Jump to content

Isotopes of livermorium

From Wikipedia, the free encyclopedia
(Redirected from Ununhexium-291)

Isotopes of livermorium (116Lv)
Main isotopes[1] Decay
abun­dance half-life (t1/2) mode pro­duct
290Lv synth 9 ms α 286Fl
SF
291Lv synth 26 ms α 287Fl
292Lv synth 16 ms α 288Fl
293Lv synth 70 ms α 289Fl
293mLv synth 80 ms α ?

Livermorium (116Lv) is a synthetic element, and thus a standard atomic weight cannot be given. Like all artificial elements, it has no stable isotopes. The first isotope to be synthesized was 293Lv in 2000. There are six known radioisotopes, with mass numbers 288–293, as well as a few suggestive indications of a possible heavier isotope 294Lv. The longest-lived known isotope is 293Lv with a half-life of 53 ms.[2]

List of isotopes

[edit]


Nuclide
[n 1]
Z N Isotopic mass (Da)[3]
[n 2][n 3]
Half-life[1]
[n 4]
Decay
mode
[1]
Daughter
isotope

Spin and
parity[1]
Excitation energy[n 4]
288Lv[4] 116 172 <1 ms α 284Fl 0+
289Lv[5] 116 173 289.19802(54)# α 285Fl
290Lv 116 174 290.19864(59)# 9(3) ms α 286Fl 0+
291Lv 116 175 291.20101(67)# 26(12) ms α 287Fl
292Lv 116 176 292.20197(82)# 16(6) ms α 288Fl 0+
293Lv 116 177 293.20458(55)# 70(30) ms α 289Fl
293mLv[n 5] 720(290)# keV 80(60) ms α
294Lv[n 5] 116 178 54# ms[6] α ? 290Fl 0+
This table header & footer:
  1. ^ mLv – Excited nuclear isomer.
  2. ^ ( ) – Uncertainty (1σ) is given in concise form in parentheses after the corresponding last digits.
  3. ^ # – Atomic mass marked #: value and uncertainty derived not from purely experimental data, but at least partly from trends from the Mass Surface (TMS).
  4. ^ a b # – Values marked # are not purely derived from experimental data, but at least partly from trends of neighboring nuclides (TNN).
  5. ^ a b This isotope is unconfirmed

Nucleosynthesis

[edit]

Target-projectile combinations leading to Z=116 compound nuclei

[edit]

The below table contains various combinations of targets and projectiles which could be used to form compound nuclei with atomic number 116.

Target Projectile CN Attempt result
208Pb 82Se 290Lv Failure to date
238U 54Cr 292Lv Successful reaction
244Pu 50Ti 294Lv Successful reaction
242Pu 50Ti 292Lv Successful reaction
250Cm 48Ca 298Lv Reaction yet to be attempted
248Cm 48Ca 296Lv Successful reaction
246Cm 48Ca 294Lv Reaction yet to be attempted
245Cm 48Ca 293Lv Successful reaction
243Cm 48Ca 291Lv Reaction yet to be attempted
248Cm 44Ca 292Lv Reaction yet to be attempted
251Cf 40Ar 291Lv Reaction yet to be attempted

Cold fusion

[edit]

208Pb(82Se,xn)290−xLv

[edit]

In 1995, the team at GSI attempted the synthesis of 290Lv as a radiative capture (x=0) product. No atoms were detected during a six-week experimental run, reaching a cross section limit of 3 pb.[7]

Hot fusion

[edit]

This section deals with the synthesis of nuclei of livermorium by so-called "hot" fusion reactions. These are processes which create compound nuclei at high excitation energy (~40–50 MeV, hence "hot"), leading to a reduced probability of survival from fission. The excited nucleus then decays to the ground state via the emission of 3–5 neutrons. Fusion reactions utilizing 48Ca nuclei usually produce compound nuclei with intermediate excitation energies (~30–35 MeV) and are sometimes referred to as "warm" fusion reactions. This leads, in part, to relatively high yields from these reactions.

238U(54Cr,xn)292−xLv (x=4)

[edit]

There are sketchy indications that this reaction was attempted by the team at GSI in 2006. There are no published results on the outcome, presumably indicating that no atoms were detected. This is expected from a study of the systematics of cross sections for 238U targets.[8]

In 2023, this reaction was studied again at the JINR's Superheavy Element Factory in Dubna, in preparation for a future synthesis attempt of element 120 using 54Cr projectiles. One atom of 288Lv was reported; it underwent alpha decay with a lifetime of less than 1 millisecond. Further analysis of the reaction and its cross section are underway.[4]

244Pu(50Ti,xn)294−xLv (x=4)

[edit]

In 2024, this reaction was performed at the LBNL, in preparation for a future synthesis attempt of element 120 using 50Ti projectiles. Two atoms of the known isotope 290Lv were successfully produced.[9][10][11] This was the first successful synthesis of a superheavy element using 50Ti projectiles and an actinide target; the cross section was reported to be 0.44+0.58
−0.28
 pb
.[12]

242Pu(50Ti,xn)292−xLv (x=3,4)

[edit]

In 2024, this reaction was studied at the JINR, as a next step after the successful 238U+54Cr reaction. Two atoms of 288Lv were detected, as well as three atoms of the new alpha-decaying isotope 289Lv. One atom of 289Mc was found in the p2n channel, which was the first time any pxn channel had been detected in a reaction of actinides with 48Ca, 50Ti, or 54Cr projectiles.[5]

248Cm(48Ca,xn)296−xLv (x=2?,3,4,5?)

[edit]

The first attempt to synthesise livermorium was performed in 1977 by Ken Hulet and his team at the Lawrence Livermore National Laboratory (LLNL). They were unable to detect any atoms of livermorium.[13] Yuri Oganessian and his team at the Flerov Laboratory of Nuclear Reactions (FLNR) subsequently attempted the reaction in 1978 and met failure. In 1985, a joint experiment between Berkeley and Peter Armbruster's team at GSI, the result was again negative with a calculated cross-section limit of 10–100 pb.[14]

In 2000, Russian scientists at Dubna finally succeeded in detecting a single atom of livermorium, assigned to the isotope 292Lv.[15] In 2001, they repeated the reaction and formed a further 2 atoms in a confirmation of their discovery experiment. A third atom was tentatively assigned to 293Lv on the basis of a missed parental alpha decay.[16] In April 2004, the team ran the experiment again at higher energy and were able to detect a new decay chain, assigned to 292Lv. On this basis, the original data were reassigned to 293Lv. The tentative chain is therefore possibly associated with a rare decay branch of this isotope or an isomer, 293mLv; given the possible reassignment of its daughter to 290Fl instead of 289Fl, it could also conceivably be 294Lv, although all these assignments are tentative and need confirmation in future experiments aimed at the 2n channel.[17][18] In this reaction, two additional atoms of 293Lv were detected.[19]

In 2007, in a GSI-SHIP experiment, besides four 292Lv chains and one 293Lv chain, another chain was observed, initially not assigned but later shown to be 291Lv. However, it is unclear whether it comes from the 248Cm(48Ca,5n) reaction or from a reaction with a lighter curium isotope (present in the target as an admixture), such as 246Cm(48Ca,3n).[20][21]

In an experiment run at the GSI during June–July 2010, scientists detected six atoms of livermorium; two atoms of 293Lv and four atoms of 292Lv. They were able to confirm both the decay data and cross sections for the fusion reaction.[22]

A 2016 experiment at RIKEN aimed at studying the 48Ca+248Cm reaction seemingly detected one atom that may be assigned to 294Lv alpha decaying to 290Fl and 286Cn, which underwent spontaneous fission; however, the first alpha from the livermorium nuclide produced was missed.[6]

245Cm(48Ca,xn)293−xLv (x=2,3)

[edit]

In order to assist in the assignment of isotope mass numbers for livermorium, in March–May 2003 the Dubna team bombarded a 245Cm target with 48Ca ions. They were able to observe two new isotopes, assigned to 291Lv and 290Lv.[23] This experiment was successfully repeated in February–March 2005 where 10 atoms were created with identical decay data to those reported in the 2003 experiment.[24]

As a decay product

[edit]

Livermorium has also been observed in the decay of oganesson. In October 2006 it was announced that three atoms of oganesson had been detected by the bombardment of californium-249 with calcium-48 ions, which then rapidly decayed into livermorium.[24]

The observation of the daughter 290Lv allowed the assignment of the parent to 294Og and confirmed the synthesis of oganesson.

Fission of compound nuclei with Z=116

[edit]

Several experiments have been performed between 2000 and 2006 at the Flerov Laboratory of Nuclear Reactions in Dubna studying the fission characteristics of the compound nuclei 296,294,290Lv. Four nuclear reactions have been used, namely 248Cm+48Ca, 246Cm+48Ca, 244Pu+50Ti, and 232Th+58Fe. The results have revealed how nuclei such as this fission predominantly by expelling 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. In addition, in comparative experiments synthesizing 294Lv using 48Ca and 50Ti projectiles, the yield from fusion-fission was roughly three times smaller for 50Ti, also suggesting a future use in SHE production.[25]

Retracted isotopes

[edit]

289Lv

[edit]

In 1999, researchers at Lawrence Berkeley National Laboratory announced the synthesis of 293Og (see oganesson), in a paper published in Physical Review Letters.[26] The claimed isotope 289Lv decayed by 11.63 MeV alpha emission with a half-life of 0.64 ms. The following year, they published a retraction after other researchers were unable to duplicate the results.[27] In June 2002, the director of the lab announced that the original claim of the discovery of these two elements had been based on data fabricated by the principal author Victor Ninov. This isotope of livermorium was finally discovered in 2024 by the JINR, in the 242Pu(50Ti,3n) reaction.[5]

Chronology of isotope discovery

[edit]
Isotope Year discovered Discovery reaction
288Lv 2023 238U(54Cr,4n)[4]
289Lv 2024 242Pu(50Ti,3n)[5]
290Lv 2002 249Cf(48Ca,3n)[24]
291Lv 2003 245Cm(48Ca,2n)[23]
292Lv 2004 248Cm(48Ca,4n)[19]
293Lv 2000 248Cm(48Ca,3n)[15]
294Lv ?? 2016 248Cm(48Ca,2n) ?

Yields of isotopes

[edit]

Hot fusion

[edit]

The table below provides cross-sections and excitation energies for hot fusion reactions producing livermorium isotopes directly. Data in bold represent maxima derived from excitation function measurements. + represents an observed exit channel.

Projectile Target CN 2n 3n 4n 5n
48Ca 248Cm 296Lv 1.1 pb, 38.9 MeV[19] 3.3 pb, 38.9 MeV[19]
48Ca 245Cm 293Lv 0.9 pb, 33.0 MeV[23] 3.7 pb, 37.9 MeV[23]

Theoretical calculations

[edit]

Decay characteristics

[edit]

Theoretical calculation in a quantum tunneling model supports the experimental data relating to the synthesis of 293Lv and 292Lv.[28][29]

Evaporation residue cross sections

[edit]

The below table contains various targets-projectile combinations for which calculations have provided estimates for cross section yields from various neutron evaporation channels. The channel with the highest expected yield is given.

DNS = Di-nuclear system; σ = cross section

Target Projectile CN Channel (product) σmax Model Ref
208Pb 82Se 290Lv 1n (289Lv) 0.1 pb DNS [30]
208Pb 79Se 287Lv 1n (286Lv) 0.5 pb DNS [30]
238U 54Cr 292Lv 2n (290Lv) 0.1 pb DNS [31]
250Cm 48Ca 298Lv 4n (294Lv) 5 pb DNS [31]
248Cm 48Ca 296Lv 4n (292Lv) 2 pb DNS [31]
247Cm 48Ca 295Lv 3n (292Lv) 3 pb DNS [31]
245Cm 48Ca 293Lv 3n (290Lv) 1.5 pb DNS [31]
243Cm 48Ca 291Lv 3n (288Lv) 1.53 pb DNS [32]
248Cm 44Ca 292Lv 4n (288Lv) 0.43 pb DNS [32]

References

[edit]
  1. ^ a b c d Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S.; Audi, G. (2021). "The NUBASE2020 evaluation of nuclear properties" (PDF). Chinese Physics C. 45 (3): 030001. doi:10.1088/1674-1137/abddae.
  2. ^ "Livermorium - Element Information (Uses and properties)". rsc.org. Retrieved October 27, 2020.
  3. ^ Wang, Meng; Huang, W.J.; Kondev, F.G.; Audi, G.; Naimi, S. (2021). "The AME 2020 atomic mass evaluation (II). Tables, graphs and references*". Chinese Physics C. 45 (3): 030003. doi:10.1088/1674-1137/abddaf.
  4. ^ a b c "В ЛЯР ОИЯИ впервые в мире синтезирован ливерморий-288" [Livermorium-288 was synthesized for the first time in the world at FLNR JINR] (in Russian). Joint Institute for Nuclear Research. 23 October 2023. Retrieved 18 November 2023.
  5. ^ a b c d Ibadullayev, Dastan (2024). "Synthesis and study of the decay properties of isotopes of superheavy element Lv in Reactions 238U + 54Cr and 242Pu + 50Ti". jinr.ru. Joint Institute for Nuclear Research. Retrieved 2 November 2024.
  6. ^ a b Kaji, Daiya; Morita, Kosuke; Morimoto, Kouji; Haba, Hiromitsu; Asai, Masato; Fujita, Kunihiro; Gan, Zaiguo; Geissel, Hans; Hasebe, Hiroo; Hofmann, Sigurd; Huang, MingHui; Komori, Yukiko; Ma, Long; Maurer, Joachim; Murakami, Masashi; Takeyama, Mirei; Tokanai, Fuyuki; Tanaka, Taiki; Wakabayashi, Yasuo; Yamaguchi, Takayuki; Yamaki, Sayaka; Yoshida, Atsushi (2017). "Study of the Reaction 48Ca + 248Cm → 296Lv* at RIKEN-GARIS". Journal of the Physical Society of Japan. 86 (3): 034201–1–7. Bibcode:2017JPSJ...86c4201K. doi:10.7566/JPSJ.86.034201.
  7. ^ Hoffman, Darleane C.; Ghiorso, Albert; Seaborg, Glenn T. (2000). The Transuranium People: The Inside Story. World Scientific. p. 367. ISBN 978-1-78-326244-1.
  8. ^ "List of experiments 2000–2006" Archived 2007-07-23 at the Wayback Machine
  9. ^ Biron, Lauren (23 July 2024). "A New Way to Make Element 116 Opens the Door to Heavier Atoms". lbl.gov. Lawrence Berkeley National Laboratory. Retrieved 24 July 2024.
  10. ^ Bourzac, Katherine (23 July 2024). "Heaviest element yet within reach after major breakthrough". Nature. doi:10.1038/d41586-024-02416-3. Retrieved 24 July 2024.
  11. ^ Service, Robert F. (23 July 2024). "U.S. back in race to forge unknown, superheavy elements". Science. Retrieved 24 July 2024.
  12. ^ Gates, P. M.; et al. (2024). "Toward the Discovery of New Elements: Production of Livermorium (Z = 116) with 50Ti". Physical Review Letters. 133 (172502). doi:10.1103/PhysRevLett.133.172502.
  13. ^ Hulet, E. K.; Lougheed, R.; Wild, J.; Landrum, J.; Stevenson, P.; Ghiorso, A.; Nitschke, J.; Otto, R.; et al. (1977). "Search for Superheavy Elements in the Bombardment of 248Cm with48Ca". Physical Review Letters. 39 (7): 385–389. Bibcode:1977PhRvL..39..385H. doi:10.1103/PhysRevLett.39.385.
  14. ^ Armbruster, P.; Agarwal, YK; Brüchle, W; Brügger, M; Dufour, JP; Gaggeler, H; Hessberger, FP; Hofmann, S; et al. (1985). "Attempts to Produce Superheavy Elements by Fusion of 48Ca with 248Cm in the Bombarding Energy Range of 4.5–5.2 MeV/u". Physical Review Letters. 54 (5): 406–409. Bibcode:1985PhRvL..54..406A. doi:10.1103/PhysRevLett.54.406. PMID 10031507.
  15. ^ a b Oganessian, Yu. Ts.; Utyonkov, V.; Lobanov, Yu.; Abdullin, F.; Polyakov, A.; Shirokovsky, I.; Tsyganov, Yu.; Gulbekian, G.; Bogomolov, S.; Gikal, B.; Mezentsev, A.; Iliev, S.; Subbotin, V.; Sukhov, A.; Ivanov, O.; Buklanov, G.; Subotic, K.; Itkis, M.; Moody, K.; Wild, J.; Stoyer, N.; Stoyer, M.; Lougheed, R.; Laue, C.; Karelin, Ye.; Tatarinov, A. (2000). "Observation of the decay of 292116". Physical Review C. 63 (1): 011301. Bibcode:2000PhRvC..63a1301O. doi:10.1103/PhysRevC.63.011301.
  16. ^ "Confirmed results of the 248Cm(48Ca,4n)292116 experiment" Archived 2016-01-30 at the Wayback Machine, Patin et al., LLNL report (2003). Retrieved 2008-03-03
  17. ^ Hofmann, Sigurd (2019). "Synthesis and properties of isotopes of the transactinides". Radiochimica Acta. 107 (9–11): 879–915. doi:10.1515/ract-2019-3104. S2CID 203848120.
  18. ^ Hofmann, S.; Heinz, S.; Mann, R.; Maurer, J.; Münzenberg, G.; Antalic, S.; Barth, W.; Burkhard, H. G.; Dahl, L.; Eberhardt, K.; Grzywacz, R.; Hamilton, J. H.; Henderson, R. A.; Kenneally, J. M.; Kindler, B.; Kojouharov, I.; Lang, R.; Lommel, B.; Miernik, K.; Miller, D.; Moody, K. J.; Morita, K.; Nishio, K.; Popeko, A. G.; Roberto, J. B.; Runke, J.; Rykaczewski, K. P.; Saro, S.; Scheidenberger, C.; Schött, H. J.; Shaughnessy, D. A.; Stoyer, M. A.; Thörle-Popiesch, P.; Tinschert, K.; Trautmann, N.; Uusitalo, J.; Yeremin, A. V. (2016). "Review of even element super-heavy nuclei and search for element 120". The European Physical Journal A. 2016 (52): 180. Bibcode:2016EPJA...52..180H. doi:10.1140/epja/i2016-16180-4. S2CID 124362890.
  19. ^ a b c d Oganessian, Yu. Ts.; Utyonkov, V.; Lobanov, Yu.; Abdullin, F.; Polyakov, A.; Shirokovsky, I.; Tsyganov, Yu.; Gulbekian, G.; Bogomolov, S.; Gikal, B.; Mezentsev, A.; Iliev, S.; Subbotin, V.; Sukhov, A.; Voinov, A.; Buklanov, G.; Subotic, K.; Zagrebaev, V.; Itkis, M.; Patin, J.; Moody, K.; Wild, J.; Stoyer, M.; Stoyer, N.; Shaughnessy, D.; Kenneally, J.; Wilk, P.; Lougheed, R.; Il’kaev, R.; Vesnovskii, S. (2004). "Measurements of cross sections and decay properties of the isotopes of elements 112, 114, and 116 produced in the fusion reactions 233,238U, 242Pu, and 248Cm+48Ca" (PDF). Physical Review C. 70 (6): 064609. Bibcode:2004PhRvC..70f4609O. doi:10.1103/PhysRevC.70.064609.
  20. ^ Hofmann, S.; Heinz, S.; Mann, R.; Maurer, J.; Khuyagbaatar, J.; Ackermann, D.; Antalic, S.; Barth, W.; Block, M.; Burkhard, H. G.; Comas, V. F.; Dahl, L.; Eberhardt, K.; Gostic, J.; Henderson, R. A.; Heredia, J. A.; Heßberger, F. P.; Kenneally, J. M.; Kindler, B.; Kojouharov, I.; Kratz, J. V.; Lang, R.; Leino, M.; Lommel, B.; Moody, K. J.; Münzenberg, G.; Nelson, S. L.; Nishio, K.; Popeko, A. G.; et al. (2012). "The reaction 48Ca + 248Cm → 296116* studied at the GSI-SHIP". The European Physical Journal A. 48 (5): 62. Bibcode:2012EPJA...48...62H. doi:10.1140/epja/i2012-12062-1. S2CID 121930293.
  21. ^ Oganessian, Yu. Ts.; Utyonkov, V. (2015). "Super-heavy element research". Reports on Progress in Physics. 78 (3): 036301. Bibcode:2015RPPh...78c6301O. doi:10.1088/0034-4885/78/3/036301. PMID 25746203. S2CID 37779526.
  22. ^ Hoffman, S.; et al. (2012). "The reaction 48Ca + 248Cm → 296116* studied at the GSI-SHIP". European Physical Journal A. 48 (62): 62. Bibcode:2012EPJA...48...62H. doi:10.1140/epja/i2012-12062-1. S2CID 121930293.
  23. ^ a b c d Oganessian, Yu. Ts.; Utyonkov, V.; Lobanov, Yu.; Abdullin, F.; Polyakov, A.; Shirokovsky, I.; Tsyganov, Yu.; Gulbekian, G.; et al. (2004). "Measurements of cross sections for the fusion-evaporation reactions244Pu(48Ca,xn)292−x114 and 245Cm(48Ca,xn)293−x116". Physical Review C. 69 (5): 054607. Bibcode:2004PhRvC..69e4607O. doi:10.1103/PhysRevC.69.054607.
  24. ^ a b c Oganessian, Yu. Ts.; Utyonkov, V. K.; Lobanov, Yu. V.; Abdullin, F. Sh.; Polyakov, A. N.; Sagaidak, R. N.; Shirokovsky, I. V.; Tsyganov, Yu. S.; et al. (2006-10-09). "Synthesis of the isotopes of elements 118 and 116 in the 249Cf and 245Cm+48Ca fusion reactions". Physical Review C. 74 (4): 044602. Bibcode:2006PhRvC..74d4602O. doi:10.1103/PhysRevC.74.044602. Retrieved 2008-01-18.
  25. ^ see Flerov lab annual reports 2000–2006
  26. ^ Ninov, V.; et al. (1999). "Observation of Superheavy Nuclei Produced in the Reaction of86Kr with 208Pb". Physical Review Letters. 83 (6): 1104–1107. Bibcode:1999PhRvL..83.1104N. doi:10.1103/PhysRevLett.83.1104.
  27. ^ Ninov, V.; Gregorich, K.; Loveland, W.; Ghiorso, A.; Hoffman, D.; Lee, D.; Nitsche, H.; Swiatecki, W.; Kirbach, U.; Laue, C.; Adams, J.; Patin, J.; Shaughnessy, D.; Strellis, D.; Wilk, P. (2002). "Editorial Note: Observation of Superheavy Nuclei Produced in the Reaction of ^{86}Kr with ^{208}Pb [Phys. Rev. Lett. 83, 1104 (1999)]". Physical Review Letters. 89 (3): 039901. Bibcode:2002PhRvL..89c9901N. doi:10.1103/PhysRevLett.89.039901.
  28. ^ P. Roy Chowdhury; C. Samanta; D. N. Basu (2006). "α decay half-lives of new superheavy elements". Physical Review C. 73 (1): 014612. arXiv:nucl-th/0507054. Bibcode:2006PhRvC..73a4612C. doi:10.1103/PhysRevC.73.014612. S2CID 118739116.
  29. ^ C. Samanta; P. Roy Chowdhury; D. N. Basu (2007). "Predictions of alpha decay half lives of heavy and superheavy elements". Nuclear Physics A. 789 (1–4): 142–154. arXiv:nucl-th/0703086. Bibcode:2007NuPhA.789..142S. doi:10.1016/j.nuclphysa.2007.04.001. S2CID 7496348.
  30. ^ a b Feng, Zhao-Qing; Jin, Gen-Ming; Li, Jun-Qing; Scheid, Werner (2007). "Formation of superheavy nuclei in cold fusion reactions". Physical Review C. 76 (4): 044606. arXiv:0707.2588. Bibcode:2007PhRvC..76d4606F. doi:10.1103/PhysRevC.76.044606. S2CID 711489.
  31. ^ a b c d e Feng, Z; Jin, G; Li, J; Scheid, W (2009). "Production of heavy and superheavy nuclei in massive fusion reactions". Nuclear Physics A. 816 (1–4): 33–51. arXiv:0803.1117. Bibcode:2009NuPhA.816...33F. doi:10.1016/j.nuclphysa.2008.11.003. S2CID 18647291.
  32. ^ a b Zhu, L.; Su, J.; Zhang, F. (2016). "Influence of the neutron numbers of projectile and target on the evaporation residue cross sections in hot fusion reactions". Physical Review C. 93 (6): 064610. Bibcode:2016PhRvC..93f4610Z. doi:10.1103/PhysRevC.93.064610.