First Measurement of Collectivity of Coexisting Shapes Based on Type II Shell Evolution: The Case of ${}^{96}\mathrm{Zr}$

Background: Type II shell evolution has recently been identified as a microscopic cause for nuclear shape coexistence. Purpose: Establish a low-lying rotational band in ${}^{96}\mathrm{Zr}$. Methods: High-resolution inelastic electron scattering and a relative analysis of transition strengths are used. Results: The $B(E2;0_1^{+}\to 2_2^{+})$ value is measured and electromagnetic decay strengths of the $2_2^{+}$ state are deduced. Conclusions: Shape coexistence is established for ${}^{96}\mathrm{Zr}$. Type II shell evolution provides a systematic and quantitative mechanism to understand deformation at low excitation energies.

Figure 1

Summed and efficiency corrected experimental data for $\theta =141°$ and $E_0=43\mathrm{MeV}$ after the radiative tail of the elastic line has been subtracted. Gray areas correspond to inactive segments of the detector system. The inlet shows a magnification of the region around the $2_2^{+}$ state of ${}^{96}\mathrm{Zr}$, which is indicated by the red rectangle.

Figure 2

Value of $R_F\sqrt{A(2_2^{+})/A(2_1^{+})}$ as a function of elastic momentum transfer $q_0$. The solid red line shows the best fit of Eq. (1) to the experimental data (blue circles). The dashed lines represent the $1\sigma$ uncertainties with respect to $T(2_2^{+},2_1^{+})$. The adopted literature lower limit from $\beta$ decay [16] is shown as a black square. The green triangles, shifted slightly to the left for readability, represent estimates from ($p$, $p^{\prime }$), ($d$, $d^{\prime }$), and polarized ($d$, $d^{\prime }$) measurements [17].

Figure 3

Low-lying $0^{+}$ and $2^{+}$ states of ${}^{96}\mathrm{Zr}$ (left) and analyzed underlying structure (right), see text. Experimental excitation energies are given in keV. Excitation energies from the present shell model calculation are indicated by red bars. Note that only the $B(E2;2_1^{+}\to 0_1^{+})$ and $B(E2;2_2^{+}\to 0_2^{+})$ transition strengths have been used in the mixing calculation. The $T$-plots on the potential energy surface are included, demonstrating different shapes for the ground-state structure (spherical) and for the band on top of the $0_2^{+}$ state (triaxial) (see Ref. [19] for details). The lower left corner of each $T$-plot corresponds to zero for the quadrupole moments $Q_2$ and $Q_0$. The energy in the contour plot increases from blue (low) to red (high).

Figure 4

Effective single-particle energies (ESPE) for neutron (top) and proton (bottom) orbitals of interest to the discussion. The occupation of the orbitals is indicated by thick (filled) and thin (empty) lines. The length of the lines is proportional to the occupation number (thick lines) or the degeneracy of the orbital (thin lines). See text for details.