Role of the $\nu g_{9/2}$ orbital in the development of collectivity in the $A\approx 60$ region: The case of ${}^{61}\mathrm{Co}$

An extensive study of the level structure of ${}^{61}\mathrm{Co}$ has been performed following the complex ${}^{26}\mathrm{Mg}({}^{48}\mathrm{Ca},2\alpha 4np\gamma ){}^{61}\mathrm{Co}$ reaction at beam energies of 275, 290, and 320 MeV using Gammasphere and the Fragment Mass Analyzer (FMA). The low-spin structure is discussed within the framework of shell-model calculations using the GXPF1A effective interaction. Two quasirotational bands consisting of stretched-$E2$ transitions have been established up to spins $I=41/2$ and $(43/2)$, and excitation energies of $\sim 17$ and $\sim 20$ MeV, respectively. These are interpreted as signature partners built on a neutron $\nu {\left(g_{9/2}\right)}^2$ configuration coupled to a proton $\pi p_{3/2}$ state, based on cranked shell model (CSM) calculations and comparisons with observations in neighboring nuclei. In addition, four $\Delta I=1$ bands were populated to high spin, with the yrast dipole band interpreted as a possible candidate for the shears mechanism, a process seldom observed thus far in this mass region.

Figure 1

Representative angular distributions for newly identified transitions in ${}^{61}\mathrm{Co}$. The solid lines represent least-squares fits using the Legendre polynomial expansion, $W\left(\theta \right)=a_o[1+a_2{P}_2(cos\theta )+a_4{P}_4(cos\theta )]$. Experimental data points are represented by open circles.

Figure 2

Experimental $F\left(\tau \right)$ values as a function of the $\gamma$-ray energy (filled circles) compared with the best-fit curve (solid line) for band $\text{QB}1$ in ${}^{61}\mathrm{Co}$. The dashed lines indicate the statistical errors only; i.e., they do not include the $\sim 10\%$ error associated with the systematic uncertainty in the stopping powers. See text for details.

Figure 3

The level structure of ${}^{61}\mathrm{Co}$ as obtained from the present study. The widths of the arrows are proportional to the relative intensities of the $\gamma$ rays. Tentative transitions are indicated by dashed lines. Note that the excitation energy of band $\text{QB}2$ is unknown (marked dash-dotted line); see text for details.

Figure 4

Representative Doppler-corrected coincidence spectra gated by transitions in ${}^{61}\mathrm{Co}$. (a) Gate on the 270-keV transition in the dipole band $\text{DB}1$. (b) Gate on the 1030-keV transition in band $\text{DB}2$. (c) Gate on the 475-keV $\gamma$ ray in band $\text{DB}3$. Some of the relevant coincidence relationships are highlighted in the text.

Figure 5

Representative Doppler-corrected coincidence spectra gated by transitions in ${}^{61}\mathrm{Co}$. (a) Gate on the 541-keV transition in the dipole band $\text{DB}4$. (b) Gate on the 1267-keV line in the quadrupole band $\text{QB}1$. (c) Gate on the 1834-keV $\gamma$ ray in the quadrupole band $\text{QB}2$.

Figure 6

Shell-model calculations of level structures in ${}^{61}\mathrm{Co}$ compared with experimental levels. The picture depicts the single-particle levels marked $\text{SP}1$ and the bandheads of the newly identified dipole bands. The calculations used the effective interaction GXPF1A with a ${}^{40}\mathrm{Ca}$ closed core.

Figure 7

Excitation energy $E_x$ as a function of spin for the $\Delta I=2$ bands in ${}^{61}\mathrm{Co}$ observed in the present investigation. Panel (a) shows the bands alone, while panel (b) compares the new bands with similar sequences in the $N=34$ isotones ${}^{60}\mathrm{Fe}$ and ${}^{62}\mathrm{Ni}$. Data and band names for the isotones are taken from Refs. [5] and [29]. Note that different scales are used in the top and bottom panels.

Figure 8

(a) Experimental kinematic moment of inertia ${\mathcal{J}}^{\left(1\right)}$ as a function of the rotational frequency $\hslash \omega$ for bands $\text{QB}1$ and $\text{QB}2$ in ${}^{61}\mathrm{Co}$, the yrast band in ${}^{60}\mathrm{Fe}$ $(\text{GSB}$ in Ref. [5]), and band $\text{D}1$ in ${}^{62}\mathrm{Ni}$ [29]. (b) Experimental alignment $I_x$ as a function of the rotational frequency $\hslash \omega$ for bands $\text{QB}1$ and $\text{QB}2$ in ${}^{61}\mathrm{Co}$, the yrast band in ${}^{60}\mathrm{Fe}$ $(\text{GSB}$ in Ref. [5]) and band $\text{D}1$ in ${}^{62}\mathrm{Ni}$ [29]. Data and band names for the isotones are taken from Refs. [5] and [29].

Figure 9

Results of cranked shell-model calculations (CSM) for the quasineutron (a) and quasiproton (b) Routhians as a function of rotational frequency $\hslash \omega$ in ${}^{61}\mathrm{Co}$. The calculation was performed with parameters of ${\beta }_2=0.3,{\beta }_4=0.0$, and $\gamma =0^{\circ }$. The line types represent unique combinations of (parity, signature), as follows: solid $(+,+1/2)$; dot $(+,-1/2)$; dash-dot $(-,+1/2)$; dash $(-,-1/2)$. Quasiparticle labels follow the convention of Ref. [48]. See text for details.

Figure 10

Excitation energies $E_x$ of states as a function of spin $I$ for (a) band $\text{DB}2$ in ${}^{61}\mathrm{Co}$ and (b) band $\text{MRB}1$ in ${}^{58}\mathrm{Fe}$. Effective interaction as a function of the shears angle $\theta$ for (c) band $\text{DB}2$ in ${}^{61}\mathrm{Co}$ and (d) band $\text{MRB}1$ in ${}^{58}\mathrm{Fe}$. The solid lines in panels (c) and (d) show the dependence of a $P_2$-type force.

Figure 11

(a) Excitation energy as a function of spin for all the observed $\Delta I=1$ bands in ${}^{61}\mathrm{Co}$. (b) Effective interaction as a function of the shears angle for band $\text{DB}1$ in ${}^{61}\mathrm{Co}$. The solid line shows the dependence of a $P_2$-type force. (c) Angular momentum and (d) kinematic moment of inertia ${\mathcal{J}}^{\left(1\right)}$ versus rotational frequency $\hslash \omega$ for bands $\text{DB}1,\text{DB}2,\text{DB}3$, and $\text{DB}4$.