BY THE SHIPTRAP FACILITY PNPI participants of the SHIPTRAP collaboration:
S.A. Eliseev, D.A. Nesterenko, Yu.N. Novikov, and G.K. Vorobjev 1. Introduction One of the intriguing problems of nuclear physics in the second half of the last century was the possible existence of the mysterious island of superheavy stable nuclides with the “magic” proton and neutron numbers Z = 114 and N = 184, respectively. It was thought that this island was situated far off the last known stable nuclides of the Periodic Table of elements. Among many open questions, it is interesting to learn whether the physical-chemical properties of the new elements in this island obey the universal law of periodicity. Besides, the unusual nuclear physical properties of very heavy nuclides (ultra-high spin values and large radii) and of heavy nuclear matter (A ≈ 300), as well as specific nuclear dynamics of their production, engrossed the attention of investigators. Dramatic efforts have been undertaken to reach this enigmatic region by methods of hot and cold complete fusion in heavy ion reactions . In addition, the search for these superheavy elements in nature has also been carried out.
Step-by-step experiments performed over many decades have led to success: a dozen of new elements was discovered by the end of the last century, mainly at the SHIP facility at GSI (Darmstadt) . However, the proton magic number of Z = 114 had not yet been reached. Only at the very beginning of the 21st century, the team from JINR (Dubna) [1, 3] succeeded in discovering nuclides of heavy elements with Z up to Z = 118. Although the doubly-magic nuclide was not observed, the performed activity unambiguously showed that superheavies are not fully unstable as the liquid drop model predicts – the measured half-lives of superheavies typically exceed 1 ms.
The position of the maximal stability (the peak of the island) is still unknown. To identify this peak in experiments, one needs to invent new ingenious methods of production. At the same time, the absolute mass mapping of the known region of superheavies can help to make certain predictions of a possible position of the maximal stability. While this mass landscape is so far unknown, it can be determined by direct measurements of masses of superheavy nuclides. Since all known superheavies have been identified by the α-decay chains and α-decay energies have been measured, an independently measured mass value (i.e., the total binding energy) of one of the nuclides in the α-chain will allow one to determine the masses of all the others. In order to fulfill the mass mapping of the known superheavies, about ten mass values of nuclides in different α-chains should be directly measured . This program of direct mass measurements of transfermium nuclides – as a first foray into the region of transuranium – was developed at the SHIPTRAP facility of GSI with participation of PNPI physicists.
Fig. 1. The scheme of the Penning trap set-up at GSI
The mass mapping can also help to identify new possible semimagic nuclides (e.g., with N = 152, etc.). The semimagic structure of superheavies may be typical for this region due to strong influence of the shell structure effects, which possibly stabilize these very heavy nuclides. However, to recognize irregularities in the mass landscape, a wide mass mapping is needed. The implementation of this program has started at GSI with the use of the ionic Penning trap – the most precise system for mass measurements presently known .
2. The experimental installation The SHIPTRAP facility is a Penning trap system installed behind the velocity filter SHIP, which was used in the past for identification of new elements of the Periodic Table . Thus, the production conditions for transfermium elements are very well known. A schematic overview of SHIPTRAP is given in Fig. 1, and a picture of SHIPTRAP is shown in Fig. 2.
Fig. 2. Overview photo of the SHIPTRAP facility
The nobelium and lawrencium isotopes were produced in fusion-evaporation reactions of Ca ions accelerated to about 4.5 MeV/u with isotopically enriched 206,207,208Pb and 209Bi target nuclides. They were separated from the primary beam by SHIP and sent to SHIPTRAP with the kinetic energy of about 40 MeV. After slowing down by the mylar degrader foils and the 2 mg/cm2-thick titanium entrance window of the gas cell, the ions were stopped in ultrahigh-purity helium gas kept at the pressure of 50 mbar. After extraction from the gas cell, they were cooled, bunched, and accumulated by the radiofrequency quadrupole ion trap (see Fig. 1). Afterwards, the ions were transferred to the double Penning trap system hosted by a superconducting 7 T solenoid magnet. In the first purification trap, the isobars can be separated with a mass resolving power of up to 105. In the second trap, the ions are excited by the external RF field, and the cyclotron frequency is determined with the time-of-flight ion-cyclotron-resonance method. For a successful fit of the resonance curve, at least about 30 ions must be detected. In the case of 256Lr, a resonance with only 48 ion counts took 93 hours. For such a long measurement, the temporal stability of the magnetic field is critical for the accurate mass measurement. To reduce the drift of the cyclotron frequency, active stabilization was implemented for the pressure in the liquid helium cryostat and also for the temperature in the bore of the superconducting magnet. As a result, the drift of only 2∙10–9 per day was obtained .
More precisely, the mass is determined by comparing the cyclotron frequency of the ion of interest with that of a reference ion with the well-known mass. In the present case, the ion of 133Cs+ has the m/q ratio similar to that of doubly-charged nobelium and lawrencium ions. The statistical uncertainty depends on the number of detected ions per resonance and on the Fourier-limit based resolution ≈ 1/, where is the observation time. In addition, the systematic uncertainties of 4.5∙10–8 are taken into account.
The time-of-flight resonance detection technique was used to measure the ion cyclotron frequency,
where q is the charge and B is the magnetic field strength, thus determining the mass m of the ion. The atomic mass value can be determined from the equation:
where meis the electron mass; matomand matom,ref denote the atomic masses; r is the ratio of the cyclotron frequencies r = νc,ref/νc; Z and Zref are the charges of the ion under investigation and of the reference ion, respectively. In the present measurement, doubly-charged nobelium and lawrencium ions were investigated (Z = 2), which led to a decrease of the relative uncertainty. Furthermore, the observation of doubly-charged ions indicates that helium gas in the cell and in the purification trap is of high purity.
For calibration of the magnetic field, singly-charged 133Cs ions from a surface ion source can be chosen as reference. The obtained weighted mean frequency ratios for 252–255No and 255,256Lr are presented in Table 1. The uncertainty includes statistical variations, nonlinear magnetic-field changes and the residual systematic uncertainty. For each nobelium isotope, at least three measurements were performed. The atomic mass matom was determined from the frequency ratios and, thus, the mass excess ME = matom – A was found. The nuclear mass can be derived from the atomic mass according to the relation mnucl(A,Z) = matom(A,Z) – Zme – Be(Z), where mnucl is the nuclear mass and Be(Z) is the electron binding energy for an atom with the atomic number Z.
3. Results As an example, in Fig. 3 we present the time-of-flight cyclotron resonance curves for 254No and 256Lr. Details of all the ions produced and investigated in this work [7, 8] are summarized in Table 1.
Fig. 3. The time-of-flight resonance curves for 254No and 256Lr ions measured by SHIPTRAP
All of our measurements have improved the accuracy of the mass values. Indeed, the earlier uncertainties in the mass of 252No and 254No were decreased by a factor of 1.4 and the masses of 255No, 255Lr and 256Lr were measured for the first time .
For even-even nuclides, the α-decay occurs predominantly from the ground-state to the ground-state. In this case, the directly measured new mass values can be combined with the results of decay spectroscopy to reach higher-Z nuclides in a straightforward way. In particular, a recent study of 270Ds performed at SHIP has discovered the α-decay branch of 262Sg, providing the missing link connecting the decay chain of 270Ds (Z = 110)to 254No. Thus, it will now be possible to determine the mass of 270Ds with an uncertainty of 40 keV and to provide the presently highest-Z anchor point in the SHE region.
Properties of investigated nobelium and lawrencium isotopes
Cross section, nb
For other investigated nuclides, the situation is more complex since the strongest α-decays populate the excited states in the daughter nucleus. For many nuclides, detailed decay-spectroscopy data are either lacking or still inconclusive because unambiguous level schemes are not available. In these cases, the new ground-state mass values from direct mass measurements provide important data. For example, the SHIPTRAP mass value of 255No can be used to determine the masses of its daughters linked by the α-decay (247Cf) and electron capture (247Bk). After evaluation of the recent α-spectroscopy data for the nuclides above 255No, the combination with the mass value of 255No will establish the mass of 271Ds (Z = 110).
Mass estimations of superheavy nuclides linked to odd-odd nuclide are even more complicated than in the cases discussed above. The heaviest radionuclide studied so far by Penning trap mass spectrometry, 256Lr, has only recently been studied by α-decay spectroscopy, and it shows a complex spectrum involving several excited states yet unassigned. In the future, the establishment of the relevant states involved in the α-decay chain starting at 272Rg (Z = 111) will allow us to use the mass of 256Lr as an anchor point to fix the mass of 272Rg. The current moderate mass uncertainty results from just a single measurement done at the lower resolution due to beam-time limitations. In future experiments, it will be improved by an order of magnitude similarly to the other studied isotopes.
The nuclides with the directly measured mass values and their links to superheavies via α-decay chains are shown on the chart of transuranium nuclides in Fig. 4.
of nobelium and lawrencium isotopes (indicated in the squares)
4. Conclusions and outlook The masses of 255No2+ and 255-256Lr2+ nuclides were directly measured with the SHIPTRAP facility for the first time, with the uncertainties ranging down to 15 keV. The masses of 254No and 252No already known from an indirect determination were measured directly, and the previous mass uncertainties were further decreased.The nuclide of 256Lr had the lowest yield (about 10 ions per minute) when investigated at the on-line Penning-trap mass spectrometer. It is the heaviest nuclide of the chart of the nuclides whose mass has ever been measured. Figure 5 shows how much the precision of the measured value is superior to the evaluated one . A combination of the present results with spectrometric data allows one to fix the masses of the nuclides as heavy as 270Ds (Z = 110). Thus, experiments with SHIPTRAP pave the way for investigation of superheavy elements and other very exotic nuclides. The performed investigation can be considered as a first step in the long-term program of the precise mass landscape determination of superheavy nuclides by means of the Penning trap mass spectrometry.
Fig. 5. Comparison of the measured (in this work) and evaluated  mass values of 256Lr
Our further plans concern the extension of the region of measurements towards rutherfordium isotopes. This can be done with the titanium beam, which is now under commissioning at the UNILAC linear accelerator at GSI. As the expected yields of rutherfordium are even smaller than those of lawrencium, suppression of the background becomes an important problem. This problem can be solved by replacement of the gas cell with the cryogenic one  that is currently under construction. However, a dramatic change in sensitivity of SHIPTRAP is expected when the method of the unperturbed Fourier transformation of the ion cyclotron resonance will be implemented.
The authors would like to thank the SHIPTRAP collaboration for invaluable contribution to this work, and especially our coauthors K. Blaum, M. Block, C. Droese, M. Dworschak, F. Herfurth, H.-J. Kluge, E. Minaya-Ramirez and L. Schweikhard for their help and support.
References 1. Yu. Oganessian, J. Phys. G 34, R165 (2007).
2. S. Hofmann and G. Muenzenberg, Rev. Mod. Phys. 72, 733 (2000).
3. Yu.Ts. Oganessian et al., Phys. Rev. Lett. 104, 142502 (2010).
4. Z. Qin et al., Radiochem. Acta 96, 455 (2008).
5. K. Blaum, Yu. Novikov and G. Werth, Contemporary Physics 51, 49 (2010).
6. C. Droese et al., Nucl. Instrum. Meth. A 632, 157 (2011).
7. M. Block et al., Nature 463, 785 (2010).
8. M. Dworschak et al., Phys. Rev. C 81, 064312 (2010).
9. E. Minaya-Ramirez et al. (in preparation).
10. Atomic Mass Evaluation. Nucl. Phys. A 729, 1 (2003).
11. S. Eliseev et al., Nucl. Instr. Meth. B 266, 4475 (2008).