Thallium (, Bismuth (), Astatine (), Francium (), Actinium () and Protactinium () are of odd-proton numbers among the mass chain A = 217. In the present work, the half-lives and gamma transitions for the six nuclei have been studied and adopted based on the recently published interactions or unevaluated nuclear data sets XUNDL. The Q (α) has been updated based on the recent published work of the Atomic Mass Evaluation AME2012 as well. Moreover, the total conversion electrons as well as the K-Shell to L-Shell, L-Shell to M-Shell and L-Shell to N-Shell Conversion Electron Ratios have been calculated using BrIcc code v2.3. An updated skeleton decay scheme for each of the above nuclei has been presented here. The decay hindrance factors (HF) calculated using the ALPHAD program, which is available from Brookhaven National Laboratory’s website, have been calculated for the α- decay data sets for 221Fr-, 221Ac- and 221Pa- α-decays.
Citation: Nafee SS, Shaheen SA, Al-Ramady AM (2016) Nuclear Data Evaluation for Mass Chain A=217:Odd-Proton Nuclei. PLoS ONE 11(1): e0146182. doi:10.1371/journal.pone.0146182
Editor: Matjaz Perc, University of Maribor, SLOVENIA
Received: October 6, 2015; Accepted: December 14, 2015; Published: January 13, 2016
Copyright: © 2016 Nafee et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All relevant data are within the paper and its Supporting Information files.
Funding: The authors would like to thank the authorities of King Abdulaziz City for Science and Technology (KASCT); Long-Term Comprehensive National Plan for Science, Technology and Innovations; and King Abdulaziz University (KAU), Saudi Arabia, for funding this project, contract number “11-MAT2037-03.”
Competing interests: The authors have declared that no competing interests exist.
Alvarez-Pol et al.,  identified 217Tl from the 9Be(238U, x) reaction when a 1 GeV/nucleon beam from the SIS18 synchrotron at the Gesellschaft für Schwerionenforschung (GSI), Germany at an intensity of 1.5 ×109 ions/spill bombarded a 9Be target of 2500 gm/cm2. The 217Tl isotope was separated by means of a high resolving power magnetic spectrometer Fragment Separator (FRS). Two plastic scintillators and two multisampling ionization chambers were used to identify the nuclide based on the magnetic rigidity, time–of -flight, energy loss and atomic number. However, the discovery of the 217Bi isotope was attributed to Pfützner et al.,  using the same facility. The spectrum was investigated by means of γ-γ, α-γ coincidence and spectrum-multiscaling measurements . The RISING array of 15 Ge clusters was used to detect the γ- rays. Each cluster has seven elements.
Fry and Thoennessen  reported that thirty–nine isotopes of Astatine (At) have been discovered based on the Hartree-Fock-Bogoliubov model (HFB-14). Meanwhile, the discovery of 217At was reported in 1947 by Hagemann et al.,  and English et al., , by studying the decay series (4n+1) of 233U. The half-life was reported to be 18 ms.
Hahn et al.,  reported the observation of 217Fr through the decay of 229Np produced in 233U(p, 5n) reactions in which a beam of protons of 32–41.6 MeV bombarded an enriched 233U target in the Oak Ridge Isochronous Cyclotron. The α emissions were measured by a surface–barrier Si(Au) detector. The measured α was reported to be 8.31±0.02 MeV.
Valli and Hyde  observed the 217Pa in 1968 through (6n) and (1p8n) fusion-evaporation reactions. In these reactions 203Tl and 206Pb targets were bombarded by 166 MeV 20Ne beams from the Berkeley HILAC. The recoils were deposited on a metallic surface in front of a semiconductor detector with a helium gas jet recoil transport apparatus . The adopted half-life by Akovali  was 3.48(9) ms. Several years later, in 1972, Nomura et al., reported the observation of 217Ac through a (5n) fusion–evaporation reaction in which a 91 MeV 14N beam from the RIKEN IPCR cyclotron bombarded a 208Pb target . Alpha-particle spectra were measured with a surface-barrier Si detector. The measured half-life for the 217Ac was 0.10± 0.01μs, whereas, the adopted one by Akovali  was 69(4) ns.
The latest nuclear decay data evaluations for the above nuclides were carried out by Akovali in 2003 . The reported half- lives for 217Bi,217At,217Fr,217Ac and 217Pa, were 93(3) s, 32.3(4) ms, 19(3) μs, 69(4) ns and 3.6(8) ms, respectively. There was no record for 217Tl in 2003. An updated evaluation for 217Tl was in 2011, whereas, for 217Bi it was in 2014, both of which are available at Brookhaven National Laboratory's website: www.nndc.bnl.gov. This paper presents the results of the evaluations of the odd-proton nuclei among the members of the mass chain A = 217 (217Tl, 217Bi, 217At), 217Fr, 217Ac and 217Pa), which have been performed in the frame of the KASCT Research Contract no. 11-MAT2037-03, using the procedures adopted by the DDEP working group. The references cut-off date was 2015, March 31. The calculated and adopted parameters will be used to update the Evaluated Nuclear Structure and Decay Data Files (ENSDF) for those nuclides under consideration, which were appraised in 2003. The complete and updated datasets for all nuclides are of great importance for the development of different aspects of nuclear technologies.
Procedure for Decay Data Evaluation
The half-life of 217At was measured using the ion-implanted technique by measuring α- and β- particles from weak 225Ac sources . The decay series of the 225Ac was studied by a 900 mm2 Canberra Passivated Implanted Planar Silicon (PIPS) detector in a quasi 2π counting system. Recoils from 225Ac were collected to measure the half-life of 221Fr, which is the parent of 217At. It was reported that the possible configuration for 217At in analogy to 215At is ((π h9/2)+2(π f7/2)(ν g9/2)-4) [13, 14].
Actinium-217 was produced from the 221Pa α- decay  and from the (HI, xnγ) reactions such as 205Tl (16O, 4n), 206Pb (15N, 4n) and 209Bi (12C, 4n) reactions using a 96 MeV 16O, 80 MeV 15N and 75 MeV 12C beams . The half-life of 217Ac was deduced from alpha-gamma (αγ), gamma-gamma (γγ), alpha-conversion electron (α-ce) and (ce-ce) coincidence experiments. Whereas, 217Fr was produced from 221Ac α- decay or from 210Pb (11B, 4nγ) using a 11B beam of energy ranges from 52 to 68 MeV . The measured spectrum has been studied using the γ-γ coincidence techniques.
The calculation of the hindrance factor(s) of β—decay or the so-called log ft value was carried out for the direct feeding(s) to the excited states in the β—decay. The electron capture (ε) decays have generally been computed by the evaluator from the I(γ+ce) intensity balances at each level. The log ft values describe the shape of the spectrum and can be discussed as follows.
The total decay constant λ for a constant nuclear matrix element η is given as: (1) where, ƒ(Z,Q) is a Fermi integral, which is constant for a given β—decay and can be calculated by numerical expressions. g is the strength of the weak interaction between the nucleons, electron and the neutrino which is constant and assigned as 0.88×10−4 MeV.fm3. me is the mass of the electron and C is the speed of light. And η is a constant nuclear matrix element representing the overlap between the final and initial nuclear states.
Eq 1 can be rewritten in terms of the half-life of the parent t1/2 as: (2)
The logarithm of the left hand side in Eq 2 is called log ft. A rapid method to calculate the log ft values has been reported in . The β—decay transitions between the initial and final states can be classified based on the log ft values from [19, 20] in Table 1.
The hindrance factors HF in the α- decay are calculated by Eq 3: (3) Where, is the partial half-life for the excited state having a given α—decay branching ratio Pi . All the theoretical half-life values in the present evaluation were obtained from the spin-independent equations of Preston . Five classes of α- transitions were found based on the HF values. For the hindrance factor between 1 and 4, the transition is called a favored transition in which the emitted α- particle is assembled from two low lying pairs of nucleons in the parent nucleus, leaving an odd nucleon in its initial orbital. For hindrance factors between 4 and 10, it indicates a mixing or favorable overlap between the initial and final nuclear states. For values between 10 and 100, it indicates that the spin projections of both initial and final states are parallel, but the wave-function overlap is not favorable. For values ranging from 100 up to1000, it indicates that the transitions occur with a change in parity but with projections of initial and final states being parallel. Finally, for hindrance factors of >1000, it indicates that the transition involves a parity change and a spin flip.
The electric quadrupole transition probability B(E2: ) and the energy ratio R(4/2) = E(4+ 1)/E(2+ 1) were calculated from the proton-neutron interaction, which is proportional to the product of the number of active protons and neutrons (NpNn).
The associated log ft values, the hindrance factors, and the statistical analysis of γ–ray data and the deduced level schemes were calculated using the computer codes LOGft, ALPHAD, BrIcc, which are available at Brookhaven National Laboratory's website: www.nndc.bnl.gov. The weighted average values for half-lives were calculated when we want to calculate an average that is based on different percentage values for several categories or when we have a group of values with frequencies associated with it using the AveTool code. All associated uncertainties are expressed at the k = 1 confidence level (i.e. 68% coverage). Using level energies from measured values of energies of transitions, the GTOL code was used to determine the intensity balance. The absolute intensities of γ-rays and the normalization factor for the transferring of the relative intensities to the intensities per 100 decays of the parent nucleus have been calculated using the GABS code. In addition, the theoretical conversion coefficients were deduced from the BrIcc code: v2.3S (29–March–2011)  with "Frozen Orbitals" approximation, and with an implicit uncertainty of 1.4% (k = 2 confidence level). The probabilities of internal conversion are represented as conversion coefficients by Eq 4: (4) Where, λe and λγ are the probabilities for emission of conversion electrons and γ’s, respectively . The total conversion coefficient represents the sum of the probabilities of conversion electrons in different atomic shells as in Eq 5: (5) where, (6)
The conversion coefficients for mixed transitions are given as a function of a mixed ratio δ as in Eq 7: (7)
The values of Q(β), Q(α), and the separation energies of the neutrons and the protons Sn and Sp were calculated using the 2012 Atomic Mass Evaluation code (AME2012), available from the Atomic Mass Data Center (AMDC), Institute of Modern Physics (IMP), Chinese Academy of Sciences .
Results and Discussions
The Q-values, the separation energies of the neutron, the proton, the two neutrons and the two protons (Sn, Sp, S(2N) and S(2P), respectively, as well as their associated uncertainties were calculated using the Atomic Mass Evaluation AME2012 for and and listed in Table 2, respectively. All energies are expressed in keV unless otherwise noted. All associated uncertainties are expressed at the k = 1 confidence level (i.e. 68% coverage).
The measured half -lives T1/2 and the Predicted spin-parity values Jπ (“from systematics and calculations”) for the ground states g.s. of the nuclides under consideration are listed in Table 3.
The decay Data for the ground state g.s for 217Bi was only available in the previous evaluation . However, new energy levels and γ- rays have been measured from the 9Be (238U,X) in [24–26]. Meanwhile, the half-life of 217Bi was adopted from the weighted average of the half-lives of the γ- transitions through the α decay of 217Po , which were 93(3) s for 254.1 γ, 100.5(13) s and 98(1) s for 264.4 γ , respectively. In Table 3, the half-life of 217Fr was adopted in  from the unweighted average measured half-lives of 22(5) μs , 16(2) μs [28, 30] and 15(3) μs , respectively. Similarly, the half-life of 217Pa is adopted in the present evaluation from the unweighted average of the measured half-lives of 4.9(6) ms, 3.4(2) ms, 2.3(+5–3) ms, 3.4(1) ms and 3.8(2) ms [32–36], respectively. Meanwhile, Jπ was predicted from systematics and calculations in . The half- life of 217At and its uncertainty were reported in .
The energy levels with their uncertainties, their spins-parities Jπ, the gamma- transition energies Eγ, their intensities Iγ (%), their associated uncertainties, their assigned multipolarities (MULTI.), the internal conversion coefficients (Ice(K)), and the total internal conversion coefficients (Icc) with their associated uncertainties calculated using BrIcc v2.3S for 217Bi, 217At, 217Fr, 217Ac and 217Pa are listed in Tables 4–8, respectively.
The α- energies, α- intensities, their associated uncertainties and the hindrance factors HF calculated by LOG ft are listed in Table 9 for 217At, 217Fr and 217Ac from the 221Fr-, 221Ac- and 221Pa- α decays, respectively.
In Table 9, Eα’s, Iα’s and their associated uncertainties for 217At were measured in , except for Eα’s = 5500 and 5530, which were measured from the α-γ coincidence spectrum in . For 217Fr and 217Ac, they were measured in  and , respectively.
The isomeric state energy levels (Elevel), their percentage decay by isomeric transition (% IT), their Jπ, and their measured half-lives for 217Bi, 217Ac and 217Pa, respectively, are listed in Table 10.
In Table 10, the half-live T1/2 for the E = 1436+x in 217Bi was measured in , whereas for 217Ac, it was measured from the γγ prompt coincidences in . Meanwhile, for 217Pa, it was calculated as an unweighted average of 1.6(10) ms , 0.(6) ms , 1.5(2) ms  and 1.5(+9–4) ms , respectively. B(E2) was calculated for 217Bi from the systematics of neighboring nuclides and ranges from 0.00062(3) for x = 20 keV for the isomeric states 1436+x keV to 0.00044(2) for x = 90 keV . In addition, an octupole deformation has been noticed in 217Fr from the large value of B(E1)/B(E2) .
Skeleton schemes for 217Tl, 217Bi, 217At, 217Fr, 217Ac and 217Pa are shown in Fig 1. The complete decay schemes of 217Bi, 217At, 217Fr, 217Ac and 217Pa based on the current evaluation (S1–S12 Datasets) are shown in Figs 2–6, respectively. Gamma transition energies with their emission probabilities, spins and parities for energy levels, hindrance factors for α- decays and band structures are included in the figures. Whereas, Intensities I(γ+ce) are expressed per 100 parent decays.
Gamma transition energy is in blue color, the black lines are for the level energies of 217Bi, whereas, the green color is for the half- lives and red color is for the decay type.
Gamma transition energy and multipolarities are in blue color, the black lines are for the level energies of 217At, whereas, the green color is for the half- lives and red color is for the α- decay properties (Eα, Iα and HF).
A) the α- decay properties (Eα, Iα and HF) in red color. B) Gamma transition energy is in blue color, the black lines are for the level energies of 217 Fr, whereas, the green color is for the half- lives.
A) the α- decay properties (Eα, Iα and HF) in red color. B) Gamma transition energy is in blue color, the black lines are for the level energies of 217 Ac, whereas, the green color is for the half- lives.
The evaluated nuclear structure data files (ENSDF) for nuclides of odd-proton numbers among the mass chain A = 217 ( and ) have been updated in the present work. All literature works have been studied until the cut-off date April 2015. The half-lives, the Q (α) and Q (β) values, the total conversion electrons as well as the K-Shell to L-Shell, L-Shell to M-Shell and L-Shell to N-Shell conversion electron ratios have been reevaluated and adopted in the present work. Moreover, an updated skeleton decay scheme for each of the above nuclei has been presented here. In addition, the updated decay schemes include the assigned multipolarities, the emission probabilities, gamma-transitions and the evaluated decay hindrance factor (HF) for α-decays whenever possible. The new ENSDF datasets for the above nuclides have been sent to the National Nuclear Data Center (NNDC) at Brookhaven National Laboratory (BNL) for consideration of online publication.
S1 Dataset. Adopted levels for 217Tl.
S2 Dataset. Adopted levels, Gammas for 217Bi.
S3 Dataset. 98E (238U, x)217Bi.
S4 Dataset. Adopted levels, Gammas for 217At.
S5 Dataset. 221Fr alpha decay
S6 Dataset. Adopted levels, Gammas for 217Fr.
S7 Dataset. 221Ac alpha decay.
S8 Dataset. 210Pb (11B, 4nγ) 217Fr.
S9 Dataset. Adopted levels, Gammas for 217Ac.
S10 Dataset. (HI, xnγ) 217Ac.
S11 Dataset. 221Pa alpha decay.
S12 Dataset. Adopted levels, Gammas for 217Pa.
The authors would like to thank the authorities of King Abdulaziz City for Science and Technology (KASCT), Long-Term Comprehensive National Plan for Science, Technology and Innovations, and King Abdulaziz University (KAU), Saudi Arabia, for funding this project, contract number ‘‘11-MAT2037-03”. The authors also, acknowledge with thanks Science and Technology Unit, King Abdulaziz University, for technical support. In addition, we express our deepest appreciations to Dr. J. Tuli, National Nuclear Data Center (NNDC), Brookhaven National Laboratory (BNL) Upton, NY, USA, for supervising this work and valuable discussions throughout the evaluation process.
Conceived and designed the experiments: SSN AMA SAS. Performed the experiments: SSN AMA SAS. Analyzed the data: SSN AMA SAS. Contributed reagents/materials/analysis tools: SSN AMA SAS. Wrote the paper: SSN AMA SAS.
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