Charge Radii of Neutron Deficient ${}^{52,53}\mathrm{Fe}$ Produced by Projectile Fragmentation

Bunched-beam collinear laser spectroscopy is performed on neutron deficient ${}^{52,53}\mathrm{Fe}$ prepared through in-flight separation followed by a gas stopping. This novel scheme is a major step to reach nuclides far from the stability line in laser spectroscopy. Differential mean-square charge radii $\delta ⟨r^2⟩$ of ${}^{52,53}\mathrm{Fe}$ are determined relative to stable ${}^{56}\mathrm{Fe}$ as $\delta ⟨r^2{⟩}^{56,52}=-0.034(13){\mathrm{fm}}^2$ and $\delta ⟨r^2{⟩}^{56,53}=-0.218(13){\mathrm{fm}}^2$, respectively, from the isotope shift of atomic hyperfine structures. The multiconfiguration Dirac-Fock method is used to calculate atomic factors to deduce $\delta ⟨r^2⟩$. The values of $\delta ⟨r^2⟩$ exhibit a minimum at the $N=28$ neutron shell closure. The nuclear density functional theory with Fayans and Skyrme energy density functionals is used to interpret the data. The trend of $\delta ⟨r^2⟩$ along the Fe isotopic chain results from an interplay between single-particle shell structure, pairing, and polarization effects and provides important data for understanding the intricate trend in the $\delta ⟨r^2⟩$ of closed-shell Ca isotopes.

Figure 1

Hyperfine spectra of ${}^{52,53,56}\mathrm{Fe}$. The open circles are the data, and the solid lines are best fits of an asymmetric Voigt profile [28, 31] to the data.

Figure 2

rms charge radii (top) of the isotopic chains of Ca (left) and Fe (right) and differential ms charge radii (bottom) of K-Fe (left). Data are taken from Refs. [21, 22, 40, 49, 50, 51], and this work. The uncertainties in the atomic factors are marked by shading. Calculations with SV-min and UNEDF0 EDFs were performed for even-even mass isotopes only. The inset shows one-neutron separation energies for the Fe chain.

Figure 3

rms charge radii (top) plotted relative to $\sqrt{⟨r^2⟩}$ at $N=28$; ${\beta }_2=0$, and potential energies (bottom) for the Ca (left) and Fe (right) chains calculated with UNEDF0 as a function of ${\beta }_2$. Results with SV-min (not shown) are similar.