Shape coexistence in ${}^{153}\text{Ho}$

The high-spin states in ${}^{153}\text{Ho}$ have been studied by the ${}_{57}{}^{139}\text{La}({}^{20}\text{Ne},6n)$ reaction at a projectile energy of 139 MeV at the Variable Energy Cyclotron Centre (VECC), Kolkata, India, utilizing an earlier campaign of the Indian National Gamma Array (INGA) setup. Data from $\gamma -\gamma$ coincidence, directional correlation, and polarization measurements have been analyzed to assign and confirm the spins and parities of the levels. We have suggested a few additions and revisions of the reported level scheme of ${}^{153}\text{Ho}$. The RF-$\gamma$ time difference spectra have been useful to confirm the half-life of an isomer in this nucleus. From the comparison of experimental and theoretical results, it is found that there are definite indications of shape coexistence in this nucleus. The experimental and calculated lifetimes of several isomers have been compared to follow the coexistence and evolution of shape with increasing spin.

Figure 1

Experimental DCO ratios ($R_{\mathrm{DCO}}$) for a few transitions in ${}^{153}\text{Ho}$. Typical values of $R_{\mathrm{DCO}}$ determined for $\mathrm{\Delta }J=0$ and 1 transitions from $E2$ gated spectra are indicated in the figure by dotted lines.

Figure 2

Asymmetry parameter $a\left(E_{\gamma }\right)$ plotted as a function of energy. The fitted straight line is shown as dotted line in the figure.

Figure 3

Polarization symmetry for a few transitions in ${}^{153}\text{Ho}$. The dotted line separates the regions corresponding to pure electric and magnetic transitions.

Figure 4

(a) The RF-$\gamma$ TAC spectrum without any gate on $\gamma$ energies (left). (b) (Right) Comparison of RF-$\gamma$ TAC spectra gated by the 913 keV prompt transition and 533 keV delayed transition decaying from the isomer at 2772 keV through 36 keV. The logarithmic (ln) values of counts (to the base $e$) are plotted against time (ns) for ease of comparison.

Figure 5

Partial level scheme of ${}^{153}\text{Ho}$.

Figure 6

Partial level scheme of ${}^{153}\text{Ho}$ below the isomer $31/2^{+}$ at 2772 keV.

Figure 7

Determination of (a) (top) prompt resolution of the TAC spectrum by fitting the decay curve of the prompt 913 keV transition decaying from the 3685 keV level, and (b) (bottom) the lifetime of the isomeric level at 2772 keV from the RF-$\gamma$ TAC spectra gated by the 533 keV transition. The logarithmic (ln) values of counts (to the base $e$) are plotted against time (ns) for ease of fitting.

Figure 8

The alignment plots for (a) positive and (b) negative parity states in ${}^{153}\text{Ho}$

Figure 9

TRS plots for the positive parity states. In the top row the plots correspond to (a) $\hslash \omega =0.2$ (left) and (b) 0.40 (right) MeV (with $J\simeq 2.5$ and 37.5, respectively). In the bottom row, they are calculated for (c) $\hslash \omega =0.25$ and (d) 0.28 MeV (with $J\simeq 9.5$ and 21.5, respectively). Shape coexistence at $\omega =0.25$ MeV is clearly indicated with yrast oblate and non-yrast prolate minimum.

Figure 10

TRS plots for the negative parity states. The plots correspond to (i) top row: (a) $\hslash \omega =0.2$ (left) and (b) 0.45 (right) MeV (with $J\simeq 6.5$ and 32.5, respectively); (ii) bottom row: (c) $\hslash \omega =0.25$ (left) and (d) 0.28 (right) MeV (with $J\simeq 12.5$ and 24.5, respectively).

Figure 11

(a) The alignment plot shows the yrast, non-yrast states of ${}^{152}\text{Dy}$. The core states (“new core”) selected for our calculations are indicated by stars. For all cases $K=0$ value has been considered for alignment calculation. (b) Experimental energy spectra of ${}^{152}\text{Dy}$ as a function of angular momentum ($J$). (c) The figure shows an expanded view of the region where vibration and rotational features compete and coexist.

Figure 12

The energy vs angular momentum plots for the positive parity states for different shape options with yrast and new cores.

Figure 13

The energy vs angular momentum plots for the positive parity states for different shape options. (a) Results from calculations with yrast core compared with experimental yrast states. (b) Results from calculations with “new core” compared with experimental states including non-yrast $49/2_2^{+}$ and $53/2_2^{+}$.

Figure 14

Comparison of experimental and theoretical energies of negative parity states in ${}^{153}\text{Ho}$.