$\beta$-delayed & neutron-induced fission
in the dynamical ejecta of mergers

    LA-UR-18-XXXXX

Matthew Mumpower

Los Alamos National Lab

INT Kilonova Meeting

Tuesday March 13$^{th}$ 2018


FIRE Collaboration
Fission In R-process Elements

Outline

Background & motivation

The old approach to delayed particle emission

The new QRPA+HF model

Application of QRPA+HF to $\beta$-delayed fission

Results & application to the $r$-process

The Problem

We want to describe the abundances observed in nature

But there is uncertainty in:

The astrophysical conditions

The nuclear physics inputs

Both are required to model the nucleosynthesis

Inputs from nuclear physics

1st order: masses, $\beta$-decay rates, reaction rates & branching ratios

See review paper: Mumpower et al. PPNP 86 (2016)

$\beta$-delayed neutron emission

Discovered in 1939 by R.B. Roberts et al.

Delayed emission with half-life of precursor

Energetically possible: $Q_\beta$ > $S_n$ Important for neutron-rich nuclei

The energy window argument

For $\beta$-delayed neutron emission

Start with the initial population from QRPA

Mumpower et al. PRC 94 064317 (2016)

The energy window argument

For $\beta$-delayed neutron emission

Spread strength using 100 keV uncertainty

Mumpower et al. PRC 94 064317 (2016)

The energy window argument

For $\beta$-delayed neutron emission

Calculate the probabilities assuming neutron emission dominates

Mumpower et al. PRC 94 064317 (2016)

The energy window argument

For $\beta$-delayed neutron emission

Calculate the probabilities assuming neutron emission dominates

Mumpower et al. PRC 94 064317 (2016)

The energy window argument

For $\beta$-delayed neutron emission

For more n-rich nuclei, sep. energies can overlap

Mumpower et al. PRC 94 064317 (2016)

The energy window argument

For $\beta$-delayed neutron emission

For more n-rich nuclei, sep. energies can overlap

Mumpower et al. PRC 94 064317 (2016)

How do we solve this problem?

We take a more microscopic approach by combining

QRPA: Initial population of excited states in daughter

Hauser-Feshbach: Follow the subsequent statistical decay

Output: branching ratios & particle spectra

Combining QRPA + HF

Initial population from the $\beta$-decay strength function from P. Möller's QRPA

Follow the statistical decay until all excitation energy is exhausted

Möller et al. PRC (1997 & 2003) • Kawano et al. PRC 94 014612 (2016) • Mumpower et al. PRC 94 064317 (2016)

Average neutron emission

Apply energy window method to the entire chart of nuclides

Problem with describing very neutron-rich nuclei

Mumpower et al. PRC 94 064317 (2016)

Average neutron emission

Apply the QRPA+HF method to the entire chart of nuclides

Problem with neutron-rich nuclei goes away

Mumpower et al. PRC 94 064317 (2016)

Extensive benchmarking

QRPA+HF GT-only $\beta$-strength are within 15% of measured $P_{1n}$ values

Adding FF transitions improves the match to measured data by 3%

Using measured masses improves the match to measured data by 3%

This yields a roughly 9% global model uncertainty to measured $P_{1n}$ values
The best in the business!

Spyrou et al. PRL 117 142701 (2016) • Mumpower et al. PRC 94 064317 (2016) • Wu et al. PRL 118, 072701 (2017)

Extension to $\beta$df

We have now extended the model to describe $\beta$-delayed fission ($\beta$df)

Barrier heights from Möller et al. PRC 91 024310 (2015)

Assumes a Hill-Wheeler form for fission transmission

Mumpower et al. arXiv:1802.04398 (2018)

Multi-chance $\beta$df

Recall: Near the dripline $Q_{beta}$ ⇡ $S_{n}$ ⇣

Multi-chance $\beta$df: each daughter may fission

The yields in this decay mode are a convolution of many fission yields!

Mumpower et al. arXiv:1802.04398 (2018)

($n$,$\gamma$,$f$) competition

Fission can successfully compete with $\gamma$-rays and neutrons

Mumpower et al. (2018)

Cumulative $\beta$df probability

$\beta$df occupies a large amount of real estate in the NZ-plane

Multi-chance $\beta$df outlined in black

Mumpower et al. arXiv:1802.04398 (2018)

Application to $r$-process

Network calculation of neutron star merger ejecta

$\beta$df alone prevents the production of superheavy elements in nature

Mumpower et al. arXiv:1802.04398 (2018)

Impact on final abundances

Network calculation of neutron star merger ejecta; FRDM2012 inputs

$\beta$df can shape the final pattern near the $A=130$ peak

Mumpower et al. arXiv:1802.04398 (2018)

Multi-chance $\beta$df contribution

Network calculation of neutron star merger ejecta; FRDM2012 inputs

Multi-chance $\beta$df contributes at both early and late times

Mumpower et al. arXiv:1802.04398 (2018)

Freeze-out matters

Network calculation of neutron star merger ejecta; FRDM2012 inputs

$\beta$df overtakes (n,f) during the decay back to stability

Mumpower et al. arXiv:1802.04398 (2018)

Neutron-induced fission rates

Apply CoH: Los Alamos statistical Hauser-Feshbach

Barrier heights from Möller et al. PRC 91 024310 (2015)

Assumes a Hill-Wheeler form for fission transmission

Many channels calculated: $(n,\gamma)$, $(n,2n)$, $(n,f)$

Mumpower et al. to be published (2018)

Special thanks to

My collaborators

E. Holmbeck, P. Jaffke, T. Kawano, S. Liddick, G. C. McLaughlin, P. Möller, T. Sprouse, A. Spyrou, R. Surman, N. Vassh, M. Verriere, J. Wu & Y. Zhu

Students Postdocs

Summary

We have recently built the QRPA+HF framework which is well benchmarked and applicable across the chart of nuclides

We have performed new calculations of neutron-induced fission & beta-delayed fission and applied them to $r$-process nuclelosynthesis calculations

Multi-chance $\beta$df in particular has been overlooked

$\beta$df impacts fission dynamics, the final abundances as well as the reheating relevant for kilonova

Results at MatthewMumpower.com