Early onset of ground-state deformation in the neutron-deficient polonium isotopes
T.E. Cocolios, W. Dexters, M.D. Seliverstov, A.N. Andreyev, S. Antalic, A.E. Barzakh, B. Bastin, J. Buscher, I.G. Darby, D.V. Fedorov, V.N. Fedosseyev, K.T. Flanagan, S. Franchoo, S. Fritzsche, G. Huber, M. Huyse, M. Keupers, U. Koster, Yu. Kudryavtsev, E. Mane, B.A. Marsh, P.L. Molkanov, R.D. Page, A.M. Sjoedin, I. Stefan, J. Van de Walle, P. Van Duppen, M. Venhart, S.G. Zemlyanoy, M. Bender, P.-H. Heenen
aa r X i v : . [ nu c l - e x ] O c t Early onset of ground-state deformation in the neutron-deficient polonium isotopes
T.E. Cocolios , , W. Dexters , M.D. Seliverstov , , , A.N. Andreyev , , S. Antalic , A.E. Barzakh ,B. Bastin ∗ , J. B¨uscher , I.G. Darby , D.V. Fedorov , V.N. Fedosseyev , K.T. Flanagan , ,S. Franchoo , S. Fritzsche , , G. Huber , M. Huyse , M. Keupers , U. K¨oster , Yu. Kudryavtsev ,E. Man´e † , B.A. Marsh , P.L. Molkanov , R.D. Page , A.M. Sjoedin , , I. Stefan , J. Van deWalle , ‡ , P. Van Duppen , M. Venhart , , S.G. Zemlyanoy , and M. Bender , P.-H. Heenen Instituut voor Kern- en Stralingsfysica, K.U. Leuven, B-3001 Leuven, Belgium ISOLDE, CERN, CH-1211 Geneva 23, Switzerland Petersburg Nuclear Physics Institute, 188350 Gatchina, Russia Institut f¨ur Physik, Johannes Gutenberg Universit¨at, D-55099 Mainz, Germany School of Engineering and Science, University of West Scotland, Paisley,PA1 2BE, United Kingdom and Scottish Universities Physics Alliance (SUPA) Department of Physics and Biophysics, Comenius University, Bratislava 842 48, Slovakia EN Department, CERN, CH-1211 Geneva 23, Switzerland Department of Physics, University of Manchester, Manchester, M60 1AD, United Kingdom Centre de Spectrom´etrie Nucl´eaire et de Spectrom´etrie de Masse, F-91405 Orsay, France Institut de Physique Nucl´eaire d’Orsay, F-91406 Orsay, France GSI Helmholtzzentrum f¨ur Schwerionenforschung, D-64291 Darmstadt, Germany Department of Physics, P.O. Box 3000, Fin-90014 University of Oulu, Finland Institut Laue-Langevin, F-38042 Grenoble, France Oliver Lodge Laboratory, University of Liverpool, Liverpool, L69 7ZE, United Kingdom KTH-Royal Institute of Technology, SE-10044 Stockholm, Sweden Institute of Physics, Slovak Academy of Sciences, Bratislava 845 11, Slovakia Joint Institute of Nuclear Research, 141980 Dubna, Moscow Region, Russia Centre d’Etudes Nucl´eaires de Bordeaux Gradignan, F-33175 Gradignan, France and Service de Physique Nucl´eaire Th´eorique, Universit´e Libre de Bruxelles, B-1050 Bruxelles, Belgium (Dated: October 25, 2018)In-source resonant ionization laser spectroscopy of the even- A polonium isotopes − , , Pohas been performed using the 6 p s S to 6 p p P ( λ = 843 .
38 nm) transition in the polo-nium atom (Po-I) at the CERN ISOLDE facility. The comparison of the measured isotope shiftsin − Po with a previous data set allows to test for the first time recent large-scale atomic cal-culations that are essential to extract the changes in the mean-square charge radius of the atomicnucleus. When going to lighter masses, a surprisingly large and early departure from sphericity isobserved, which is only partly reproduced by Beyond Mean Field calculations.
PACS numbers: 21.10.Ft, 27.80.+w, 29.38.-c, 31.15.-p
In spite of substantial progress in understanding thestructure of light atomic nuclei using ab-initio calcula-tions [1], heavy nuclei are still modeled using shell-modelcalculations, symmetry-based approaches or mean-fielddescriptions. These concepts address an interestingaspect of the finite ensemble of strongly interactingfermions that makes the atomic nucleus, namely the sub-tle interplay between microscopic (individual nucleon)and macroscopic properties (collective behavior). Thelead isotopes are a good example: while the doublyclosed-shell nucleus
Pb, with Z = 82 and N = 126, isa textbook case of a shell-model nucleus [2], signaturesof particle-hole symmetries have been found [3]. Fur-thermore, shape coexistence has been observed in theneutron-deficient isotopes, whereby states with different ∗ Present address: GANIL, France † Present address: TRIUMF, Canada ‡ Present address: KVI, The Netherlands shapes occur at low excitation energy [4]. In spite of thelatter effect, recent studies have shown that the groundstate of the very neutron-deficient lead isotopes remainsessentially spherical, confirming the robustness of the Z = 82 shell closure in those isotopes [5, 6]. In the neigh-boring mercury isotopes ( Z = 80), a significant deviationfrom sphericity has been deduced around N = 104, midway between N = 82 and N = 126, from, e.g., the mea-surement of the changes in the mean-square charge radius( δ h r i ) [7]. From symmetry arguments a similar effect isexpected to occur in the neutron-deficient polonium iso-topes ( Z = 84) [8, 9].By approaching N = 104, the intrusion of a presumedoblate band was seen at low energy in Po [10, 11]. In
Po, evidence for a prolate configuration in the polo-nium isotopes was obtained [12], which is believed to be-come the ground state in
Po [13, 14]. In order to un-derstand the change in the configuration, a direct mea-surement of ground-state properties independent of nu-clear models is crucial. The δ h r i can be extracted fromisotope shifts measurements using laser spectroscopy in amodel-independent procedure, provided that the atomicparameters (electronic factor F and specific mass shift M SMS ) are known [15]. However, since there is no stableisotope of polonium, those measurements are extremelychallenging. In particular, the information on the atomicstructure of the polonium atom itself was hitherto ratherscarce and limited in precision [16]. Hence a previousstudy of the δ h r i in − Po by laser spectroscopy [17]had to rely on a nuclear model (Finite Range DropletModel - FRDM [18]) in order to extract the δ h r i fromthe isotope shifts.In the last 20 years, the progress in atomic structuretheory has enabled large-scale calculations for open-shellatoms and ions [19] providing the necessary input to an-alyze laser-spectroscopic data. However, one still has toassess the accuracy and reliability of those calculations,especially in heavy systems, as they are needed to accessthe atomic and chemical properties of the super heavyelements.In this Letter, we report on the measurement of theisotope shifts of the neutron-deficient, even- A poloniumisotopes from Po down to
Po ( T / = 33 ms) andof the neutron-rich isotopes , Po using in-source res-onant photoionization spectroscopy. Combining the iso-tope shifts of the present and previous data set [17] al-lowed us to test large-scale atomic calculations for thefirst time and to evaluate their accuracy. The measuredshifts and calculated atomic parameters are then used toextract δ h r i and those are discussed in terms of nuclearmodels.The polonium isotopes were produced at the CERNISOLDE facility by 1.4 GeV proton-induced spallationreactions of a thick depleted UC x target as describedin Ref. [20] over two experimental campaigns using theresonant ionization laser ion source [21]: − Po in2007 and , , − , , Po in 2009. For
A >
A >
204 polonium isotopes were insteadstudied without proton irradiation, using precursors pre-viously accumulated in the target. Without proton irra-diation, the short-lived, fast-releasing francium contami-nation disappears as it does not have any precursor. Theisotopes − Po were obtained via the β + /EC decayof the isobaric astatine nuclei while the isotopes , Powere produced via the α decay of Ra and
Rn, re-spectively.The α -decaying isotopes − , , Po were stud-ied as described in Ref. [20]. The β -decaying isotopes − Po were sent to the ISOLDE tape station andtheir decay measured using a plastic scintillator and asingle coaxial HPGe detector. The isotopes − Powere directly counted in a Faraday cup. The measure-ments were performed by scanning the narrowband laserat 843 .
38 nm from the 6 p s S to the 6 p p P ex-cited state of the ionization scheme [21] and monitoring Po Po Po Po Po -1.1-1-0.9-0.8-0.7 Po -0.2-0.100.10.20.30.40.5 Po -1.2-1.1-1-0.9-0.8-0.7-0.6-0.5 Po Po Po Po Frequency [GHz]-15 -10 -5 0 5 10 15 Po FIG. 1: From top to bottom: example of a laser scan aroundthe 843 .
38 nm transition between the 6 p s S and 6 p p P atomic excited states in even- A Po-I for A = 218 downto A = 192. For A = 192, several scans have been addedtogether to obtain sufficient statistics. The line is the resultfrom a fit of those spectra using an asymmetric Voigt profile;more information on this asymmetry can be found in the text. the yields as a function of the frequency. The frequencyscans are shown in Fig. 1. The shape of the resonancecan be described as a deformed Voigt profile. The 2007data were analyzed as described in Ref. [6]. For the 2009data, an asymmetry in the fit function was introducedthrough a different Lorentzian width parameter on eachside of the resonance. The difference comes from the useof different pump lasers between the two runs. The de-duced isotope shifts with respect to Po ( δν A, exp ) arepresented in Table I.The large overlap in the studied isotopes between thepresent data set and the previous study using the 255 . F while the y intercept is a linear combination of the M SMS from eachtransition. The M SMS and F can also be calculated onthe basis of the Dirac-Coulomb-Breit Hamiltonian and aFermi-like distribution of the different isotopes. A seriesof relativistic configuration interaction calculations havebeen carried out with systematically enlarged wave func-tion expansions within a restricted active space, includ-ing the polarization of the electronic core and single anddouble excitations into three additional layers of correla-tion orbitals ( n = 8 , , F , while the M SMS values appear more sensitive tothe details of the calculations. The results are shown in
TABLE I: Isotope shifts δν A, exp in the 843 .
38 nm transition ofPo-I and changes in the mean-square charge radii δ h r i A, exp of the polonium isotopes with respect to Po from this work.The systematic uncertainty on the δ h r i A, exp originates fromthe Specific Mass Shift.Mass δν A, exp [GHz] δ h r i A, exp [fm ] a − . . { } − . . { }
210 0 0208 1 . − . { }
206 3 . − . { }
204 4 . − . { }
202 5 . − . { }
200 6 . − . { }
198 7 . − . { }
196 7 . − . { }
194 7 . − . { }
192 6 . − . { } a (statistical uncertainty) { systematic uncertainty } Modified isotope shift (255.8 nm) [GHz]0 1000 2000 3000 4000 M od i f i e d i s o t op e s h i f t ( . n m ) [ GH z ] -2000-1500-1000-50000 1 2 3 4-2-1.5-1-0.500 1 2 3 4 FIG. 2: (Color online) King plot between the transitions at255 . x axis) and at 843 .
83 nm (present work, y axis) for − Po. The solid line is a linear fit through thedata points; the dotted red line is the calculated relation fromthe large-scale atomic calculation and lies within 1 σ of thefit. Table II. The red dotted line in Fig. 2 displays the corre-sponding relation according to the calculated parametersand lies within 1 σ of the fitted trend. The good agree-ment between the slope of the calculated parameters andthat of the fit shows the predictive power of the calcula-tions for F . The difference in the y intercept, however,raises some questions on the theoretical accuracy of thecalculated M SMS .The δ h r i of the even- A isotopes − , , Po wereextracted using those parameters and a 0 .
932 correctionfor higher moments [22]. In order to take into accountthe uncertainty of the different M SMS in the calculation,
TABLE II: Calculated atomic electronic factors F and specificmass shifts M SMS .Transition [nm] F [GHz/fm ] M SMS [GHz · amu]255 . .
363 51843 . − . −
100 110 120 130 140 ] > [f m < r δ Pt Hg PbPoRn Ra
Neutron number N100 110 120 130 140 F R D M > < r δ > - < r δ Experimental dataFRDMSLy4 * SLy4
FIG. 3: (Color online) (top) δ h r i for the even- Z isotopesfrom platinum ( Z = 78) to radium ( Z = 88) [5, 7, 24–28]. Thesolid black line represents the predictions from the sphericalFRDM [18] using the second parametrization from Ref. [23].(bottom) Difference between the measured δ h r i to the spheri-cal FRDM. The dotted lines represent the Beyond Mean Fieldcalculations with the SLy4 and SLy4 ∗ (with reduced pairing)interactions [29, 30]. a systematic error was introduced. It was deduced as thedifference between the δ h r i values using only the calcu-lated atomic parameters for the 843 .
38 nm line and thoseobtained via the King plot and the calculated atomic pa-rameters from the 255 . δ h r i (seeTable I) are compared with the predictions from thespherical FRDM [18] using the second parametrizationfrom Ref. [23] (see Fig. 3). On the neutron-deficient side,a surprisingly large deviation from sphericity can be seenstarting from Po that becomes increasingly markedfor the lighter isotopes. The deviation is larger in magni-tude and occurs for larger neutron numbers than in the Z ≤
82 isotones. The data in the neutron-deficient radonand radium isotopes [24] do not extend far enough in theneutron-deficient side to compare with the polonium iso-topes.In order to understand the unexpectedly large andearly deviation from sphericity in the polonium isotopes,the δ h r i have been calculated using the same BeyondMean Field method as in Ref. [29, 30]. The most im-portant feature of the method for this study is that theground-state wave function is constructed as a superposi-tion of mean-field wave functions corresponding to a largeset of axial quadrupole deformations, projected on angu-lar momentum and particle number. The coefficients ofthe expansion are determined by varying the energy cor-responding to a Skyrme energy density functional. TheSLy4 Skyrme parametrization has been tested togetherwith the effect of a reduced pairing strength (SLy4 ∗ ).Within this framework, one cannot assign an intrinsicdeformation to the wave functions. Instead, they are amixture of mean-field states of different deformation andtherefore different radii. In general, deformed configu-rations have larger radii than spherical ones. The twomain effects that increase the radii of neutron-deficientpolonium isotopes, compared to the global A / trendset by spherical configurations, are the spread of thecollective wave function in deformation space and theshift of the dominant configurations from near-sphericalto oblate. The increasing softness of the deformationenergy surfaces, when going down from Po to
Po,leads to collective ground-state wave functions of increas-ing spread, but which remain centered around sphericalshapes. For , Po, the ground-state wave functionbecomes centered around an oblate minimum in the de-formation energy surface and the contribution from near-spherical configurations (or smaller radii) becomes sup-pressed.The calculated δ h r i are compared with the experimen-tal data at the bottom of Fig. 3, after subtraction of theFRDM value. There is a qualitative agreement betweentheory and experiment, although deficiencies exist, es-pecially for , Po, where the data indicate a strongerdeviation from sphericity. The effect of a reduced pairingstrength, which clearly improves the agreement betweentheory and experiment for the lightest nuclei, is meantto put a larger weight on deformed oblate configurations.One still needs to construct more flexible energy func-tionals to correct the deficiencies of the actual ones.Finally, the neutron-rich isotopes , Po show aclear break from the trend of the polonium isotopes below N = 126. The magnitude of this kink is similar to what isobserved in the neutron-rich neighboring lead ( Z = 82)[26], bismuth ( Z = 83) [31] and heavier isotopes. Theunderlying mechanism is still an open question.In conclusion, in-source resonant ionization laser spec-troscopy has been performed on the polonium isotopesfrom Po to
Po. The overlap with the previous dataset available in the literature has allowed testing of thelarge-scale atomic calculations for the F and the M SMS ,although the latter remain slightly less well determinedfor such heavy atoms. This first experimental evidence ofthe reliability of such calculations is crucial for the studyof laser spectroscopy in complex systems [15]. Moreover,it shows that reliable information can be extracted for thevery heavy elements, where limited or no atomic data areavailable yet.The δ h r i of the even- A polonium isotopes − , , Po have been extracted and comparedwith systematics of this region and recent calculations.An unexpectedly large departure from sphericity wasobserved compared with the Z ≤
82 isotones. Com-parison to Beyond Mean Field calculations indicatethat the coexistence of the different shapes at lowexcitation energies leads to a very soft nature of themost neutron-deficient polonium nuclei. The differenttrend with respect to the Z ≤
82 nuclei might suggestthat high- j orbitals occupied by the protons play acritical role. The study of the more neutron-deficientradon ( Z = 86) and radium ( Z = 88) isotopes couldeventually shed more light on the aspect.We would like to thank the ISOLDE collabora-tion for providing excellent beams and the GSI Tar-get Group for manufacturing the carbon foils. Thiswork was supported by FWO-Vlaanderen (Belgium),by GOA/2004/03 (BOF-K.U.Leuven), by the IUAP -Belgian State Belgian Science Policy - (BriX networkP6/23), by the European Commission within the SixthFramework Programme through I3-EURONS (ContractRII3-CT-2004-506065), by the U.K. Science and Technol-ogy Facilities Council, by the FiDiPro programme of theFinnish Academy and by the Slovak grant agency VEGA(Contract No. 1/0091/10). [1] P. Maris et al., Phys. Rev. C , 014308 (2009).[2] O. Sorlin and M. G. Porquet, Prog. Part. Nucl. Phys. ,602 (2008).[3] R. B. Cakirli et al., Phys. Rev. Lett. , 092501 (2005).[4] A. N. Andreyev et al., Nature , 430 (2000).[5] H. De Witte et al., Phys. Rev. Lett. , 112502 (2007).[6] M. D. Seliverstov et al., Eur. Phys, J. A , 315 (2009).[7] G. Ulm et al., Z. f¨ur Phys. A , 247 (1986).[8] K. Heyde et al., Phys. Rep. , 291 (1983).[9] J. L. Wood et al., Phys. Rep. , 101 (1992).[10] K. Helariutta et al., Phys. Rev. C , R2799 (1996).[11] N. Fotiades et al., Phys. Rev. C , 1724 (1997).[12] D. R. Wiseman et al., Eur. Phys, J. A , 275 (2007).[13] K. Van de Vel et al., Phys. Rev. C , 054311 (2003).[14] A. N. Andreyev et al., Phys. Rev. C , 044324 (2006).[15] B. Cheal and K. T. Flanagan, J. of Phys. G , 113101(2010).[16] G. W. Charles, J. of the Opt. Soc. of America , 1292(1966).[17] D. Kowalewska et al., Phys. Rev. A , R1442 (1991).[18] W. D. Myers and K. H. Schmidt, Nucl. Phys. A , 61(1983).[19] S. Fritzsche, Phys. Scripta T100 , 37 (2002).[20] T. E. Cocolios et al., J. of Phys. G p. in print (2010).[21] T. E. Cocolios et al., Nucl. Intrum. and Meth. B ,4403 (2008).[22] G. Torbohm, B. Fricke, and A. Ros´en, Z. f¨ur Phys. A , 141 (1985).[23] D. Berdichevsky and F. Tondeur, Z. f¨ur Phys. A , 2038(1985).[24] G. Fricke and K. Heilig, Nuclear charge radii (Springer,
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