Spectroscopy of weakly deformed bands in ${}^{87}\mathrm{Zr}$: First observation of the shears mechanism in a Zr isotope

Excited states of ${}^{87}\mathrm{Zr}$, populated in the reaction ${}^{60}\mathrm{Ni}({}^{31}\mathrm{P}$, $3pn$) at a beam energy of 112.5 MeV, have been studied. Experimental information on two negative-parity bands has been significantly upgraded with the addition of new $\gamma$ rays and levels. Small values of the reduced transition probability $B(E2$) and a general absence of a measurable Doppler shift in the transitions suggest that the states are weakly deformed. Several positive-parity levels have been grouped into two bands based on their observed properties. Spin parities have been proposed for a majority of the states belonging to the different bands. Lifetimes have been measured for the eight states belonging to the two positive-parity bands from Doppler shift attenuation data, including an upper limit for the highest energy state. The behavior of the deduced $B(M1$) and $B(E2$) values as a function of level spin supports the interpretation of one of these bands within the framework of the shears mechanism. A study of these reduced transition probabilities in the light of the semiclassical model of the shears mechanism, proposed by Macchiavelli and co-workers, confirms this interpretation. The effective gyromagnetic ratio and the interaction strength between the two blades of the shears have been estimated from this study.

Figure 1

Level scheme of ${}^{87}\mathrm{Zr}$ deduced from the present work. The relative intensities of the transitions are indicated by the widths of the transitions. New transitions and levels are marked with asterisks.

Figure 2

Gated spectra in support of the placement of new transitions (marked with asterisk) in bands 1 and 2. (a) and (b) in the upper panel show the low- and high-energy regions, respectively, of the sum of the double-gated spectra gated by ($1133.4+110.9$) and ($1004.7+239.6$) keV $\gamma$ rays. Panels (c) and (d) represent the low- and high-energy regions, respectively, of the sum of the double-gated spectra gated by ($967.6+627.8$) and ($683.8+627.8$) keV $\gamma$ rays. All spectra are corrected for $\gamma$-ray relative efficiencies.

Figure 3

Gated spectra in support of the placement of new transitions (marked with asterisk) in bands 1 and 2. The vertical axis for (a) is shown on the extreme left and those for (b) and (c) are indicated at extreme right. Panel (a) shows the sum of single gates on the 286.3 and 1197.3 keV transitions. Gamma rays marked u1 and u2 with energies 655 and 660 keV, respectively, belong to ${}^{85}\mathrm{Y}$ and u3 with energy 721 keV belongs to ${}^{88}\mathrm{Zr}$. Panels (b) and (c) show double-gated spectra with gates on the ($239.6+1352.1$) and ($676.4+683.8$) keV $\gamma$ rays, respectively. The spectra are corrected for $\gamma$-ray relative efficiencies.

Figure 4

Experimental DCO ratios for $\gamma$ rays belonging to (a) bands 1 and 2 and (b) bands 3 and 4. Filled squares represent DCO ratios for $\mathrm{\Delta }I=1$ transitions and open squares represent DCO ratios for $\mathrm{\Delta }I=2$ transitions. The 1004.7 keV, $13/2^{-}\to 13/2^{+}\gamma$ ray (see Fig. 1) is a pure nonstretched dipole transition and its DCO ratio is represented by a filled triangle in (a). The DCO ratios were obtained by gating on stretched $E2$ transitions. The $R_{\mathrm{DCO}}$ results are given in the Supplemental Material [28].

Figure 5

Gamma-ray multipole mixing ratios $\delta$ for (a) bands 1 and 2 and (b) bands 3 and 4. Only the 925.4 keV $\gamma$ ray in (a) and the 692.6 keV $\gamma$ ray in (b) are electric quadrupole in nature. Mixing ratio results are given in the Supplemental Material [28].

Figure 6

Gated spectra in support of the placement of new transitions (marked with asterisk) in bands 3 and 4. Figure shows the sum of the double-gated $\gamma$-ray spectra with gates on ($1070.5+431.9$) and ($1133.4+431.9$) keV. Panel (a) shows the low-energy part of the summed spectrum for $\gamma$ rays with energies up to 1200 keV and panel (b) shows the spectrum for the higher-energy $\gamma$ rays. The spectra are corrected for $\gamma$-ray relative efficiencies.

Figure 7

DSA line shapes for the 486.7, 562.8, 588.3, and 525.1 keV $\gamma$ rays belonging to band 3 at ${90}^{\circ }$ (bottom panels) and ${157}^{\circ }$ (top panels) to the beam direction. The spectra in (a), (b), and (c) are from gates on lower-lying $E2\gamma$ rays and the spectra in (d) are gated by the 486.7 keV dipole $\gamma$ ray. The bold lines are the calculated fits to the experimental data using the code lineshape [27]. Weak contaminant peaks present in the spectra in (c) and (d) are also included in the fits.

Figure 8

Plot of the excitation energies ($E_x$) of the states belonging to band 2 in ${}^{87}\mathrm{Zr}$, established in the present work, versus the excitation energies of similar negative-parity bands in ${}^{85}\mathrm{Sr}$ [16] and ${}^{89}\mathrm{Mo}$ [32].

Figure 9

Figure shows the angular momentum vectors $j_{\parallel }=4\hslash$ and $j_{\perp }=8.5\hslash$ for band 3 at the bandhead (continuous lines) at spin $I=21/2$ and for the state at $I=29/2$ (dashed lines). The corresponding vector sums $I$ are also shown. The configuration for band 3 is given in the text. The shears angle $\theta (=75.6^{\circ }$) and the proton angle ${\theta }_{\pi }(=53.4^{\circ }$) at the bandhead are indicated. Also shown are the components of the magnetic dipole moments perpendicular to $I$ at $I=23/2$ (continuous line) and $I=29/2$ (dashed line).

Figure 10

Plots of experimental (a) $B(M1$), (b) $B(E2$) values and (c) $\left[B\right(M1$)/$B(E2$)] ratios as functions of level spin for states of band 3. The continuous lines in (a) and (b) are fits of the reduced transition probabilities calculated from the semiclassical model of Macchiavelli et al. [37] to the experimental results. Plot (d) shows the $B(M1$) values as a function of the shears angle $\theta$. The continuous line represents the theoretical $B(M1$) values fitted to the observed results. The plot in (e) presents the experimental excitation energy of band 3 versus level spin. The corresponding shears angles are shown along the axis at the top. The full line is the interaction energy according to Eq. (4) in the text.