A finite-temperature density functional study of electron self-trapping in 3He and 4He

We introduce a compact finite-temperature density functional model to study electron self-trapping in both liquid and vapor (3)He and (4)He. This model can quantitatively reproduce the most essential thermodynamic properties of (3)He and (4)He along their liquid-vapor coexistence lines. The structures and energetics of self-trapped electron bubbles on the 1S ground state and 1P excited state are particularly investigated. Our results show that 1S and 1P bubbles exist in liquid at any temperature, whereas 1S bubbles exist in vapor only above 1.6 K in (3)He and above 2.8 K in (4)He, 1P bubbles exist in vapor only above 2.5 K in (3)He and 4.0 K in (4)He. An initially spherical 1P bubble is unstable against deformation towards a peanut shape. In liquid, a peanut-shaped 1P bubble is held from fission by surface tension until reaching the liquid-vapor critical point, whereas in vapor it always splits into two smaller bubbles. The existence of 1P bubbles in finite-temperature liquid helium and their fission instability in helium vapor reveal interesting physics in this system.