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

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 193 Fr, 193 Rn, 193 At, 193 Po, 193 Bi, 193 Pb, 193 Tl, 193 Hg. Inst. Fisica, Universidade de Sao Paulo, Brasil: Evaluator: V.Vanin 193 Au, 193 Pt, 193 Ir, 193 Os, 193 Re. Evaluations include : Decay, Reaction and  spectroscopy data.

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

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

The Q-values can be obtained from: a)Systematics trend extrapolations from 1995Au04 and/or 1997Au04. b)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). c)In the particular case of Q  determinations, this value may be obtained using a measured E , and the atomic mass values from, e.g., 2000Ra23/2002No01 for the recoil correction.

The corresponding Q-values and their errors (uncertainties) for the nucleus 193 Po Q  S n S p QQ Method a) 1995Au Au (360)7095 (390) Method b) 2000Ra No01 Method c) (using E  ) (140) (490) 8410 (140) 8460 (350) 1950 (140)7085 (140) (35)

 -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.  -transition, the value HF=1. For odd-A and odd-odd nuclei, the radius parameters (r 0 ) 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 r 0 =1.55 value for the 197 Rn  -decay, but without any comment about the source for this value. The same goes for the HF value. One can estimate the r 0 for 193 Po running the ALPHAD code for the above mentioned even-even Po isotopes, requiring a HF=1.0 (0+ g.s. ==> 0+ g.s.  -transition). One obtains r 0 ( 192 Po) = 1.522(20) and r 0 ( 194 Po) = 1.550(8). This latter value agrees with the one quoted in 1998Ak04. Consequently, the mean value for r 0 ( 193 Po) is 1.546(10).

How does the chosen value of r 0 affect the estimate for the HF? (Results from runs of ALPHAD for 193 Po) 197 Rn  -decay r 0 (fm) T 1/2 (ms) HF T 1/2 = 67 ms E  = 7260 keV T 1/2 = 21ms E  = 7358keV

Symmetric and asymmetric errors For x 1,...,x n measurement results with symmetric error  1,...,  n then: =  v i x i /  v i where v i = (  i ) -2 If each x i measurement has an asymmetric error  i + and  i - (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 x i and assuming a symmetric uncertainty given by the larger value of  i + and |  i - |. For example, if the 197 Rn  decay has a half-life of  1/2 = , we would assume for this case a mean value of = 65 +/- 25

 i - x i  i + didi Method 1: d i = (  i + +  i - )/2, w i = [(  i + -  i - )/2] -2 However, the result should have been shifted towards the high tail !!! =  w i (x i +d i ) /  w i where d i and w i have to be determined. With this procedure (Option b) we obtain = 71 +/- 20 Two methods are proposed by Audi et al. (NPA 674, 1 (1997):

Method 2: d i = (  /8) 1/2 (  i + +  i - ), w i = [(1-2/  )(  i + +  i - ) 2 -  i +  i - ] -1 The idea is to consider our measurements x i 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

Option a) ( d i =0) Option b) Method 1 (1997Au04 Option c) Method 2 (1997Au04) x 1 +d / / /- 20 x 2 +d / / / / / /- 16 For the measured values of the 197 Rn  193 Po a -decay we have: two measurements x 1 and x 2 whose values are and , 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.

CONCLUSIONS Up to here we have partially evaluated the following three isotopes: 193 Po, 193 Bi and 193 At. 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 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 r 0 (nuclear radius parameter) to determine the  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 ? Outstanding questions: