and implications for the $r$-process

LA-UR-19-30940

*Workshop on nuclear fission dynamics*

Monday Oct. 28$^{th}$ 2019

FIRE Collaboration

Fission In R-process Elements

Requires deep knowledge of a range of fields, including:

The theoretical modeling of astrophysical environments

Multi-messenger observations (gravitational waves, EM waves, etc.)

Nuclear theory predictions for exotic nuclei

Precision experiments to constrain nuclear theory

Data and observations are limited

We must be clever when deciphering what is going on with nucleosynthesis...

Rapid neutron capture that occurs in astrophysical environments allowing for the production of heavy elements

Neutron captures are initially much faster than $\beta$-decays

Relative slowdown in the nuclear flow (right) produces peak structures in the observed abundances (left)

Astrophysical environment must produce a lot of free neutrons in order for this process to proceed

Aprahamian *et al.* (2018) • Horowitz *et al.* J Phys G 083001 (2019)

One possibility is in (rare?) supernovae

For standard supernovae (left) neutrino physics still needs to be well understood

Jets in magnetorotational driven supernovae (right) may also provide the necessary conditions

Another option is the disk winds of collapsars - black hole forms after core collapse of a rapidly rotating star

Meyer ApJ (1989) • MacFadyen & Woosley ApJ (1999) • Figure from **Mumpower** *et al.* in prep. (2019)

Another possibility is in compact object mergers

A binary merger of neutron stars is an exciting possibility (some indirect evidence exists)

Another option is in the disk of a black hole neutron star binary

Lattimer & Schramm (1974) • Korobkin *et al.* (2012) • Figure from **Mumpower** *et al.* in prep. (2019)

We want to describe the abundances observed in nature

But there is uncertainty in:

The astrophysical conditions (large variations in current simulations)

The nuclear physics inputs (1000's of unknown species / properties)

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

Dillmann *et al.* EPJA (2002) • Aprahamian **et al.** (2018) • See review paper: **Mumpower** *et al.* PPNP 86 (2016)

PRISM: Portable Routines for Integrated nucleoSynthesis Modeling

Sprouse & **Mumpower** in prep (2019)

**The fission process:**

A heavy nucleus splits into two lighter fragments

Subsequent particle emission and decays then occur

Many events gives rise to fission yield

Meitner & Frisch (1938) • Bohr & Wheeler (1939) • Figure from Verriere **et al.** in prep. (2019)

**Influence on the $r$-process:**

Fission rates and branching determine re-cycling (robustness)

Fragment yields place material at lower mass number; barriers determine hot spots

Large Q-value ⇒ impacts thermalization and therefore possibly observations

Responsible for what is left in the heavy mass region when nucleosynthesis is complete ⇒ "smoking gun"

Holmbeck *et al.* ApJ 870 1 (2019) • Vassh **et al.** J. Phys. G (2019) • Figure from Verriere **et al.** in prep. (2019)

(Maximum) FRLDM Barrier heights

Low barrier ↦ fission ⇑

$r$-process hot spots follow low barriers

Möller *et al.* PRC 91 024310 (2015)

(Maximum) HFB-14 Barrier heights

Low barrier ↦ fission ⇑

Used in (n,f) and $\beta$df calculations

http://www.astro.ulb.ac.be/pmwiki/Brusslib/HomePage

We've taken a look at the region where fission seems to occur the most

With variations in both astrophysical conditions and nuclear models

Nuclei which influence the final abundances are colored for (n,f) and ($\beta$,f)

Vassh **et al.** J. Phys. G (2019)

We use statistical Hauser-Feshbach theory updated to account for fission transmission

**Model inputs:** nuclear level density, $\gamma$-ray strength functions, optical model potentials and fission barriers

Kawano *et al.* PRC 94 014612 (2016) • **Mumpower** & Kawano in prep. (2019)

Use statistical Hauser-Feshbach for competition between neutrons, $\gamma$s and fission

Barrier heights Möller (2015) / FRDM2012 masses

Large region that will fission cycle $r$-process

Use statistical Hauser-Feshbach for competition between neutrons, $\gamma$s and fission

Barrier heights from HFB-14 / HFB-17 masses

Similar results are obtained for other nuclear models

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

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

Problem with neutron-rich nuclei goes away

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!__

Can we extend this model to other phenomena ... fission?

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

We have recently extended our QRPA+HF 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

Yokoyama

**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!

Yokoyama

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

Multi-chance $\beta$df outlined in black

Network calculation of neutron star merger ejecta; FRDM2012 inputs

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

PRISM network calculation of neutron star merger ejecta

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

Thielemann *et al.* Zeitschrift fur Physik A Atoms and Nuclei 309 4 (1983) • **Mumpower** *et al.* ApJ 869 1 (2018)

Network calculation of tidal ejecta from a neutron star merger (FRDM2012)

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

This is because of a relatively long fission timescale

Conclusion ⇒ we need a good description of fission yields to understand abundances near $A\sim130$.

Kodama & Takahashi (1975) • Shibagaki *et al.* ApJ (2016) • **Mumpower** *et al.* ApJ 869 1 (2018) • Vassh **et al.** J. Phys. G (2019)

Follow progression of the nucleus from compact to highly elongated shapes

Many possible shape degrees of freedom - but we have to isolate the most important

Möller *et al.* PRC (2009) • Möller **et al.** PRC (2015)

Change in nuclear shape acts as a driving force for bulk rearrangement of material

This results in a collective kinetic energy

The macroscopic shape degrees of freedom couple to individual nucleonic motion

Resulting in an evolution that is both damped and diffuse

This can be approximated as Brownian shape motion

Randrup *et al.* PRL (2011) • Randrup *et al.* PRC (2011) • Randrup *et al.* PRC (2013) • Möller **et al.** PRC (2015)

Amounts to random walk across potential energy surface

Count the number of peaks in the mass yield, $Y(A)$, distribution

Rather smooth variation in number of peaks across chart of nuclides.

$r$-process region: 2 or 3 peaks are the norm given our prediction of fission hot spots

Measure the distance in $A$ between the maxima of $Y(A)$ and $Y(A_{\rm f}/2)$

Abrupt changes can be seen when the maxima shift from symmetric to asymmetric

Symmetric followed by asymmetric distributions can be expected in $r$-process simulations

Measure the spread of the daughter products in $A$

Strong dependence can be seen with the fission system

Wiggles in the yield (number of peaks or asymmetry) don't matter if the distribution is wide!

Measure the placement of material of the highest peak in $A$

Notice the transition between 3 and 2 peaks plays an important role

$r$-process conditions from astro. simulations suggest population of $A\sim150$ to ligher nuclei

Abundance output using common old nuclear fission data and our new model predictions

Co-production of light nuclei from $Z\sim 45$ to the actinides (dynamical merger ejecta only!)

Universality may extend further down to lighter nuclei than commonly accepted in the literature

Vassh *et al.* in prep. (2019)

My collaborators

A. Aprahamian, J. Barnes, A. Burrows, J. Clark, B. Côté, J. Dolance, W. Even, C. Fontes, C. Fryer, E. Holmbeck, A. Hungerford, P. Jaffke, T. Kawano, O. Korobkin, J. Lippuner, G. C. McLaughlin, J. Miller, W. Misch, P. Möller, R. Orford, J. Randrup, G. Savard, T. Sprouse, R. Surman, N. Vassh, M. Verriere, R. Vogt, R. Wollaeger, Y. Zhu

& many more...

▣ Student ▣ Postdoc ▣ CTA Staff ▣ FIRE PI

The $r$-process requires a deep understanding of fission

**Recent calculations give insight into:**

Re-cycling material ▴ Production of heaviest elements ▴ Late-time observations

FRIB, etc. will help to constrain nuclear models, but the heaviest elements will remain relatively inaccessible

We therefore need to keep developing and studying theoretical models of nuclear physics, especially fission

Nuclear modeling is absolutely crucial if we want to prove definitively that heavy elements such as the actinides were made in an event

Results / Data / Papers **@** MatthewMumpower.com

In some simulations actinides seem to be overproduced versus lanthanides

A sufficient amount of dilution with ligher $r$-process material is required to match the solar isotopic residuals

∴ Fission theory has implications far beyond nucleosynthetic outcomes; e.g. for galactic chemical evolution, etc.

Holmbeck *et al.* ApJ 870 1 (2019) • Vassh **et al.** J. Phys. G (2019)

Is there any possible precursor to show that actinide nucleosynthesis has occurred in an event?... Maybe!

The spontaneous fission of $^{254}$Cf can be a __ primary__ contributor to nuclear heating at late-time epochs

The $T_{1/2}\sim 60$ days; found from nuclear weapons testing

Baade *et al.* PASP (1956) • Conway *et al.* JOSA (1962) • Wanajo *et al.* ApJL (2014) • Y. Zhu *et al.* ApJL 863 2 (2018)

Vassh**et al.** J. Phys. G (2019)

Vassh

Primary feeder seems to be from $\beta$-decay

Production of this nucleus been explored over a range of nuclear models; some high - some low

Remains to be seen if we can disentangle from other late-time heating sources (e.g. puslar or accreetion fallback)

Wanajo *et al.* (2014) • Y. Zhu *et al.* ApJL 863 2 (2018) • Vassh **et al.** J. Phys. G (2019) • Wollaeger *et al.* ApJ (2019) • Wu *et al.* PRL (2019)

Both near- and middle- IR are impacted by the presence of $^{254}$Cf

Late-time epoch brightness can be used as a proxy for actinide nucleosynthesis

Future JWST will be detectable out to 250 days with the presence of $^{254}$Cf

This also has implications for merger morphology...

Wanajo *et al.* (2014) • Y. Zhu *et al.* ApJL 863 2 (2018) • Vassh **et al.** J. Phys. G (2019) • Wollaeger *et al.* ApJ (2019) • Wu *et al.* PRL (2019)