A new approach to estimating the probability for delayed neutron emission

E. A. McCutchanA.A. SonzogniT.D. Johnson

National Nuclear Data CenterBrookhaven National Laboratory, NY USA

Outline

• Motivation

• Traditional systematics

• A new parameterization

• A closer look

-delayed neutrons and their use

• Reactor control and post-processing of fuel

• r-process nucleosynthesis and abundances

• Basic structure physics

214 nuclei with measured Pn values

http://www.nndc.bnl.gov/nudat2

Relevance of reliable systematics

Some terminology

AZ+1

Q

AZ

Sn

A-1Z+1

Qn

n

Pn : the probability to emit a neutron following decay

6

Kratz -Herrmann Formula (KHF)

𝑃𝑛≈𝑎 [𝑄 𝛽−𝑆𝑛

𝑄𝛽−𝐶 ]𝑏

Cut off parameter C (MeV)

𝐶=0𝐶=

13

√𝐴𝐶=

26

√𝐴

even-even

even-odd

odd-odd

Traditional systematic studies

K.-L. Kratz and G. Herrmann, Z. Phys. A 263, 435 (1973)

Two parameter fit with ‘a’ and ‘b’

Log-log plot gives straight linewith slope=b

B. Pfeiffer et al., Prog. Nucl. Energy 41, 39 (2002).

The standard for systematic studies

Linear regression

Weighted least-squares

a = 106(38)b = 5.5(6)

red 2 = 81

a = 119(42)b = 5.45(48)red 2 = 146

Audi and Meng (2011)

Effect of improved Q values

a = 106(38)b = 5.5(6)

red 2 = 81

Masses from :Audi and Wapstra (1995)

A better parameterization?

Strength function Fermi integral

𝑃𝑛

𝑇1 /2𝑎(𝑄 𝛽𝑛)

𝑏

Applying same concept as KHF

A more compact trajectory

a = 0.0097(9)b = 4.87(7)red 2 = 35

a = 119(42)b = 5.45(48)red 2 = 146

Light fission fragment region

Heavy fission fragment region

a = 141(48)b = 5.08(37)red 2 = 78

a = 0.016(2)b = 4.55(13)red 2 = 55

A more compact trajectory

A surprising correlation

a = 45(6)b = 4.4(4)

red 2 = 280

a = 0.037(9)b = 4.11(9)red 2 = 87

Light nuclei, Z <26

A closer lookLight fission fragment region

• Very linear trend• Few outliers

100Rb102Rb

A closer lookHeavy fission fragment region

• Few outliers• Less linear trend• Possible shell

effects?

How do we do ??

KHF-2002: B. Pfeiffer et al., Prog. Nucl. Energy 41, 39 (2002).QRPA-1: P. Moller et al., Phys. Rev. C 67, 055802 (2003).

Another surprising correlation

P. Moller et al., Phys. Rev. C 67, 055802 (2003).

Summary

• New prescription for systematics of Pn values

• Ratio of Pn to T1/2

• More compact trajectory

• Works across nuclear chart

• For the future

• Extract information about strength function from slope ??

Relevance to ENSDF

• Some evaluators give Pfeiffer KHF results (2002Pf04) for cases where Pn has not been measured

• Should we replace with values from new systematics ?

Another surprising correlation

P. Moller et al., Phys. Rev. C 67, 055802 (2003).