Proton–hole excitation in the closed shell nucleus 205Au

Proton–hole excitation in the closed shell nucleus 205Au Zs. Podolyák a,∗, G.F. Farrelly a, P.H. Regan a, A.B. Garnsworthy a, S.J. Steer a, M. Górska b, J. Benlliure c, E. Casarejos c, S. Pietri a, J. Gerl b, H.J. Wollersheim b, R. Kumar d, F. Molina e, A. Algora e,f, N. Alkhomashi a, G. Benzoni g, A. Blazhev h, P. Boutachkov b, A.M. Bruce i, L. Caceres b,j, I.J. Cullen a, A.M. Denis Bacelar i, P. Doornenbal b, M.E. Estevez c, Y. Fujita k, W. Gelletly a, H. Geissel b, H. Grawe b, J. Grȩbosz b,l, R. Hoischen m,b, I. Kojouharov b, S. Lalkovski i, Z. Liu a, K.H. Maier n,l, C. Mihai o, D. Mücher h, B. Rubio e, H. Schaffner b, A. Tamii k, S. Tashenov b, J.J. Valiente-Dobón p, P.M. Walker a, P.J. Woods q

The neutron-rich N = 126 nucleus 205 Au has been populated following the relativistic energy projectile fragmentation of E/ A = 1 GeV 208 Pb, and studied via charged-particle decay spectroscopy. An internal decay with a transition energy of 907(5) keV and a half-life of T 1/2 = 6(2) s has been identified through the observation of the corresponding K and L internal conversion electron lines. The 907 keV energy level corresponds to the πh −1 11/2 proton-hole state and decays both internally into the πd −1 Studies of magic nuclei are of fundamental importance in our understanding of nuclear structure since they allow direct tests of the purity of shell model wave functions. Information on the single-particle energies can be derived from the experimental observables such as energies of the excited states and transition probabilities.
The doubly magic 208 Pb nucleus, with 82 protons and 126 neutrons, provides the heaviest classic shell model core. Current experimental information on the neutron-rich N = 126 nuclei is very scarce. The data on the excited states of proton-hole N = 126 iso-* Corresponding author.  [3]. In the case of 205 79 Au, only a tentative spin-parity of the groundstate is known [4,5]. The experimental information on the structure of these nuclei can be used as building blocks for calculating more complex configurations. More information is available, more robust predictions can be made on the properties of more neutron-rich species. These are of particular importance as the r-process path nuclei, experimentally unreachable in this mass region so far, are approached [6].
The lack of information on proton-hole nuclei compared to the 208 Pb core arises from difficulties in populating such neutron-rich nuclei. Projectile fragmentation has proved to be an efficient tool to produce exotic nuclear species. When projectile fragmentation is combined with high sensitivity gamma detection arrays, struc-  [3]). The highest sensitivity is achieved with decay spectroscopy. In this technique the delayed gamma rays are correlated with the individually identified ion, therefore minimising the associated background radiation [7][8][9]. Here we employed a different version of the technique. Conversion electron spectroscopy following relativistic energy fragmentation was performed (according to our knowledge) for the first time.
In this Letter results on the N = 126 nucleus 205 Au are reported.
A beryllium target of thickness 2.5 g/cm 2 was bombarded with an E/ A = 1 GeV 208 Pb beam provided by the SIS accelerator at GSI, Darmstadt, Germany. The nuclei of interest, populated in relativistic energy projectile fragmentation, were separated and identified using the FRagment Separator (FRS) [10] operated in monochromatic mode with a wedge-shaped aluminium degrader in the intermediate focal plane of the separator. Niobium foils were placed after both the target and the degrader in order to maximise the electron stripping.
The mass-to-charge ratio of the ions, A/q, was determined from their time of flight and magnetic rigidity measurements in the second part of the FRS. The measured change of the magnetic rigidity of ions before and after they passed through this degrader was used to obtain unambiguous charge identification. The energy deposition of the identified fragments, which gives information on Z , was measured as they passed through two gas ionisation chambers. By determining A/q, the charge state and Z , an unambiguous event-by-event identification has been obtained. The transmitted (and identified) ions were slowed down in a variable thickness aluminium degrader and finally stopped in an active catcher.
The catcher consisted of three 1 mm thick 5 × 5 cm 2 double sided silicon strip detectors. Each Si had 16 X-strips and 16 Ystrips. The catcher allowed for the detection of both the implanted ion and the subsequent charged particle decay. A charged-particle decay observed in a given pixel was correlated with the previous implant detected in the very same pixel. Due to the large number of pixels, correlation between the implanted ion and the subsequent charged particle decay could be obtained over periods longer than seconds. Semilogarithmic preamplifiers were used, providing linear amplification up to 10 MeV and logarithmic for the 10 MeV-3 GeV range. The linear part allowed for the spectroscopy of the charged particle decay and was calibrated using an open internal conversion electron 207 Bi source, yielding an energy resolution of FWHM = 20 keV and a minimum detection threshold of 150 keV [11]. The logarithmic part allowed for the determination of the implantation position and was calibrated with a pulser. For details on the Si catcher and its electronics see Ref. [11]. Scintillation detectors were placed both in front of and behind the catcher, allowing the offline suppression of the majority of fragments destroyed in the slowing down process.
The catcher was surrounded by the high-efficiency, high granularity RISING γ -ray spectrometer in the "Stopped Beam" configuration [12]. The array consists of 15 former Euroball cluster Ge detectors and has a full peak efficiency of 15% at 662 keV [12].
Time-correlated γ decays following both internal-decay and βdecay have been recorded. The experiment was monitored using the Cracow analysis software [13]. A dedicated fragment separator setting was used to study the neutron-rich 205 Au nucleus. After the production target the magnetic rigidity of the fully stripped 205 Au nuclei is close to those of the intense He-like primary 208 Pb beam. In order to avoid this contamination, the first half of the fragment separator was set to transmit the H-like 205 Au ions. Although only an estimated 6.5% of the ions of interest were in their H-like charged state [14], the high production cross section in the order of 10 −2 mbarn [15] ensures sufficient statistics for the current measurement. In the second part of the fragment separator, after the monochromatic  degrader, 205 Au was transmitted in its fully stripped charged state. This setting provided a beam consisting predominantly (∼ 55%) of 205 Au nuclei, as shown in Fig. 1.
The primary 208 Pb beam intensity was 7 × 10 8 ion/spill, with the spill consisting of 1 s beam-on period followed by 10 s beamoff. The average implantation yield was ∼ 30 205 Au ion/spill, corresponding to a total of 76 × 10 3 collected ions. The observation of the previously identified γ -ray transitions in 205 Hg in coincidence with the β-decay of the ground-state 205 Au [4] confirmed the identification (see Fig. 1).
The use of the fragment separator in monochromatic mode allowed for the implantation of 205 Au in a thin layer of Si, maximising the efficiency of the charged particle detection. Fig. 2 shows the simulated range distribution within the 1 mm thick silicon detector. According to these simulations, performed with the LISE code [16], 70% of the implanted ions were 205 Au. The delayed charged particle spectrum measured in the Si detector and correlated to the implanted 205 Au ions is presented in Fig. 3. In addition to the continuous energy spectrum of the β electron from the 205 Au decay, two discrete peaks can be observed. These are interpreted as the K and L internal conversion electrons associated to a γ -ray transition with an energy of 907 (5)  The energy difference between the K and L lines, as well as the intensity ratio of the two peaks supports this interpretation. The measured lifetime of the decay is T 1/2 = 6(2) s. This lifetime suggests a transition with M4 or E4 character (considering a transition strength between 10 −4 and 10 +3 W.u.).
The γ -ray spectrum associated to the β decay of 205 Au is shown in Fig. 1. When compared with that of the previous study of Ch. Wennemann et al. [4], one notices that the spectrum contains two additional transitions with energies of 967 and 1016 keV.
These γ lines are clearly visible when a maximum implantationdecay correlation time in the order of seconds is used (5 s in Fig. 1), and they disappear in the background if a much longer maximum correlation time is chosen. These γ lines were previously identified in 205 Hg (but not from β decay) and they deexcite states with spin-parities 7/2 − and 9/2 − , respectively [5]. These spins are high when compared to that of the 3/2 + groundstate of 205 Au, therefore it is unlikely that these γ -ray transitions originate from the β decay of the 205 Au groundstate. The lifetimes associated to these two γ -ray transitions are consistent with the 6 s half-life of the conversion electron, and in the case of the stronger 967 keV transition inconsistent with the much longer lifetime of the groundstate β decay. All these experimental findings suggest the identification of an isomeric state in 205 Au, and that this state decays both internally and via β decay. The branching ratio between these decays cannot be determined due to poor knowledge of the full peak conversion electron detection efficiency.  In order to obtain a quantitative understanding of the underlying single-particle structure of the excited states of 205 Au, shellmodel calculations have been performed employing the OXBASH code [17]. The standard interaction two-body matrix elements (TBMEs) were used as taken from Ref. [18]. They are based on the Kuo-Brown interaction including core polarisation [19,20], with slight modifications introduced to obtain an improved description of the experimental data available at the time. The proton-hole energies were taken from the experimental level scheme of 207 Tl [1]. This parameterisation gives a good description of the reported excited states in the two proton-hole 206 Hg [2] and reasonable description for the four proton-hole nucleus 204 Pt [3]. In order to get a good description for all available information on the N = 126 isotones below lead, both on excitation energies and transition strengths, small modifications of the standard TBMEs were required [3]. Calculations with these modified matrix elements were also performed. The results of the calculations for 205 Au, using both sets of TBMEs, are compared with the experimental level schemes in Fig. 4. The dominant configurations are also indicated.
The measured energy of the isomeric state with the proposed 11/2 − spin-parity is in good agreement with the shell model calculations. The calculations also predict a 5/2 + state to lie below the 11/2 − isomer, therefore the isomer could decay into it via an E3 transition. The Weisskopf estimate for the partial lifetime of this transition is in the order of 0.1 s. This transition, even if it exists, could not be observed in the present experiment: the energy of the corresponding conversion electron is low and could not be discerned from the background; the γ branch could have not been correlated with the 205 Au ions due to the long lifetime of the isomer. As a consequence, the M4/E3 branching ratio could not be ascertained in the current work. Since the 11/2 − isomeric state β decays and possibly decays internally through an E3 branch, only an upper limit for the B(M4) transition strength was determined, B(M4) 1.7(7) W.u. This limit is somewhat lower than that of the equivalent M4 transition strength, 3.2(3) W.u. [1], in 207 Tl, and similar to those determined in lighter gold isotopes: 2.4(8) W.u. in 197 Au [22] and 2.2(3) W.u. in 195 Au [23]. This suggests that the E3 branching might be missing altogether, possible because the 5/2 + state lies above the 11/2 − isomer.
In conclusion, an excited state in the neutron-rich N = 126 205 Au nucleus has been identified through conversion electron spectroscopy. It has an excitation energy of 907(5) keV and a halflife of T 1/2 = 6(2) s. It corresponds to the πh −1 11/2 single proton-hole excitation and decays both internally into the πd −1 3/2 groundstate and via β decay into excited states of 205 Hg. The energy of the isomeric state is in good agreement with the shell-model calculations.