of 294[[ununoctium|Uuo]] measured in experiments at Dubna. Similar experiments have indicated a similar phenomenon at Z=124 (see [[unbiquadium]]) but not for [[flerovium]], suggesting that the next proton shell does in fact lie at Z>120.<ref>{{cite journal|doi=10.1103/Physics.1.12|title=How stable are the heaviest nuclei?|year=2008|author=Natowitz, Joseph|journal=Physics|volume=1|pages=12|bibcode = 2008PhyOJ...1...12N }}</ref><ref>{{cite journal|journal=Phys. Rev. Lett.|volume=101|year=2008|page=072701|title=Fission Time Measurements: A New Probe into Superheavy Element Stability|author=Morjean, M. et al.|doi=10.1103/PhysRevLett.101.072701|pmid=18764526|bibcode=2008PhRvL.101g2701M|issue=7}}</ref>
The team at RIKEN have begun a program utilizing 248Cm targets and have indicated future experiments to probe the possibility of Z=120 being the next magic number using the aforementioned nuclear reactions to form 302Ubn.<ref>see slide 11 in [http://www-win.gsi.de/tasca07/contributions/TASCA07_Contribution_Morita.pdf Future Plan of the Experimental Program on Synthesizing the Heaviest Element at RIKEN]</ref>

====Target-projectile combinations leading to Z=120 compound nuclei====
The below table contains various combinations of targets and projectiles which could be used to form compound nuclei with an atomic number of 120.

{|class="wikitable" style="text-align:center"
! Target !! Projectile !! CN !! Attempt result
|-
!208Pb
|88Sr||296Ubn||{{unk|Reaction yet to be attempted<ref name=Haire/>}}
|-
!238U
|64Ni||302Ubn||{{no|Failure to date, σ < 94 fb}}
|-
!244Pu
|58Fe||302Ubn||{{no|Failure to date, σ < 0.4 pb}}
|-
!248Cm
|54Cr||302Ubn||{{no|Failure to date, not all details available}}
|-
!250Cm
|54Cr||304Ubn||{{unk|Reaction yet to be attempted}}
|-
!249Cf
|50Ti||299Ubn||{{unk|Results are not yet available}}
|-
!252Cf
|50Ti||302Ubn||{{unk|Reaction yet to be attempted}}
|-
!257Fm
|48Ca||305Ubn||{{unk|Reaction yet to be attempted}}
|}

===Unbibium===
The first attempt to synthesize unbibium was performed in 1972 by [[Georgy Flerov|Flerov]] ''et al.'' at [[JINR]], using the hot fusion reaction:<ref name="emsley"/>

:<math>\,^{238}_{92}\mathrm{U} + \,^{66}_{30}\mathrm{Zn} \to \,^{304}_{122}\mathrm{Ubb} ^{*} \to \ \mbox{no atoms}.</math>

No atoms were detected and a yield limit of 5 [[Barn (unit)|mb]] (5,000,000,000 [[barn (unit)|pb]]) was measured. Current results (see [[flerovium]]) have shown that the sensitivity of this experiment was too low by at least 6 orders of magnitude.{{Citation needed|date=February 2012}}

In 2000, the [[Gesellschaft für Schwerionenforschung]] (GSI) performed a very similar experiment with much higher sensitivity:<ref name="emsley">{{cite book|last=Emsley|first=John|title=Nature's Building Blocks: An A-Z Guide to the Elements|edition=New|year=2011|publisher=Oxford University Press|location=New York, NY|isbn=978-0-19-960563-7|page=588}}</ref>

:<math>\,^{238}_{92}\mathrm{U} + \,^{70}_{30}\mathrm{Zn} \to \,^{308}_{122}\mathrm{Ubb} ^{*} \to \ \mbox{no atoms}.</math>

These results indicate that the synthesis of such heavier elements remains a significant challenge and further improvements of beam intensity and experimental efficiency is required. The sensitivity should be increased to 1 [[barn (unit)|fb]].{{Citation needed|date=February 2012}}

Another unsuccessful attempt to synthesize unbibium was carried out in 1978 at the GSI, where a natural [[erbium]] target was bombarded with [[xenon-136]] ions:<ref name="emsley"/>

:<math>\,^{nat}_{68}\mathrm{Er} + \,^{136}_{54}\mathrm{Xe} \to \,^{298,300,302,303,304,306}\mathrm{Ubb} ^{*} \to \ \mbox{no atoms}.</math>

The two attempts in the 1970s to synthesize unbibium were caused by research investigating whether superheavy elements could potentially be naturally occurring.<ref name="emsley"/>
Several experiments have been performed between 2000-2004 at the Flerov laboratory of Nuclear Reactions studying the fission characteristics of the compound nucleus 306Ubb. Two nuclear reactions have been used, namely 248Cm + 58Fe and 242Pu + 64Ni.<ref name="emsley"/> The results have revealed how nuclei such as this fission predominantly by expelling [[nuclear shell model|closed shell]] nuclei such as 132Sn (Z=50, N=82). It was also found that the yield for the fusion-fission pathway was similar between 48Ca and 58Fe projectiles, indicating a possible future use of 58Fe projectiles in superheavy element formation.<ref>see Flerov lab annual reports 2000–2004 inclusive http://www1.jinr.ru/Reports/Reports_eng_arh.html</ref>

===Unbiquadium===
In a series of experiments, scientists at GANIL have attempted to measure the direct and delayed fission of compound nuclei of elements with Z=114, 120, and 124 in order to probe [[nuclear shell|shell]] effects in this region and to pinpoint the next spherical proton shell. This is because having complete nuclear shells (or, equivalently, having a [[magic number (physics)|magic number]] of [[proton]]s or [[neutron]]s) would confer more stability on the nuclei of such superheavy elements, thus moving closer to the [[island of stability]]. In 2006, with full results published in 2008, the team provided results from a reaction involving the bombardment of a natural germanium target with uranium ions:

:<math>\,^{238}_{92}\mathrm{U} + \,^{nat}_{32}\mathrm{Ge} \to \,^{308,310,311,312,314}\mathrm{Ubq} ^{*} \to \ fission.</math>

The team reported that they had been able to identify compound nuclei fissioning with half-lives > 10−18 s. A compound nucleus is a loose combination of [[nucleon]]s that have not arranged themselves into nuclear shells yet. It has no internal structure and is held together only by the collision forces between the target and projectile nuclei. It is estimated that it requires around 10−14 s for the nucleons to arrange themselves into nuclear shells, at which point the compound nucleus becomes an [[nuclide]], and this number is used by [[IUPAC]] as the minimum [[half-life]] a claimed isotope must have to potentially be recognised as being discovered. Thus, the GANIL experiments do not count as a discovery of element 124.<ref name="emsley">{{cite book|last=Emsley|first=John|title=Nature's Building Blocks: An A-Z Guide to the Elements|edition=New|year=2011|publisher=Oxford University Press|location=New York, NY|isbn=978-0-19-960563-7|page=590}}</ref>

===Unbihexium===
The first and only attempt to synthesize unbihexium, which was unsuccessful, was performed in 1971 at [[CERN]] by [[René Bimbot]] and John M. Alexander using the hot fusion reaction:<ref name="emsley"/>

: {{nuclide2|thorium|232|link=y}} + {{nuclide2|krypton|84|link=y}} → {{nuclide2|unbihexium|316}}* → ''no atoms''

A high energy [[alpha particle]] was observed and taken as possible evidence for the synthesis of unbihexium. Recent research{{which|date=October 2011}} suggests that this is highly unlikely as the sensitivity of experiments performed in 1971 would have been several orders of magnitude too low according to current understanding.

===Unbiseptium===
Unbiseptium has had one failed attempt at [[Synthetic element|synthesis]] in 1978 at the Darmstadt UNILAC accelerator by bombarding a natural [[tantalum]] target with [[xenon]] ions:<ref name="emsley">{{cite book|last=Emsley|first=John|title=Nature's Building Blocks: An A-Z Guide to the Elements|edition=New|year=2011|publisher=Oxford University Press|location=New York, NY|isbn=978-0-19-960563-7|page=593}}</ref>

:<math>\,^{nat}_{73}\mathrm{Ta} + \,^{136}_{54}\mathrm{Xe} \to \,^{316, 317}\mathrm{Ubs} ^{*} \to \mbox{no atoms}.</math>

====Target-projectile combinations leading to Z=127 compound nuclei====

The below table shows various combinations of targets and projectiles leading to compound nuclei with an atomic number of 127.

{|class="wikitable" style="text-align:center"
|-
! Target !! Projectile !! CN !! Attempt result
|-
!180mTa
|136Xe||316Ubs||{{no|Failure to date}}
|-
!181Ta
|136Xe||317Ubs||{{no|Failure to date}}
|-
|}

==See also==
* [[Extended periodic table]]: extension of the table beyond the 7th period
* [[Nucleon drip line]]
* [[Period 9 element]]

==Notes==
{{reflist|group=note}}

==References==
{{reflist}}


{{PeriodicTablesFooter}}
{{Compact extended periodic table}}

{{DEFAULTSORT:Period 8 Element}}
[[Category:Periodic table]]
[[Category:Hypothetical chemical elements]]

Levi-Civita symbol

2014-01-11T17:44:58Z

195.202.243.48: /* Determinants */

{{Redirect|Étalon|the ''commune'' in [[Somme]], [[France]]|Étalon, Somme}}
[[File:Fabry Perot Etalon Rings Fringes.png|right|thumb|200px|Interference fringes, showing [[fine structure]], from a Fabry–Pérot etalon. The source is a cooled [[deuterium]] lamp.]]
In [[optics]], a '''Fabry–Pérot interferometer''' or '''etalon''' is typically made of a transparent plate with two [[Reflection (physics)|reflecting]] surfaces, or two parallel highly reflecting mirrors. (Technically the former is an etalon and the latter is an [[interferometer]], but the terminology is often used inconsistently.) Its transmission [[optical spectrum|spectrum]] as a function of [[wavelength]] exhibits peaks of large transmission corresponding to resonances of the etalon. It is named after [[Charles Fabry]] and [[Alfred Perot]].<ref>Perot frequently spelled his name with an accent—Pérot—in scientific publications, and so the name of the interferometer is commonly written with the accent. {{cite journal
| first=Françoise |last=Métivier
|title=Jean-Baptiste Alfred Perot
|date=September–October 2006
| journal=Photoniques |issue= 25| language=French
|url=http://www.sabix.org/documents/perot.pdf |format=pdf
|accessdate=2007-10-02}} Page 2: "Pérot ou Perot?"</ref> "Etalon" is from the French ''étalon'', meaning "measuring gauge" or "standard".<ref>''[[Oxford English Dictionary]]''</ref>

Etalons are widely used in [[telecommunication]]s, [[laser]]s and [[spectroscopy]] to control and measure the [[wavelength]]s of light. Recent advances in fabrication technique allow the creation of very precise tunable Fabry–Pérot interferometers.

== Basic description ==
[[File:Fabry Perot Interferometer - diagram.png|thumb|300px|Fabry–Pérot interferometer, using a pair of partially reflective, slightly wedged optical flats. The wedge angle is highly exaggerated in this illustration; only a fraction of a degree is actually necessary. Low-finesse versus high-finesse images correspond to mirror reflectivities of 4% (bare glass) and 95%.]]
The heart of the Fabry–Pérot interferometer is a pair of partially reflective glass [[optical flat]]s spaced millimeters to centimeters apart, with the reflective surfaces facing each other. (Alternatively, a Fabry–Pérot ''etalon'' uses a single plate with two parallel reflecting surfaces.) The flats in an interferometer are often made in a wedge shape to prevent the rear surfaces from producing interference fringes; the rear surfaces often also have an [[anti-reflective coating]].

In a typical system, illumination is provided by a diffuse source set at the [[focal plane]] of a [[collimating lens]]. A focusing lens after the pair of flats would produce an inverted image of the source if the flats were not present; all light emitted from a point on the source is focused to a single point in the system's image plane. In the accompanying illustration, only one ray emitted from point A on the source is traced. As the ray passes through the paired flats, it is multiply reflected to produce multiple transmitted rays which are collected by the focusing lens and brought to point A' on the screen. The complete interference pattern takes the appearance of a set of concentric rings. The sharpness of the rings depends on the reflectivity of the flats. If the reflectivity is high, resulting in a high [[Q factor]], [[monochromatic light]] produces a set of narrow bright rings against a dark background. A Fabry–Pérot interferometer with high Q is said to have high ''finesse''.

== Applications ==
[[Image:LASCO C1a.png|thumb|right|A picture of the solar corona taken with the [[Large Angle and Spectrometric Coronagraph|LASCO]] C1 coronagraph which employed a tunable Fabry–Pérot interferometer to recover scans of the solar corona at a number of wavelengths near the FeXIV green line at 5308 Å. The picture is a color-coded image of the [[Doppler effect|doppler shift]] of the line, which may be associated with the [[Corona|coronal plasma]] velocity towards or away from the satellite camera. In calculating the velocity, the velocity due to [[solar rotation]] has been subtracted.]]
[[File:Dispositif Fabry-Perot .jpg|thumb|A commercial Fabry-Perot device]]

* Telecommunications networks employing [[wavelength division multiplexing]] have [[add-drop multiplexer]]s with banks of miniature tuned [[fused silica]] or [[diamond]] etalons. These are small iridescent cubes about 2 mm on a side, mounted in small high-precision racks. The materials are chosen to maintain stable mirror-to-mirror distances, and to keep stable frequencies even when the temperature varies. Diamond is preferred because it has greater heat conduction and still has a low coefficient of expansion. In 2005, some telecommunications equipment companies began using solid etalons that are themselves optical fibers. This eliminates most mounting, alignment and cooling difficulties.

* [[Dichroic filter]]s are made by depositing a series of etalonic layers on an optical surface by [[Vacuum deposition|vapor deposition]]. These [[optical filter]]s usually have more exact reflective and pass bands than absorptive filters. When properly designed, they run cooler than absorptive filters because they can reflect unwanted wavelengths. Dichroic filters are widely used in optical equipment such as light sources, cameras, astronomical equipment, and laser systems.

* Optical [[wavemeter]]s use Fabry–Pérot interferometers with different free spectral ranges to determine the wavelength of light with great precision.

*[[Optical cavity|Laser resonators]] are often described as Fabry–Pérot resonators, although for many types of laser the reflectivity of one mirror is close to 100%, making it more similar to a [[Gires–Tournois interferometer]]. Semiconductor [[diode laser]]s sometimes use a true Fabry–Pérot geometry, due to the difficulty of coating the end facets of the chip.

*Etalons are often placed inside the laser resonator when constructing single-mode lasers. Without an etalon, a laser will generally produce light over a wavelength range corresponding to a number of [[Optical cavity|cavity]] modes, which are similar to Fabry–Pérot modes. Inserting an etalon into the laser cavity, with well-chosen finesse and free-spectral range, can suppress all cavity modes except for one, thus changing the operation of the [[laser]] from multi-mode to single-mode.

*Fabry–Pérot etalons can be used to prolong the interaction length in [[laser absorption spectrometry]], particularly [[cavity ring-down spectroscopy|cavity ring-down]], techniques.

*A Fabry–Pérot etalon can be used to make a [[spectrometer]] capable of observing the [[Zeeman effect]], where the [[spectral lines]] are far too close together to distinguish with a normal spectrometer.

*In [[astronomy]] an etalon is used to select a single [[atomic transition]] for imaging. The most common is the [[H-alpha]] line of the [[sun]]. The [[Calcium#H_and_K_lines|Ca-K]] line from the sun is also commonly imaged using etalons.

*In [[gravitational wave]] detection, a Fabry–Pérot cavity is used to ''store'' [[photon]]s for almost a millisecond while they bounce up and down between the mirrors. This increases the time a gravitational wave can interact with the light, which results in a better sensitivity at low frequencies. This principle is used by detectors such as [[LIGO]] and [[Virgo interferometer|Virgo]], which consist of a [[Michelson interferometer]] with a Fabry–Pérot cavity with a length of several kilometers in both arms. Smaller cavities, usually called ''mode cleaners'', are used for [[spatial filter]]ing and frequency stabilization of the main laser.

== Theory ==
[[File:Etalon-2.svg|frame|right|A Fabry–Pérot etalon. Light enters the etalon and undergoes multiple internal reflections.]]

The varying transmission function of an etalon is caused by [[Interference (wave propagation)|interference]] between the multiple reflections of light between the two reflecting surfaces. Constructive interference occurs if the transmitted beams are in [[phase (waves)|phase]], and this corresponds to a high-transmission peak of the etalon. If the transmitted beams are out-of-phase, destructive interference occurs and this corresponds to a transmission minimum. Whether the multiply reflected beams are in phase or not depends on the wavelength (λ) of the light (in vacuum), the angle the light travels through the etalon (θ), the thickness of the etalon (''ℓ'') and the [[refractive index]] of the material between the reflecting surfaces (''n'').

The phase difference between each successive transmitted pair (i.e. T2 - T1 in the diagram) is given by δ:<ref name="Lipson, Optical Physics" >{{cite book
|first=S.G. |last=Lipson |first2=H. |last2=Lipson |first3=D.S. |last3=Tannhauser
|year=1995
|title=Optical Physics
|edition=3rd
|pages=248
|ref=Lipson, Optical Physics
|isbn=0-521-06926-2
|publisher=Cambridge U.P.
|location=London
}}</ref>

:<math>\delta = \left( \frac{2 \pi}{\lambda} \right) 2 n \ell \cos\theta. </math>

If both surfaces have a [[reflectance]] ''R'', the [[transmission coefficient|transmittance function]] of the etalon is given by

:<math>T_e = \frac{(1-R)^2}{1+R^2-2R\cos\delta}=\frac{1}{1+F\sin^2(\delta/2)},</math>

where

:<math> F = \frac{4R}{{(1-R)^2}}</math>

is the ''coefficient of finesse''.

[[Image:Etalon-2.png|frame|right|The transmission of an etalon as a function of wavelength. A high-finesse etalon (red line) shows sharper peaks and lower transmission minima than a low-finesse etalon (blue).]]

Maximum transmission (<math>T_e=1</math>) occurs when the [[optical path length]] difference (<math>2 n l \cos\theta</math>) between each transmitted beam is an integer multiple of the wavelength. In the absence of absorption, the reflectance of the etalon ''R''e is the complement of the transmittance, such that <math>T_e+R_e=1</math>. The maximum reflectivity is given by:

:<math>R_\max = 1-\frac{1}{1+F}= \frac {4R}{(1+R)^2} </math>

and this occurs when the path-length difference is equal to half an odd multiple of the wavelength.

[[File:Etalon-finesse-vs-reflectivity-2012-May-15.svg|thumb|400px|right|Finesse as a function of reflectivity. Very high finesse factors require highly reflective mirrors.]]

The wavelength separation between adjacent transmission peaks is called the [[free spectral range]] (FSR) of the etalon, Δλ, and is given by:

:<math>\Delta\lambda = \frac{ \lambda_0^2}{2n\ell \cos\theta + \lambda_0 } \approx \frac{ \lambda_0^2}{2n\ell \cos\theta } </math>

where λ0 is the central wavelength of the nearest transmission peak. The FSR is related to the full-width half-maximum, δλ, of any one transmission band by a quantity known as the ''finesse'':

:<math> \mathcal{F} = \frac{\Delta\lambda}{\delta\lambda}=\frac{\pi}{2 \arcsin(1/\sqrt F)}</math>.

This is commonly approximated (for ''R'' > 0.5) by

:<math> \mathcal{F} \approx \frac{\pi \sqrt{F}}{2}=\frac{\pi R^{1/2} }{1-R} </math>

Etalons with high finesse show sharper transmission peaks with lower minimum transmission coefficients. In the oblique incidence case, the finesse will depend on the polarization state of the beam, since the value of "R", given by the [[Fresnel equations]], is generally different for p and s polarizations.

A Fabry–Pérot interferometer differs from a Fabry–Pérot etalon in the fact that the distance ''ℓ'' between the plates can be tuned in order to change the wavelengths at which transmission peaks occur in the interferometer. Due to the angle dependence of the transmission, the peaks can also be shifted by rotating the etalon with respect to the beam.

Fabry–Pérot interferometers or etalons are used in [[optics|optical]] [[modem]]s, [[spectroscopy]], [[laser]]s, and [[astronomy]].

A related device is the [[Gires–Tournois etalon]].

{{clear}}

=== Detailed analysis ===
{{Unreferenced section|date=October 2011}}
[[Image:Fabry Perot Diagram1.svg|320px|right]]

Two beams are shown in the diagram at the right, one of which (T0) is transmitted through the etalon, and the other of which (T1) is reflected twice before being transmitted. At each reflection, the amplitude is reduced by <math>\sqrt R</math>, while at each transmission through an interface the amplitude is reduced by <math>\sqrt T</math>. Assuming no absorption, [[conservation of energy]] requires ''T'' + ''R'' = 1. In the derivation below, ''n'' is the index of refraction inside the etalon, and ''n''0 is that outside the etalon. It is presumed that ''n'' > ''n''0. The incident amplitude at point a is taken to be one, and [[phasor]]s are used to represent the amplitude of the radiation. The transmitted amplitude at point b will then be

:<math>t_0 = T\,e^{ik\ell/\cos\theta}</math>,

where <math>k=2\pi n/\lambda</math> is the wavenumber inside the etalon and λ is the vacuum wavelength. At point c the transmitted amplitude will be

:<math>t'_1 = TR\,e^{3ik\ell/\cos\theta}</math>.

The total amplitude of both beams will be the sum of the amplitudes of the two beams measured along a line perpendicular to the direction of the beam. The amplitude ''t''0 at point b can therefore be added to ''t'''1 retarded in phase by an amount <math>k_0 \ell_0</math> where <math>k_0=2\pi n_0/\lambda</math> is the wavenumber outside of the etalon. Thus

:<math>t_1 = TR\,e^{3ik\ell/\cos\theta-ik_0 \ell_0}</math>,

where ℓ0 is

:<math>\ell_0=2\ell\tan\theta\sin\theta_0\,</math>.

The phase difference between the two beams is

:<math>\delta={2k\ell\over\cos\theta} - k_0 \ell_0\,</math>.

The relationship between ''θ'' and ''θ''0 is given by [[Snell's law]]:

:<math>n\sin\theta=n_0\sin\theta_0\,</math>,

so that the phase difference may be written:

:<math>\delta=2k\ell\,\cos\theta\,</math>.

To within a constant multiplicative phase factor, the amplitude of the ''m''th transmitted beam can be written as:

:<math>t_m=TR^m e^{im\delta}\,</math>.

The total transmitted amplitude is the sum of all individual beams' amplitudes:

:<math>t=\sum_{m=0}^\infty t_m=T\sum_{m=0}^\infty R^m\,e^{im\delta}</math>

The series is a [[geometric series]] whose sum can be expressed analytically. The amplitude can be rewritten as

:<math>t=\frac{T}{1-Re^{i\delta}}</math>.

The intensity of the beam will be just ''t'' times its [[complex conjugate]]. Since the incident beam was assumed to have an intensity of one, this will also give the transmission function:

:<math>T_e=tt^*=\frac{T^2}{1+R^2-2R\cos\delta}</math>

===Another expression for the transmission function===

Defining <math>\gamma=\ln(1/R)</math> the above expression may be written as:

:<math>T_e=\frac{T^2}{1-R^2}\left(\frac{\sinh\gamma}{\cosh\gamma-\cos\delta}\right)</math>

The second term is proportional to a [[wrapped Cauchy distribution|wrapped Lorentzian distribution]] so that the transmission function may be written as a series of [[Cauchy distribution|Lorentzian functions]]:

:<math>T_e=\frac{2\pi\,T^2}{1-R^2}\,\sum_{\ell=-\infty}^\infty L(\delta-2\pi\ell;\gamma)</math>

where

:<math>L(x;\gamma) = \frac{\gamma}{\pi(x^2+\gamma^2)}</math>

== See also ==
* [[Lummer–Gehrcke interferometer]]
* [[Atomic line filter]]
* [[ARROW waveguide]]
* [[Distributed Bragg reflector]]
* [[Fiber Bragg grating]]
* [[Optical microcavity]]
* [[Thin-film interference]]

==Notes and references==
{{reflist}}
*{{cite book
| first = G. | last = Hernandez
| year = 1986
| title = Fabry–Pérot Interferometers
| publisher = Cambridge University Press | location = Cambridge
| isbn = 0-521-32238-3
}}

==External links==
* [http://www.infratec.de/fileadmin/media/Sensorik/pdf/Appl_Notes/Application_note_FP_detectors.pdf Compact FP interferometer for gas analysis]
*[http://www.precisionphotonics.com/technology/EtalonAdvanced.pdf Advanced Design of Etalons]- by Precision Photonics Corporation

{{DEFAULTSORT:Fabry Perot Interferometer}}
[[Category:Interferometers]]