Shape evolution with increasing angular momentum in the ${}^{66}\mathrm{Ga}$ nucleus

The high-spin nuclear structure of the odd-odd ${}^{66}\mathrm{Ga}$ nucleus was probed using heavy-ion induced fusion-evaporation reaction. The de-exciting $\gamma$ rays were detected by using the Indian National Gamma Array (INGA) consisting of high resolution Compton suppressed clover detectors. The level scheme of ${}^{66}\mathrm{Ga}$ was extended up to an excitation energy $\left(E_x\right)$ of $\sim 10.6$ MeV with spin parity of ${21}^{(+)}$. Two new quadrupole bandlike structures, one positive and one negative parity, based on the states having spin parity of $J^{\pi }={11}^{+}$ and ${10}^{-}$, respectively, were found. The experimental energy levels are compared with calculations within the framework of shell model calculation using $jj44bpn$ effective interaction. The agreement between experiment and theory is good. The total Routhian surface calculations were performed to understand the shape of the ${}^{66}\mathrm{Ga}$ nucleus associated with the configurations $\nu \left(g_{9/2}\right){}^3\nu \left(f_{5/2}\right){}^2\pi \left(g_{9/2}\right){}^1\pi \left(f_{5/2}\right){}^2$ and $\nu \left(g_{9/2}\right){}^2\nu \left(f_{5/2}\right){}^1\pi \left(g_{9/2}\right){}^1\pi \left(f_{5/2}\right){}^2$ assigned to the positive and negative parity bands, respectively. In the frequency domain $\omega =0.20\text{–}0.30$ MeV, both the negative and positive parity quadrupole structures, favor prolate deformation whereas at $\omega =0.50$ MeV there is a sudden change to noncollective oblate shape in both the bands.

Figure 1

Theoretical $R_{\mathrm{DCO}}$ values for different $\sigma /j$ value of the reaction for the present experimental setup, calculated using the angcor program. Experimental $R_{\mathrm{DCO}}$ ratios for the transitions of energy 1084-keV ($7^{-}\to 6^{+}$), 1409-keV ($9/2^{+}\to 7/2^{-}$), 1510-keV ($5^{-}\to 4^{+}$), and 1381 ($5^{-}\to 4^{+}$)-keV transitions in ${}^{60}\mathrm{Ni}$, ${}^{61}\mathrm{Cu}$, ${}^{66}\mathrm{Ge}$, and ${}^{68}\mathrm{Ge}$ nuclei, respectively. Mean value of $\sigma /j=0.29$.

Figure 2

Plot of asymmetry factor $a$ with energy for a ${90}^{\circ }$ clover detector (with respect to beam direction) in the present setup. The solid line shows a linear fit to the data points.

Figure 3

Plot of the polarization sensitivity with energy for different $\gamma$-ray transitions observed in the present experiment. The solid curve is obtained by fitting the data with Eq. (4).

Figure 4

Plot of the experimental and theoretical value of polarization for different $\gamma$-ray transitions observed in the present experiment.

Figure 5

Total projection spectrum of $E_{\gamma }-E_{\gamma }$ matrix from ${}^{12}\mathrm{C}+{}^{56}\mathrm{Fe}$ reaction at $E_{\mathrm{lab}}=62$ MeV shows $\gamma$ rays of nuclei populated in the present reaction. Contaminant peaks are identified with C. Nuclei in $A\sim 150$ region were populated from the reaction of ${}^{12}\mathrm{C}$ beam with the ${}^{150}\mathrm{Nd}$ target.

Figure 6

Gated spectrum on 1189-keV ($9^{+}\to 7^{+}$) and 1540-keV (${10}^{-}\to 9^{+}$) transitions in ${}^{66}\mathrm{Ga}$. Transitions belonging to the ${}^{66}\mathrm{Ga}$ nucleus are labeled with the respective energies and new transitions are indicated by asterisks (*) while contaminant peaks are identified with C.

Figure 7

Proposed partial level scheme of ${}^{66}\mathrm{Ga}$ nucleus obtained from the present work. Transitions marked with asterisks (*) are newly observed in the current measurement. Widths of the arrows are proportional to the transition intensities. Tentatively identified transition is indicated by dotted line.

Figure 8

Plot of theoretical $R_{\mathrm{DCO}}$ values for different $\delta I$ mixing represented by the solid blue, red, and black colored lines. Experimental $R_{\mathrm{DCO}}$ for 1119-keV transition are represented by the solid black horizontal lines.

Figure 9

Angular distribution fit for the 1119-keV (${11}^{+}\to 9^{+}$) transition in the ${}^{66}\mathrm{Ga}$ nucleus and the corresponding ${\chi }^2$ analysis for obtaining the mixing ratio.

Figure 10

Comparison of energy levels of ${}^{66}\mathrm{Ga}$ observed in the present data (denoted by Expt) with shell model calculations using $jj44bpn$ [36] effective interaction (denoted by SM) for both positive as well as negative parity states.

Figure 11

Variation of experimental quasiparticle (a) aligned angular momentum and (b) Routhian for positive and negative parity band structures (band I and band II) in ${}^{66}\mathrm{Ga}$ with frequency. Harris parameters used for the calculation are ${\mathit{J}}_{\mathit{0}}=6.0{\hslash }^2{\mathrm{MeV}}^{-1}$ and ${\mathit{J}}_{\mathit{1}}=3.5{\hslash }^4{\mathrm{MeV}}^{-3}$ [40].

Figure 12

Calculated quasineutron energy levels for $N=35$ corresponding to the ${}^{66}\mathrm{Ga}$ nucleus. Positive parity, positive, and negative signature, and negative parity, positive, and negative signature orbitals are denoted by green, blue, red, and magenta colors, respectively.

Figure 13

Calculated quasiproton energy levels for $Z=31$ corresponding to the ${}^{66}\mathrm{Ga}$ nucleus. Positive parity, positive and negative signature and negative parity positive and negative signature orbitals are denoted by green, blue, red, and magenta colors, respectively.

Figure 14

Contour plots of the TRS calculations for the $\nu \left(g_{9/2}\right){}^3\nu \left(f_{5/2}\right){}^2\pi \left(g_{9/2}\right){}^1\pi \left(f_{5/2}\right){}^2$ configuration of the positive parity band structure in ${}^{66}\mathrm{Ga}$. The rotational frequency ($\hslash \omega$) for the calculations are (a) 0.200, (b) 0.300, (c) 0.500, and (d) 0.900 MeV. The energy difference between two contours is 0.250 MeV.

Figure 15

Contour plots of the TRS calculations for the $\nu \left(g_{9/2}\right){}^2\nu \left(f_{5/2}\right){}^1\pi \left(g_{9/2}\right){}^1\pi \left(f_{5/2}\right){}^2$ configuration of the negative parity structure in ${}^{66}\mathrm{Ga}$. The rotational frequency ($\hslash \omega$) for the calculations are (a) 0.200, (b) 0.300, (c) 0.500, and (d) 0.900 MeV. The energy difference between two contours is 0.250 MeV.