**GROUND AND ISOMER STATE PROPERTIES OF NEUTRON-DEFICIENT LEAD, POLONIUM AND TALLIUM ISOTOPES INVESTIGATED BY LASER ION SOURCE SPECTROSCOPY **
**AT THE ISOLDE FACILITY **
**A.E. Barzakh , D.V. Fedorov, V.S. Ivanov, P.L. Molkanov, **
**V.N. Panteleev, M.D. Seliverstov, Yu.M. Volkov**
**In collaboration with** Institut für Physik, Johannes Gutenberg Universität; Oliver Lodge Laboratory, University of Liverpool; TRIUMF, Vancouver; Instituut voor Kern- en Stralingsfysica, K.U. Leuven; Institut de Physique Nucléaire, Université Paris-Sud, Orsay; ISOLDE, CERN; Laboratoire de Physique subatomique et de cosmologie, Université Joseph Fourier, Grenoble; Institut Laue-Langevin, Grenoble; Department of Physics, University of Manchester.
**1. Shape coexistence in Pb region studied by laser spectroscopy**
For neutron-deficient nuclides around the closed proton shell at *Z *= 82, subtle interplay between individual and collective behavior of nucleons leads to the appearance of states with different shapes at low excitation energy. These the so-called shape coexisting states can be interpreted as particle-hole excitations across the closed proton shell gap, whereby the interaction of the valence proton particles and holes with the neutrons drives the nucleus to deformation. The phenomenon of shape-coexistence is a subject of intensive experimental and theoretical studies. The excited bands built on top of the 0^{+} states were observed in ^{182–190}Pb, and recent lifetime measurements confirmed the deformed character of these bands. For ^{186,188}Pb, it was concluded that the ground state and the 2_{1}^{+} state have a very different structure, the 0^{+}ground state is predominantly spherical, while the 2_{1}^{+} state is predominantly prolate. Monopole transition strengths between the 0^{+} states were used to estimate the mixing between the normal and intruder configurations and they revealed a limited configuration mixing in the ground-state wave functions of ^{190}^{,}^{192}^{,}^{194}Pb. At the same time, as the excited 0^{+} states become lower in energy when approaching *N *= 104, the mixing could increase substantially. All models that provide a consistent picture of the available data suggest that the ground states of lead isotopes are dominated by spherical configurations, even when the prolate and oblate rotational bands come down very low in energy around *N *= 104, and the barrier that separates the corresponding structures in the total energy surface is very small. Most experimental data, however, concern transitions to the ground state, which depend on the structure of the initial state. Note that the observables which give detailed information on the ground-state wave function are the charge radii determined in atomic spectroscopy.
Approaching *N *= 104, the intrusion of a presumed oblate band was seen at low energy in ^{192}Po also. In ^{190}Po, an evidence for a prolate configuration in the polonium isotopes was obtained, which is believed to become the ground state in ^{188}Po. In order to understand the change in the configuration, a direct measurement of ground-state properties independent of nuclear models through the charge radii studies is crucial.
We have measured isotopic shifts in the atomic spectra of the very neutron-deficient ^{182–188}Pb isotopes, neutron-deficient polonium isotopes from ^{210}Po down to ^{191}Po (*T*_{1/2} = 22 ms) and of the neutron-rich isotopes ^{216,218}Po and deduced the corresponding changes in mean square charge radii. The in-source laser spectroscopy technique was first used at PNPI. By combining the in-source laser spectroscopy technique with efficient alpha detection, the mean square charge radii data were obtained for nuclides, which were detected with a rate of about 1 ion per second. The radioactive isotopes were produced at the PSB-ISOLDE facility at CERN, in a proton-induced (*E*_{p}* = *1.4 GeV) spallation reaction on a thick (50 g/cm^{2}) UC_{x} target. The reaction products diffuse out of the target toward the ion source cavity, heated to around 2050^{0}C. In this cavity, the isotopes were selectively ionized in a three-step laser ionization process. With copper-vapor pumped tunable dye lasers, atomic electrons were promoted out of the ground state toward the excited state (λ_{1 }= 283.3 nm for Pb and λ_{1 }= 255.8 nm for Po). In a second excitation step, the second tunable dye laser was tuned to λ = 600.19 nm for Pb and λ = 843.38 nm for Po. The final ionizing step was supplied by the pumping laser (see Fig. 1).
In order to determine the isotope shift of the optical line, the first excitation step for Pb and the second step for Po were set to a narrow linewidth of 1.2 GHz, and its frequency was scanned over the resonance. After ionization and extraction, the radioactive ions of interest were accelerated to 60 keV, mass separated and subsequently implanted in one of ten identical 20 µg/cm^{2} carbon foils, mounted on a rotating wheel. A Si-detector (area 150 mm^{2}, thickness 300 m), placed behind the foil, measured the α-radiation during a fixed implantation time. After this period, a new wavelength was set, and a fresh carbon foil was introduced by turning the wheel. The implanted lead ions were counted via their characteristic *α*-decay and the intensities of the *α *lines as functions of the laser frequency revealed the optical isotope shift.
**Fig. 1.** Ionization schemes used for Pb (left) and for Po (right) laser spectroscopy
The isotopes ^{199–204}Po and ^{189,190}Pb were detected via their β-decay and the subsequent characteristic γ-ray emission at the ISOLDE tape station. The polonium isotopes ^{206-210}Po were measured with a Faraday cup. To determine the absolute wavelength calibration and the shape of the resonance curve, laser scans using the mass separated ion current of the stable isotope ^{208}Pb and the reference isotope ^{202}Po were performed regularly. By scanning the frequency of the narrow band laser over the resonance, together with simultaneous counting of the mass-separated photo-ions, the isotope shift (IS) and hyperfine structure (hfs) constants of the atomic spectra lines can be measured. From these data the change in nuclear mean square charge radii (*δ*^{2}*>*) and the electromagnetic moments can be determined according to the well-known formulas (see Eqs. (1) and (2) in *A.E. Barzakh, et al.* in the present volume). *
*Figure 2 shows examples of the obtained frequency scans for even Po isotopes. In Fig. 3, the mean square charge radii for polonium, bismuth, lead, mercury, thallium, and gold isotopes are displayed. For the sake of clarity, the data for different elements are shifted relative to each other by a vertical offset. In our experiments the data for ^{218,216,211,203,201,199–191}Po (*N *= 134, 132, 127, 119, 117, 107–116), ^{182–189}Pb (*N *= 100–107) and the corresponding isomers were obtained for the first time.
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**Fig. 2.** Examples of optical spectra measured for even Po isotopes
t is generally acknowledged that the isotopic trend of *δ*^{2}*> *is described by the Droplet Model (DM). Deviations from the DM trend are attributed to the advance of the mean squared quadrupole deformation (see Eq. (3) in *A.E. Barzakh, D.V. Fedorov, V.S. Ivanov et al.* in the present volume). The large deviation observed for the ground state of the odd-mass mercury isotopes and the odd- and even-mass gold isotopes around *N *= 104 has been interpreted as due to the onset of a strong prolate deformation.
**Fig. 3.** Changes of the mean square charge radii for polonium, bismuth, lead, mercury, thallium, and gold isotopes. Hollow symbols mark the isomers. For the sake of clarity the data for different elements are shifted relative to each other by a vertical offset
In the case of lead, a modest deviation is observed, and Fig. 4 shows the difference between the experimental charge radii and the droplet model predictions.
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**Fig. 4. **Difference between the experimental *δ*^{2}*>* for Pb isotopes and the DM calculations for spherical nuclei
*rom *^{196}Pb downwards, the spherical droplet model predictions deviate from the data, with an underestimation around 0.1 fm^{2} from ^{190}Pb to ^{184}Pb. Introduction of a static deformation into the droplet model with *β*_{2 }*= *0.1 improves the agreement with the data for ^{184–190}Pb, but is inconsistent with spectroscopic properties. A more realistic approach that provides good description of the coexisting bands in the neutron-deficient lead isotopes is beyond the mean-field calculations. This model mixes the mean-field wave functions which all have different axial quadrupole deformations. Around the midshell where lead isotopes are soft, the collective wave function is spread over a large number of configurations, and the notion of a spherical or deformed nucleus becomes ill defined.
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*Calculations with this model show that isotopic shifts are very sensitive to correlations in the ground-state wave functions of lead. A slight reduction of the pairing strength has a significant effect on precise balance between the excited prolate and oblate configurations, but leads only to a very small increase in the mean deformation of the ground state.
The values of ***r*^{2} for Po isotopes are compared with those predicted also by the spherical DM (see Fig. 5). On the neutron-deficient side, a surprisingly large deviation from sphericity can be seen starting from ^{198}Po that becomes increasingly marked for lighter isotopes.
The deviation is larger in magnitude and occurs for larger neutron numbers than in the *Z* 82 isotones. In order to understand the unexpectedly large and early deviation from sphericity in polonium isotopes, the values of ***r*^{2} were calculated using the same beyond mean field method.
The SLy4 Skyrme parametrization was tested together with the effect of reduced pairing strength. The results of these calculations are shown on Fig. 5.
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**Fig. 5. **Difference between the measured values of ***r*^{2} and those predicted by the spherical DM. Dotted lines represent the beyond mean field calculations with the SLy4 and SLy4* (with reduced pairing) interactions
wo main effects that increase the radii of neutron-deficient polonium isotopes, compared to the global trend set by spherical configurations, are the spread of the collective wave function in deformation space and the shift of the dominant configurations from near-spherical to oblate. The increasing softness of the deformation energy surfaces, when going down from ^{210}Po to ^{194}Po, leads to collective ground-state wave functions of increasing spread, but which remain centred in spherical shapes. For ^{192,190}Po, the ground-state wave function becomes centred in an oblate minimum in the deformation energy surface, and the contribution from near-spherical configurations (or smaller radii) becomes suppressed, while from ^{188}Po onwards, the ground-state wave function becomes more localized in a deformed minimum. The calculated values of ***r*^{2} are compared with the experimental data in Fig. 5, after subtraction of the DM value. There is a qualitative agreement between theory and experiment, although some discrepancies exist, especially for ^{192,194}Po, where the data indicate a significant deviation from sphericity. The effect of a reduced pairing strength, which clearly improves the agreement between theory and experiment for the lightest nuclei, implies a larger contribution of deformed oblate configurations. From our calculations, it can be concluded that none of the polonium isotopes measured in this work have a static deformation. One still needs to construct more flexible energy functionals to correct the deficiencies of the actual ones.
In conclusion, the in-source resonant ionization laser spectroscopy has been performed on polonium and lead isotopes. From ^{190}Pb downwards, the ***r*^{2} data show a distinct deviation from the spherical droplet model suggesting ground-state deformation, but comparisons of the data with model calculations show that ***r*^{2}** is very sensitive to correlations in the ground-state wave functions and that the lead isotopes stay essentially spherical in their ground states even at and beyond the *N = *104 midshell region. The ***r*^{2} values for even-*A* polonium isotopes have been compared with systematics of this region and recent calculations. An unexpectedly large divergence from sphericity was observed compared with the *Z *= 82 isotones. A comparison to beyond mean field calculations indicates that the coexistence of different shapes at low excitation energies leads to a very soft nature of the most neutron-deficient polonium nuclei. The different trend with respect to the *Z *= 82 nuclei might suggest that high-*j* orbitals occupied by the protons play a critical role.
**2. New type of asymmetric fission in proton-rich nuclei**
Usually, the fission process is described by the interplay between the macroscopic (liquid-drop) and microscopic nuclear (shell corrections) degrees of freedom. Only in fission below or slightly above the barrier, the so-called low-energy fission, this interplay can be most fully explored. Until recently, such low-energy fission studies were limited to nuclei from around thorium (Th) to fermium (Fm) using spontaneous fission, fission induced by thermal neutrons, or by β-delayed fission. These studies have shown the dominance of asymmetric fission over symmetric fission for most isotopes of these elements and suggested that structure effects due to the spherical shell structure of doubly magic ^{132}Sn dominate the mass split. Recently, the low energy fission studied by Coulomb-excited fission of radioactive nuclei demonstrated the transition from mostly asymmetric fission in the actinides towards symmetric fission as the dominant mode in the light thorium to astatine region. Another way to study low-energy fission is through β-delayed fission (βDF). In this two-step nuclear process, a parent nucleus first undergoes β decay, in this case electron capture (EC), populating the states in the daughter nucleus which may be fissile, provided the energy release *Q*_{EC} of the parent nuclide is comparable to the fission-barrier height *B*_{f} of the daughter nucleus. The β-delayed fission is of special interest because it allows to study the low-energy fission properties of exotic nuclei possessing unusual neutron to proton ratios, e.g., *N*/*Z *= 1.25 for ^{180}Hg, in contrast to a typical ratio of *N/Z *= 1.55–1.59 in the U region.
We have carried out a dedicated βDF study of ^{180}Tl at the ISOLDE mass separator at CERN. A 1.4 GeV proton beam with an average intensity of 1.2 µA impinges on a 50 g/cm^{2} UC_{x} target, producing a large variety of nuclides. To obtain a high-purity source of ^{180}Tl, allowing a precise study of its decay, a combination of resonance laser ionization and mass separation was used, resulting in a unique isotopic selection. The scheme of resonance ionization of Tl atoms is presented in Fig. 6.
After selective ionization, acceleration up to 30 keV and mass separation, a pure ^{180}Tl beam of ~150 atoms/s passed through a hole in an annular silicon detector and was implanted into a carbon foil of 20 µg/cm^{2} thickness. A second Si detector was placed 3 mm behind the foil. By using the two silicon detectors (both of 300 µm thickness), the single α and fission decays, as well as the double-fold fission-fragment coincidences, could be measured. The total registration efficiency for a single α or fission decay in one of the Si detectors was ~ 66%, while the coincident fission fragments were registered with an efficiency of ~ 20%.
**Fig. 6.** Scheme of Tl resonance ionization
A segmented MINIBALL Ge cluster, consisting of three individual germanium crystals, and a planar Ge detector were installed around the detection chamber to allow γ and *K* *X*-ray measurements in coincidence with particle events. Approximately, 1.4∙10^{6} α decays of ^{180}Tl were detected in total. All observed α lines originated from ^{180}Tl or its subsequent decays (cf. the decay scheme in Fig. 7) as they were reduced by a factor of ~70 when laser light was blocked, preventing laser ionization of Tl. No direct production of ^{180}Hg was possible as it could be ionized neither by surface ionization nor by laser ionization tuned to Tl isotopes. This proved the purity of the ^{180}Tl source, which allowed an accurate determination of different branching ratios. The half-life value of *T*_{1/2}(^{180}Tl) = 1.09(1) s was deduced, more precise than the literature value 1.4(3) s. The total of 1111 single fission events in the region 30–90 MeV were observed when the lasers were tuned to Tl ionization.
In total, 346 dual coincidences between fission fragments were observed. Finally, the prompt coincidences between the fission fragments and Hg *K*-line *X* rays were registered. These observations together unambiguously prove the observation of prompt fission of the excited states in ^{180}Hg fed by the β decay of ^{180}Tl.
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**Fig. 7.** A simplified decay scheme of ^{180}Tl with the deduced halflife and branching ratios for its various decay modes
he purity of the ^{180}Tl sample allowed the absolute branching ratios of its decay channels to be deduced by comparison of the summed numbers of ^{180}Tl α decays and βDF events to the number of ^{180}Hg α decays using the well-known α branching ratio of ^{180}Hg [48(2)%] and the corrections for the different half-lives due to the implantation-decay cycle. This resulted in the β^{+}/EC branching ratio of 94(4)% and the βDF probability *P*_{βDF}(^{180}Tl) = 3.6(7)∙10^{-3}% for ^{180}Tl. A fission-fragment mass distribution from the 346 coincident fission events of ^{180}Hg, could be obtained through a well-established procedure. The resulting spectrum as a function of the total kinetic energy and the fission-fragment mass is shown in Fig. 8. The mass distribution is clearly asymmetric. The most probable *Z* values of the heavy and light fission fragments were deduced to be *Z*_{H}_{ }= 44(2) and *Z*_{L}_{ }= 36(2), respectively, assuming that the *N*/*Z* ratio of the parent nucleus ^{180}Hg is preserved in the fission fragments. Thus, the most abundantly produced fission fragments were ^{100}Ru and ^{80}Kr and their neighbors.
The most surprising result of this study was the asymmetric mass distribution of the fission fragments of ^{180}Hg. Indeed, one might have expected a symmetric fission fragment mass distribution, as this was observed to be the main mode of the low-energy fission in a broad neutron-deficient region below Th. In addition, very common arguments applied e.g. for fission of heavy actinides that shell effects in fragments (rather than shell effects in the fissioning nucleus in the region near the saddle) determine the mass distributions would also lead to an expectation of symmetry.
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**Fig. 8**. The derived fission-fragment distribution of ^{180}Hg as a function of the fragment mass and the total kinetic energy
his is because there are no strong ground-state shell effects in the measured asymmetric fragments of ^{180}Hg, while a weak shell effect for the nucleus ^{90}Zr, with the magic *N *= 50 and semimagic *Z *= 40 would, if it were determinative, lead to symmetric splitting. A realistic description of the fission process needs the structure of the entire, multidimensional fission potential energy surface based on at least five independent shape parameters. A dynamical model would be required to make a specific prediction of the mass split implied by these potential-energy calculations. In the actinide region, one can identify a connection between the asymmetric fission-fragment distribution and the strong shell effects in the region near the saddle, extending and increasing as one moves towards the scission point.
These shell effects are related to the extra binding energy of the doubly magic nucleus ^{132}Sn. In contrast, in the neutron-deficient Hg region such a combined effect of magic proton and neutron shells in the observed fission fragments is completely absent, and the asymmetric splitting is determined by relatively small microscopic effects that do not persist to scission but which cause the fission saddle point and a nearby valley to be mass-asymmetric. This new mode, which should survive only in very low energy fission, arises from the complex interplay between macroscopic and microscopic contributions to the total energy as a function of shape and is observed for the first time. Prediction of this mass asymmetry and related properties comprises a stringent test for any nuclear structure model. It is a challenge to the experimental approaches as well as current theories to elucidate this new fission mode which gives the opportunity to study the topography and dynamics of the saddle to scission region, the least understood part of the fission process.
**References**
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3. M.D. Seliverstov* et al*., Eur. Phys. J. **A** 41, 315 (2009).
4. A.N. Andreyev *et al.*, Phys. Rev. Lett. **105**, 252502 (2010).
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