Nuclear Data Evaluation for Mass Chain A=217:Odd-Proton Nuclei

Thallium (Tl81217), Bismuth (Bi83217), Astatine (At85217), Francium (Fr87217), Actinium (Ac89217) and Protactinium (Pa91217) 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.


Introduction
Alvarez-Pol et al., [1] identified 217 Tl from the 9 Be( 238 U, 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 ×10 9 ions/spill bombarded a 9 Be target of 2500 gm/cm 2 . The 217 Tl 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 217 Bi isotope was attributed to Pfützner et al., [2] using the same facility. The spectrum was investigated by means of γ-γ, α-γ coincidence and spectrum-multiscaling measurements [3]. The RISING array of 15 Ge clusters was used to detect the γrays. Each cluster has seven elements.
Fry and Thoennessen [4] reported that thirty-nine isotopes of Astatine (At) have been discovered based on the Hartree-Fock-Bogoliubov model . Meanwhile, the discovery of The total decay constant λ for a constant nuclear matrix element η is given as: where, ƒ(Z,Q) is a Fermi integral, which is constant for a given βdecay 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.fm 3 . m e 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 t 1/2 as: 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 [18]. The βdecay 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 αdecay are calculated by Eq 3: Where, T Exp 1=2 a i ð Þ is the partial half-life for the excited state having a given α-decay branching All the theoretical half-life values in the present evaluation T Theory 1=2 a i ð Þ were obtained from the spin-independent equations of Preston [21]. Five classes of αtransitions 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 αparticle 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: 2 þ 1 À 0 þ 1 ) 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) [22] 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: Where, λ e and λ γ are the probabilities for emission of conversion electrons and γ's, respectively [23]. The total conversion coefficient represents the sum of the probabilities of conversion electrons in different atomic shells as in Eq 5: where, The conversion coefficients for mixed transitions are given as a function of a mixed ratio δ as in Eq 7: The values of Q(β), Q(α), and the separation energies of the neutrons and the protons S n and S p 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 [24].

Results and Discussions
The Q-values, the separation energies of the neutron, the proton, the two neutrons and the two protons (S n , S p , S(2N) and S(2P), respectively, as well as their associated uncertainties were calculated using the Atomic Mass Evaluation 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 T 1/2 and the Predicted spin-parity values J π ("from systematics and calculations") for the ground states g.s. of the nuclides under consideration are listed in Table 3.
The energy levels with their uncertainties, their spins-parities J π , the gamma-transition energies E γ , their intensities I γ (%), 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 217 Bi,217 At, 217 Fr, 217 Ac and 217 Pa are listed in Tables 4-8, respectively. The αenergies, αintensities, their associated uncertainties and the hindrance factors HF calculated by LOG ft are listed in Table 9 for 217 At, 217 Fr and 217 Ac from the 221 Fr-, 221 Ac-and 221 Pa-α decays, respectively. In Table 9, E α 's, I α 's and their associated uncertainties for 217 At were measured in [41], except for E α 's = 5500 and 5530, which were measured from the α-γ coincidence spectrum in [42]. For 217 Fr and 217 Ac, they were measured in [42] and [29], respectively.
** is β-decay followed by a neutron emission Q-value.
***ECP is the electron capture followed by a proton emission.
*** The Multipolarities were deduced by [17] from gamma-ray angular distributions and angular correlations. Since no delay component was observed in γγ(t), M2 multipolarities were ruled out for quadrupole transitions in 217 Fr.
Skeleton schemes for 217 Tl, 217 Bi, 217 At, 217 Fr, 217 Ac and 217 Pa are shown in Fig 1. The complete decay schemes of 217 Bi,217 At, 217 Fr, 217 Ac and 217 Pa 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 αdecays and band structures are included in the figures. Whereas, Intensities I(γ+ce) are expressed per 100 parent decays. Table 8. 217 Pa nuclear energy levels and associated properties [10,[39][40].
doi:10.1371/journal.pone.0146182.t008  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.