Simultaneous $\gamma$-ray and electron spectroscopy of ${}^{182,184,186}\mathrm{Hg}$ isotopes

Background: The mercury isotopes around $N=104$ are a well-known example of nuclei exhibiting shape coexistence. Mixing of configurations can be studied by measuring the monopole strength ${\rho }^2\left(E0\right)$, however, currently the experimental information is scarce and lacks precision, especially for the $I^{\pi }\to I^{\pi }$ ($I\ne 0$) transitions.

Purpose: The goals of this study were to increase the precision of the known branching ratios and internal conversion coefficients, to increase the amount of available information regarding excited states in ${}^{182,184,186}\mathrm{Hg}$, and to interpret the results in the framework of shape coexistence using different models.

Method: The low-energy structures in ${}^{182,184,186}\mathrm{Hg}$ were populated in the $\beta$ decay of ${}^{182,184,186}\mathrm{Tl}$, produced at ISOLDE, CERN and purified by laser ionization and mass separation. The $\gamma$-ray and internal conversion electron events were detected by five germanium clover detectors and a segmented silicon detector, respectively, and correlated in time to build decay schemes.

Results: In total, 193, 178, and 156 transitions, including 144, 140, and 108 observed for the first time in a $\beta$-decay experiment, were assigned to ${}^{182,184,186}\mathrm{Hg}$, respectively. Internal conversion coefficients were determined for 23 transitions, out of which 12 had an $E0$ component. Extracted branching ratios allowed the sign of the interference term in ${}^{182}\mathrm{Hg}$ as well as ${\rho }^2(E0;0_2^{+}\to 0_1^{+})$ and $B(E2;0_2^{+}\to 2_1^{+})$ in ${}^{184}\mathrm{Hg}$ to be determined. By means of electron-electron coincidences, the $0_3^{+}$ state was identified in ${}^{184}\mathrm{Hg}$. The experimental results were qualitatively reproduced by five theoretical approaches, the interacting boson model with configuration mixing with two different parametrizations, the general Bohr Hamiltonian, the beyond mean-field model, and the symmetry-conserving configuration-mixing model. However, a quantitative description is lacking.

Conclusions: The presence of shape coexistence in neutron-deficient mercury isotopes was confirmed and evidence for the phenomenon existing at higher energies was found. The new experimental results provide important spectroscopic input for future Coulomb excitation studies.

Figure 1

Portion of the electron singles energy spectrum collected with the ${}^{182}\mathrm{Tl}$ beam. The electron lines associated with ${}^{182}\mathrm{Hg}$ have been marked with the transition energy and corresponding atomic orbital, whereas transitions arising from the $A=182$ decay chain are marked with the nucleus of origin.

Figure 2

Portion of the $\gamma$-ray energy spectrum gated on the 351-keV ($2_1^{+}\to 0_1^{+}$) $\gamma$-ray transition in ${}^{182}\mathrm{Hg}$. The most prominent lines have been labeled with the transition energy in keV.

Figure 3

Partial level scheme of excited states in ${}^{182}\mathrm{Hg}$ populated in the $\beta$ decay of ${}^{182}\mathrm{Tl}$ extracted in this work. For the full version, see Supplemental Material [31]. Levels and transitions known from the previous $\beta$-decay studies are plotted in black, shifted in the decay scheme in blue, known from other than $\beta$-decay studies in green and newly identified in red. Transitions not observed in this work for which the intensity limits have been determined are plotted with dashed lines. Spins, parities, and proposed transition multipolarities are taken from this work and Ref. [32].

Figure 4

A fit (black solid line) to the portion of the electron energy spectrum spectrum, gated on the 723- and 773-keV $\gamma$ rays in ${}^{182}\mathrm{Hg}$. The visible peaks stem from the K-ICE of the 335-keV ($0_2^{+}\to 0_1^{+}$) and 351-keV ($2_1^{+}\to 0_1^{+}$) transitions. The contribution from asymmetric Gaussian functions is plotted in solid red lines and the constant background in dashed purple line.

Figure 5

$\gamma$-ray (top) and electron (bottom) energy spectra gated on the 526-, 576-, 748-, and 1171-keV $\gamma$-ray transitions feeding the $2_2^{+}$ state in ${}^{182}\mathrm{Hg}$. The peaks of interest are labeled by the energy given in keV.

Figure 6

A fit (black solid line) to a portion of the electron energy spectrum spectrum, gated on the 526-, 576-, 748-, and 1171-keV $\gamma$ rays feeding the 548 keV $2_2^{+}$ state in ${}^{182}\mathrm{Hg}$. The visible peaks stem from the $L$- and $M+$-ICE of the 197-keV transition and the $L$-ICE of the 213-keV transition. A contribution from asymmetric Gaussian functions is plotted in solid red lines and the constant background is shown by the dashed purple line.

Figure 7

$\gamma$-ray (top) and electron (bottom) energy spectra gated on the 701-keV $\gamma$ ray in ${}^{182}\mathrm{Hg}$. The peaks of interest are labeled by the energy given in keV. The energy range 440–650 keV of electron energy spectrum has been magnified by a factor 10 for visualization purposes.

Figure 8

$\gamma$-ray (top) and electron (bottom) energy spectra gated on the 1156-keV $\gamma$ ray in ${}^{182}\mathrm{Hg}$. The position of the nonobserved 211-keV $\gamma$ ray is indicated with a shaded area.

Figure 9

Portion of an electron energy spectrum gated on the 261-keV ($4_1^{+}\to 2_1^{+}$) $\gamma$ ray in ${}^{182}\mathrm{Hg}$. Peaks stemming from the ICEs of the yrast cascade as well as from the 512-keV transition are labeled.

Figure 10

Portion of the electron singles energy spectrum collected with the ${}^{184}\mathrm{Tl}$ beam. The electron lines associated with ${}^{184}\mathrm{Hg}$ have been marked with the transition energy and corresponding atomic orbital, whereas transitions arising from the $A=184$ decay chain are marked with the nucleus of origin.

Figure 11

Portion of the $\gamma$-ray energy spectrum gated on the 367-keV ($2_1^{+}\to 0_1^{+}$) $\gamma$-ray transition in ${}^{184}\mathrm{Hg}$. The most prominent lines have been labeled with the transition energy in keV.

Figure 12

Portion of the $\gamma$-ray energy spectrum gated on the 375-keV ($0_2^{+}\to 0_1^{+}$) $K$-ICE in ${}^{184}\mathrm{Hg}$. The negative peaks are stemming from the background subtraction. Main coincident lines are labeled by the energy given in keV.

Figure 13

Partial level scheme of excited states in ${}^{184}\mathrm{Hg}$ populated in the $\beta$ decay of ${}^{184}\mathrm{Tl}$ extracted in this work. For the full version, see Supplemental Material [31]. Levels and transitions known from the previous $\beta$-decay studies are plotted in black, known from other studies in green and the newly identified ones in red. Transitions not observed in this work for which the intensity limits have been determined are plotted with dashed lines. Spins, parities, and proposed transition multipolarities are taken from this work and Refs. [13, 40].

Figure 14

Portion of the electron energy spectrum gated on the $K$-ICE of the 375-keV $0_2^{+}\to 0_1^{+}$ transition in ${}^{184}\mathrm{Hg}$. The observed peaks are labeled by the energy of the transition they are originate from. Inset: portion of the $\gamma$-ray energy spectrum gated on the $K$-ICE of the 375-keV $0_2^{+}\to 0_1^{+}$ transition with the position of the nonobserved 749-keV $\gamma$ ray indicated with a shaded area.

Figure 15

$\gamma$-ray (top) and electron (bottom) energy spectra gated on the 367-keV ($2_1^{+}\to 0_1^{+}$) $\gamma$ ray in ${}^{184}\mathrm{Hg}$. A peak labeled as ‘CS’ stems for the Compton scattering of strong $\gamma$ rays between different clovers.

Figure 16

Portion of the $\gamma$-ray energy spectrum gated on the $\gamma$ rays feeding the 535-keV state in ${}^{184}\mathrm{Hg}$, used to determine the total ICC of the 168-keV $2_2^{+}\to 2_1^{+}$ transition by the imbalance method, see text for details. Main peaks are labeled by the energy given in keV.

Figure 17

$\gamma$-ray (top) and electron (bottom) energy spectra gated on the 535-keV ($2_2^{+}\to 0_1^{+}$) $\gamma$ ray in ${}^{184}\mathrm{Hg}$. The main $\gamma$-ray peaks are labeled with the energy given in keV. The position of the nonobserved 449-keV $\gamma$ ray is indicated with a shaded area.

Figure 18

$\gamma$-ray (top) and electron (bottom) energy spectra gated on the 720-keV ($4_2^{+}\to 2_1^{+}$) $\gamma$ ray in ${}^{184}\mathrm{Hg}$. A position of the nonobserved 214-keV $\gamma$ ray is indicated with a shaded area.

Figure 19

Portion of the $\gamma$-ray energy spectrum gated on the 403-keV ($4_1^{+}\to 2_1^{+}$) and 406-keV ($2_1^{+}\to 0_1^{+}$) $\gamma$-ray transitions in ${}^{186}\mathrm{Hg}$. The most prominent lines have been labeled with the transition energy in keV.

Figure 20

Portion of the $\gamma$-ray energy spectrum gated on the 524-keV ($0_2^{+}\to 0_1^{+}$) $K$-ICE in ${}^{186}\mathrm{Hg}$. Main coincident lines are labeled by the energy given in keV.

Figure 21

Partial level scheme of excited states in ${}^{186}\mathrm{Hg}$ populated in the $\beta$ decay of ${}^{186}\mathrm{Tl}$ extracted in this work. For the full version, see Supplemental Material [31]. Levels and transitions known from the previous $\beta$-decay studies are plotted in black, shifted in the decay scheme in blue, known from other studies in green, and newly identified in red. Transitions not observed in this work for which the intensity limits have been determined are plotted with dashed lines. Spins, parities, and proposed transition multipolarities are taken from this work and Ref. [43].

Figure 22

Portion of the $\gamma$-ray energy spectrum gated on the 1248-keV $\gamma$ ray in ${}^{186}\mathrm{Hg}$.

Figure 23

Portion of the $\gamma$-ray energy spectrum gated on the 542-keV ${12}_1^{+}\to {10}_1^{+}\gamma$ ray in ${}^{186}\mathrm{Hg}$. The yrast transitions and the 511-keV annihilation peak are labeled by the energy given in keV.

Figure 24

$\gamma$-ray (top) and electron (bottom) energy spectra gated on the 406-keV ($2_1^{+}\to 0_1^{+}$) $\gamma$ ray in ${}^{186}\mathrm{Hg}$.

Figure 25

$\gamma$-ray (top) and electron (bottom) energy spectra gated on the 675-keV ($4_2^{+}\to 2_1^{+}$) $\gamma$ ray in ${}^{186}\mathrm{Hg}$. The position of the non-observed 353-keV $\gamma$ ray is marked with a shaded area.

Figure 26

$\gamma$-ray (top) and electron (bottom) energy spectra gated on the 811-keV ($8_2^{+}\to 6_1^{+}$) $\gamma$ ray in ${}^{186}\mathrm{Hg}$. The position of the non-observed K-ICE from the 242-keV transition is indicated with a shaded area.

Figure 27

The ${\chi }^2$ plot as a function of the $\left|\delta \right|$ and $q_K^2$ mixing parameters of the $2_2^{+}\to 2_1^{+}$ 197 keV transition in ${}^{182}\mathrm{Hg}$. The ${\chi }^2$ value is given by the color scale.

Figure 28

The energy curves as a function of the deformation parameter ${\beta }_2$ obtained within the SCCM calculations for (a) ${}^{182}\mathrm{Hg}$, (b) ${}^{184}\mathrm{Hg}$, and (c) ${}^{186}\mathrm{Hg}$, after particle-number projection (PN-VAP method, dashed lines) and angular momentum projection (PNAMP method, continuous lines).

Figure 29

Comparison of the experimental energies of the selected excited states in ${}^{182,184,186}\mathrm{Hg}$ with the theoretical calculations. The dashed lines, provided to guide the eye, are connecting the states of the same spin and order.

Figure 30

Collective wave functions from the SCCM calculations for (a) ${}^{182}\mathrm{Hg}$, (b) ${}^{184}\mathrm{Hg}$, and (c) ${}^{186}\mathrm{Hg}$. The first, second, and third states of each spin are plotted in full, short-dashed, and dashed lines, respectively.