Investigation of the high spin structure of ${}^{88}\mathrm{Zr}$

High spin states of ${}^{88}\mathrm{Zr}$ were populated with ${}^{80}\mathrm{Se}$(${}^{13}\mathrm{C}$, $5n$) fusion evaporation reaction. A thin target as well as Au backed target were used in two different experiments for the present study. Excited levels of ${}^{88}\mathrm{Zr}$ have been observed up to spin $\sim 20\hslash$ and an excitation energy of $\sim 10$ MeV. Spin and parity of most of the states have been determined from directional correlation and polarization measurements. The level scheme was substantially extended with the addition of a number of high spin states and transitions. The comparison of the measured levels of ${}^{88}\mathrm{Zr}$ with large shell model calculations based on the full unrestricted $f_{5/2}p{g}_{9/2}$ model space established the dominance of shell-model excitation up to the highest observed spin.

Figure 1

Prompt and delayed coincidence spectrum of ${}^{88}\mathrm{Zr}$ with a gate on the 1022 keV transition are shown in (a) and (b), respectively. Due to the presence of a $T_{1/2}=1.7$ $\mu$s isomeric level at 2888 keV, energy in the prompt coincidence (within a time window of 100 ns) spectrum none of the transitions below this level are observed. However, the strong transitions below the isomer could be exclusively identified from the delayed coincidence spectrum as shown in the inset. The $\gamma$ rays that have been newly observed in the present experiment are marked with asterisks.

Figure 2

Partial level scheme of ${}^{88}\mathrm{Zr}$ developed in the present work. The energies of the observed excited states and $\gamma$-ray transitions are given in keV. The thickness of the arrows above the 2888 keV level are roughly proportional to the $\gamma$-ray intensity mentioned in Table 1. The new and rearranged $\gamma$ rays are marked with red and green color, respectively.

Figure 3

Spectrum generated by the sum of the double gates of 503-587, 1022-587, 816-587, and 721-587 keV transitions. The strong transitions having energies of 288 and 604 keV belong to the cascade P1. The 2042 keV $\gamma$-ray links the cascades P2 and P1 at the 7431 keV level. The 1422, 1731, and 1808 keV $\gamma$ rays belong to the sequence of levels marked as P4. The $\gamma$ rays that have been newly observed in the present experiment are marked with asterisks.

Figure 4

Spectrum generated by the sum of the double gates of 503-551, 1022-551, 816-551, and 721-551 keV transitions. The strong transitions having energies of 325, 605, and 678 keV belong to cascade P1, while 409, 457, and 628 keV transitions belong to cascade P2 and the 437 and 572 keV transition belongs to the cascade P3 of positive parity part of the level scheme. The $\gamma$ rays that have been newly observed in the present experiment are marked with asterisks.

Figure 5

Spectrum generated by the sum of the double gates of 503-409, 1022-409, 816-409, and 1757-409 keV transitions. The strong transitions having energies of 628, 457, and 992 keV belong to P2 while the 285 and 551 keV transitions belong to P1 of the positive parity part of the level scheme. The $\gamma$ rays that have been newly observed in the present experiment are marked with asterisks.

Figure 6

Spectrum generated by the double gate of 101 and 84 keV transitions showing various $\gamma$ rays associated with the decay of the negative parity states. The $\gamma$ rays that have been newly observed in the present experiment are marked with asterisks.

Figure 7

A comparison of the measured positive parity states (middle) of ${}^{88}\mathrm{Zr}$ with the shell model calculation using the JUN45 (left) and jj44b (right) interactions in the model space incorporating the $p_{3/2}$, $f_{5/2}$, $p_{1/2}$, and $g_{9/2}$ orbitals. For a given spin whenever more than one state is present, they have been marked with red (second excited state) and green (third excited state).

Figure 8

A comparison of the measured negative parity states (middle) of ${}^{88}\mathrm{Zr}$ with the shell model calculation using the JUN45 (left) and jj44b (right) interactions in the model space incorporating the $p_{3/2}$, $f_{5/2}$, $p_{1/2}$, and $g_{9/2}$ orbitals. The second excited states observed for certain spin values have been marked as red.

Figure 9

Contribution of different configurations in the yrast 16${}^{+}$ and 2${}^{+}$ levels as calculated with the JUN45 interaction are shown in the pie charts. The configuration which has the largest contribution is shown with black color. The figure shows larger configuration mixing in the 2${}^{+}$ state than in the 16${}^{+}$ state. The first and the second square brackets in the legend represent the number of protons and neutrons in different orbitals corresponding to various configurations, respectively. The entries in the square brackets corresponds to the number of particles in $p_{3/2}$, $f_{5/2}$, $p_{1/2}$, and $g_{9/2}$, respectively.

Figure 10

Shell model calculation of particle occupation with the JUN45 interaction for the observed yrast levels of ${}^{88}\mathrm{Zr}$ positive parity states showing the probability of protons occupying the $g_{9/2}$ level is increased, whereas the same is decreased for the $p_{1/2}$ and $f_{5/2}$ levels at higher spin states. No significant change in particle occupation in $p_{3/2}$ has been observed. In the neutron shell no significant change in particle occupation is observed.