$ \ce{^{A}_{Z}X} + n \longrightarrow \ce{^{(A+1)}_{Z}X} $ Neutron capture is a process in which an atomic nucleus ($\ce{^{A}_{Z}X}$) and one or more neutrons ($n$) collide and merge to form an isotope with one higher atomic mass ($A+1$). If the new isotope is stable, a series of increases in mass can occur, but if it is unstable, then [[Beta Decay#Beta-Minus Decay]] will occur, producing an element of the next higher atomic number ($A-1, Z+1$). Neutron capture can proceed in two ways depending on the neutron flux: as a rapid process ([[#r-process]]) or a slow process ([[#s-process]]). > [!note] > Since neutrons have no electric charge, they can enter a nucleus more easily than a charged particle, which has to overcome or tunnel through the high Coulomb Barrier. This allows neutron capture to play a significant role in the cosmic nucleosynthesis of elements heavier than iron ($A=56$), whereas elements with $A>56$ cannot be formed through thermonuclear reactions. ### s-process ![[s-process.png|align:center]] $ \ce{^{A}_{Z}X} + n \longrightarrow \ce{^{(A+1)}_{Z}X} \hspace{1cm} \underbrace{\textcolor{gray}{\left[ \ce{^{A}_{Z}X} \longrightarrow \ce{^{A}_{(Z+1)}X'} + e^{-} + \bar{\nu}_{e} \right]}}_{\rm \beta^{-} \ decay} \hspace{1cm} \longrightarrow \hspace{1cm} \ce{^{(A+N)}_{Z'}X'} $ The s-process (slow neutron-capture process) occurs when an atomic nucleus ($\ce{^{A}_{Z}X}$) undergoes successive [[#Neutron Capture|neutron captures]], but the neutron flux is low enough that [[Beta Decay#Beta-Minus Decay|beta-minus decay]] **can** occur between captures. *(hence, a "slow" process)* **Important Notes:** - Accounts for approximately half the atomic nuclei heavier than iron. - Each branch of the s-process reaction chain terminates at a cycle involving... - Bismuth *(heaviest "stable" element -- technically, radioactive with half-life $\approx 10^{19} \; {\rm yr}$)* - Polonium *(first non-primordial element after bismuth -- half-life $\approx 138 \; {\rm day}$)* - Lead *(decay remanent from Polonium)* - Timescale: $\sim \mathcal{O}(10 \; {\rm yr})$ between successive neutron captures, such that the full process in the reaction chain can take $\sim \mathcal{O}(1000 \; {\rm yr})$ **S-Process Sites:** - The [[Hertzsprung-Russell Diagram#Asymptotic Giant Branch]] ### r-process ![[r-process.png|align:center|500]] $ \ce{^{A}_{Z}X} + Nn \longrightarrow \ce{^{(A+N)}_{Z}X} \hspace{1cm} \underbrace{\textcolor{gray}{\left[ \ce{^{A}_{Z}X} \longrightarrow \ce{^{A}_{Z+1}X'} + e^{-} + \bar{\nu}_{e} \right]}}_{\rm \beta^{-} \ decay} \hspace{1cm} \longrightarrow \hspace{1cm} \ce{^{(A+N)}_{Z'}X'} $ The r-process (rapid neutron-capture process) occurs when an atomic nucleus ($\ce{^{A}_{Z}X}$) undergoes successive [[Neutron Capture|neutron captures]], but the neutron flux is high enough that [[Beta Decay#Beta-Minus Decay|beta-minus decay]] **cannot** occur between captures. *(hence, a "fast"/"rapid" process)* This allows the nuclei to become neutron-rich and highly unstable. This process can continue until the nuclei becomes neutron-saturated (i.e. neutron drip line), and then it will undergo many [[Beta Decay#Beta-Minus Decay|beta-minus decay]] in quick succession until it enters the valley of stability. > [!note] Seed Nuclei > The r-process creates their own seed nuclei, such that they might proceed in massive stars that contain no heavy seed nuclei. This is unlike the [[#s-process]] which needs a seed nuclei of iron-56 or heavier. **Important Notes:** - Accounts for approximately half the atomic nuclei heavier than iron. - Creates the most neutron-rich stable isotopes of each heavy element - Typically, the heaviest four isotopes of every heavy element; heaviest two come only from the r-process - Restricted by the limit of stability (i.e. neutron drip line) where a nuclei is physically unable to retain neutrons, due to the short range nuclear force. - Timescale: $\sim \mathcal{O}(0.01 \; {\rm s})$ between successive neutron captures *(100 captures per second)* **R-Process Sites:** - Center of a core-collapse supernova - Kilonova (binary neutron star merger) - Thermonuclear weapon explosions - *Maybe in collapsars (massive star collapse)* Need locations with a high density of free neutrons. The necessary neutron density is estimated to be $\sim \mathcal{O}(1000 \; {\rm /cm^{3}})$ at $T \approx 2 \; {\rm GK}$ by matching neutron drip line peaks with mass number abundance peaks on the nuclide table.