Isotopes of darmstadtium

Darmstadtium (Ds) is a synthetic element, and thus a standard atomic mass cannot be given. Like all synthetic elements, it has no stable isotopes. The first isotope to be synthesized was ²⁶⁹Ds in 1994. There are 7 or 8 known radioisotopes from ²⁶⁷Ds (or ²⁶⁹Ds) to ²⁸¹Ds (with many gaps) and 2 or 3 known isomers. The longest-lived isotope is ²⁸¹Ds with a half-life of 9.6 seconds.

Table

nuclide symbol	Z(p)	N(n)	isotopic mass (u)	half-life	decay mode(s)[n 1]	daughter isotope(s)	nuclear spin
	excitation energy
^267Ds[n 2]	110	157	267.14377(15)#	3(+6−2) µs			9/2+#
^269Ds	110	159	269.14475(3)	230(110) µs [179(+245−66) µs]	α	^265Hs	3/2+#
^270Ds	110	160	270.14458(5)	160(100) µs [0.10(+14−4) ms]	α	^266Hs	0+
^270mDs	1140(70) keV			10(6) ms [6.0(+82−22) ms]	α	^266Hs	(10)(−#)
^271Ds	110	161	271.14595(10)#	210(170) ms	α	^267Hs	11/2−#
^271mDs	29(29) keV			1.3(5) ms	α	^267Hs	9/2+#
^273Ds	110	163	273.14856(14)#	0.17(+17−6) ms	α	^269Hs	13/2−#
^277Ds[n 3]	110	167	277.15591(41)#	4.1 ms[1]	α	^273Hs	11/2+#
^279Ds[n 4]	110	169	279.16010(64)#	0.18(+5−3) s	SF (90%)	(various)
					α (10%)	^275Hs
^281Ds[n 5]	110	171	281.16451(59)#	9.6 s	SF (94%)	(various)	3/2+#
					α (6%)	^277Hs
^281mDs[n 6][n 5]				3.7 min	α	^277mHs

1. Abbreviations:
   SF: Spontaneous fission
2. Unconfirmed isotope
3. Not directly synthesized, occurs in decay chain of ²⁸⁵Fl
4. Not directly synthesized, occurs as decay product of ²⁸³Cn
5. Not directly synthesized, occurs in decay chain of ²⁸⁹Fl
6. This isomer is unconfirmed

Notes

• Values marked # are not purely derived from experimental data, but at least partly from systematic trends. Spins with weak assignment arguments are enclosed in parentheses.
• Uncertainties are given in concise form in parentheses after the corresponding last digits. Uncertainty values denote one standard deviation, except isotopic composition and standard atomic mass from IUPAC, which use expanded uncertainties.

Isotopes and nuclear properties

Nucleosynthesis

Super-heavy 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.^[2]

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.^[3] 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.^[2] The latter is a distinct concept from that of where nuclear fusion claimed to be achieved at room temperature conditions (see cold fusion).^[4]

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 1986. 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.^[5] This reaction was successfully repeated in 2000 by GSI (4 atoms), in 2000^[6][7] and 2004^[8] by the Lawrence Berkeley National Laboratory (LBNL) (9 atoms in total) and in 2002 by RIKEN (14 atoms).^[9] 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.^[5] A fourth decay chain was measured but was subsequently retracted.^[10]

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 8 atoms of ²⁷⁰Ds, relating to a ground state isomer, ²⁷⁰Ds, and a high-spin metastable state, ^270mDs.^[11]

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.^[12]

Hot fusion

In September 1994, the team at Dubna detected a single atom of ²⁷³Ds by bombarding a plutonium-244 target with accelerated sulfur-34 nuclei.^[13]

Experiments have been performed in 2004 at the Flerov Laboratory of Nuclear Reactions in Dubna studying the fission characteristics of the compound nucleus ²⁸⁰Ds, produced through the nuclear 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.^[14] 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 to potentially be recognised as being discovered. Thus, the isotope ²⁸⁰Ds currently remains unknown.^[15][16]

As decay product

List of darmstadtium isotopes observed by decay

Evaporation residue	Observed darmstadtium isotope
^277Cn	^273Ds[17]
^285Fl, ^281Cn	^277Ds[18]
^291Lv, ^287Fl, ^283Cn	^279Ds[19]
^293Lv, ^289Fl, ^285Cn	^281Ds[20]

Darmstadtium has been observed as decay products of copernicium. Copernicium currently has six known isotopes, four of which have been shown to undergo alpha decays to become darmstadtium nuclei, with mass numbers between 273 and 281. Darmstadtium isotopes with mass numbers 277, 279 and 281 to date have only been produced by copernicium nuclei decay. Parent copernicium nuclei can be themselves decay products of flerovium or livermorium. To date, no other elements have been known to decay to darmstadtium.^[16] For example, in 2004, the Dubna team (JINR) identified darmstadtium-281 as a product in the decay of livermorium via an alpha decay sequence:^[20]

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 is currently unknown.

²⁷⁷Ds

In the claimed synthesis of ²⁹³Uuo 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.^[21]

^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). 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^[11]

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.^[20]

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.^[22]

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.^[11]

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 nucleus²⁸⁰Ds. 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).^[23]

Theoretical calculations

Decay characteristics

Theoretical calculation in a quantum tunneling model reproduces the experimental alpha decay half live data.^[24][25] It also predicts that the isotope ²⁹⁴110 would have alpha decay half-life of the order of 311 years.^[26][27]

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	[28]
^232Th	^48Ca	^280Ds	4n (^276Ds)	0.2 pb	DNS	[29]
^230Th	^48Ca	^278Ds	4n (^274Ds)	1 pb	DNS	[29]
^238U	^40Ar	^278Ds	4n (^274Ds)	2 pb	DNS	[29]

References

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14. Flerov lab annual report 2004
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21. see ununoctium
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