Main

The chemical characterization of heavy elements at the end of the actinides and of all transactinides, performed to probe their positions in the periodic table4,5,6,7,8,9,10, has been, so far, conducted by rapid chemical separation techniques, such as gas-phase and liquid-phase chromatography. The influence of relativistic effects on electronic orbitals has been inferred indirectly, through a comparison of the chemical properties of the heavy elements with those of their lighter homologues and those predicted by theoretical calculations. The first ionization potential, one of the most fundamental physical and chemical properties of an element, gives direct information about the binding energy of an electron in the outermost electronic orbital of an atom. Accurate IP1 values of heavy elements provide crucial tests for our understanding of their electronic structure. IP1 values of weighable amounts of nuclear-reactor-produced heavy elements up to einsteinium (atomic number Z = 99) have been successfully measured by resonance ionization mass spectroscopy (RIMS)11,12. RIMS was also used in an investigation of fermium (Fm, Z = 100) with a sample of 2.7 × 1010 atoms of 255Fm (half-life T1/2 = 20.1 h). In that experiment, the atomic level structure, but not the IP1, was determined13. Recently, resonance ionization laser ion source (RILIS) studies optimized for short-lived atoms made it possible to determine the IP1 of astatine (At, Z = 85) using 199At (T1/2 = 7.2 s) produced in the proton-induced spallation reaction of uranium14. IP1 values of heavy elements with Z ≥ 100, however, could not be determined experimentally, because production rates drastically decrease for elements as their atomic number increases. The study of these elements therefore requires new techniques, on an atom-at-a-time scale.

The ground-state electronic configuration of Lr is predicted to be [Rn]5f147s27p1/2, in contrast to that of its lanthanide homologue Lu, [Xe]4f146s25d, as the 7p1/2 orbital is expected to be stabilized below the 6d orbital in Lr by strong relativistic effects15,16,17,18,19. The determination of IP1 sheds light on the important role of relativistic effects in heavy elements by comparison with theoretical predictions. For Lr, theory predicts an exceptionally low IP1 value. A sufficiently long-lived and detectable isotope for ionization experiments is 256Lr (T1/2 = 27 s). It is produced at a rate of one atom per several seconds in the fusion-evaporation reaction of a 249Cf target with a 11B beam20. With this constraint, a new and highly efficient experimental set-up based on the ionization and detection of the 256Lr+ ion has been devised and implemented to determine the IP1 value of Lr.

The surface ionization process takes place on a solid surface kept at high temperature, which is coupled to an on-line mass separator; that is, an atom is ionized to the 1+ charge state via the interaction with a solid (metal) surface at high temperature and is selectively mass-separated from nuclear reaction by-products. Figure 1 depicts the experimental set-up schematically. Short-lived 256Lr atoms recoiling off a 249Cf target were promptly transported to the ionization site (ionization cavity) by He/CdI2 gas-jet transport, and surface-ionized 256Lr atoms were extracted and mass-separated. The number of 256Lr ions after the mass-separation was determined by α-particle spectroscopy. Experimental details are provided in the Methods section and in ref. 20.

Figure 1: Schematic experimental set-up used to measure the IP1 of Lr on an atom-at-a-time scale.
figure 1

256Lr atoms produced in the nuclear reaction 249Cf(11B, 4n) are transported (blue line) by the He/CdI2 gas jet to a tantalum ionization cavity via a skimmer component. The 256Lr atoms are ionized on the tantalum surface. The 256Lr+ ions produced are extracted electrostatically from the cavity by the extraction electrode, accelerated by 30 kV, and mass-separated by a dipole magnet. See Methods for details. The number of mass-separated 256Lr+ ions is determined by α-particle spectroscopy at the detector position.

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Based on the Saha-Langmuir equation21,22, an analytical model23 describes the surface ionization process in a hollow tube (cavity)-type ion-source. The ionization efficiency Ieff can be expressed as:

where ϕ is the work function, which is material-dependent, k the Boltzmann constant, T the temperature of the ionizing surface, and N a parameter that depends on the effective number of atom–surface interactions in the cavity. IP1*, the effective IP1, is directly related to IP1 as22:

where Qi and Q0 are the partition functions at a given temperature for the ion and the atom, respectively, which can be calculated using excitation energies and statistical weights of their ground and excited states. Tantalum (Ta) was chosen as the cavity material. The ionization experiments were conducted at T = 2,700 K and 2,800 K. For 256Lr, Ieff values of (33 ± 4)% and (36 ± 7)%, respectively, were determined by the procedure given in ref. 20.

The following procedure was applied to determine the value of the free parameter N in equation (1): short-lived lanthanide and alkali isotopes 142,143Eu, 143Sm, 148Tb, 153,154Ho, 157Er, 162Tm, 165Yb, 168Lu and 80Rb were produced in nuclear reactions of 11B beams with target materials of 136Ce, 141Pr, 142Nd, 147Sm, Eu, 156Gd, 159Tb, 162Dy and Ge, respectively, and their Ieff values were experimentally determined at T = 2,700 K and 2,800 K. Figure 2 shows the Ieff values at 2,700 K as a function of IP1*. The IP1* value for each element was calculated with equation (2). Energies and statistical weights of low-lying states in the ion and the atom of each element were taken from the National Institute of Standards and Technology (NIST) atomic database24. The Ieff values determined for all isotopes were best fitted with equation (1) using N values of 43 ± 3 and 50 ± 3 at T = 2,700 K and 2,800 K, respectively.

Figure 2: The ionization efficiency (Ieff) of various short-lived isotopes as a function of the effective IP1 (IP1*) at 2,700 K.
figure 2

The short-dashed curve is obtained by fitting the experimental data using equation (1), which describes a relationship between Ieff and IP1* in our present system. The position of the measured Ieff value of Lr, (33 ± 4)%, is also shown. From the fitted equation (1) with N = 43 ± 3, IP1* of Lr is calculated to be eV. This corresponds to an IP1 value of eV at 2,700 K. Error bars, ±1s.d.

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The Lr IP1* values of eV and eV were determined from equation (1) at T = 2,700 K and 2,800 K, respectively. The result at 2,700 K is illustrated in Fig. 2. Errors on the IP1* values mainly came from three sources of uncertainty: surface temperatures, Ieff (which is based on counting statistics) and fitting procedures. The Lr IP1 can be calculated from IP1* using equation (2) with Qi and Q0. No experimental data on excited states of the Lr atom and ion are available. Thus, the energies and statistical weights for calculating Qi and Q0 were taken from relativistic Fock space coupled cluster (FSCC) calculations18. The average absolute error for the 20 lowest excitation energies of Lu (where comparison with experiment is possible) was 0.05 eV using the same approach18. We expected a similar accuracy for the predicted transition energies of Lr. The evaluated values of kT ln(Qi/Q0) for Lr at T = 2,700 K and 2,800 K are and , respectively. The errors include uncertainties in the calculated excitation energies indicated in ref. 18, 0.087 eV (700 cm−1) for each state, and in the temperatures. From this, IP1 values of eV and eV were obtained at T = 2,700 K and 2,800 K, respectively. Based on these results, our experimentally determined value for IP1 of Lr is eV.

A theoretical calculation of the IP1 of Lr was also performed, using the relativistic coupled cluster approach with single, double, and perturbative triple excitations (DC CCSD(T)), and corrected for the Breit contribution and Lamb shift (Methods). The calculated 7s27p1/2 level of Lr is lower by ∼180 meV than 7s26d3/2, confirming earlier identification of the former as the atomic ground state. This is due to relativistic effects; a non-relativistic calculation puts the energy of the 7s26d configuration about 2.2 eV below that of 7s27p. To assess the accuracy of our predicted IP1 of Lr, the same approach was applied to its lighter homologue Lu. The calculated ground state of the latter is experimentally confirmed as 6s25d. The Lr+ ion has a closed-shell [Rn]5f147s2 ground-state configuration. The IP1 was obtained by taking the difference between the calculated energies of the neutral state and the 1+ state. The calculated IP1 values are 5.418 eV for Lu and 4.963 eV for Lr. Corrections for the Breit contribution were 6 meV for Lu and −12 meV for Lr, and corrections for the Lamb shift were 0.3 meV for Lu and 16 meV for Lr (ref. 25). The calculated IP1 for Lu is in very good agreement with the experimental IP1 of 5.425871(12) eV (ref. 26); similar accuracy is expected for the calculated IP1 of Lr.

The experimental and calculated IP1 results obtained in our work are shown in Table 1 together with earlier theoretical predictions. It should be noted that the calculated excitation energies of Lr, which we used to get Qi and Q0 values to derive the experimental IP1 from IP1*, were obtained with a method different to the one employed here for the calculation of the IP1 itself. As the two calculations are independent, we can compare the present experimental and theoretical IP1 values. Our experimental result on the first ionization potential of Lr of eV is in excellent agreement with the theoretical value of 4.963(15) eV also obtained in this work.

Table 1 Theoretical and experimental IP1 values of Lr
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Thus, we have experimentally shown that the IP1 of Lr is distinctly lower than that of Lu. Lr, the heaviest actinide, has the lowest IP1 value of all lanthanides and actinides; this quantitatively reflects and confirms the theoretically predicted situation of closed 5f14 and 7s2 shells with an additional weakly-bound electron in the valence orbital. We note that the surface ionization method, successfully applied here to determine the IP1 of Lr, can provide experimental data that can benchmark quantum chemical calculations of the heaviest elements. In addition, it opens up new perspectives on determining basic atomic properties of the superheavy elements.

Methods

Ionization experiments

The set-up consists of a target-recoil chamber coupled to an aerosol gas-jet transport system, a surface ion-source, a mass separator, and a detection system for nuclear decays20. For the Lr experiment, a 249Cf target (thickness 260 μg cm−2) in the target-recoil chamber was irradiated with a 67.9-MeV 11B4+ beam delivered from the Tandem accelerator at the Japan Atomic Energy Agency (JAEA), Tokai20,29. 256Lr atoms, recoiling from the target, attached onto CdI2 particles produced by sublimation of CdI2, were transported to the ionization cavity of the ion-source installed in the Isotope Separator On-Line (JAEA-ISOL)20,30. Before entering the ionization cavity, aerosol particles with the attached 256Lr passed through a skimmer structure, installed to remove the He carrier gas to achieve high vacuum conditions at the ion-source (typically 2 × 10−2 Pa). In the cavity, the aerosol particles were vaporized and 256Lr atoms were surface ionized. The temperature of the cavity was monitored with a calibrated radiation thermometer with ±50 K accuracy. The cavity can be heated up to 2,850 K. Ions were extracted and accelerated by an electrostatic potential of 30 kV. 256Lr+ ions were mass separated in the dipole magnet of the JAEA-ISOL and were transported to the detection device. The nuclear decay of 256Lr was measured with eight pairs of Si PIN photodiodes of a rotating catcher wheel apparatus, MANON (Measurement system of Alpha particle and spontaneous fissioN events ON-line) for efficient α-particle measurements20.

For the short-lived isotope experiments to obtain a relationship between Ieff and IP1* in the present system, various isotopes, 142,143Eu, 143Sm, 148Tb, 153,154Ho, 157Er, 162Tm, 165Yb, 168Lu and 80Rb, were employed. These isotopes were produced in reactions of 11B with targets consisting of 136Ce, 141Pr, 142Nd, 147Sm, Eu, 156Gd, 159Tb, 162Dy and Ge, respectively. Mass-separated ions were collected on an aluminized Mylar tape in a tape transport system installed between the end of the ISOL beam line and the MANON set-up20. A high-purity germanium (HP-Ge) detector was placed at the tape transport system to determine the number of the ions by γ spectroscopy.

Calculation of Ieff and IP1*

To calculate the Ieff value of each isotope, the number of atoms transported to the ion-source was determined by a direct-catch measurement. Nuclear reaction products were directly collected at a separate collection site where their radioactivity was measured before the ISOL experiments. Here, the measurement of 256Lr was performed using another MANON set-up. For the measurements of the other isotopes, aerosol particles from the target recoil chamber were collected on a glass fibre filter. The γ-rays of each isotope on the glass fibre filter were measured using a HP-Ge detector. Because of the low IP1 of Rb, it is justified to assume that the Ieff of 80Rb should be 100% in the surface ionization. By using 80Rb as a reference material, Ieff of the other elements were calculated20.

For a calculation of IP1*, equation (2) is applied to each element. Qi and Q0 in equation (2) are described as follows22,

where and are the statistical weights of the jth quantum state of the ion and the atom, respectively. The j = 0 corresponds to the ground state. Here, and are the energies of excitation to the jth quantum state of the ion and the atom, respectively. Excited states whose excitation energy is much higher than kT can be neglected because is approaching zero. Using equations (3), Qi and Q0 values were calculated. Applying these results to the IP1* value for each element, the IP1 value was calculated by equation (2).

Theoretical calculation

The CCSD(T) calculations of the IP1 of Lu and Lr were carried out using the DIRAC13 computational program package31, in the framework of the relativistic Dirac-Coulomb Hamiltonian. The IP1 was obtained as the difference between the calculated energies of the neutral and mono-cation species. The Faegri dual family basis sets of uncontracted Gaussian-type orbitals32 were used. These sets were augmented by high angular momentum and diffuse functions up to convergence of the calculated IP1 values. The final basis sets consist of 25s 23p 15d 14f 6g 3h orbitals for Lu and 27s 25p 17d 14f 6g 3h 2i orbitals for Lr. The finite nucleus model with Gaussian charge distribution was used33.

Effects of higher-order terms of the Hamiltonian on the IP1 values, namely the frequency independent Breit operator and the Lamb shift, were also calculated. These terms are not implemented in the DIRAC13 program; the Breit term was therefore calculated using the TRAFS-3C (Tel-Aviv Relativistic Atomic Fock Space coupled cluster code) package34, and the Lamb energy shift was obtained by the recently developed effective potential method, implemented in the QEDMOD program25. The contributions of the Breit term were 6 meV for Lu and −12 meV for Lr; the effect of the Lamb shift on the IP was −0.3 meV for Lu and 16 meV for Lr. These contributions were added to the CCSD(T) results obtained using the DIRAC13 program.

Sample size

No statistical methods were used to predetermine sample size.