Fig. 1. Wavefunctions for the 1s and 2s states of Li, Be⁺, and B²⁺ atoms as functions of the radial coordinate r for the unconfined atoms. The curves are our results, while the symbols are from Ref. 28.

Fig. 2. Orbital energies for the 1s, 2s, 2p, 3s, and 3p states of Li, Be⁺, and B²⁺ atoms confined by a spherical impenetrable cavity as a function of the confinement radius R₀: (a) 3s and 3p states; (b) 2s and 2p states; (c) 1s ground state. The crossing points between the ns–np levels are highlighted by circles for better visualization. The curves without symbols are for the ns states, while the curves with symbols are for the np states. For comparison, the HF results of Weiss³³ for the unconfined atom energy levels are also shown at R₀ = 30 a.u (▿).

Fig. 3. Total HF energy, Eq. (6), as a function of cavity radius R₀ for Li, Be⁺, and B²⁺ atoms. In the case of Li, the symbols show the theoretical results from Sañu-Ginarte et al.²⁹ (×), Le Sech and Banerjee³⁷ (□), Sarsa and Le Sech³⁸ (○), and Sarsa et al.¹³ (▵). The HF results for unconfined atoms as reported by Weiss³³ are shown at R₀ = 5 a.u (▿).

Fig. 4. Static pressure induced by the cavity as a function of cavity size R₀ for Li, Be⁺, and B²⁺ atoms confined by an impenetrable spherical cavity. The open square symbols (□) indicate the cavity size and pressure at which the 2s → 2p transition occurs. Some naturally occurring pressures are also shown.

Fig. 5. Dipole oscillator strength for the is → 2p and is → 3p electronic transitions as a function of the impenetrable spherical cavity size R₀ for Li, Be⁺, and B²⁺ atoms for i = 1 (core) and i = 2 (valence) electrons. The curves without symbols are for the is → 2p transition of the valence i = 2 electron, while the curves with symbols are for the i = 1 core electron.

Fig. 6. Static dipole polarizabilities αs2s (a) and αs1s (b) as functions of cavity size R₀ for Li, Be⁺, and B²⁺ atoms. The solid triangle (▴) and the solid circle (•) at R₀ = 30 a.u. are the HF results of Schwerdtfeger and Nagle¹¹ and Tang et al.,³² respectively.

Fig. 7. (a) Mean excitation energies I01s (curves with symbols) and I02s (curves without symbols) as functions of cavity size R₀ for Li, Be⁺, and B²⁺ atoms. For comparison, we also show at R₀ = 30 a.u. the values of the free atoms obtained by Oddershede and Sabin²⁷ (○), Kamakura⁴¹ (▵), and Dehmer et al.⁴² (□). (b) Total mean excitation energy I₀.

Fig. 8. Slater’s X-α parameter α_X as a function of cavity size R₀ for Li, Be⁺, and B²⁺ atoms.

Table 1. Unconfined ground state properties for free Li, Be⁺, and B²⁺ atoms. We report values for the core (i = 1) and valence (i = 2) electrons for the ground (${ϵ}_0^{is}$) and excited (${ϵ}_0^{2p}$) orbital energies, the total HF energy E_HF, the DOS $f_{is2p}^i$, the static dipole polarizability ${\alpha }_s^i$, and the mean excitation energy $I_0^i$. Slater’s α_X parameter, Eq. (9), takes the values ${\alpha }_X^{\mathrm{L}\mathrm{i}}=0.58002$, ${\alpha }_X^{{\mathrm{B}\mathrm{e}}^{+}}=0.52632$, and ${\alpha }_X^{{\mathrm{B}}^{2+}}=0.49922$.

Table 2. Similar to Table I, but for a Li atom confined by an impenetrable spherical cavity for several selected values of the cavity size R₀. The values in parentheses are the theoretical results from Sañu-Ginarte et al.²⁹

Table 3. Similar to Table II, but for the Be⁺ and B²⁺ atoms.