Mass Spectrometry—The Early Years

Home , Arthur Jeffrey Dempster, Ernest Rutherford, Eugen Goldstein, Francis William Aston, Frederick Soddy

International Journal of Mass Spectrometry 349–350 (2013) 3–8

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International Journal of Mass Spectrometry

j ournal homepage: www.elsevier.com/locate/ijms

Mass spectrometry—The early years

∗

K.S. Sharma

Department of Physics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2

a r t i c l e i n f o a b s t r a c t

Article history: In 1913 J.J. Thomson constructed his famous positive-ray parabola apparatus at Cambridge and discovered

Received 21 March 2013

two isotopes of neon. He subsequently discovered other isotopes. His work conﬁrmed the concept of

Received in revised form 22 May 2013

isotopes and provided an explanation for deviations of atomic weights determined through chemical

Accepted 23 May 2013

techniques from the “whole number rule”. This achievement marks the beginning of the ﬁeld of mass

Available online 5 June 2013

spectroscopy which is celebrating its 100th anniversary in 2013. His student Aston extended this work by

constructing an instrument that we properly term a mass spectrometer and contributed signiﬁcantly to

Keywords:

our ﬁrst glimpses into the binding energy of the nucleus. Independently, Dempster constructed a similar

Atomic masses

instrument at the University of Chicago also provided contributions to our knowledge of nuclear masses.

Nuclear physics

The birth of this ﬁeld of measurement has its roots in nuclear physics and chemistry. It has grown to be

Mass spectrometry

History the driver of a huge international industry and is utilized as a tool in almost every ﬁeld of science. This

Instrumental paper will recount the early days of the ﬁeld.

1. Introduction Studies of these electrical discharges provided us with our

ﬁrst understanding of the electrical nature of gases and other

Mass spectrometers as their name suggests are instruments substances. In the 1870s, Eugen Goldstein, working at the Berlin

used to analyse beams of ions according to the masses of the ionic Observatory, conducted a series of systematic investigations of

species that are present. It is therefore not surprising that the tech- the constituents of these electrical discharges in a Crookes dis-

nique owes a considerable part of its utility to the techniques of charge tube. He conﬁrmed earlier reports that negatively charged

producing ion beams and the origin of the ﬁeld is linked to studies rays (cathode rays) were emitted from the cathode and travelled

of the electrical nature of matter. The study of electrical discharges towards the anode of the discharge tube. He surmised that these

in gases provided us with the ﬁrst glimpse into this aspect of nature. rays carried energy and could be detected by the ﬂuorescence of

One of the ﬁrst studies of these phenomena was reported in 1675 the glass envelope behind the anode. He also observed that there

by the French astronomer Jean-Felix Picard who observed ﬂashes were also positively charged rays emitted from the anode that trav-

of light in the empty space above the column of mercury in his elled towards the cathode. Holes in the cathode allowed these rays

barometer when the column was agitated [1]. Many investigators to pass through the cathode and excite ﬂuorescence in the glass

tried to determine the cause of the phenomenon. In 1705 Francis envelope of the tube. He named these positive rays “kanalstrahlen”

Hauksbee demonstrated that a small amount of mercury placed in a or canal rays [2]. There were competing explanations of whether

partially evacuated bulb and charged by static electricity could pro- these rays were some form of wave or whether they were made

duce enough light to read by. These events together with advances up of charged corpuscles. Wien deﬂected the canal rays in mag-

in technology set the stage for the development of low-pressure netic and electric ﬁelds and discovered that the positively charged

gas discharge tubes. Heinrich Geissler, a German glassblower, con- rays had a much smaller charge to mass ratio (by a factor of ∼2000)

structed (in 1857) artistic cold-cathode gas discharge tubes that than the cathode rays. Similar studies were conducted by numerous

glowed with many vibrant colours. The technology was further researchers but the results were unclear because of the effects of

developed by French engineer Georges Claude in 1910 and became residual gas pressure inside the discharge tubes, the varying ener-

the basis for the many “neon” signs that we see around us today. gies of the particles and the presence of ions from molecular species

Between 1869 and 1875 William Crookes and others invented and and other contaminants in the gas.

experimented with low pressure discharge tubes that made many

of the scientiﬁc experiments on the nature of these phenomena 2. The ﬁrst mass spectrometers

possible.

Joseph John Thomson (Fig. 1) was born in Manchester in 1856.

He entered Trinity College, Cambridge as a minor scholar in 1876

∗

and became a Fellow of Trinity College in 1880 where he remained

Tel.: +1 204 474 6181; fax: +1 204 474 7622.

E-mail address: [email protected] a member of the College for the rest of his life, becoming Lecturer

4 K.S. Sharma / International Journal of Mass Spectrometry 349–350 (2013) 3–8

Fig. 2. Cathode ray tube used by Thomson in a measurement of e/m for the electron.

From Science Museum. The electrical discharge was struck in the bulb on the left.

The electrical deﬂection was effected by the two plates seen in the middle. The coils

used to create the magnetic ﬁeld are displayed below.

Reproduced with permission from http://www.scienceandsociety.co.uk/results.

asp?image=10324719&itemw=4&itemf=0002&itemstep=1&itemx=4.

conducted by Ernest Rutherford and ﬁnd expression in the atomic

theory constructed by Bohr.

Early work in Chemistry had, through the laws of simple and

multiple proportions in stoichiometry lead Dalton in 1808 to

conclude that chemical reactions appeared to involve the com-

bination of basic elemental entities termed “atoms”. In 1815 the

English chemist, William Prout, noted that atomic weights of the

elements appeared to be nearly integer multiples of the atomic

Fig. 1. J.J. Thomson at work.

Reproduced from http://commons.wikimedia.org/wiki/File:JJ Thomson %28Nobel weight of hydrogen [4]. These developments motivated Thomson

%29.jpg; by the Nobel Foundation, 1906. to search for a basic building block from which atoms could be

constructed. The existence of some elements that notably deviated

from this whole number rule (like neon and chlorine) was known.

in 1883 and Master in 1918. He was Cavendish Professor of Exper- In 1912 another British radiochemist, Frederick Soddy deduced

imental Physics at Cambridge from 1884 to 1918 and Honorary the existence of isotopes for some radioactive elements that he

Professor of Physics, Cambridge and Royal Institution, London. was studying. He was awarded the Nobel Prize in Chemistry, in

Throughout his career Thomson attempted to discover the funda- 1921, for this discovery. From 1905 to 1914 Thomson turned his

mental structure of matter and its basic building blocks. He was attention to the positively charged canal rays. He built a device,

convinced that the study of cathode and anode rays would reveal shown schematically in Fig. 3, [5] that would deﬂect the posi-

these fundamental constituents of positive and negative matter. His tive rays with magnetic and electric ﬁelds. Thomson was trying

work on “vortex rings” as these fundamental particles inspired his to ﬁnd a fundamental corpuscle of positive electricity as he had

investigations of the products of gas discharges. He was noted for found with negative electricity. An experimental proof of the exist-

his skill at ﬁnding interpretations for complicated scientiﬁc obser- ence of these isotopes and an accurate measure of their relative

vations and suggesting new avenues of investigation but did not abundances could be a convincing proof of these theories. His pre-

love the task of carefully constructing scientiﬁc apparatus and the conceptions about the structure of matter and technical challenges

travails of coaxing results from it. His visionary approach to sci- with the instrument initially made the results hard to interpret and

ence combined with the superb experimental skills of men who progress difﬁcult (for a more deﬁnitive account see [6]). He was

worked with him, like Aston and Rutherford, resulted in some very joined by F.W. Aston in 1910 as a research assistant. Aston’s early

important discoveries about the nature of matter. researches on electrical conduction in gas discharges made him an

In 1897, working with a discharge tube with a much improved expert on the construction and operation of discharge tubes and the

vacuum, J.J. Thomson used electric and magnetic ﬁelds to deﬂect phenomena associated with them. Aston’s superb skills as an exper-

cathode rays (see Fig. 2). Through his results he concluded that imental physicist played a major part in the successes that Thomson

the cathode rays were composed of “charges of negative electricity enjoyed with his positive-ray parabola apparatus. In this apparatus

carried by particles of matter” [3]. He was convinced that these Thomson deﬂected the positive rays, simultaneously, in two direc-

particles formed a fundamental constituent of matter. Thomson tions perpendicular to their initial direction of travel using parallel,

was awarded the Nobel Prize in 1906 “in recognition of the great coterminous electric and magnetic ﬁelds. The deﬂected ions were

merits of his theoretical and experimental investigations on the detected on a photographic plate.

conduction of electricity by gases”. He is credited for the discovery Let us assume a perfectly collimated ion beam that is initially

of the electron in his studies of cathode rays in 1897 [3]. The actual travelling in the z direction with a velocity v0. The ions enter a

conﬁrmation of these particles as electrons and a clearer picture region, of length L along the z-direction, where they are acted on

of the structure of matter would come much later in the studies by an electric ﬁeld, E, directed along the positive y-direction, and

K.S. Sharma / International Journal of Mass Spectrometry 349–350 (2013) 3–8 5

Fig. 3. A schematic view of Thomson’s positive ray parabola apparatus. The ions approach from the left and pass through a region of length L where they are deﬂected by an

electric, E, and magnetic, B, field. The subsequently travel a distance D through a field free region before striking a photographic plate. The electric field deflects the ions in

the y-direction while the magnetic ﬁeld deﬂects them in the x-direction.

a magnetic ﬁeld, B, directed in the opposite direction. The ions by Thomson to join him in his work on the positive ray parabola

emerge from this region and travel a further distance D, along the apparatus.

z-axis, where they strike a photographic plate. The coordinates of Thomson encouraged Aston to continue the investigations about

the point of impact on the plate are given by: isotopes. Aston built a series of 3 instruments each with improved

characteristics (Figs. 5 and 6). He employed a gas discharge tube as

L DL 1 an ion source. A very narrow, well collimated ion beam was pro-

x = R 1 − 1 − + (1)

R2 R 2 2 duced using two narrow slits. The ions were then deﬂected ﬁrst by

1 − L /R

a parallel plate deﬂector and subsequently with a magnetic ﬁeld.

Both deﬂections were in the same plane. The combination of the

q E L2 electric and magnetic deﬂections resulted in a ﬁnal location for

y = + LD (2)

m 2 2 the ions on the focal plane of the instrument that depended on

the charge-to-mass ratio of the ion but was independent of the ion

v0 energy. This was the ﬁrst mass spectrometer with energy focussing.

R =

where qB

Aston used the ﬁrst instrument [8] he constructed, in 1919, to fur-

When R L, the deﬂection along the x axis simpliﬁes to:

ther explore the isotopic nature of chemical and the whole number q BDL

x = (3) m v0

From Eqs. (2) and (3) it is easily seen that y ∝ x and each species

of ion present, lands on a locus of points (on a photographic plate)

that form a parabola whose shape is uniquely deﬁned by their

charge to mass ratio. These parabolas were similar to the mass

spectral lines produced by mass spectrometers. These positive ray

spectra allowed an identiﬁcation of the components even if the gas

was contaminated and could be reliable used for chemical anal-

+ +

ysis. With this apparatus Thomson identiﬁed the ions of H , H2 ,

22 20

He and the isotopes Ne and Ne. This was the ﬁrst conﬁrmation

that isotopes of elements existed. Quantitative determination of

isotopic abundances was difﬁcult with the photographic detector

so Thomson modiﬁed the apparatus to include a slit with a faraday

cup behind it to replace the photographic plate. Ions of different

charge-to-mass ratios were brought to the slit sequentially by scan-

ning the magnetic ﬁeld. This electrical detection technique made

the reliable quantitative measurement of the intensities of different

ions possible [7].

Francis William Aston (Fig. 4) was born in Birmingham in 1877.

He attended what is now the University of Birmingham where he

studied Chemistry and Physics. He conducted researches in organic

chemistry and started working on fermentation chemistry. This

lead to his brief employment by W. Butler &Co. Brewery after which

he returned to the University of Birmingham to study Physics as

an associate with Poynting. It was during this period that Aston

turned his attention to gas discharge tubes. He constructed much

of his own apparatus and became adept at the experimental tech-

niques needed to produce the low pressures needed to conduct his

Fig. 4. F.W. Aston.

experiments. The dark space in the discharge, near the cathode,

Reproduced from http://commons.wikimedia.org/wiki/File:Francis William

was named the Aston dark space after him. In 1910 he was invited Aston.jpg; author unknown, 1922.

6 K.S. Sharma / International Journal of Mass Spectrometry 349–350 (2013) 3–8

Fig. 5. Aston’s ﬁrst Mass Spectrometer. The large bulb in the foreground is the gas discharge tube that functioned as the ion source. The pole pieces and the coils for the

magnetic form the background.

Reproduced with permission from http://www.scienceandsociety.co.uk/results.asp?image=10313936&itemw=4&itemf=0001&itemstep=1&itemx=3, 1927.

rule for atomic masses. More than 50 elements were analysed with deviations from the whole number rule were properly interpreted

this instrument and small deviations from the whole number rule as an expression of the binding energy of the nucleus and these

were noted. A large deviation approaching 1% was observed for accurate results made it possible to predict the energies involved

H. Successive instruments with better characteristics were built in nuclear reactions. This launched the ﬁeld of nuclear chemistry.

to explore this effect more carefully. Aston was awarded the Nobel Prize in Chemistry, in 1922, “for his

The second, more reﬁned, instrument designed by Aston [9] was discovery, by means of his mass spectrograph, of isotopes, in a large

capable of a precision of 1 part in 10,000 and incorporated the number of non-radioactive elements, and for his enunciation of

focussing properties of sector electric and magnetic ﬁelds. Using the whole number rule”. In his lecture to the History of Science

the mass of O as a standard (deﬁned to have a mass of 16 units) Committee in 1936 Aston speculated about nuclear reactions and

the ‘packing fractions’ of a large number of elements were deter- nuclear energy.

mined and the results reported in his Bakerian Lecture given in At the same time as the ﬁrst activities of Aston and Thomson

1927. Aston’s third instrument [10] improved the precision of his at Cambridge, Arthur Jeffrey Dempster, a Canadian working at the

measurements by another order of magnitude. At this time the University of Chicago, constructed an instrument that could be

Fig. 6. A replica of Aston’s third mass spectrometer.

Reproduced from http://commons.wikimedia.org/wiki/File:Early Mass Spectrometer (replica).jpg, by Jeff Dahl September 2009.

K.S. Sharma / International Journal of Mass Spectrometry 349–350 (2013) 3–8 7

characterized as the ﬁrst modern mass spectrometer [11]. Demp- design of ion-optical systems for the transport of charged particle

ster was born (into a family that is famous across Canada for its beams as well. As progress was made in ion-optics, quadrupolar

bakeries) in Toronto, Canada in 1886. He received his Bachelor and and other higher order ﬁelds found use in the correction of aberra-

Master degree from the University of Toronto in 1910. He brieﬂy tions. Improved apparatus for vacuum systems, ion sources and the

joined Wien’s group at the University of Wuerzburg to study gas detection of ions became available and the ﬁeld of mass spectrom-

discharges for his doctoral studies but returned to Canada at the etry expanded enormously. The advent of commercial instruments

outbreak of World War I. He completed his doctorate at the Uni- in the 1950s brought mass spectrometers out of specialized labo-

versity of Chicago in 1916 where he replicated Thomson’s parabola ratories and made them a common analytic tool in many ﬁelds.

apparatus and equipped it with a gas discharge ion-source employ- The advances in the design of ion-optical systems were accom-

ing a Wehnelt cathode to produce ions with slower and better panied by the construction of many instruments with ever

deﬁned velocities [12]. An added beneﬁt was that the pressure in increasing performance in Germany, the UK, the United States

the gas discharge tube could be lower and better controlled. Follow- of America, Canada, Japan and other locations worldwide. An

ing a brief service in the army, he joined the Physics Department excellent summary of the progress made can be found in Mass

there in 1919 and constructed the ﬁrst of his mass spectrometers. Spectroscopy by Duckworth, Barber and Venkatasubramanian [16].

Dempster’s ﬁrst mass spectrometer employed the direction

focussing properties of 180 deﬂection in a magnetic ﬁeld. The ions

3. Mass spectrometry in nuclear physics

were produced by surface ionization or electron-bombardment

ion-sources allowing the study of ions from solid samples. The

In the ensuing period, numerous instruments were constructed

accuracy of the mass determination was superior to that obtained

which rapidly furnished highly precise values for the nuclear bind-

by Thomson’s parabola apparatus. While the direction focussing

ing energies for the approximately 340 nuclides that are found

properties of the instrument improved its performance it required

naturally. When combined with other data available from nuclear

a relatively monoenergetic ion beam which limited its applica-

reaction and decay studies this forms a body of accurately known

tion to particular ion sources. Dempster used this instrument for

data on the masses of nuclides that lie at the bottom of the valley

abundance studies of isotopes of magnesium and later of lithium,

of stability which has been called the “backbone of well-known

potassium, calcium and zinc. To investigate elements that were

masses” and reveals considerable detail about the structure of

hard to ionize with standard techniques, Dempster turned to a high

nuclei. Signiﬁcant mass spectrometric contributions were made

frequency oscillating spark source. The large spreads in the ener-

by the groups in Manitoba (headed by H.E. Duckworth and R.C.

gies of the ions so produced lead him to construct an improved

Barber) and the group in Minnesota (headed by W.H. Johnson).

mass spectrometer. Based on calculations performed by Bartky

◦ ◦ The enormous task of examining this huge collection of data and

[13], a 90 electric sector was added to the 180 magnetic sector

extracting a set of self-consistent data was carried out by Mattauch

to construct an instrument that focussed the ions both in direc-

and collaborators in their formulation of the ﬁrst Atomic Mass Eval-

tion and energy. With this instrument Dempster was able to study

235 uation in 1965 [17]. The AME was enthusiastically carried out in

ions from the heavier elements and discovered U. The nuclear

an approximately 4 year cycle by Wapstra till he passed away in

binding energies of these species were soon to be of consider-

2006. It was then conducted by Audi and is currently being carried

able strategic importance to the world. Many North American mass

out by Audi and Wang [18]. The technique was extended to mea-

spectroscopists like Duckworth and Bainbridge found their start in

surements among radioactive nuclei at ISOLDE in the 1970s. In the

Dempster’s work and subsequently spawned productive research

1980s, techniques using Penning traps to measure the cyclotron

programmes of their own. Dempster remained at the University of

frequencies of trapped ions came into use. Since then the focus has

Chicago till his death in 1950. He was appointed the director of the

shifted to detailed studies of the masses of nuclei far from stability

Argonne National Laboratory’s Division of Mass Spectroscopy and

using Penning traps. An excellent review of these techniques can

Crystallography in 1946.

be found in the review by Klaus Blaum [19]. The extreme sensi-

The works of Thomson, Aston, Dempster and Bainbridge were

tivity and their immunity to systematic errors have added to this

conducted despite grave limitations in the available technology and

progress. The highest precision to which the charge-to-mass ratio

were based on rudimentary principles of ion optics. The ﬁrst appli- 11

of an ion is approaching 1 part in 10 [20], 3 orders of magnitude

cation of the focussing properties of a magnetic sector ﬁelds was by

better than the typical result from measurements using conven-

Dempster. These properties were most likely known to Aston but

tional mass spectrometers. These new achievements imply that

are not mentioned in his papers. This situation began to change

new opportunities for the exploration of fundamental physics may

in the 1930s with the work by Herzog that put ion optics on a

be on the horizon.

ﬁrm analytical footing. His approach treated the focussing prop-

erties of electric and magnetic sector ﬁelds in a 1st order, paraxial

approximation that was similar to that used in the design of optical 4. Conclusion

systems. The analysis was extended to 2nd order by for combi-

nations of cylindrical electrostatic analysers and uniform magnetic The search for a model to explain the fundamental structure

ﬁeld sectors by Hintenberger and Koenig [14] who published a table of matter was undertaken by physicists and chemists in the late

of suggested geometries for instruments. The designs described 1800s. The advances made were the result of a combination of

in this table allowed the construction of several notable instru- insights from the results of investigations in both chemistry and

ments including the one constructed by Barber at the University of physics. Several types of instruments and techniques arose from

Manitoba in the early 1960s [15]. With the improvement of com- this work and mass spectrometry is one of them. Elements of mod-

puting capabilities, the approximations were upgraded to include ern deﬂection-type mass spectrometers are recognizable in the

2nd order terms. Matrix methods for calculating the properties of instruments used by Wein, Thomson, Aston and Dempster. They

ion-optical systems were employed by Brown, Wollnik, Enge and all incorporate the deﬂection of charged particles in a combination

others in the 1960s. The analysis was advanced to 3rd order by of electric and magnetic ﬁelds. Thomson‘s positive-ray parabola

Wollnik, Matsuda, Matsuo and others in the 1970s. This progress apparatus was the ﬁrst to have identiﬁable mass spectral lines and

in the systematic description of the trajectories of particles in elec- later incorporated some form of electronic detection for the ion

tric and magnetic ﬁelds made great improvements in the design of current. Aston’s and Dempster’s mass spectrometers bear an even

mass spectrometers possible and found many applications in the stronger resemblance to modern instruments. In 1951 Dempster

8 K.S. Sharma / International Journal of Mass Spectrometry 349–350 (2013) 3–8

was granted a US patent 2,572,600 in 1951 for a “mass spectro- I would also like to acknowledge my many conversations with

graph”. These early instruments can clearly be identiﬁed as the my Ph.D. supervisor Dr. R.C. Barber for instilling in me a sense of

progenitor of modern mass spectrometers. In writing this article the history of this ﬁeld and with the late Dr. H.E. Duckworth who

I have been fairly loose in calling instruments mass spectroscopes, pioneered the ﬁeld of mass measurements in Canada.

mass spectrographs and mass spectrometers. In general I have tried

to reserve the term spectroscopes for those instruments where the References

observations were made directly by eye. Instruments using pho-

[1] J.F. Picard, Journal des Savants (Paris edition) (May) (1676) 112.

tographic plates for a detector are called spectrographs. Where

[2] E. Goldstein, Analen der Physik 300 (1) (1898) 38.

electrical detection is employed I have used the term spectrometer.

[3] J.J. Thomson, Philosophical Magazine 44 (1897) 293.

[4] W. Prout, Annals of Philosophy 6 (1915) 321–330.

Acknowledgements [5] J.J. Thomson, Philosophical Magazine 21 (1911) 225.

[6] I. Falconer, http://www.jstor.org/stable/27757604?origin=JSTOR-pdf; also see

Historical Studies in the Physical and Biological Sciences, vol. 18, no. 2 p. 265

In writing this article I have made use of many resources both (1988).

[7] J.J. Thomson, Philosophical Magazine 24 (1912) 209.

in print and online to try and deﬁne the sequence of events that

[8] F.W. Aston, Philosophical Magazine 38 (1919) 707.

brought mass spectrometry to its current status. I have tried where

[9] F.W. Aston, Proceedings of the Royal Society of London Series A 115 (1927)

possible to identify documents that describe particular advances 487.

but these must necessarily be incomplete in a historical article [10] F.W. Aston, Proceedings of the Royal Society of London Series A 163 (1937)

391.

like this. My apologies if I have omitted some of your favourite

[11] A.J. Dempster, Physical Review 11 (1918) 316.

characters.

[12] Measuring mass: from positive rays to proteins, in: M.A. Grayson (Ed.), ASMS

These are some of the resources that I have found particularly 50th Anniversary Volume, American Society for Mass Spectrometry, Chemical

helpful: Heritage Press, Philadelphia, USA, 2002.

[13] W. Bartky, A.J. Dempster, Physical Review 33 (1929) 1019.

[14] H. Hintenberger, L.A. Koenig, in: J.D. Waldron (Ed.), Advances in Mass Spec-

•

The historical posters prepared by the American Society for trometry, vol. 1, Pergamon Press, London, 1959, p. 16.

[15] R.C. Barber, R.L. Bishop, J.O. Meredith, F.C.G. Southon, P. Williams, H.E. Duck-

Mass Spectrometry (for their 50th anniversary) found online at

worth, P. van, Rookhuyzen, Review of Scientiﬁc Instruments 42 (1971) 1.

http://www.asms.org/publications/historical

[16] H.E. Duckworth, R.C. Barber, V.S. Venkatasubramanian, Mass Spectroscopy, 2nd

•

The information provided on the website for the Nobel Prize: ed., Cambridge University Press, Cambridge, UK, 1986.

www.nobelprize.org [17] J.H.E. Mattauch, W. Thiele, A.H. Wapstra, Nuclear Physics 67 (1965) 1.

• [18] G. Audi, M. Wang, A.H. Wapstra, F.G. Kondev, M. MacCormick, X. Xu, B. Pfeiffer,

Mass Spectroscopy by Duckworth, Barber and Venkatasubrama-

Chinese Physics C(HEP & NP) 36 (12) (2012) 1287.

nian [16]. [19] K. Blaum, Physics Reports 425 (2006) 1.

• [20] W. Shi, M. Redshaw, E.G. Myers, Phys. Rev. A 72 (2005), 022510.

The ever ubiquitous wikipedia.