The spectral linewidth of 5. However, such a linewidth completely masked the ground-state hyperfine splitting, essential for the spin and quadrupole moment determination. Finally, low-temperature and low-pressure conditions were obtained in the supersonic jet, where laser ionization and spectroscopy studies on the , Ac isotopes were performed. The hfs of Ac obtained in the jet experiments is compared with the in-gas-cell results in Fig. The reduction of both collisional and temperature-associated broadening in the jet experiments led to a fold improvement of the spectral resolution, which enabled a precise fitting of the ground-state hfs, as shown in Fig.
Even with this small duty cycle, the efficiency was similar to that in the gas-cell studies. The experimental systematic uncertainties originate from the instability and nonlinearity of the different wavelength meters used in the three experiments and from the pressure dependence in case of the in-gas-cell data. Out of these isotope-dependent atomic observables, we could deduce a number of nuclear ground-state properties for the different isotopes, also given in Table 2. The spectral resolution obtained in the offline and in-gas-jet measurements, made it possible to unambiguously determine the nuclear spins I of the isotopes investigated.
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The in-gas-cell data for , Ac does not enable a firm spin assignment. Based on the observed experimental trend in the magnetic moments of ,, Ac see Fig. The values obtained after applying the additivity rule dashed lines using the indicated spin and nucleon configuration are also shown for the odd—odd isotopes. The literature values are taken from ref. As B 0 and V zz depend only on the electronic configuration and not on the specific isotope, one can usually circumvent this by means of a scaling relation with experimentally measured hyperfine-splitting constants and the independently measured magnetic dipole or electric quadrupole moment of a known isotope.
The uncertainty on these values reflects the s. Although the obtained values are in agreement with the literature values and have similar error bars, they are more reliable as they are based on superior experimental input and advanced atomic model calculations. Using these values as reference, the magnetic dipole moments were deduced for — Ac from the in-gas-cell measurements and for , Ac, with a higher precision, from the in-gas-jet measurements. Only with the in-gas-jet method could the electric-quadrupole moments for , Ac be obtained.
The errors from the Ac reference values are not propagated, leaving the possibility for later improvements of the obtained results once the moments of Ac can be measured in an independent way or the precision of atomic model calculations is improved. In Fig. For the odd—odd , Ac isotopes, the results are also compared with values from the additivity relation using the magnetic moment of , Ra refs 22 , 23 , respectively, and the magnetic moment of Ac.
Both calculations are further explained in the Methods section. Further developments on atomic theory or an independent measurement of the magnetic dipole moment in Ac are needed to clarify this discrepancy. As shown in Fig.
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The isotope shift originates from the change in nuclear mass A and nuclear charge distribution. This will be discussed in detail in a forthcoming publication. Spatial constraints and limitations of the pumping system in the present setup prevented a high-quality jet formation and, as a consequence, an optimal laser-atom overlap in space and time.
These will be overcome in future experiments when dedicated IGLIS setups are in operation at new-generation radioactive beam facilities see for example, ref. Table 1 compares the presently obtained in-gas-jet performance third column with the projected performance of the technique under optimal conditions fourth column , which also include a new gas-cell design with better transport and extraction characteristics As the technique is based on laser spectroscopy, fundamental atomic properties such as ionization potentials, transition energies and rates can also be determined.
The advantages of this, now proven, approach are obvious when compared with the low-resolution in-source 7 , 31 or in-gas-cell 8 , 10 approach but are also evident when compared with the collinear laser spectroscopy technique 9 , 32 , which has a superior spectral resolution but is ultimately limited by the production mechanism of the desired radioactive ion beam and needs at least ions per second. All radioactive isotopes with published optical data are shown with orange squares on the nuclear chart in Fig. One notices a rather sudden dearth of radionuclides which have been probed as one enters the actinide region and beyond.
This echoes a number of significant obstacles in accessing the heaviest of elements including low production cross-sections, strongly competing reaction channels and limited atomic information mainly due to a lack of stable or long-lived isotopes. The reach of the IGLIS technique, based on the projected performance of the in-gas-jet method see Table 1 and on experimental and estimated cross sections blue and green squares, respectively , can be seen in the inset of Fig.
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Furthermore, in the medium-mass region the in-gas-jet laser ionization and spectroscopy method can also be used to study those nuclei, which are inaccessible to conventional laser-spectroscopy techniques, owing to the physico-chemical properties of the involved elements, such as the refractory elements around molybdenum and tantalum. Chart of nuclides showing the current status of the isotopes investigated by optical spectroscopy 9. In the blow-up of the actinide and heavier mass region, blue green squares are isotopes that, based on experimental calculated cross-sections, can be produced in sufficient amounts to be studied by the IGLIS technique.
In conclusion, the feasibility and impact of the in-gas-jet laser ionization and spectroscopy method have been demonstrated on-line by measuring nuclear and atomic properties of the short-lived isotopes Ac and Ac. The obtained efficiency and spectral resolution demonstrate that basic ground- and isomeric-state nuclear properties of heavier actinides and eventually super-heavy elements, as well as their atomic properties, can be determined to high precision. The technique presented has also far reaching consequences for the exploration of the refractory elements, so far hardly accessible to high-resolution laser spectroscopy techniques.
In addition, the highly selective ionization enables the production of high-quality, high-purity isotopic and isomeric radioactive ion beams that can be used for other applications in nuclear physics, chemistry and astrophysics, as well as in atomic physics. We chose the transition from the ground state 6 d 7 s 2 at We characterized in detail the hfs of eight transitions of actinium including that at The short-lived , Ac and , Ac isotopes were produced at the Leuven Isotope Separator On Line facility in the fusion reaction of 0.
For the determination of the efficiency of the in-gas-cell and in-gas-jet technique, the experimental cross-sections from refs 29 , 36 were used. The change in cross-section as a function of the energy loss of the neon beam in the target was taken into account to calculate the production rate. More information on the preparation of the experiments can be found in ref. To characterize the frequency shift due to atom—atom interactions in the high-pressure gas-cell environment, we scanned the singlet hyperfine transition in Ac number VI in Fig. The Gaussian linewidth contribution reported in Table 2 was calculated from the gas temperature and the laser linewidth 1.
Dedicated spectra of the triplet, doublet and singlet multiplets see Fig. This enabled to separate the contributions of collisional broadening and the natural linewidth Lorentz from temperature-associated, laser linewidth and gas-jet divergence broadening Gauss , see Table 2. For the spectroscopic measurements, the energy per pulse of the first step was set around 0. The efficiency in the in-gas-cell experiments, where in contrast all atoms are irradiated, is comparable with the in-gas-jet result.
This points to collisional de-excitation losses in the ionization process due to the high-pressure environment. For the high-resolution data obtained in the offline and in the gas-jet experiments, the fitting procedure converged only for a particular spin value. This made an unambiguous spin assignment for the isotopes ,, Ac possible. We obtained the hfs constants, a and b , and the centre of gravity of the hfs for each isotope from least-square minimization fits of a peak Voigt profile to the data points.
We deduced the magnetic dipole moment of the short-lived actinium isotopes from the scaling relation. The experimentally observed levels were identified and subsequently their hyperfine coupling constants a and b were calculated. Furthermore, we determined the isotope-shift parameters M and F for the transition at Virtual excitations from a set of reference configurations to a systematically enlarged set of up to five layers of correlation orbitals with angular momenta up to g are used to generate the multiconfiguration basis.
Here we took single, double and triple excitations from the valence shells into account. Core-valence correlation was accounted for by performing single excitations from the 6 p -shell together with a second excitation from one of the valence shells. Furthermore, core polarization was also included in our calculations by including single excitations from all core orbitals into the active space.
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In a subsequent step, the obtained wave functions were used to extract the isotope-shift parameters and the hyperfine coupling constants a and b. The mass-shift constant M was obtained by calculating the expectation value of the relativistic recoil operator in the generated eigenfunctions as described in ref.
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A series of configuration interaction calculations was performed to obtain the isotope-shift between different isotopes for a model nucleus. Subsequently, the field-shift was extracted from these differences in the transition energy. This method, applied to other elements as heavy as polonium 41 , 42 , resembles the experimental approach and we refer to ref. Several independent calculations were carried out and the resulting differences were used to estimate the uncertainties.
This in turn implied tuning of the pairing strength, to describe the evolution of occupation and single-particle energies with increasing distance from the core nucleus Pb in a satisfactory way. The degree of truncation was benchmarked using the francium isotopes where experimental data are known. Only the value for both isomers agree with the experimental value 0.
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Semi-magic nuclei can be described in a seniority scheme In this framework, the E 2 matrix element is given by and is linear in n and changes sign in the half-filled orbit. In the analysis of the odd—odd nuclei we compare our results for the magnetic moments with those provided by the additivity rule 48 for different spin values. For both isotopes , Ac the experimental values are predicted by simple coupling rules in combination with the suitable nucleon configuration involving only the experimental magnetic moments of the neighbouring odd- A nuclei, namely , Ra refs 22 , 23 for the neutrons and the in-gas-jet result of Ac for the protons see Table 2.
All the relevant data supporting the findings of these studies are available from the corresponding author upon request. How to cite this article: Ferrer, R. Towards high-resolution laser ionization spectroscopy of the heaviest elements in supersonic gas jet expansion.
Oganessian, Yu, Ts. Production and decay of the heaviest nuclei , and A , — Sato, T. Measurement of the first ionization potential of lawrencium, element Nature , — Sewtz, M. Laatiaoui, M. Atom-at-a-time laser resonance ionization spectroscopy of nobelium. Fedosseev, V. Resonance laser ionization of atoms for nuclear physics. Backe, H. Prospects for laser spectroscopy, ion chemistry and mobility measurements of superheavy elements in buffer-gas traps. Campbell, P. Laser spectroscopy for nuclear structure physics. Cocolios, T. Magnetic dipole moment of 57,59 Cu measured by in-gas-cell laser spectroscopy.
Ferrer, R. B , — Kudryavtsev, Yu. The in-gas-jet laser ion source: resonance ionization spectroscopy of radioactive atoms in supersonic gas jets.
B , 7—22 Kudryavtsev, Y. Beams of short lived nuclei produced by selective laser ionization in a gas cell. Meggers, W.