Acknowledgements

Almudena Arcones   Melina Avila   Camilla Juul Hansen  

Peter Mohr   Fernando Montes   Wei Jia Ong Hendrik Schatz

The periodic table from
a Galactic Chemical Evolution perspective

What do the ancient stars show us?

The periodic table from
a Galactic Chemical Evolution perspective

The weak $r$-process

• Where?

  In neutrino-driven outflows of explosive environments (ccSNe or NSMs)

• When?

  During the expansion of the hot and dense outflows ($Y_e \equiv n_p/(n_p+n_n),s,\tau$)

• How?

  After an $\alpha$-rich freeze-out from NSE at T= 5-2 GK $(\alpha,n)$ reactions produce heavy elements

• What?

  Can synthesize heavy elements around Z = 47 (silver) found in metal-poor stars

How much do we know the $(\alpha,xn)$ reaction rates?

The $(\alpha,xn)$ reaction rates are sensitive to the $\alpha$-nucleus potential
and their uncertainties can be up to two orders of magnitude.

Framework of the sensitivity study

A. Parikh et al., Astrophys. J., Suppl. Ser. 178, 110 (2008)
N. Nishimura et al., Mon. Not. R. Astron. Soc 489, 1379 (2019)
J. Bliss et al., Phys. Rev. C 101, 055807 (2020)
P.A. Denissenkov et al., Mon. Not. R. Astron. Soc 503, 3913 (2021)

• Relevant thermodynamic profiles spanning the astrophysical phase-space ($Y_e$, $s$, $\tau$)
  J. Bliss et al., Astrophys. J 855, 135 (2018)


• $(\alpha, xn)$ reaction rates based on the Atomki-v2 $\alpha$-nucleus potential
  P. Mohr et al., At. Data Nucl. Data Tables 132, 101453 (2021)
• MC sampling of the $(\alpha,xn)$ reaction rates (10⁴ calculations)


• Find the most impactful $(\alpha,xn)$ reactions and compare with observations

For more details: A. Psaltis et al., Astrophys. J 935, 27 (2022)

The impact of updated $(\alpha,n)$ reaction rates to elemental abundances

Same model, but different $(\alpha, xn)$ reaction rates!

The impact of new $(\alpha,n)$ reaction rates to elemental abundance ratios

Combine observations, astrophysical modeling and nuclear physics uncertainties

Finding the most important $(\alpha,n)$ reactions for the weak $r$-process

Search for the (anti)correlations! 🔍

The most important $(\alpha,n)$ reactions for the weak $r$-process

N=50 shell closure is a bottleneck for T= 4-5 GK due to the $(n,\gamma) \leftrightarrow (\gamma,n)$ equilibrium

Most of the relevant beams are accessible!

What has been measured so far?

• $\mathrm{^{86}Kr(\alpha,n)}$, $\mathrm{^{96}Zr(\alpha,n)}$ and $\mathrm{^{100}Mo(\alpha,n)}$ at ATOMKI
  
  G.G. Kiss et al., Astrophys. J 908, 202 (2021) • T.N. Szegedi et al., Phys. Rev. C 104, 035804 (2021)
  


• $\mathrm{^{75}Ga(\alpha,n)}$, $\mathrm{^{85,86}Kr(\alpha,xn)}$, $\mathrm{^{85}Br(\alpha,xn)}$ at NSCL/FRIB (HabaNERO/SECAR)
  F. Montes, J. Pereira et al.
  


• $\mathrm{^{86}Kr(\alpha,xn)}$, $\mathrm{^{87}Rb(\alpha,xn)}$, $\mathrm{^{88}Sr(\alpha,xn)}$, $\mathrm{^{100}Mo(\alpha,xn)}$ at Argonne (MUSIC)
  M. L. Avila, C. Fougères et al.
  W. J. Ong et al., Phys. Rev. C 105, 055803 (2022)


• $\mathrm{^{86}Kr(\alpha,n)}$ and $\mathrm{^{94}Sr(\alpha,n)}$ at TRIUMF (EMMA)
  C. Aa. Diget, A. M. Laird, M. Williams et al.
  C. Angus et al., EPJ Web of Conferences, NPA-X (2023)

First measurement of the $\boldsymbol{\mathrm{^{93}Sr}(\alpha,xn)}$ reaction at Argonne with MUSIC

$\mathrm{^{93}Sr}(\alpha,xn)$ at Argonne with MUSIC

M. L. Avila et al., NIM A 859, 63 (2017)

• Re-accelerated $\mathrm{^{93}Sr}$ beam from $\nu$CARIBU.


• MUSIC has close to 100% efficiency due to its segmented anode structure.


• Use a single beam energy to measure a large range of excitation functions of angle integrated cross sections.

We formed linear combinations using trajectories of various astrophysical conditions to compare with observations of metal-poor stars.

The case of HD122563

Results for HD122563 using two trajectories

Results using two trajectories for our star sample

Proton-rich conditions are more favourable than neutron-rich

High entropy and short expansion timescale is preferred

Secrets in the stardust?

Summary

1. The weak $r$-process in neutrino-driven outflows can contribute to the production of elements between strontium and silver that are observed in Galactic metal-poor stars.


2. We explored the impact of $(\alpha,xn)$ reactions to the weak $r$-process and identified the most important of them to motivate future experiments in stable and radioactive ion beam facilities.


3. We investigated which are the most common astrophysical conditions of the neutrino-driven outflows that fit the observational patterns of metal-poor stars.


4. Experiments in the current and next-generation RIB facilities, multimessenger observations and theoretical modeling will enhance our understanding of the origin of the light heavy elements.

Methods

We formed linear combinations using various astrophysical conditions ($Y_e, s, \tau$)
to compare with observations of metal-poor stars.

$$P = \sum_{i=1}^N w_i Y_i$$

where $w_i>0$ is a multiplication factor and $Y_i$ is the abundance pattern of the $i^{th}$ trajectory.

Total number of unique combinations: $C_r = N! / r! (N - r)!$
for example 2 trajectories out of 46 yields 1035 unique combinations

Methods

$$\mathrm{minimize}~ ||A w - O||^2$$ where $O$ is the observational pattern and $$A = \begin{bmatrix} Y_{11} & \cdots & Y_{1k}\\ \vdots & \ddots & \vdots \\ Y_{N1} & \cdots & Y_{Nk} \end{bmatrix} , w = \begin{bmatrix} w_1 \\ \vdots \\ w_k \end{bmatrix}$$

Goal: solve the least-squares problem using $\texttt{sklearn}$