Finite-nuclear-size effect for hydrogenlike ions under high external pressure

Abstract

The influence of pressure on finite-nuclear-size corrections to atomic energy levels and electron-capture decay rate is investigated in confined hydrogenlike ions. The ions are modeled inside an impenetrable spherical cavity, with a Gaussian distribution used to represent the nuclear charge distribution. For each confinement radius used to simulate external pressure, the energies and wave functions of the lowest-lying bound states are determined by numerically solving the Dirac equation via the kinetically balanced generalized pseudospectral method. In contrast to unconfined ions, both the FNS corrections and electron-capture decay rates increase markedly under pressure and exhibit parallel trends with increasing confinement. Pressure also removes level degeneracies and alters the relative magnitudes of FNS corrections across different bound states. Moreover, the nuclear charge radius is found to significantly affect the pressure-enhanced electron-capture decay rate.

Figures (5)

• Figure 1: The absolute energy values $|E_{1s}|$ (a) and the corresponding FNS correction $\Delta E_{\mathrm{FNS} }$ (b) for the $1s_{1/2}$ state of hydrogenlike ions $^{7}\mathrm{Be}^{3+}$, $^{56}\mathrm{Fe}^{25+}$, $^{120}\mathrm{Sn}^{49+}$ and $^{208}\mathrm{Pb}^{81+}$ as a function of pressure. The vertical dashed line of (a) represents the pressure where the energy level is zero. At the top of (b), some characteristic pressures are labeled that represent several orders of magnitude.
• Figure 2: Absolute values of energy levels (a) and FNS corrections to energy levels $\Delta E_{\mathrm{FNS} }$ (b) for $1s_{1/2}$, $2s_{1/2}$ and $2p_{1/2}$ states of hydrogenlike ion $^{120}\mathrm{Sn}^{49+}$ as a function of pressure.
• Figure 3: $\Delta E_{\mathrm{FNS} }$ for the $1s_{1/2}$ state of hydrogenlike ions $^{7}\mathrm{Be}^{3+}$ and $^{120}\mathrm{Sn}^{49+}$ in the relativistic case, are compared with the nonrelativistic case.
• Figure 4: The ratio of the electron-capture decay rate with and without pressure for the $1s_{1/2}$ state of hydrogenlike ions $^{7}\mathrm{Be}^{3+}$, $^{64}\mathrm{Cu}^{28+}$, $^{140}\mathrm{Pr}^{58+}$ and $^{205}\mathrm{Pb}^{81+}$ as a function of pressure. The vertical dashed line denotes the critical pressure for the corresponding hydrogenlike ions.
• Figure 5: The fractional increase of the decay rate at the $1s_{1/2}$ state of hydrogenlike ions of Pr isotopes. (a) Fixed different pressures at $10^6$ GPa, (b) $10^8$ GPa, (c) $10^{10}$ GPa, (d) $10^{12}$ GPa, (e) $10^{14}$ GPa, and (f) $10^{16}$ GPa.