Isotopes of darmstadtium

Darmstadtium (₁₁₀Ds) is a synthetic element, and thus a standard atomic weight cannot be given. Like all synthetic elements, it has no stable isotopes. The first isotope to be synthesized was ²⁶⁹Ds in 1994. There are 11 known radioisotopes from ²⁶⁷Ds to ²⁸¹Ds (with many gaps) and 2 or 3 known isomers. The longest-lived isotope is ²⁸¹Ds with a half-life of 14 seconds. However, the unconfirmed ²⁸²Ds might have an even longer half-life of 67 seconds.^[2]

Isotopes of darmstadtium (₁₁₀Ds)

Main isotopes[1] Decay abun­dance half-life (t1/2) mode pro­duct 279Ds synth 0.2 s α10% 275Hs SF90% – 281Ds synth 14 s SF94% – α6% 277Hs

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List of isotopes

Nuclide [n 1]	Z	N	Isotopic mass (Da)[3] [n 2][n 3]	Half-life[1]	Decay mode[1] [n 4]	Daughter isotope	Spin and parity[1] [n 5][n 6]
	Excitation energy
267Ds[n 7]	110	157	267.14373(22)#	10(8) μs [2.8+13.0 −1.3 μs]	α	263Hs	3/2+#
269Ds	110	159	269.14475(3)	230(110) μs [170+160 −60 μs]	α	265Hs
270Ds	110	160	270.14459(4)	205(48) μs	α	266Hs	0+
270mDs	1390(60) keV			4.3(1.2) ms [3.9+1.5 −0.8 ms]	α (70%)	266Hs	10−#
					IT (30%)	270Ds
271Ds[n 8]	110	161	271.14595(10)#	144(53) ms	SF (75%)	(various)
					α (25%)	267Hs
271mDs[n 8]	68(27) keV			1.7(4) ms [1.63+0.44 −0.29 ms]	α	267Hs
273Ds	110	163	273.14846(15)#	240(100) μs [190+140 −60 μs]	α	269Hs
273mDs[n 7]	198(20) keV			120 ms	α	269Hs
275Ds[4]	110	165	275.15209(37)#	430+290 −120 μs	α	271Hs	3/2#
276Ds[5]	110	166	276.15302(59)#	150+100 −40 μs	SF (57%)	(various)	0+
					α (43%)	272Hs
277Ds[n 9]	110	167	277.15576(42)#	6(3) ms [4.1+3.7 −1.3 ms]	α	273Hs
279Ds[n 10]	110	169	279.15998(65)#	186+21 −17 ms[6]	SF (87%)[6]	(various)
					α (13%)	275Hs
280Ds[n 11]	110	170	280.16138(80)#	360+172 −16 μs[7][8][9]	SF	(various)	0+
281Ds[n 12][n 8]	110	171	281.16455(53)#	14(3) s	SF (90%)	(various)
					α (10%)	277Hs
281mDs[n 13][n 8]	80(240)# keV			0.9(7) ms [0.25+1.18 −0.11 s]	α	277Hs
282Ds[n 14]	110	172	282.16617(32)#	4.2(3.3) min [67+320 −30 s]	α	278Hs	0+
This table header & footer: view

1. ^mDs – 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. Modes of decay:

   SF:	Spontaneous fission

5. ( ) spin value – Indicates spin with weak assignment arguments.
6. # – Values marked # are not purely derived from experimental data, but at least partly from trends of neighboring nuclides (TNN).
7. Unconfirmed isotope
8. Order of ground state and isomer is uncertain.
9. Not directly synthesized, occurs in decay chain of ²⁸⁵Fl
10. Not directly synthesized, occurs as decay product of ²⁸³Cn
11. Not directly synthesized, occurs in decay chain of ²⁸⁸Fl
12. Not directly synthesized, occurs in decay chain of ²⁸⁹Fl
13. Not directly synthesized, occurs in decay chain of ²⁹³Lv, unconfirmed
14. Not directly synthesized, occurs in decay chain of ²⁹⁰Fl, unconfirmed

Isotopes and nuclear properties

Nucleosynthesis

Superheavy elements such as darmstadtium are produced by bombarding lighter elements in particle accelerators that induce fusion reactions. Whereas most of the isotopes of darmstadtium can be synthesized directly this way, some heavier ones have only been observed as decay products of elements with higher atomic numbers.^[10]

Depending on the energies involved, the former are separated into "hot" and "cold". In hot fusion reactions, very light, high-energy projectiles are accelerated toward very heavy targets (actinides), giving rise to compound nuclei at high excitation energy (~40–50 MeV) that may either fission or evaporate several (3 to 5) neutrons.^[11] In cold fusion reactions, the produced fused nuclei have a relatively low excitation energy (~10–20 MeV), which decreases the probability that these products will undergo fission reactions. As the fused nuclei cool to the ground state, they require emission of only one or two neutrons, and thus, allows for the generation of more neutron-rich products.^[10] The latter is a distinct concept from that of where nuclear fusion claimed to be achieved at room temperature conditions (see cold fusion).^[12]

The table below contains various combinations of targets and projectiles which could be used to form compound nuclei with Z = 110.

Target	Projectile	CN	Attempt result
208Pb	62Ni	270Ds	Successful reaction
207Pb	64Ni	271Ds	Successful reaction
208Pb	64Ni	272Ds	Successful reaction
209Bi	59Co	268Ds	Successful reaction
226Ra	50Ti	276Ds	Reaction yet to be attempted
232Th	44Ca	276Ds	Failure to date
232Th	48Ca	280Ds	Successful reaction
233U	40Ar	273Ds	Failure to date[13]
235U	40Ar	275Ds	Failure to date[13]
238U	40Ar	278Ds	Successful reaction
244Pu	34S	278Ds	Successful reaction
244Pu	36S	280Ds	Reaction yet to be attempted
248Cm	30Si	278Ds	Reaction yet to be attempted
250Cm	30Si	280Ds	Reaction yet to be attempted

Cold fusion

Before the first successful synthesis of darmstadtium in 1994 by the GSI team, scientists at GSI also tried to synthesize darmstadtium by bombarding lead-208 with nickel-64 in 1985. No darmstadtium atoms were identified. After an upgrade of their facilities, the team at GSI successfully detected 9 atoms of ²⁷¹Ds in two runs of their discovery experiment in 1994.^[14] This reaction was successfully repeated in 2000 by GSI (4 atoms), in 2000^[15][16] and 2004^[17] by the Lawrence Berkeley National Laboratory (LBNL) (9 atoms in total) and in 2002 by RIKEN (14 atoms).^[18] The GSI team studied the analogous reaction with nickel-62 instead of nickel-64 in 1994 as part of their discovery experiment. Three atoms of ²⁶⁹Ds were detected.^[14] A fourth decay chain was measured but was subsequently retracted.^[19]

In addition to the official discovery reactions, in October–November 2000, the team at GSI also studied the analogous reaction using a lead-207 target in order to synthesize the new isotope ²⁷⁰Ds. They succeeded in synthesising eight atoms of ²⁷⁰Ds, relating to a ground state isomer, ²⁷⁰Ds, and a high-spin metastable state, ^270mDs.^[20]

In 1986, a team at the Joint Institute for Nuclear Research (JINR) in Dubna, Russia, studied the reaction:

²⁰⁹
₈₃Bi + ⁵⁹
₂₇Co → ²⁶⁷
₁₁₀Ds + ¹
₀n

They were unable to detect any darmstadtium atoms. In 1995, the team at LBNL reported that they had succeeded in detecting a single atom of ²⁶⁷Ds using this reaction. However, several decays were not measured and further research is required to confirm this discovery.^[21]

Hot fusion

In the late 1980s, the GSI team attempted to synthesize element 110 by bombarding a target consisting of various uranium isotopes—²³³U, ²³⁵U, and ²³⁸U—with accelerated argon-40 ions. No atoms were detected;^[22] a limiting cross section of 21 pb was reported.^[13]

In September 1994, the team at Dubna detected a single atom of ²⁷³Ds by bombarding a plutonium-244 target with accelerated sulfur-34 ions.^[23]

Experiments were done in 2004 at the Flerov Laboratory of Nuclear Reactions (FLNR) in Dubna studying the fission characteristics of the compound nucleus ²⁸⁰Ds, produced in the reaction:

²³²
₉₀Th + ⁴⁸
₂₀Ca → ²⁸⁰
₁₁₀Ds* → fission

The result revealed how compound nuclei such as this fission predominantly by expelling magic and doubly magic nuclei such as ¹³²Sn (Z = 50, N = 82). No darmstadtium atoms were obtained.^[24] A compound nucleus is a loose combination of nucleons 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 a nuclide, and this number is used by IUPAC as the minimum half-life a claimed isotope must have in order to be recognized as being discovered.^[25][26]

The ²³²Th+⁴⁸Ca reaction was attempted again at the FLNR in 2022; it was predicted that the ⁴⁸Ca-induced reaction leading to element 110 would have a lower yield than those leading to lighter or heavier elements. Seven atoms of ²⁷⁶Ds were reported, with lifetimes ranging between 9.3 μs and 983.1 μs; four decayed by spontaneous fission and three decayed via a two-alpha sequence to ²⁷²Hs and the spontaneously fissioning ²⁶⁸Sg.^[5] The maximum reported cross section for the production of ²⁷⁶Ds was about 0.7 pb and a sensitivity limit an order of magnitude lower was reached. This reported cross section is lower than that of all reactions using ⁴⁸Ca as a projectile, with the exception of ²⁴⁹Cf + ⁴⁸Ca, and it further supports the existence of magic numbers at Z = 108, N = 162 and Z = 114, N = 184.^[5] In 2023, the JINR team repeated this reaction at a higher beam energy and also found ²⁷⁵Ds.^[27] They intend to further study the reaction to search for ²⁷⁴Ds.^[27] The FLNR also successfully synthesised ²⁷³Ds in the ²³⁸U+⁴⁰Ar reaction.^[4]

As decay product

List of darmstadtium isotopes observed by decay

Evaporation residue	Observed darmstadtium isotope
277Cn	273Ds[28]
285Fl, 281Cn	277Ds[29]
291Lv, 287Fl, 283Cn	279Ds[30]
288Fl, 284Cn	280Ds
288Mc, 284Nh, 280Rg ?	280Ds ?
293Lv, 289Fl, 285Cn	281Ds[31]
290Fl, 286Cn ?	282Ds ?[2]

Darmstadtium has been observed as a decay product of copernicium. Copernicium currently has seven known isotopes, four of which have been shown to alpha decay into darmstadtium, with mass numbers 273, 277, and 279–281. To date, all of these bar ²⁷³Ds have only been produced by decay of copernicium. Parent copernicium nuclei can be themselves decay products of flerovium or livermorium. Darmstadtium may also have been produced in the electron capture decay of roentgenium nuclei which are themselves daughters of nihonium and moscovium.^[26] For example, in 2004, the Dubna team (JINR) identified darmstadtium-281 as a product in the decay of livermorium via an alpha decay sequence:^[31]

²⁹³
₁₁₆Lv
→ ²⁸⁹
₁₁₄Fl
+ ⁴
₂He

²⁸⁹
₁₁₄Fl
→ ²⁸⁵
₁₁₂Cn
+ ⁴
₂He

²⁸⁵
₁₁₂Cn
→ ²⁸¹
₁₁₀Ds
+ ⁴
₂He

Retracted isotopes

²⁸⁰Ds

The first synthesis of element 114 resulted in two atoms assigned to ²⁸⁸Fl, decaying to the ²⁸⁰Ds, which underwent spontaneous fission. The assignment was later changed to ²⁸⁹Fl and the darmstadtium isotope to ²⁸¹Ds. Hence, ²⁸⁰Ds remained unknown until 2016, when it was populated by the hitherto unknown alpha decay of ²⁸⁴Cn (previously, that nucleus was only known to undergo spontaneous fission). The discovery of ²⁸⁰Ds in this decay chain was confirmed in 2021; it undergoes spontaneous fission with a half-life of 360 μs.^[7]

²⁷⁷Ds

In the claimed synthesis of ²⁹³Og in 1999, the isotope ²⁷⁷Ds was identified as decaying by 10.18 MeV alpha emission with a half-life of 3.0 ms. This claim was retracted in 2001. This isotope was finally created in 2010 and its decay data supported the fabrication of previous data.^[32]

^273mDs

In the synthesis of ²⁷⁷Cn in 1996 by GSI (see copernicium), one decay chain proceeded via ²⁷³Ds, which decayed by emission of a 9.73 MeV alpha particle with a lifetime of 170 ms. This would have been assigned to an isomeric level. This data could not be confirmed and thus this isotope is currently unknown or unconfirmed.

²⁷²Ds

In the first attempt to synthesize darmstadtium, a 10 ms SF activity was assigned to ²⁷²Ds in the reaction ²³²Th(⁴⁴Ca,4n).^[13] Given current understanding regarding stability, this isotope has been retracted from the table of isotopes.

Nuclear isomerism

The current partial decay level scheme for ²⁷⁰Ds proposed following the work of Hofmann et al. in 2000 at GSI^[20]

²⁸¹Ds

The production of ²⁸¹Ds by the decay of ²⁸⁹Fl or ²⁹³Lv has produced two very different decay modes. The most common and readily confirmed mode is spontaneous fission with a half-life of 11 s. A much rarer and as yet unconfirmed mode is alpha decay by emission of an alpha particle with energy 8.77 MeV with an observed half-life of around 3.7 min. This decay is associated with a unique decay pathway from the parent nuclides and must be assigned to an isomeric level. The half-life suggests that it must be assigned to an isomeric state but further research is required to confirm these reports.^[31] It was suggested in 2016 that this unknown activity might be due to ²⁸²Mt, the great-granddaughter of ²⁹⁰Fl via electron capture and two consecutive alpha decays.^[2]

²⁷¹Ds

Decay data from the direct synthesis of ²⁷¹Ds clearly indicates the presence of two nuclear isomers. The first emits alpha particles with energies 10.74 and 10.69 MeV and has a half-life of 1.63 ms. The other only emits alpha particles with an energy of 10.71 MeV and has a half-life of 69 ms. The first has been assigned to the ground state and the latter to an isomeric level. It has been suggested that the closeness of the alpha decay energies indicates that the isomeric level may decay primarily by delayed isomeric transition to the ground state, resulting in an identical measured alpha energy and a combined half-life for the two processes.^[33]

²⁷⁰Ds

The direct production of ²⁷⁰Ds has clearly identified two nuclear isomers. The ground state decays by alpha emission into the ground state of ²⁶⁶Hs by emitting an alpha particle with energy 11.03 MeV and has a half-life of 0.10 ms. The metastable state decays by alpha emission, emitting alpha particles with energies of 12.15, 11.15, and 10.95 MeV, and has a half-life of 6 ms. When the metastable state emits an alpha particle of energy 12.15 MeV, it decays into the ground state of ²⁶⁶Hs, indicating that it has 1.12 MeV of excess energy.^[20]

Chemical yields of isotopes

Cold fusion

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

Projectile	Target	CN	1n	2n	3n
62Ni	208Pb	270Ds	3.5 pb
64Ni	208Pb	272Ds	15 pb, 9.9 MeV

Fission of compound nuclei with Z = 110

Experiments have been performed in 2004 at the Flerov Laboratory of Nuclear Reactions in Dubna studying the fission characteristics of the compound nucleus ²⁸⁰Ds. The nuclear reaction used is ²³²Th+⁴⁸Ca. The result revealed how nuclei such as this fission predominantly by expelling closed shell nuclei such as ¹³²Sn (Z = 50, N = 82).^[34]

Theoretical calculations

Decay characteristics

Theoretical calculation in a quantum tunneling model reproduces the experimental alpha decay half-live data.^[35][36] It also predicts that the isotope ²⁹⁴Ds would have alpha decay half-life of the order of 311 years.^[37][38]

Evaporation residue cross sections

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	64Ni	272Ds	1n (271Ds)	10 pb	DNS	[39]
232Th	48Ca	280Ds	4n (276Ds)	0.2 pb	DNS	[40]
230Th	48Ca	278Ds	4n (274Ds)	1 pb	DNS	[40]
238U	40Ar	278Ds	4n (274Ds)	2 pb	DNS	[40]
244Pu	36S	280Ds	4n (276Ds)	0.61 pb	DNS	[41]
248Cm	30Si	278Ds	4n (274Ds)	65.32 pb	DNS	[41]
250Cm	30Si	280Ds	4n (276Ds)	3.54 pb	DNS	[41]

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