A=193 Mass Chain evaluation: A summary

1. A=193 Mass Chain evaluation: A summary IAEA-ICTP Workshop on Nuclear Structure and Decay Data: Theory and Evaluation, Trieste, Italy November 17-28 - 2003 Guillermo V. Marti Department of Physics – Tandar Laboratory CNEA – Buenos Aires - Argentina

2. Evaluation of nuclear data for the NSDD network (IAEA) Coordinated Research Project: Evaluate nuclear data for nuclides with mass numberA=193, 191, and 178 (3 years). For the first year (2003): A=193 Mass chain evaluation ( eleven isotopes to be evaluated). Tandar Laboratory, CNEA, Argentina: Evaluators: E.Achterberg, O.A.Capurro, G.V.Marti 193Fr, 193Rn, 193At, 193Po, 193Bi, 193Pb, 193Tl, 193Hg. Inst. Fisica, Universidade de Sao Paulo, Brasil: Evaluator: V.Vanin 193Au, 193Pt, 193Ir, 193Os, 193Re. Evaluations include : Decay, Reaction and g-spectroscopy data.

3. 193Fr and 193Rn: No previous ENSDF file for these nuclides and there is no spectroscopy information available up to our cutoff date: September 30/03. 193At, 193Po and 193Bi: ENSDF files ready and sent for pre-review by project coordinator (Dr E.Browne-Moreno). 193Pb and 193Tl: First rough versions of new ENSDF files, under current evaluation. 193Hg: Bibliography evaluated and systemized, ENSDF file not yet started.

6. Three questions about: • 1-Q values determination • 2- a-Hindrance Factors determination • 3- Asymmetric errors and their evaluation In what follows I will show some examples obtained throughout the 193Po isotope evaluation.

7. The Q-values can be obtained from: • Systematics trend extrapolations from 1995Au04 and/or 1997Au04. • Atomic mass excess data deduced from experimental atomic masses determined using, e.g., Schottky Mass Spectroscopy (2000Ra23), and extension of these results using additional information for known alpha-ray energies from alpha-decay chains (2002No01). • In the particular case of Qa determinations, this value may be obtained using a measured Ea, and the atomic mass values from, e.g., 2000Ra23/2002No01 for the recoil correction.

8. The corresponding Q-values and their errors (uncertainties) for the nucleus 193Po -8470 (490) 8460 (350) 1950 (140) 7085 (140) -8110 (140) 8410 (140) 7093.7 (35)

10. a-decay Hindrance Factors and their determination ENSDF policy: the nuclear radius for each even-even nucleus is determined by defining, for the g.s. to g.s. a-transition, the value HF=1. For odd-A and odd-odd nuclei, the radius parameters (r0) are chosen to be the average of the radii for the adjacent even-even nuclei (see e.g. 1998Ak04). The previous evaluator of the A=193 mass chain used a r0=1.55 value for the 197Rn a-decay, but without any comment about the source for this value. The same goes for the HF value. One can estimate the r0 for 193Po running the ALPHAD code for the above mentioned even-even Po isotopes, requiring a HF=1.0 (0+ g.s. ==> 0+ g.s. a-transition). One obtains r0(192Po) = 1.522(20) and r0(194Po) = 1.550(8). This latter value agrees with the one quoted in 1998Ak04. Consequently, the mean value for r0(193Po) is 1.546(10).

11. How does the chosen value of r0 affect the estimate for the HF? (Results from runs of ALPHAD for 193 Po)

12. Symmetric and asymmetric errors For x1,...,xn measurement results with symmetric error s1 ,...,sn then: <x> = S vixi / S viwherevi = (si)-2 If each xi measurement has an asymmetric error si+andsi- (i.e. in half-lives measurements), the question is: How should a weighted mean be formed from results with these asymmetric errors?. A simple answer could be “symmetrizing the uncertainties”. Option a) Keeping the measured value xi andassuming a symmetric uncertainty given by the larger value of si+ and|si-|. For example, if the 197Rn a decay has a half-life of t1/2=65-14+25 , we would assume for this case a mean value of <x> = 65 +/- 25

13. However, the result should have been shifted towards the high tail !!! <x> = S wi(xi+di) / S wiwhere di and wi have to be determined. Two methods are proposed by Audi et al. (NPA 674, 1 (1997): Method 1: di = ( si + +si - )/2 , wi = [( si+ -si- )/2]-2 si- xi si+ di With this procedure (Option b) we obtain <x> = 71 +/- 20

14. Method 2: di = (p/8)1/2(si+ +si-) , wi = [(1-2/p)(si+ +si-)2-si+si-]-1 The idea is to consider our measurements xi as a random variable where its probability density is an asymmetric normal distribution. The average value of this distribution divides the distribution into two equal areas, and will be the mean value of our assumed symmetric normal distribution. In this case (Option c) we obtain for our example a value 72 +/- 20

15. For the measured values of the 197Rn 193Po a-decay we have: two measurements x1 and x2 whose values are 65-14+25 and 51-15+35 , we obtain the following results after a given “symmetrization procedure”: NOTE: Option c) [Method 2 from 1997Au04] is the method used for the compilation of the Audi-Wapstra tables reported in 1995Au04 and 1997Au04.

16. CONCLUSIONS Up to here we have partially evaluated the following three isotopes: 193Po, 193Bi and 193At. The ENSDF files are in the pre-review stage. For the rest of the isotopes it is expected to finish by the end of Jan. 2004 Outstanding questions: 1- Should Q values determined from experimental atomic masses have precedence over Q values calculated from systematic trend extrapolations for the Q records in ENSDF files ? 2- Although the policy for the determination of r0 (nuclear radius parameter) to determine the a HF values is clear, some authors do not quote the sources for this value, but the influence of this value is significant in the determination of HFs. 3- Should the techniques used to handle the cases of asymmetric errors be reconsidered ?