The mass of an atom incorporates all its constituents and their interactions1. The difference between the mass of an atom and the sum of its building blocks (the binding energy) is a manifestation of Einstein’s famous relation E = mc2. The binding energy determines the energy available for nuclear reactions and decays (and thus the creation of elements by stellar nucleosynthesis), and holds the key to the fundamental question of how heavy the elements can be. Superheavy elements have been observed in challenging production experiments2,3,4, but our present knowledge of the binding energy of these nuclides is based only on the detection of their decay products. The reconstruction from extended decay chains introduces uncertainties that render the interpretation difficult. Here we report direct mass measurements of trans-uranium nuclides. Located at the farthest tip of the actinide species on the proton number–neutron number diagram, these nuclides represent the gateway to the predicted island of stability. In particular, we have determined the mass values of 252-254No (atomic number 102) with the Penning trap mass spectrometer SHIPTRAP5. The uncertainties are of the order of 10 keV/c2 (representing a relative precision of 0.05 p.p.m.), despite minute production rates of less than one atom per second. Our experiments advance direct mass measurements by ten atomic numbers with no loss in accuracy, and provide reliable anchor points en route to the island of stability.
Exotic nuclei at the limits of stability exhibit new features not present in stable nuclei and therefore provide deeper insight into the nature of the nuclear interaction. At the limit of very high proton and neutron numbers is the habitat of the superheavy elements. Far from being simply large clusters of nucleons, these fascinating species owe their very existence to subtle contributions to the nuclear binding energy. As a consequence, an entire island of stability is predicted far above uranium, around proton number Z ≈ 120 and neutron number N = 184 (refs 6–8). These predictions triggered a worldwide search for these remarkable objects that can only be produced in fusion reactions at accelerator facilities. Even with today’s most intense ion beams, the resulting production rates for superheavy elements are minute—for example, about one atom per week for element Z = 112. Nonetheless, discoveries of new elements up to Z = 118 have been reported2,3,4. The centre of the putative island of stability is close, but the final landing has yet to be made and the intriguing question of how heavy the elements can be is still open.
Accurate nuclear binding energies in the region above Z = 100 are crucial for understanding the structure of superheavy elements. They provide important benchmarks for competing theoretical models6,7,8, most of which disagree in their predictions of the island of stability. Remarkably, no binding energies in the region of superheavy elements have ever been measured directly. Our knowledge comes exclusively from measurements of the decay products en route to lighter species. The reconstruction of binding energies from these decay chains introduces significant uncertainties, in particular for odd-even nuclei where the α-decay often includes excited states. First, the already large statistical uncertainties rapidly accumulate according to error propagation with increasing distance to the well-known reference nuclides. Second, the uncertainties of the population of the nuclear states, of their ordering, and of the transition energies between them, all contribute to the total uncertainties of the resulting masses and corresponding systematic errors cannot be excluded. Therefore, direct mass measurements with high precision using Penning traps are of utmost importance to ensure that the mass values are accurate.
In contrast to the mass differences obtained from nuclear-decay spectroscopy, Penning-trap mass measurements directly yield binding energies. Moreover, they provide outstanding accuracy, which is superior to that of other mass measurement techniques. Relative mass uncertainties of δm/m ≈ 10-11 have been achieved for stable nuclides9 and down to δm/m ≈ 10-9 for short-lived exotic species10. In addition, Penning traps allow experiments on single particles at rest under perturbation-free conditions. Thus, they have been used for high-precision measurements of fundamental constants, such as the electron mass and magnetic moment and the fine-structure constant11. Several Penning-trap facilities have come on-line recently, particularly for short-lived nuclides12,13. Owing to their accuracy and very high resolving power they have also contributed to, for example, the spin-parity assignment of ground-state configurations14 and the discovery of new isomers15 and isotopes16. However, no such measurement had been performed for elements above uranium before the present study.
The double Penning-trap mass spectrometer SHIPTRAP5 at GSI Helmholtzzentrum für Schwerionenforschung was conceived for this type of experiment. It is installed behind the velocity filter SHIP where the elements with Z = 107–112 were discovered2. Since 2005, high-precision mass measurements of about 60 rare isotopes have been performed with SHIPTRAP, contributing to nuclear astrophysics studies17,18 and the mapping of the proton drip line by direct mass measurements of proton-unbound nuclei19.
In August 2008, SHIPTRAP made the first foray into the region of trans-uranium elements, performing high-precision mass measurements of the nobelium isotopes 252–254No (Z = 102). These rare isotopes were produced by fusion reactions of 48Ca projectiles with 206–208Pb targets. In the case of 252No, less than one ion per second was entering the SHIPTRAP gas cell after separation by the velocity filter SHIP from the primary beam of 6 × 1012 particles per second. The exotic particles were slowed down and thermalized in high-purity helium gas at a pressure of 60 mbar. Mainly doubly-charged ions were extracted from the gas cell within a few milliseconds by a combination of static and oscillating electric fields with continuous gas flow. They were cooled, accumulated and bunched by radio frequency quadrupole structures before the injection into a purification Penning trap inside a 7-T superconducting solenoid. Here, a mass-selective buffer-gas cooling technique with a resolving power of about 50,000 was applied. The mass-selected ion sample was transferred into a precision Penning trap situated in the same solenoid. A time-of-flight resonance detection technique20 was used to measure the ion cyclotron frequency, νc = qB/(2πm) (where q is the charge and B is the magnetic field strength), from which the mass m of the ion was determined. As an example, a cyclotron resonance of 253No2+ is shown in Fig. 1. One such measurement took about four hours. For calibration of the magnetic field, singly charged 133Cs+ ions from a surface ion source were chosen as reference. The weighted mean frequency ratios νc(133Cs+)/νc(252No2+) = 0.948376768(126), νc(133Cs+)/νc(253No2+) = 0.952144941(51) and νc(133Cs+)/νc(254No2+) = 0.955908553(58) were obtained. The uncertainty includes statistical variations, nonlinear magnetic-field changes5, and a residual systematic uncertainty21. For each nobelium isotope at least three measurements were performed. From the frequency ratios the atomic mass mA was determined and thus the mass excess, ME = m - A u (where A is the mass number and u the unified atomic mass unit), was found to be ME(252No) = 82,850(31) keV/c2, ME(253No) = 84,356(13) keV/c2 and ME(254No) = 84,733(14) keV/c2. The nuclear mass can be derived from the atomic mass according to the relation22 mN = mA – Zme + Be(Z), where mN and me are the nuclear and electron mass, respectively, and Be(Z) is the electron binding energy for an atom with atomic number Z. There are no experimental data for the total electron binding energies of trans-uranium elements, but calculations for nobelium22 yield Be(Z = 102) ≈ 1 MeV. The uncertainty of the calculation is difficult to quantify but is estimated to be smaller than our experimental uncertainty for the atomic mass.
The investigated nobelium isotopes have isomeric states23,24,25. However, the overall ion-preparation time of about 500 ms ensured that even the long-lived K-isomers in 252No and 254No had decayed before the ions reached the precision trap. Therefore, we have measured unambiguously the mass of the ground state in all cases.
For the most recent atomic-mass evaluation (AME)22, before the present measurements, the masses of 252–254No were deduced from spectroscopy data26,27,28 of the corresponding decays 252–254No(α)248–250Fm. In the even-even nuclides, the observed α-decay connects ground state to ground state and thus the mass determination is straightforward, resulting in uncertainties of 13 keV for 252No and 18 keV for 254No. As discussed above, the situation is more complex for 253No. Its α-decay chain involves excited states in 249Fm and 245Cm whose energies and ordering were mostly unknown, resulting in an estimated mass uncertainty of 100 keV. Recently, a level scheme for the 253No decay has been established, indicating that the strongest α-transition populates an excited state in 249Fm at about 280 keV (ref. 29). However, the 253No ground-state mass was still ambiguous owing to insufficient knowledge of a low-lying excited state in the granddaughter 245Cm that decays by internal conversion. The direct mass measurements by SHIPTRAP are free from such ambiguities.
The SHIPTRAP results for all three nobelium isotopes are compared to the results from the latest AME (AME2003; ref. 22) in Fig. 2. They agree within their uncertainties, and provide the first independent confirmation of these mass values based on experimental Qα values (where Qα is the energy equivalent to the mass difference between mother and daughter nuclide in α-decay). In the case of 253No the uncertainty was reduced by a factor of five, and the mass is now unambiguously fixed. The new nobelium masses serve as accurate reference points in this mass region. For example, the masses of heavier nuclides, at present not accessible with our technique owing to their short half-lives, are connected by α-decay links (compare Fig. 3). The decay chains passing through the investigated nobelium isotopes reach all the way up to darmstadtium (Ds, Z = 110). In addition, we can determine the neutron pairing energy Δn , a very important quantity for nuclear models, from the three-point mass difference30 Δn(Z,N) = (-1) N [m(Z,N - 1) - 2m(Z,N) + m(Z,N + 1)]/2 from the three measured masses of consecutive nuclides. We obtain a value of Δn(Z = 102, N = 151) = -1/2[m(252No) - 2m(253No) + m(254No)] = 565(21) keV.
Whereas previous high-precision direct mass measurements were limited to the elements up to uranium (Z = 92), our work has extended them to Z = 102. Furthermore, our work opens up many new perspectives for the observation of very heavy elements with traps. In addition to mass measurements, laser spectroscopic studies will become possible. These allow the study of relativistic effects that strongly influence the atomic structure of the very heavy nuclides, as well as studies of nuclear properties such as spins, charge radii and nuclear moments independently of a particular nuclear model. The identification of new elements, at present based on the observation of long decay chains ending in known nuclides, is an example where mass spectrometry in combination with laser spectroscopy yielding Z-information will provide a new approach. This is particularly important when the decay chains end by spontaneous fission before the region of known nuclides is reached, as for most chains of Z = 114–118 nuclides observed at Dubna4. Some of these chains end in isotopes of rutherfordium and dubnium that are sufficiently long-lived to be accessed with SHIPTRAP. In addition, this identification method will be applicable to very long-lived superheavy elements where the decay-correlation identification will no longer be applicable.
In summary, we have performed the first direct mass measurements of the nobelium isotopes 252–254No with relative uncertainties of about 0.05 p.p.m. The isotope 252No is the lowest-production-rate radionuclide whose mass has been measured with a Penning trap, and 254No is the heaviest radionuclide for which a direct mass measurement has been performed. The new mass values provide accurate reference points in the region above Z = 100 that can act as benchmarks for theoretical models. In combination with experimental Qα values, these anchor points reach to the superheavy elements. Thus, even the masses of short-lived neutron-deficient isotopes of such elements, at present not accessible for a direct mass measurement, can be determined accurately. The application of low-energy techniques to trans-uranium elements opens the door to novel experiments in our approach to the superheavy island of stability. One of the next goals of SHIPTRAP is to extend the accurate direct mass determinations to the transactinide region, starting with long-lived rutherfordium isotopes that terminate decay chains originating from Z = 116.
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We thank D. Lunney for help with the preparation of the manuscript. The project was supported in part by the German Federal Ministry of Education and Research, the Max-Planck Society, and the Helmholtz Association. D.R. acknowledges support from Junta de Andalucia.
Author Contributions M.B. and M.D. performed the data analysis. M.B., K.B. and L.S. prepared the manuscript. All authors helped to perform the experiment, discussed the results, and commented on the manuscript at all stages.
The authors declare no competing financial interests.
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Block, M., Ackermann, D., Blaum, K. et al. Direct mass measurements above uranium bridge the gap to the island of stability. Nature 463, 785–788 (2010) doi:10.1038/nature08774
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