Changes in mean-squared charge radii and magnetic moments of ${}^{179–184}\mathrm{Tl}$ measured by in-source laser spectroscopy

Hyperfine structure and isotope shifts have been measured for the ground and isomeric states in the neutron-deficient isotopes ${}^{179–184}\mathrm{Tl}$ using the 276.9-nm transition. The experiment has been performed at the CERN-Isotope Separator On-Line facility using the in-source resonance-ionization laser spectroscopy technique. Spins for the ground states in ${}^{179,181,183}\mathrm{Tl}$ have been determined as $I=1/2$. Magnetic moments and changes in the nuclear mean-square charge radii have been deduced. By applying the additivity relation for magnetic moments of the odd-odd Tl nuclei the leading configuration assignments were confirmed. A deviation of magnetic moments for isomeric states in ${}^{182,184}\mathrm{Tl}$ from the trend of the heavier Tl nuclei is observed. The charge radii of the ground states of the isotopes ${}^{179–184}\mathrm{Tl}$ follow the trend for isotonic (spherical) lead nuclei. The noticeable difference in charge radii for ground and isomeric states of ${}^{183,184}\mathrm{Tl}$ has been observed, suggesting a larger deformation for the intruder-based $9/2^{-}$ and ${10}^{-}$ states compared to the ground states. An unexpected growth of the isomer shift for ${}^{183}\mathrm{Tl}$ has been found.

Figure 1

The hfs spectra of selected Tl isotopes. In the insets the spin of the corresponding nuclide and the energies of the γ- or α-decay lines used for the photoion current monitoring are shown. The solid lines depict the Voigt-profile fit to the data. The vertical dashed lines mark the center of gravity of the corresponding hfs. The zero point on the frequency scale corresponds to a wave number of $18059.0\mathrm{c}{\mathrm{m}}^{-1}$.

Figure 2

Hyperfine structure spectrum of ${}^{181}\mathrm{Tl}^g$. The full line represents fitting with $I=1/2$, and the dashed line represents fitting with $I=3/2$.

Figure 3

Isotopic dependence of the changes in the mean-square charge radii for the Tl isotopes. Present data are marked by the star symbols. Literature data are taken from Ref. [7] (see also references therein). Full squares: ground states with $I=1/2$; hollow squares: intruder isomers [$I=(9/2)$, (10)]; upward triangles: nuclei with $I=\left(2\right)$; downward triangles: nuclei with $I=\left(7\right)$. The dashed lines represent the droplet model prediction with different constant mean-square deformations. Only statistical errors are displayed.

Figure 4

Magnetic moments for the $\mathrm{T}{\mathrm{l}}^g\left(I=1/2\right)$ isotopes. Squares: literature data (see Ref. [7] and references therein). Stars: present paper. A parabolic fit is shown by the dashed curve.

Figure 5

Magnetic moments for $\mathrm{T}{\mathrm{l}}^m\left(I=9/2\right)$ isotopes. Squares: literature data (Ref. [7] and references therein). Star: present paper.

Figure 6

Hyperfine structure pattern for different γ lines in the ${}^{182}\mathrm{Tl}$ β decay: squares: $E_{\gamma }=351\mathrm{keV}$; triangles: $E_{\gamma }=413$ and 332 keV (multiplied by 2.6). The solid and dashed lines represent the fits by the two hfs mixtures.

Figure 7

Comparison of the hfs patterns for ${}^{180}\mathrm{Tl}$ (triangles: the same data as in Fig. 1) and for ${}^{182}\mathrm{Tl}$ (squares), deduced (a) via the 6165-keV α-decay line of ${}^{182}\mathrm{Tl}$ and (b) via the 5867-keV α-decay line of the daughter isotope ${}^{182}\mathrm{Hg}$. The data for ${}^{180}\mathrm{Tl}$ are shifted by 670 MHz to overlap the data of both isotopes.

Figure 8

Magnetic moments of Tl and Bi isomers with $I=10$. Squares: Bi isomers (full squares: Ref. [49]; hollow squares: Ref. [50]). Triangles: Tl isomers (hollow triangle: present paper; full triangle: Ref. [7]). The results of a calculation using the additivity relation [Eq. (5)] with different assumptions for ${\mu }_n$ are shown by lines (see the text for details).

Figure 9

Magnetic moments for Tl isotopes with $I=7$. Squares: literature data (see Ref. [7] and references therein). Stars: present paper. Dashed line: calculation by the additivity relation [Eq. (5)] with ${\mu }_p$ and ${\mu }_n$ values from experimental magnetic moments of the adjacent odd-$A$ nuclei.

Figure 10

Relative changes in $\delta \langle r^2\rangle$ for the even-neutron thallium and lead nuclei. Triangles: Pb [30, 6]. Full squares: Tl (ground states) (Ref. [7] and references therein). Hollow squares: Tl (intruder isomers) (Ref. [7] and references therein). Full stars: Tl (ground states), present paper. Hollow star: Tl (intruder isomer), present paper.

Figure 11

Relative changes in $\delta \langle r^2\rangle$ for the odd-neutron thallium and lead nuclei. Triangles: Pb ($\nu 1i_{13/2}$ states) [30, 6]. Full squares: Tl (${[\pi 3s_{1/2},\nu 1{i_1}_{3/2}]}_{7^{+}}$ states) (Ref. [7] and references therein). Hollow square: Tl (intruder isomer) [7]. Full stars: Tl (${[\pi 3s_{1/2},\nu 1{i_1}_{3/2}]}_{7^{+}}$ states), present paper. Hollow star: Tl (intruder isomer), present paper. Semihollow star: ${}^{180}\mathrm{Tl}$, present paper.

Figure 12

Isomer shift between intruder and normal states for Tl isotopes. Stars: present paper. Squares: literature data (see Ref. [7] and references therein). Only statistical errors are shown.