M. Birch and B. Singh ( McMaster University) D. Abriola (NDS-IAEA)

1. Compilation and Evaluation of Beta-Delayed Neutron emission probabilities and half-lives of precursors in the Non-Fission Region (A ≤ 72) M. Birch and B. Singh (McMaster University) D. Abriola (NDS-IAEA) T.D. Johnson, E.A. McCutchan and A.A. Sonzogni (NNDC, BNL) Presented by B. Singh at DDEP workshop, Oct 8-10, 2012 LNHB/CEA Saclay, France

2. Beta Delayed Neutron Emission Process • In neutron rich nuclei, if the Q-value of the beta decay of the parent (precursor) is greater than the neutron separation energy of the daughter then neutron unbound levels in the beta-daughter nuclide may be populated which decay by neutron emission • We define this energy window as Qβ-n = Qβ(A,Z)– Sn(A,Z+1) • Need Qβ-n > 0 for delayed neutron emission to occur

3. Beta Delayed Neutron Emission Process

4. Previous Evaluations of the A ≤ 72 Region • Only a few nuclides were present in earlier evaluations: • L. Tomlinson, ADNDT 12, 179 (1973): 5 nuclides • 8He, 9Li, 12Be, 13B, 17N • P. del Marmol, ADNDT A6, 141 (1969): • 8He, 9Li, 12Be, 17N • Since 1973 many new measurements have been made in this mass region • Current work is the first comprehensive compilation and evaluation of Pn for this mass region

5. Potential Precursors in the A ≤ 72 Region • The delayed neutron emission probabilities have been experimentally measured for 101 precursors. These measurements have been compiled and evaluated. • 112 additional nuclides have been identified as potential precursors based on Qβ-n > 0 using mass values from G. Audi et al., 2011 interim mass evaluation file (2011AuZZ) • For 172 of these nuclides (including all but one of the 101 measured precursors) half-life measurements are also available. These too have been compiled and evaluated.

6. Potential Precursors in the A ≤ 72 Region

7. Potential Precursors in the A ≤ 72 Region • Some of these nuclides can emit two or more delayed neutrons if Qβ > S2n or Qβ > S3n • Each measured multiple delayed neutron emission probability has also been evaluated • Predictions based on Q(β-2n) > 0 and Q(β-3n) > 0, where Q(β-2n) = Qβ(A,Z) – S2n(A,Z+1) Qβ-3n = Qβ(A,Z) – S3n(A,Z+1) S3n(A,Z) = M(A-3,Z) + 3n – M(A,Z) • One four-neutron emission has also been observed (17B)

8. Potential Precursors in the A ≤ 72 Region Three-Neutron Emission Two-Neutron Emission

9. Compilation and Evaluation Procedures • Compilation consists of complete documentation of all measurements including: • Which quantity was measured (T1/2, P1n, P2n, etc.) • The method by which it was measured (list of methods in an IAEA-NDS-2011 report) • Whether a neutron spectrum was measured and reported • Comments concerning the methodology of the experiment and reliability of the result • The evaluation is done by considering the methodology of the experiments to determine which results are most reliable, and using an averaging procedure (e.g. weighted average) when several independent measurements may be considered equally reliable • When an average is taken, quoted uncertainty in the recommended value is never lower than the lowest uncertainty cited in the selected data set of measured values • Full documentation is kept concerning how the evaluated result was obtained (e.g. which results were considered for averaging, and which averaging procedure was used)

10. Sample Compilation and Evaluation Tables Compilation Table Evaluation Table

11. Systematics in the A ≤ 72 Region • The Kratz-Herrmann Formula (KHF) • Z. Physik 263, 435 (1973) Pn=a([Qβ – Sn]/[Qβ – C])b • a, b are fitted parameters; C is a cut-off parameter with a value which depends on the odd-even character of the precursor C = 0 (e-e) C = 13/√A (o-e/e-o) C = 26/√A (o-o) • Poor fit in this region, can only predict Pnwithin two orders of magnitude

12. KHF Systematics in the A ≤ 72 region

13. Systematics in the A ≤ 72 Region • Better systematics may be obtained using both half-life and delayed neutron emission probability by the following consideration: • Both T1/2 and Pn may be schematically represented as a sum of the product of the beta strength function and Fermi function (statistical rate function) over the energy region of interest • T1/2 = (Σ0≤Ei ≤ Qβ [Sβ(Ei) f(Z,Qβ – Ei)])-1 • Pn = (ΣSn ≤ Ei ≤ Qβ [Sβ(Ei) f(Z,Qβ – Ei)])/(Σ0<Ei<Qβ [Sβ(Ei) f(Z,Qβ – Ei)]) • ⇒ Pn /T1/2 = ΣSn ≤ Ei ≤ Qβ [Sβ(Ei) f(Z,Qβ – Ei)] • The energies in the sum can then be re-indexed with respect to the energy window for the delayed neutron process: Qβ-n = Qβ – Sn • ⇒ Pn /T1/2 = Σ0 ≤ E’i ≤ Qβ-n [Sβ(E’i + Sn) f(Z,Qβ-n – E’i)] • We now simplify by assuming the beta strength function is constant over this energy range and using the approximation Σ0 ≤ E’i ≤ Qβ-n [f(Z,Qβ-n – E’i)] ~ Qβ-nb

14. Systematics in the A ≤ 72 Region • Thus the following relation is obtained: Pn/T1/2 = A(Qβ – Sn)b • A (intercept on a log-log plot), and b (slope on a log-log plot) are fitted parameters, where beta strength function is assumed to be equal to the constant A and b is expected to be greater than 0 based on the derivation of the formula • The fitted values are A=0.0659(20), b=3.921(13) with Pn in percent, T1/2 in seconds and Qβ – Sn in MeV. • This formula can predict delayed neutron emission probability within an order of magnitude if the half-life is known.

15. Systematics in the A ≤ 72 Region

16. Comparison of KHF to T1/2/Pn Systematics KHF Birch et al. Pn/T1/2

17. Comparison with Theory • QRPA calculations from 1997Mo25: Moller et al. ADNDT 66,131 (1997) are available; later in 2003Mo09 • These results predict T1/2,Pn and P2n for neutron rich nuclides

18. Comparison with Theory: 1997Mo25

19. Comparison with Theory: 1997Mo25

20. Comparison with Theory • A revised theoretical calculation was performed in a later work, 2003Mo09: Phys. Rev. C 67, 055802 (2003) • These results show no improvement in calculating half-life and performs more poorly when calculating Pn

21. Comparison with Theory: 2003Mo09

22. Comparison with Theory: 2003Mo09

23. Systematics of Other Mass Regions Submitted to PRC - Rapid Communication (Reviewed Oct 3, minor comments)

24. Systematics of Other Mass Regions: Ni - TcData source: ENSDF + Nuclear Wallet CardsKHF McCutchan et al.

25. Systematics of Other Mass Regions: Rh - LaData source: ENSDF + Nuclear Wallet CardsKHF McCutchan et al.

26. Conclusion and Future Work • The beta-delayed (multiple) neutron emission probabilities and/or half-lives have been evaluated for a total of 173 nuclides in the A ≤ 72 mass region • This evaluation was accomplished by a complete compilation and documentation of all available experimental data • This work has been prompted by an IAEA- CRPapproved in Sept 2012 concerning beta-delayed neutron emitters • The IAEA-CRP hopes to provide a comprehensive reference database of all delayed neutron-related measurements which have been made along with recommended values (similar to what has been done here) for the entire chart of nuclides The CRP also aims at new measurements of Pn values, especially, in the mass regions which have never been touched (e.g. A>150).