Lifetime determination in ${}^{190,192,194,196}\mathrm{Hg}$ via $\gamma -\gamma$ fast-timing spectroscopy

Lifetimes of $2_1^{+}$ and $4_1^{+}$ states in ${}^{190,192,194,196}\mathrm{Hg}$ and of some negative parity band members were measured using the $\gamma -\gamma$ fast-timing technique with a high-purity germanium and ${\mathrm{LaBr}}_3$(Ce) detector array. The excited states were populated via fusion-evaporation reactions using the Tandem Van de Graaff accelerator of the Institute of Nuclear Physics in Cologne, Germany. The derived reduced transition probabilities of the $2_1^{+}\to 0_1^{+}$ and $4_1^{+}\to 2_1^{+}$ transitions are discussed in the framework of the interacting boson approximation with two models using configuration mixing: a phenomenological one and a microscopical one. Both models describe the observed quantities of the nuclei within the experimental uncertainties.

Figure 1

The calibrated PRD curve relative to the energy $E=344\mathrm{keV}$. The data points, which are coincident to different transitions (244, 411, and $444\mathrm{keV}$) were shifted in parallel to fit a smooth curve. The standard deviation is calculated and the $3\sigma$ interval is chosen to be the error of the PRD curve with $3\mathrm{ps}$.

Figure 2

(a) Relevant level scheme of ${}^{196}\mathrm{Hg}$ up to $2.4\mathrm{MeV}$. (b) Obtained delayed (blue) and antidelayed (red) time distributions for the $2_1^{+}$ state with the feeding transition energy of $E_{\text{feeder}}=635.4\mathrm{keV}$ and the decay transition energy of $E_{\text{decay}}=426.0\mathrm{keV}$. (c) Doubly gated HPGe (blue) and LaBr (red) spectrum to show the separation of the feeding transition. (d) Doubly gated HPGe (blue) and LaBr (red) spectrum to show the separation of the decaying transition. (e) The interpolated background time response with the reference energy $426.0\mathrm{keV}$ for the feeding transition of the $2_1^{+}$ state. In addition, the experimental determined centroid difference is shown. (f) The interpolated background time response with the reference energy $635.4\mathrm{keV}$ for the decaying transition of the $2_1^{+}$ state. Additionally the experimental centroid difference of the cascade is shown.

Figure 3

Relevant level schemes up to $3\mathrm{MeV}$, HPGe and LaBr singles spectra for ${}^{190}\mathrm{Hg}$ [(a), (b)], ${}^{192}\mathrm{Hg}$ [(c), (d)] and ${}^{194}\mathrm{Hg}$ [(e), (f)]. The relevant transitions to determine the lifetimes of the $2_1^{+}$ and $4_1^{+}$ are marked. The peaks marked with a “C” are contaminants from other reaction channels.

Figure 4

Theoretical IBM-2 (a) [18], experimental (b) [3, 15, 39, 40], and IBM-CM (c) [17] level energies of the $2_1^{+}, 4_1^{+}, 6_1^{+}, 8_1^{+}, {10}_1^{+}$, and ${12}_1^{+}$ states as functions of neutron number from ${}^{172}\mathrm{Hg}$ up to ${}^{204}\mathrm{Hg} [{}^{200}\mathrm{Hg}$ for the IBM-CM in Fig. 4].

Figure 5

$R_{4/2}=E\left(4^{+}\right)/E\left(2^{+}\right)$ ratio for the even-even mercury isotopes ${}^{172}\mathrm{Hg}$ to ${}^{204}\mathrm{Hg}$. Because of the shape coexistence in ${}^{182–186}\mathrm{Hg}$ ($N=102–106$) the yrast $4^{+}$ state is not part of the ground state band. Therefore, the $R_{4/2}$ ratio of these nuclei is shown for the energy of the ground state members (red) and the energy of the yrast states (blue).

Figure 6

Comparison of experimental and calculated $B\left(E2\right)$ values for the $2_1^{+}\to 0_1^{+}$ (a) and $4_1^{+}\to 2_1^{+}$ (b) transitions in the mercury isotopes $N=92–124$. The experimental lifetimes or $B\left(E2\right)$ values are taken from ${}^{180}\mathrm{Hg}$ [4],${}^{182}\mathrm{Hg}$ [4], ${}^{184}\mathrm{Hg}$ [6, 7], ${}^{186}\mathrm{Hg}$ [5, 6, 7], ${}^{188}\mathrm{Hg}$ [5], ${}^{198}\mathrm{Hg}$ [8, 9, 11, 12], ${}^{200}\mathrm{Hg}$ [10, 11, 12], ${}^{202}\mathrm{Hg}$ [10, 11, 14, 42], and ${}^{204}\mathrm{Hg}$ [11, 43, 44]. The model calculations are taken from [18] for the IBM-2 and [17] for the IBM-CM.