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


P. del Marmol, ADNDT A6, 141 (1969):



8He, 9Li, 12Be, 13B, 17N
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
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)
Number of
cases with
measured
P2n , P3n
P2n
P3n
19
4
Potential
115
number of
precursors
(2011AuZZ)
80
Potential Precursors in the A ≤ 72 Region
Three-Neutron Emission
Two-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
2.5
2
1.5
LOG(Pn )
1
0.5
Data
KHF Fit
0
-1.1
-0.9
-0.7
-0.5
-0.5
-1
-1.5
-2
LOG([Qβ -S n ]/[Qβ -C])
-0.3
-0.1
0.1
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
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 loglog 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
5
4
LOG(Pn/T1/2)
3
2
Data
Fit
1
0
-0.4
-0.2
0
0.2
0.4
0.6
-1
-2
LOG(Qβ -S n )
0.8
1
1.2
1.4
Comparison of KHF to T1/2/Pn Systematics
2.5
KHF
2
1.5
0.5
Data
KHF Fit
0
-1.1
-0.9
-0.7
-0.5
-0.3
-0.1
0.1
-0.5
-1
Birch et al.
-1.5
-2
LOG([Qβ -S n ]/[Qβ -C])
5
4
3
LOG(Pn/T1/2)
LOG(Pn )
1
2
Data
Fit
1
0
-0.4
-0.2
0
0.2
0.4
0.6
-1
Pn/T1/2
-2
LOG(Qβ -S n )
0.8
1
1.2
1.4
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 P n to Experimental
100
Pn(th)/Pn(exp)
10
1
10
15
20
25
0.1
0.01
0.001
Neutron Number
30
35
40
45
Comparison with Theory: 1997Mo25
Moller97: Ratio of Calculated T 1/2 to Experimental
100
T1/2(th)/T1/2(exp)
10
1
10
15
20
25
0.1
0.01
Neutron Number
30
35
40
45
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
10
1
P n (th)/P n (exp)
10
15
20
25
0.1
0.01
0.001
0.0001
Nuetron Number
30
35
Comparison with Theory: 2003Mo09
Moller03: Ratio of Calculated T 1/2 to Experimental
1000
T1/2(th)/T1/2(exp)
100
10
1
10
15
20
25
30
0.1
0.01
Nuetron Number
35
40
45
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).