1. A METHOD FOR YIELD CALCULATIONS Measurements of yields for isotopes with isomers through mixed transitions observed in  -decay Collaboration: A. Andrighetto, O. Bajeat, A.E. Barzakh, E. Del Piero, M. Dubois, S. Essabaa, D.V. Fedorov, G. Gaubert, A.M. Ionan, V.S. Ivanov, P. Jardin, A. Lanchais, C. Lau, N. Lecesne, R. Leroy, G. Lhersonneau, K.A. Mezilev, F.V. Moroz, S.Y. Orlov, J.Y. Pacquet, V.N. Panteleev, V. Rizzi, M.G. Saint Laurent, L. Stroe, L. Tecchio, Y.M. Volkov, A.C.C. Villari.

2. Summary  Experimental Setup.  Measurement conditions.  Analysis Method.  Cs and Rb example: yield and release efficiency measurements. efficiency measurements.  Conclusions.

3. Beam: E p = 1 GeV I p ≈ 70 nA Target temp: 1900°C 2100°C IRIS Facility – P.N.P.I, Gatchina (Russia) Experimental Setup UCx -Gatchina Target- p GeGe* GatchinaTarget: rod 4.5 g/cm 2 Orsay-type Target: 8 tablets 2.8 g/cm 2

4. SATURATION n0n0 Time Int. t1t1 t2t2 t tape t irr n 0 MIS t meas = t 2 - t 1 = t irr - target in saturation condition - constant ion beam from the target ISOTOPES: Am Z X E A Z X   A Z+1 Y Isomer (metastable state) Ground state m.s.=  m g.s.=  g -- -- I.T AZXAZX j m, E1 j g, E 0 =0 FISSION Yield: Branching ratios:  1 → b m1, b g1  2 → b m2, b g2 I.T → b mg Mixing of  lines Measurements

5. Produced nuclei during the irradiation (a): Collected nuclei after the irradiation (b): Number of decays (measured with spectroscopic methods): Analysis Method

6. Release Efficiency [B. Roussiere et al., NIM B 194 (2002) 151] Determination of the release time from the comparison of the yields after separation (experimental yield) with the yield expected in the target (calculated yield): PURE EFFUSION:DIFFUSION IN SPHERICAL GRAINS:  = atoms/s in target (cross section  from M. Bernas et al., NPA 725 (2003) 213)  T = ions/s on tape  S = overall efficiency T R = release time where

7. Rubidium data Parrne Target (Rb,1900°C) Gatchina Target (Rb, 1900°C) x 7.7·10 -4 x 5.5·10 -4

8. Cesium data Gatchina Target (Cs, 1900°C) Parrne Target (Cs, 1900°C) From A. L. Lanchais x 3.6·10 -3 x 1.4·10 -3

9. Conclusions Yield Calculation Method for Mixed  -lines: - Calculation based on the experimental conditions. - Possibility to separate isomer and g.s. contributions. - Accurate evaluation of errors. Problems and Limits of the procedure: - Feeding from  -decay of parents. - Inaccuracy of branchings data in literature (i.e.: 92 Rb). Good Results for Cs and Rb Chains: - Smooth and regular trend of the yield curves. Estimation of the release times for the two targets from the normalized exp_yield/calc_yield ratio. From the comparison between Gatchina and Parrne targets: Parrne target is faster!

10. Appendix I Matrices A and B:

11. Measured quantities: number of counts I TOTAL YIELD p: Appendix II

12. Normalization of I: A = S/N rep S = area of  peak N rep = number of repetitions  tot  =   1  trans   = efficiency of  detector  trans = transmission efficiency n = n 1 T life Appendix III Dead Time

13. Sources of error: C) Transmission efficiency: it’s a systematic error. A)Areas and  efficiency  p is the sum of p m e p g : they are correlated through I 1 e I 2. The correlation is derived from the  2 definition. B) Branching ratios and half-lives: the error is calculated as maximum error. Appendix IV

14. Correlation between p m and p g : from def. of    and I = (C·B·A) -1 ·p = M·p (minimum  2 ) Negligible Errors: areas and  efficiency Appendix V

15. Errors: branchings and half lives Branching b k plus error. Branching b k minus error. Appendix VI PROCEDURE: the yield p m,g is calculated for each value b k +/- of branching and j +/- of life time; the error contribution for the b k and j is the half-difference of the yields relative to b k +/- and j +/-.

16. During irradiation: After irradiation: Without isomers: Appendix VII

17. Appendix VIII Release Times: Rb (Gatchina T.) Rb (Parrne T.) Cs (Gatchina T.) Cs (Parrne T.) DIFFUSION (s) 46 +14-11 8 ±2 26 +14-8 4 +4-1 EFFUSION (s) 15 +4-3 2.6 +1.3-0.2 5 ±1 1.5 +1.0-0.1

18. Appendix IX

19. Rb - Gatchina Target Cs - Gatchina Target Rb - Parrne Target Cs - Parrne Target Appendix: yields

20. Appendix: efficiencies