Collective modes of excitation in ${}^{64}\mathrm{Cu}$

Medium and high-spin level sequences in ${}^{64}\mathrm{Cu}$ were investigated using the complex ${}^{26}\mathrm{Mg}({}^{48}\mathrm{Ca},\alpha p5n\gamma )$ multinucleon transfer reaction. The experiment was performed at the ATLAS accelerator facility at the Argonne National Laboratory using the Gammasphere array and the fragment mass analyzer (FMA). Two high-spin, quasirotational bands consisting of stretched-$E2$ transitions were observed in coincidence with the known low-spin structure for the first time. These bands share remarkable similarities with highly deformed and/or superdeformed bands observed in the $A\approx 60–70$ mass region. In addition, a regular dipole sequence with weak $E2$ crossover transitions was observed. A general discussion of the observed structures, complemented by theoretical calculations carried out within the framework of the adiabatic and configuration-fixed constrained covariant density functional theory and the quantum particle-rotor model, are presented. The results are interpreted in the context of shell-structure evolution and the collectivity in the mass region.

Figure 1

Angular distributions for some relevant ${}^{64}\mathrm{Cu}$ transitions. Experimental data are shown as black circles, while the angular-distribution fits correspond to the red curve.

Figure 2

Experimental (points) and calculated (dashed line) values of the fractional Doppler shift $F\left(\tau \right)$ as a function of $E_{\gamma }$ for Band 1 in ${}^{64}\mathrm{Cu}$. The best fit is represented by the dashed-red line.

Figure 3

Lower part of the partial level scheme of ${}^{64}\mathrm{Cu}$ as observed in the present study. Newly placed transitions are indicated in blue while those that have been reassigned from previous work are given in red. Black-colored transitions are previously known transitions that have been confirmed in the present work. Details of the spin-parity assignments for earlier-known, reassigned, and new transitions are provided in the text and in Table 1. Although Band 1 is firmly connected to the low-spin part of the level scheme, the placement of Band 2 is schematic since the absolute excitation energy, spin, and parity are unknown; see text for further details. Transitions indicated with dashed arrows and enclosed in parentheses are uncertain.

Figure 4

Continuation of the high-spin part of the level scheme of ${}^{64}\mathrm{Cu}$ as observed in the present study.

Figure 5

Background-corrected total projection spectrum obtained from the ${}^{64}\mathrm{Cu}\gamma \text{−}\gamma \text{−}\gamma$ coincidence matrix. Transitions within the low-spin region are indicated in black, those within the dipole band are in red, and transitions within rotational Bands 1 and 2 are in blue and green, respectively. The dashed line divides the two regions of the spectrum which correspond to the two different zooms of the $y$ axis: The left axis for the region on the left of the dashed line and the right axis (x3) for the one on the right.

Figure 6

Coincidence spectrum resulting from a double gate on the 159- and 203-keV. Transitions within the dipole band (labeled in red) and those within rotational Bands 1 and 2 (blue and green, respectively) are indicated. The dashed line divides the two regions of the spectrum which correspond to the two different zooms of the $y$ axis: the left axis for the region on the left of the dashed line and the right axis (x2) for the one on the right.

Figure 7

Coincidence spectra obtained by double gating on (a) the 314- and 479- keV transitions, and (b) the 479- and 481- keV ones. Newly placed transitions are indicated in blue while those that have been reassigned from previous work are given in red. Black-colored $\gamma$ rays are previously known transitions that have been confirmed in the present work.

Figure 8

Coincidence spectrum obtained by double gating on the 250- and 479- keV transitions. Newly placed $\gamma$ rays are indicated in blue while those that have been reassigned from previous work are given in red. Black-colored $\gamma$ rays are previously-known transitions that have been confirmed in the present work.

Figure 9

Coincidence spectra resulting from (a) a double gate on the 369- and 540-keV transitions, (b) a double gate on the 278- and 540-keV ones and (c) a double gate on the 199- and 540-keV lines. Newly-placed transitions are indicated in blue while those that have been reassigned from previous work are given in red. Black-colored transitions are previously known ones that have been confirmed in the present work.

Figure 10

Coincidence spectrum resulting from a double coincidence gate on 790- and 817-keV transitions. A $\gamma$ ray reassigned from previous work is given in red. Black-colored transitions are previously known ones that have been confirmed in the present work.

Figure 11

Coincidence spectra resulting from a gate on the sum of all possible in-band transitions of (a) Band 1 and (b) Band 2. An almost constant energy spacing between the in-band $\gamma$-ray transitions in these bands indicates the onset of collectivity.

Figure 12

Coincidence spectra resulting from (a) a double coincidence gate on 2216- and 1387-keV transitions and (b) a double gate on 1916- and 2216-keV ones. Gamma rays from band 2 (green) appear in coincidence with those arising from the low-lying level structure (black). The green arrows point to the gating transitions.

Figure 13

Coincidence spectra resulting from (a) a double gate on the 2116- and 2423- keV transitions and (b) a double gate on 1624- and 1860-keV ones. Gamma rays from Band 1 (blue) appear in coincidence with those arising from the low-lying level structure (black). The blue arrows point to the gating transitions.

Figure 14

Angular momentum as a function of transition energy for Band 1 (red circles) and Band 2 (blue triangles) in ${}^{64}\mathrm{Cu}$. $I_{\circ }$ is the bandhead spin. Also shown for comparison are the rotational bands in ${}^{64}\mathrm{Zn}$ [39], ${}^{68}\mathrm{Zn}$ [19], ${}^{59}\mathrm{Cu}$ [15], and ${}^{58}\mathrm{Cu}$ [14].

Figure 15

Experimental dynamic moment of inertia ${\mathcal{J}}^2$ as a function of the rotational frequency $\hslash \omega$ for Band 1 (red circles) and Band 2 (blue triangles) in ${}^{64}\mathrm{Cu}$. Also shown for comparison are the rotational bands in ${}^{64}\mathrm{Zn}$ [39], ${}^{68}\mathrm{Zn}$ [19], ${}^{59}\mathrm{Cu}$ [15], and ${}^{58}\mathrm{Cu}$ [14].

Figure 16

Potential-energy surface in the $\beta -\gamma$ plane ($0\le \beta \le 0.6, 0^{\circ }\le \gamma \le {60}^{\circ }$) for the ground state configuration of ${}^{64}\mathrm{Cu}$ in CDFT calculations with the PC-PK1 effective interaction. All energies are normalized with respect to that of the absolute minimum (in MeV) indicated by the red circle. The square denotes the local minimum. The energy separation between each contour line is 0.5 MeV.

Figure 17

Single-proton and single-neutron levels near the Fermi surface in ${}^{64}\mathrm{Cu}$ for the ground state (left) and the states in the local minimum (right).

Figure 18

Same as Fig. 17, but for the configurations of Band 1 (left) and Band 2 (right).

Figure 19

PRM calculations compared with the available data for ${}^{64}\mathrm{Cu}$: (a) energy minus a rotor contribution, (b) computed reduced electric quadrupole transition probabilities $B\left(E2\right)$, and (c) calculated transition quadrupole moment $Q_t$, for Bands 1 and 2 together with the single value for Band 3.