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

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

Beta Delayed Neutron Emission Process

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

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.

Potential Precursors in the A ≤ 72 Region

Some of these nuclides can emit two or more delayed neutrons if Qβ > S2n or Qβ > S3n

Potential Precursors in the A ≤ 72 Region

P2n P3n

Number of cases with measured P2n , P3n

19 4

Potential number of precursors (2011AuZZ)

115 80

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)

Potential Precursors in the A ≤ 72 Region

Two-Neutron Emission

Three-Neutron Emission

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)

Sample Compilation and Evaluation Tables

Compilation Table

Evaluation Table

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 Pn within two

orders of magnitude

KHF Systematics in the A ≤ 72 region

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1

LOG([Qβ-Sn]/[Qβ-C])

LO

G(P n

)

Data

KHF Fit

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-n

b

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.

Systematics in the A ≤ 72 Region

Systematics in the A ≤ 72 Region

-2

-1

0

1

2

3

4

5

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

LOG(Qβ-Sn)

LO

G(P n/T

1/2)

Data

Fit

Comparison of KHF to T1/2/Pn Systematics

KHF

Pn/T1/2

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

-1.1 -0.9 -0.7 -0.5 -0.3 -0.1 0.1

LOG([Qβ-Sn]/[Qβ-C])

LO

G(P n

)

Data

KHF Fit

-2

-1

0

1

2

3

4

5

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4

LOG(Qβ-Sn)

LO

G(P n/T

1/2)

Data

Fit

Birch et al.

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

Comparison with Theory: 1997Mo25

Ratio of Calculated Pn to Experimental

0.001

0.01

0.1

1

10

100

10 15 20 25 30 35 40 45

Neutron Number

Pn(t

h)/

P n(e

xp

)

Comparison with Theory: 1997Mo25

Moller97: Ratio of Calculated T1/2 to Experimental

0.01

0.1

1

10

100

10 15 20 25 30 35 40 45

Neutron Number

T1

/2(t

h)/

T 1/2(e

xp

)

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

Comparison with Theory: 2003Mo09

Moller03: Ratio of Calculated Pn to Experimental

0.0001

0.001

0.01

0.1

1

10

10 15 20 25 30 35

Nuetron Number

Pn(th

)/Pn(e

xp)

Comparison with Theory: 2003Mo09

Moller03: Ratio of Calculated T1/2 to Experimental

0.01

0.1

1

10

100

1000

10 15 20 25 30 35 40 45

Nuetron Number

T1/

2(th

)/T1/

2(e

xp)

Systematics of Other Mass Regions

Submitted to PRC - Rapid Communication (Reviewed Oct 3, minor comments)

Systematics of Other Mass Regions: Ni - Tc Data source: ENSDF + Nuclear Wallet Cards

KHF McCutchan et al.

Systematics of Other Mass Regions: Rh - La Data source: ENSDF + Nuclear Wallet Cards

KHF McCutchan et al.

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- CRP approved 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).