Deformed band structures at high spin in ${}^{200}\mathrm{Tl}$

High-spin band structures of ${}^{200}\mathrm{Tl}$ have been studied by $\gamma$-ray spectroscopic methods using the ${}^{198}\mathrm{Pt}({}^7\mathrm{Li},5n){}^{200}\mathrm{Tl}$ reaction at 45 MeV of beam energy. The level scheme of ${}^{200}\mathrm{Tl}$ has been extended significantly and several new band structures have been established with the observation of 60 new transitions. The $\pi h_{9/2}\otimes \nu i_{13/2}$ oblate band has been extended beyond the particle alignment frequencies. The band structures and the other excited states have been compared with the neighboring odd-odd Tl isotopes. Total Routhian surface calculations have been performed to study the deformation and shape changes as a function of spin in this nucleus. These calculations could reproduce the particle alignment frequency and suggest that the neutron pair alignment in $\nu i_{13/2}$ orbital induces $\gamma$ softness in ${}^{200}\mathrm{Tl}$.

Figure 1

Spectrum of $\gamma$ rays detected in coincidence with the 119, 217, 230, or 348 keV $\gamma$ transitions. (a) The lower-energy part and (b) the higher-energy part of the spectrum. The new peaks observed in the present work are marked as “*.”

Figure 2

DCO ratio vs polarization asymmetry of various transitions in ${}^{200}\mathrm{Tl}$ obtained with different quadrupole gates as indicated. The dotted lines at the $X$ axis correspond to the values for a dipole and quadrupole transitions in a pure quadrupole gate, respectively, and are shown to guide the eye. The dotted line at the $Y$ axis is to guide the eye for +ve and $-\text{ve}$ values of IPDCO for electric and magnetic transitions, respectively.

Figure 3

Angular distribution of various transitions in ${}^{200}\mathrm{Tl}$ obtained in the present work: (a), (c), (e) quadrupole transitions; (b), (d), (f) dipole transitions.

Figure 4

Level scheme of ${}^{200}\mathrm{Tl}$, as obtained from the present work. New transitions are marked as “*.”

Figure 5

Coincidence spectra corresponding to double gates of (a) 348 and 278 keV, (b) 348 and 311 keV, and (c) 1076 and 278 keV transitions pertaining to the bands B1 and B3 in ${}^{200}\mathrm{Tl}$. Transitions marked with “*” are newly placed in the level scheme.

Figure 6

Coincidence spectra corresponding to double gates of (a) 734 and 192 keV, (b) 790 and 192 keV, (c) 192 and 192 keV corresponding to the transitions of bands B1 and B2 in ${}^{200}\mathrm{Tl}$. Transitions marked with “*” are newly placed in level scheme.

Figure 7

Coincidence spectra corresponding to double gates of (a) 420 and 702 keV, (b) 420 and 543 keV, (c) 132 and 288 keV transitions corresponding to the band B4 in ${}^{200}\mathrm{Tl}$.

Figure 8

${\chi }^2$($\delta$) analysis of angular distribution and polarization of 490 keV transition.

Figure 9

Alignment plot for the $\pi h_{9/2}\otimes \nu i_{13/2}$ bands in odd-odd Tl isotopes. The level energies of the same bands of ${}^{194–198}\mathrm{Tl}$ are taken from Refs. [9, 10, 14], respectively. The Harris reference parameters are taken as $J_0=8{\hslash }^2{\text{MeV}}^{-1}$ and $J_1=40{\hslash }^4{\text{MeV}}^{-3}$.

Figure 10

Alignment $i_x$ as a function of rotational frequency $\hslash \omega$ for the bands in ${}^{200}\mathrm{Tl}$. The same for the $9/2^{-}$ band in the odd-proton nucleus ${}^{197}\mathrm{Tl}$ is also shown. The Harris reference parameters are taken as $J_0=8{\hslash }^2{\text{MeV}}^{-1}$ and $J_1=40{\hslash }^4{\text{MeV}}^{-3}$.

Figure 11

Staggering [$S\left(I\right)=\left[E\right(I)-E(I-1\left)\right]/2I$] plot for the $\pi h_{9/2}\otimes \nu i_{13/2}$ bands in odd-odd Tl isotopes. Data for ${}^{194–198}\mathrm{Tl}$ are taken from Refs. [9, 10, 14], respectively.

Figure 12

Experimental $B\left(M1\right)/B\left(E2\right)$ of band B1 before and after band crossing is compared with that of calculation for two- and four-quasiparticle (qp) configurations (see text).

Figure 13

Spin vs excitation energy plots of different bands in ${}^{200}\mathrm{Tl}$.

Figure 14

Total Routhian surface (TRS) calculations for the band B1 with configuration of $\pi h_{9/2}\otimes \nu i_{13/2}$ in ${}^{200}\mathrm{Tl}$ for rotational frequency $\hslash \omega =0.0$ MeV. $\gamma =0^{\circ }$ and $\gamma =-{60}^{\circ }$ lines correspond to prolate and oblate deformations, respectively. The contours are in 400 keV intervals.

Figure 15

Same as Fig. 14 but for $\hslash \omega =0.45$ MeV.

Figure 16

Calculated configuration-constrained potential-energy surface for the $7^{-}$ state with the configuration of $\pi 9/2^{-}\left[505\right]\otimes \nu 5/2^{+}\left[642\right]$ in ${}^{200}\mathrm{Tl}$. The contours are in 400 keV intervals.

Figure 17

Same as Fig. 14 but for the $\pi h_{9/2}\otimes \nu i_{13/2}^{-2}\left(f_{5/2}{p}_{3/2}\right)$ four-qp configuration corresponding to the band B3 in ${}^{200}\mathrm{Tl}$ at the rotational frequency $\hslash \omega =0.11$ MeV. The contours are 400 keV apart.

Figure 18

Plots of single-proton (left) and single-neutron (right) Routhians of ${}^{200}\mathrm{Tl}$ as a function of rotational frequency $\hslash \omega$ for deformation parameter ${\beta }_2=0.12$ and $\gamma =-{60}^{\circ }$ (corresponding to the calculated deformation of band B1). Solid (green) and dotted (cyan) lines correspond $\alpha =+1/2$ and $\alpha =-1/2$ signature partners, respectively, for the positive-parity orbitals while large-dashed (pink) and dashed (red) lines correspond to the same signature partners for the negative-parity orbitals.

Figure 19

Same as Fig. 18 but for deformation parameter ${\beta }_2=0.14$ and $\gamma ={40}^{\circ }$ corresponding to the calculated deformation of band B3.