Binding two and three <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> particles in cold neutron matter

We elucidate the fate of neighboring two and three-$\alpha$ particles in cold neutron matter by focusing on an analogy between such $\alpha$ systems Fermi polarons realized ultracold atoms. describe in-medium excitation properties particle neutron-mediated two- interactions using theoretical approaches developed for studies atomic systems. numerically solve few-body Schr\"odinger equation within standard cluster models combined with particles. point out that resultant two-$\alpha$ ground state first excited state, which correspond to $^8$Be Hoyle respectively, known as main components triple-$\alpha$ reaction, can become bound states a many-neutron background although these are unstable vacuum. Our results suggest significance not only astrophysical environments core-collapsed supernova explosions star mergers but also neutron-rich nuclei.