in the dynamical ejecta of mergers

LA-UR-18-XXXXX

Los Alamos National Lab

*INT Kilonova Meeting*

Tuesday March 13$^{th}$ 2018

FIRE Collaboration

Fission In R-process Elements

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

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

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

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

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

For $\beta$-delayed neutron emission

Start with the initial population from QRPA

Mumpower *et al.* PRC 94 064317 (2016)

For $\beta$-delayed neutron emission

Spread strength using 100 keV uncertainty

Mumpower *et al.* PRC 94 064317 (2016)

For $\beta$-delayed neutron emission

Calculate the probabilities assuming neutron emission dominates

Mumpower *et al.* PRC 94 064317 (2016)

For $\beta$-delayed neutron emission

Calculate the probabilities assuming neutron emission dominates

Mumpower *et al.* PRC 94 064317 (2016)

For $\beta$-delayed neutron emission

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

Mumpower *et al.* PRC 94 064317 (2016)

For $\beta$-delayed neutron emission

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

Mumpower *et al.* PRC 94 064317 (2016)

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

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)

Apply energy window method to the entire chart of nuclides

Problem with describing very neutron-rich nuclei

Mumpower *et al.* PRC 94 064317 (2016)

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)

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)

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)

**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)

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

Mumpower *et al.* (2018)

$\beta$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)

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)

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)

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)

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)

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)

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

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