Radiation astronomy/Hadrons

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Hadrons are subatomic particles of a type including baryons and mesons that can take part in the strong interaction and may be useful in radiation astronomy.

Hadrons[edit]

A hadron, like an atomic nucleus, is a composite particle held together by the strong force. Hadrons are categorized into two families: baryons (such as protons and neutrons) and mesons.

Baryons[edit]

A baryon is a composite subatomic particle bound together by the strong interaction, whereas leptons are not. The most familiar baryons are the protons and neutrons that make up most of the mass of the visible matter in the universe. Electrons (the other major component of the atom) are leptons. Each baryon has a corresponding antiparticle (antibaryon).

Baryonic matter is matter composed mostly of baryons (by mass), which includes atoms of any sort (and thus includes nearly all matter that may be encountered or experienced in everyday life).

Omegas[edit]

Ω0
c
has a rest mass of 2695.2 ± 1.7 MeV/c2.[1]

Ω
b
has a rest mass of 6071 ± 40 MeV/c2.[1]

Xis[edit]

Ξ0 has a rest mass of 1314.86 ± 0.20 MeV/c2.[1]

Ξ has a rest mass of 1321.71 ± 0.07 MeV/c2.[1]

Ξ0
b
has a rest mass of 5787.8 ± 5.0 ± 1.3 MeV/c2.[1]

Sigmas[edit]

Σ+ has a rest mass of 1189.37 ± 0.07 MeV/c2.[1]

Σ0 has a rest mass of 1192.642 ± 0.024 MeV/c2.[1]

Σ
b
has a rest mass of 5815.5 +0.6 −0.5 ± 1.7 MeV/c2.[1]

Lambdas[edit]

Λ0 has a rest mass of 1115.683 ± 0.006 MeV/c2.[2]

Λ+
c
has a rest mass of 2286.46 ± 0.146 MeV/c2.[2]

On 13 July 2015, the LHCb collaboration at CERN reported results consistent with pentaquark states in the decay of bottom Lambda baryons (Λ0
b
).[3]

Rest mass = 5619.4 ± 0.6 MeV/c2.

Deltas[edit]

Δ++ has a rest mass of 1,232 ± 2 MeV/c2.[2]

Δ+ has a rest mass of 1,232 ± 2 MeV/c2.[2]

Δ0 has a rest mass of 1,232 ± 2 MeV/c2.[2]

Δ has a rest mass of 1,232 ± 2 MeV/c2.[2]

Neutrons[edit]

"Due to the very low energy of the colliding protons in the Sun, only states with no angular momentum (s-waves) contribute significantly. One can consider it as a head-on collision, so that angular momentum plays no role. Consequently, the total angular momentum is the sum of the spins, and the spins alone control the reaction. Because of Pauli's exclusion principle, the incoming protons must have opposite spins. On the other hand, in the only bound state of deuterium, the spins of the neutron and proton are aligned. Hence a spin flip must take place [...] The strength of the nuclear force which holds the neutron and the proton together depends on the spin of the particles. The force between an aligned proton and neutron is sufficient to give a bound state, but the interaction between two protons does not yield a bound state under any circumstances. Deuterium has only one bound state."[4]

The "force acting between the protons and the neutrons [is] the strong force".[4]

"A potential of 36 MeV is needed to get just one energy state."[4]

The width of a bound proton and neutron is "2.02 x 10-13 cm".[4]

"Another possibility [regarding neutron stars, called "baryon matter",] is that in the absence of gravity high-density baryonic matter is bound by purely strong forces. [...] nongravitationally bound bulk hadronic matter is consistent with nuclear physics data [...] and low-energy strong interaction data [...] The effective field theory approach has many successes in nuclear physics [...] suggesting that bulk hadronic matter is just as likely to be a correct description of matter at high densities as conventional, unbound hadronic matter."[5]

"The idea behind baryon matter is that a macroscopic state may exist in which a smaller effective baryon mass inside some region makes the state energetically favored over free particles. [...] This state will appear in the limit of large baryon number as an electrically neutral coherent bound state of neutrons, protons, and electrons in β-decay equilibrium."[5]

Antiprotons[edit]

The antiproton (p, pronounced p-baer) is the antiparticle of the proton. Antiprotons are stable, but they are typically short-lived since any collision with a proton will cause both particles to be annihilated in a burst of energy.

Antiprotons have been detected in cosmic rays for over 25 years, first by balloon-borne experiments and more recently by satellite-based detectors. The standard picture for their presence in cosmic rays is that they are produced in collisions of cosmic ray protons with nuclei in the interstellar medium, via the reaction, where A represents a nucleus:

p + A → p + p + p + A

The secondary antiprotons (p) then propagate through the galaxy, confined by the galactic magnetic fields. Their energy spectrum is modified by collisions with other atoms in the interstellar medium. The antiproton cosmic ray energy spectrum is now measured reliably and is consistent with this standard picture of antiproton production by cosmic ray collisions.[6]

Protons[edit]

A "new type of neutron star model (Q stars) [is such that] high-density, electrically neutral baryonic matter is a coherent classical solution to an effective field theory of strong forces and is bound in the absence of gravity. [...] allows massive compact objects, [...] and has no macroscopic minimum mass."[5]

"Compact objects in astronomy are usually analyzed in terms of theoretical characteristics of neutron stars or black holes that are based upon calculations of equations of state for matter at very high densities. At such high densities, the effects of strong forces cannot be neglected. There are several conventional approaches to describing nuclear forces, all of which find that for a baryon number greater than ~250, a nucleus will become energetically unbound. High-density hadronic matter is not stable in these theories until there are enough baryons for gravitational binding to form a neutron star, typically with a minimum mass ≳ 0.1 M and maximum mass ≲ 3 M."[5]

Mesons[edit]

A meson is a composite subatomic particle bound together by the strong interaction.

Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometre, which is about 2/3 the size of a proton or neutron. All mesons are unstable, with the longest-lived lasting for only a few hundredths of a microsecond. Charged mesons decay (sometimes through intermediate particles) to form electrons and neutrinos. Uncharged mesons may decay to photons.

Mesons are not produced by radioactive decay, but appear in nature only as short-lived products of very high-energy interactions in matter. In cosmic ray interactions, for example, such particles are ordinary protons and neutrons. Mesons are also frequently produced artificially in high-energy particle accelerators that collide protons, anti-protons, or other particles.

In nature, the importance of lighter mesons is that they are the associated quantum-field particles that transmit the nuclear force, in the same way that photons are the particles that transmit the electromagnetic force.

Each type of meson has a corresponding antiparticle (antimeson) in which quarks are replaced by their corresponding antiquarks and vice-versa.

Mesons are subject to both the weak and strong interactions. Mesons with net electric charge also participate in the electromagnetic interaction.

While no meson is stable, those of lower mass are nonetheless more stable than the most massive mesons, and are easier to observe and study in particle accelerators or in cosmic ray experiments. They are also typically less massive than baryons, meaning that they are more easily produced in experiments, and thus exhibit certain higher energy phenomena more readily than baryons composed of the same quarks would.

B mesons[edit]

"The K0-K0 bar, D0-D0 bar, and B0-B0 bar oscillations are extremely sensitive to the K0 and K0 bar energy at rest. The energy is determined by the values mc2 with the related mass as well as the energy of the gravitational interaction. Assuming the CPT theorem for the inertial masses and estimating the gravitational potential through the dominant contribution of the gravitational potential of our Galaxy center, we obtain from the experimental data on the K0-K0 bar oscillations the following constraint: |(mg/mi)K0 - (mg/mi)K0 bar| ≤ 8·10-13, CL=90%. This estimation is model dependent and in particular it depends on a way we estimate the gravitational potential. Examining the K0-K0 bar, B0-B0 bar, and D0-D0 bar oscillations provides us also with weaker, but model independent constraints, which in particular rule out the very possibility of antigravity for antimatter."[7]

"In spite of the apparent parity non-invariance of the ordinary particles, the universe could still be left-right symmetric if [charge conjugation parity] CP were an exact symmetry[11]. But this option is [...] ruled out by experiments on kaons and B-mesons!)."[8]

Upsilon mesons[edit]

A plot of the invariant mass of muon pairs, the peak at about 9.5 GeV is due to the contribution of the Upsilon meson. Credit: Leon Lederman and the E288 collaboration, Fermilab.

The plot on the right shows a peak at about 9.5 GeV due to the Upsilon meson.

Psions[edit]

J/Ψ production is graphed. Credit: Fermilab.

On the right is a graph of the production of psi mesons (psions) at Fermilab.

The "discovery of the psi meson in 1974, independently by Samuel C.C. Ting and Burton Richter [22, 23] [pointed out] its lifetime, which was about a thousand times longer than any other similar particle’s lifetime."[9]

The "SLAC-LBL group looked between a pair of 100-MeV "milestones" and discovered the extremely narrow psi resonance that sent the counting rate up by more than a factor of 100, within the space of 1 MeV and within an observing time interval of 2 hours."[10]

Omega mesons[edit]

Omega meson production:[11]

Omega meson ω(782) decay modes:[11]

  1. Γ1:
  2. Γ2:
  3. Γ3:
  4. Γ4:
  5. Γ5:
  6. Γ6:
  7. Γ7:
  8. Γ8:
  9. Γ9:
  10. Γ10:
  11. Γ11:
  12. Γ12:
  13. Γ13:
  14. Γ14:
  15. Γ15:
  16. Γ16:
  17. Γ17:
  18. Γ18:
  19. Γ19:

Phi mesons[edit]

The phi meson (1020) has a mass of 1019.445 MeV. It decays per[12]

Rho mesons[edit]

Rho mesons occur in three states: ρ+, ρ-, and ρ0.[12] The rest masses are apparently the same at 775.4±0.4 and 775.49±0.34.[12] Decay products are π± + π0 or π+ + π-, respectively.[12]

Eta mesons[edit]

Eta mesons (547.863 ± 0.018 MeV) have the decay schemes:[11]

  1. η :
  2. η :
  3. η :

Eta prime mesons (957.78 ± 0.06 MeV) have the decay schemes:[11]

  1. η' :
  2. η' :

The charmed eta meson ηC(1S) has a rest mass of 2983.6 ± 0.7 MeV.[11]

D mesons[edit]

[13]
D mesons
Particle name Particle
symbol
Antiparticle
symbol
Rest mass (MeV/speed of light|c2) IG JPC S C B' Mean lifetime (s) Commonly decays to

(>5% of decays)

D meson[14]
D+

D
1,869.62 ± 0.20 12 0 0 +1 0 1.040 ± 0.007 × 10−12 See
D+
decay modes
D meson[15]
D0

D0
1,864.84 ± 0.17 12 0 0 +1 0 4.101 ± 0.015 × 10−13 See
D0
decay modes
Strange D meson[16]
D+
s

D-
s
1,968.47±0.33 0 0 +1 +1 0 (5.00±0.07) x 10-13 See
D+
s
decay modes
D meson[17]
D∗+
(2010)

D∗−
(2010)
2,010.27.62 ± 0.17 12 1 0 +1 0 6.9 ± 1.9 × 10−21[a]
D0
+ π+ or


D+
+ π0
D meson[18]
D∗0
(2007)

D∗0
(2007)
2,006.97 ± 0.19 12 1 0 +1 0 >3.1 × 10−22[a]
D0
+ π0 or


D0
+ γ

[a] PDG reports the resonance width (Γ). Here the conversion τ = ħΓ is given instead.

Kaons[edit]

"The muons created through decays of secondary pions and kaons are fully polarized, which results in electron/positron decay asymmetry, which in turn causes a difference in their production spectra."[19]

The "highest energy neutrinos from GRBs mainly come from kaons."[20]

Pions[edit]

Single π0 production occurs "in neutral current neutrino interactions with water by a 1.3 GeV wide band neutrino beam."[21]

"The Gamma-Ray Spectrometer (GRS) on [Solar Maximum Mission] SMM has detected [...] at least two of the flares have spectral properties >40 MeV that require gamma rays from the decay of neutral pions. [Pion] production can occur early in the impulsive phase as defined by hard X-rays near 100 keV."[22]

Gamma-ray "emission matches remarkably well both the position and shape of the inner [supernova remnant] SNR shocked plasma. Furthermore, the gamma-ray spectrum shows a prominent peak near 1 GeV with a clear decrement at energies below a few hundreds of MeV as expected from neutral pion decay."[23]

"If protons are accelerated by the shock wave of a supernova remnant, they could interact with the surrounding interstellar gas to produce short-lived particles called π0 mesons, which in turn would decay to produce γ-rays at very high, TeV, energies (1 TeV = 1012 electron volts)."[24]

Tauons[edit]

"For ultrahigh energies the neutrino spectrum at the detector is influenced by neutrino-nucleon interactions and tauon decays during the passage through the interior of the earth."[25]

Theoretical hadron astronomy[edit]

Def. a strongly interacting particle or a particle which is affected by the strong nuclear force is called a hadron.

Here's a theoretical definition:

Def. astronomy that benefits from a study and detection of hadrons is called hadron astronomy, or hadron radiation astronomy.

Neutrinos[edit]

"Atmospheric neutrinos can interact with the detector producing also hadrons. The most probable of these reactions is the single pion production [20][21]:"[26]

"There is also a small loss due to inelastic hadronic interactions of the decay particles before they are stopped."[26]

The "optical properties of mixtures of PXE [phenyl-o-xylylethane] and derivatives of mineral oils are under investigation [3]."[26]

Strong interactions[edit]

The strong interaction is observable in two areas: on a larger scale (about 1 to 3 femtometers (fm)), it is the force that binds protons and neutrons (nucleons) together to form the nucleus of an atom. On the smaller scale (less than about 0.8 fm, the radius of a nucleon), it is also the force that forms and holds together protons, neutrons and other hadron particles.

In the context of binding protons and neutrons together to form atoms, the strong interaction is called the nuclear force (or residual strong force). The strong interaction obeys a quite different distance-dependent behavior between nucleons.

Unlike the electromagnetic and weak interactions, the strong force does not diminish in strength with increasing distance. After a limiting distance (about the size of a hadron) has been reached, it remains at a strength of about 10,000 newtons, no matter how much farther the distance between hadrons.[27] The force between hadrons remains constant at any distance after the hadrons travel only a tiny distance from each other, and is equal to that needed to raise one ton, which is 1000 kg x 9.8 N = ~ 10,000 N.[27]

The amount of work done against a force of 10,000 newtons (about the weight of a one-metric ton mass on the surface of the Earth) is enough to create particle-antiparticle pairs within a very short distance of an interaction.

The strong force is nearly absent between such hadrons (i.e., between baryons or mesons). In this case, only a residual force called the residual strong force acts between these hadrons, and this residual force diminishes rapidly with distance, and is thus very short-range (effectively a few femtometers).

Hypotheses[edit]

  1. Hadrons can be used in astronomy to discern information about their sources.

See also[edit]

References[edit]

  1. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 J. Beringer et al. (2012) and 2013 partial update for the 2014 edition: Particle summary tables – Baryons
  2. 2.0 2.1 2.2 2.3 2.4 2.5 C. Amsler et al. Particle Data Group (2008). "Review of Particle Physics". Physics Letters B 667 (1): 1. doi:10.1016/j.physletb.2008.07.018. 
  3. R. Aaij et al. LHCb collaboration (2015). "Observation of J/ψp resonances consistent with pentaquark states in Λ0
    b
    →J/ψKp decays". Physical Review Letters 115 (7). doi:10.1103/PhysRevLett.115.072001.
     
  4. 4.0 4.1 4.2 4.3 Giora Shaviv (2013). Giora Shaviv, ed. Towards the Bottom of the Nuclear Binding Energy, In: The Synthesis of the Elements. Berlin: Springer-Verlag. pp. 169–94. doi:10.1007/978-3-642-28385-7_5. ISBN 978-3-642-28384-0. Retrieved 2013-12-19.
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  6. Dallas C. Kennedy (2000). "Cosmic Ray Antiprotons". Proc. SPIE 2806: 113. doi:10.1117/12.253971. https://books.google.com/books?hl=en&lr=&id=8tnDViJoOIYC&oi=fnd&pg=PA438&ots=7WbrnBWJDS&sig=W5AePyLLDvDbnJd43a8wcBRCYe8#v=onepage&f=false. 
  7. Savely G. Karshenboim (2009). "Oscillations of neutral mesons and the equivalence principle for particles and antiparticles". Pis'ma v Zhurnal 'Fizika Ehlementarnykh Chastits i Atomnogo Yadra' 6 (155): 745-53. https://inis.iaea.org/search/search.aspx?orig_q=RN:41133347. Retrieved 2014-10-02. 
  8. R. Foot and Z. K. Silagadze (January 2005). "Supernova explosions, 511 keV photons, gamma ray bursts and mirror matter". International Journal of Modern Physics D Gravitation; Astrophysics and Cosmology 14 (01): 143-52. doi:10.1142/S0218271805006523. https://arxiv.org/pdf/astro-ph/0404515. Retrieved 2017-04-20. 
  9. Simon Apers (2 June 2014). Improving the IceCube sensitivity with a wavelength (PDF). Ghent, Belgium: Universiteit Gent. p. 88. Retrieved 2017-04-20.
  10. Luis W. Alvarez (January 1983). "Experimental evidence that an asteroid impact led to the extinction of many species 65 million years ago". Proceedings of the National Academy of Sciences of the United States of America 80: 627-42. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC393431/pdf/pnas00628-0326.pdf. Retrieved 2017-04-20. 
  11. 11.0 11.1 11.2 11.3 11.4 K.A. Olive et al. (Particle Data Group) (2014). Chinese Physics C38: 090001. http://pdg.lbl.gov/2014/listings/rpp2014-list-omega-782.pdf. Retrieved 2015-02-11. 
  12. 12.0 12.1 12.2 12.3 C. Amsler; et al. (2008). Particle listings (PDF).CS1 maint: Explicit use of et al. (link)
  13. K. Kodama, N. Ushida1, C. Andreopoulos, N. Saoulidou, G. Tzanakos, P. Yager, B. Baller, D. Boehnlein, W. Freeman, B. Lundberg, J. Morfin, R. Rameika, J.C. Yun, J.S. Song, C.S. Yoon, S.H.Chung, P. Berghaus, M. Kubanstev, N.W. Reay, R. Sidwell, N. Stanton, S. Yoshida, S. Aoki, T. Hara, J.T. Rhee, D. Ciampa, C. Erickson, M. Graham, K. Heller, R. Rusack, R. Schwienhorst, J. Sielaff, J. Trammell, J. Wilcox, K. Hoshino, H. Jiko, M. Miyanishi, M. Komatsu, M. Nakamura, T. Nakano, K. Niwa, N. Nonaka, K. Okada, O. Sato, T. Akdogan, V. Paolone, C. Rosenfeld, A. Kulik, T. Kafka, W. Oliver, T. Patzak, and J. Schneps (April 12, 2001). "Observation of tau neutrino interactions". Physics Letters B 504 (3): 218-24. http://www.sciencedirect.com/science/article/pii/S0370269301003070. Retrieved 2014-03-10. 
  14. C. Amsler et al.. (2008): Particle listings –
    D±
  15. C. Amsler et al.. (2008): Particle listings –
    D0
  16. N. Nakamura et al. (2010): Particle listings –
    D±
    s
  17. C. Amsler et al.. (2008): Particle listings –
    D∗±
    (2010)
  18. C. Amsler et al.. (2008): Particle listings –
    D∗0
    (2007)
  19. I. V. Moskalenko and A. W. Strong (February 1, 1998). "Production and propagation of cosmic-ray positrons and electrons". The Astrophysical Journal 493 (2): 694-707. doi:10.1086/305152. http://iopscience.iop.org/0004-637X/493/2/694. Retrieved 2014-02-01. 
  20. K. Asano and S. Nagataki (20 March 2006). "Very High Energy Neutrinos Originating from Kaons in Gamma-Ray Bursts". The Astrophysical Journal Letters 640 (1): L9. doi:10.1086/503291. http://arxiv.org/pdf/astro-ph/0603107.pdf. Retrieved 2014-10-02. 
  21. S. Nakayama, C. Mauger, M.H. Ahn, S. Aoki, Y. Ashie, H. Bhang, S. Boyd, D. Casper, J.H. Choi, S. Fukuda, Y. Fukuda, R. Gran, T. Hara, M. Hasegawa, T. Hasegawa, K. Hayashi, Y. Hayato, J. Hill, A.K. Ichikawa, A. Ikeda, T. Inagaki, T. Ishida, T. Ishii, M. Ishitsuka, Y. Itow, T. Iwashita, H.I. Jang, J.S. Jang, E.J. Jeon, K.K. Joo, C.K. Jung, T. Kajita, J. Kameda, K. Kaneyuki, I. Kato, E. Kearns, A. Kibayashi, D. Kielczewska, B.J. Kim, C.O. Kim, J.Y. Kim, S.B. Kim, K. Kobayashi, T. Kobayashi, Y. Koshio, W.R. Kropp, J.G. Learned, S.H. Lim, I.T. Lim, H. Maesaka, T. Maruyama, S. Matsuno, C. Mcgrew, A. Minamino, S. Mine, M. Miura, K. Miyano, T. Morita, S. Moriyama, M. Nakahata, K. Nakamura, I. Nakano, F. Nakata, T. Nakaya, T. Namba, R. Nambu, K. Nishikawa, S. Nishiyama, K .Nitta, S. Noda, Y. Obayashi, A. Okada, Y. Oyama, M.Y. Pac, H. Park, C. Saji, M. Sakuda, A. Sarrat, T. Sasaki, N. Sasao, K. Scholberg, M. Sekiguchi, E. Sharkey, M. Shiozawa, K.K. Shiraishi, M. Smy, H.W. Sobel, J.L. Stone, Y. Suga, L.R. Sulak, A. Suzuki, Y. Suzuki, Y. Takeuchi, N. Tamura, M. Tanaka, Y. Totsuka, S. Ueda, M.R. Vagins, C.W. Walter, W. Wang, R.J. Wilkes, S. Yamada, S. Yamamoto, C. Yanagisawa, H. Yokoyama, J. Yoo, M. Yoshida, and J. Zalipska (July 2005). "Measurement of single π0 production in neutral current neutrino interactions with water by a 1.3 GeV wide band muon neutrino beam". Physics Letters B 619 (3-4): 255-62. http://arxiv.org/pdf/hep-ex/0408134.pdf?origin=publication_detail. Retrieved 2014-03-22. 
  22. Forrest, D. J., Vestrand, W. T., Chupp, E. L., Rieger, E., Cooper, J. F., & Share, G. H. (August 1985). Neutral Pion Production in Solar Flares, In: 19th International Cosmic Ray Conference. 4. NASA. pp. 146–9. Bibcode:1985ICRC....4..146F. Retrieved 2014-10-01.CS1 maint: Multiple names: authors list (link)
  23. A. Giuliani, M. Cardillo, M. Tavani, Y. Fukui, S. Yoshiike, K. Torii, G. Dubner, G. Castelletti, G. Barbiellini, A. Bulgarelli, P. Caraveo, E. Costa, P.W. Cattaneo, A. Chen, T. Contessi, E. Del Monte, I. Donnarumma, Y. Evangelista, M. Feroci, F. Gianotti, F. Lazzarotto, F. Lucarelli, F. Longo, M. Marisaldi, S. Mereghetti, L. Pacciani, A. Pellizzoni, G. Piano, P. Picozza, C. Pittori, G. Pucella, M. Rapisarda, A. Rappoldi, S. Sabatini, P. Soffitta, E. Striani, M. Trifoglio, A. Trois, S. Vercellone, F. Verrecchia, V. Vittorin, S. Colafrancesco, P. Giommi, and G. Bignami (1 December 2011). "Neutral Pion Emission from Accelerated Protons in the Supernova Remnant W44". The Astrophysical Journal Letters 742 (2): L30. doi:10.1088/2041-8205/742/2/L30. http://arxiv.org/pdf/1111.4868. Retrieved 2014-10-02. 
  24. Felix Aharonian (25 April 2002). "Astronomy: The cosmic accelerator". Nature 416 (6883): 797-8. doi:10.1038/416797a. http://www.nature.com/nature/journal/v416/n6883/full/416797a.html. Retrieved 2017-04-20. 
  25. Hettlage, C.; Mannheim, K. (20-25 September 1999). "Tau Sources in the Sky". AG Abstract Services 15 (04). http://adsabs.harvard.edu//abs/1999AGM....15..I04H. Retrieved 2014-10-02. 
  26. 26.0 26.1 26.2 T. Marrodán Undagoitia, F. von Feilitzsch, M. Göger-Neff, C. Grieb, K. A. Hochmuth, L. Oberauer, W. Potzel, and M. Wurm (1 October 2005). "Search for the proton decay p→ K+ ν in the large liquid scintillator low energy neutrino astronomy detector LENA". Physical Review D 72 (7): 075014. doi:10.1103/PhysRevD.72.075014. http://arxiv.org/pdf/hep-ph/0511230.pdf. Retrieved 2015-06-21. 
  27. 27.0 27.1 Fritzsch, op. cite, p. 164.

External links[edit]