Investigation of the alignment mechanism and loss of collectivity in ${}^{135}\mathrm{Pm}$

High-spin excited states of ${}^{135}\mathrm{Pm}$ have been investigated using the ${}^{107}\mathrm{Ag}({}^{32}\mathrm{S}$, $2p2n$) reaction at 145-MeV beam energy. Three negative-parity bands have been investigated up to $\sim 9.0-$, $7.6-$, and $6.9-\mathrm{MeV}$ excitation energies with spin parities $(55/2^{-})$, $(49/2^{-})$, and $(47/2^{-})\hslash$, respectively. The experimental results have been interpreted using the triaxial projected shell model. It is shown that the observation of the parallel band structures can be explained in terms of crossing of two $s$ bands with the yrast band, which is a rare phenomenon for an odd-$A$ nucleus. Further, the lifetimes of levels in yrast band have been extracted using Doppler shift attenuation method. The evaluated $B\left(E2\right)$ values of yrast states show the loss of collectivity at higher spin, attributed to the alignment process.

Figure 1

Partial level scheme of ${}^{135}\mathrm{Pm}$ consisting of negative-parity states obtained from the present work. The level energies are given relative to the ${\mathrm{11/2}}^{-}$ state of Band 1. The new transitions are shown in red while the rearranged transitions are shown in blue. The arrow widths are proportional to the transition intensity and the white portion corresponds to the internal-conversion component. The energies of levels and gamma transitions given in keV are rounded off to the nearest integer values.

Figure 2

Spectrum obtained from the double gate on (a) A/B, where A is the list gate of 286, 513, 658 keV and B is the list gate of 749, 805, 846, 898, 964, and 1030 keV; (b) C/C, where C is the list gate of 520, 612, 649, 697, and 767 keV; and (c) 286 and 649 keV. The new and rearranged transition energy values are marked red and blue, respectively.

Figure 3

Spectrum obtained from the (a) double gate on 286/620 keV and (b) sum of L/751-keV and L/927-keV double gates, where L is the list gate of 604, 620, 697, and 827 keV. The new and rearranged transition energy values are marked red and blue, respectively.

Figure 4

The theoretically fitted line-shape spectra for 658-, 749-, 805- and 846-keV quadrupole transitions of the yrast band in ${}^{135}\mathrm{Pm}$. The, contaminant peaks, and total line shapes of the above-mentioned transitions are represented in dashed (blue), dot-dashed (green), and solid (red) lines, respectively.

Figure 5

Experimental alignment, $i_x$ for the negative-parity bands in ${}^{135}\mathrm{Pm}$ is plotted against the rotational frequency ($\hslash \omega$). Harris parameters $J{}_0$ = 12.5 ${\hslash }^2{\mathrm{MeV}}^{-1}$ and $J{}_1$ = 20 ${\hslash }^4{\mathrm{MeV}}^{-3}$ were used.

Figure 6

TPSM projected energies, before band mixing, of negative-parity states for ${}^{135}\mathrm{Pm}$. Bands are labeled by $(K,\#)$ that designate the quasiparticle states with $K$ quantum number and $\#$ the number of quasiparticles. For instance, (3/2, $1\pi$), (7/2, $1\pi$), (11/2, $1\pi$) correspond to the $K=3/2,7/2,11/2$ one-proton quasiparticle state. The three-quasiparticle states with configurations (1/2, $1\pi 2\nu$), (5/2, $1\pi 2\nu$), (9/2, $1\pi 2\nu$), (3/2, $3\pi$), (7/2, $3\pi$), (11/2, $3\pi$) corresponding to the $K=1/2,5/2,9/2,3/2,7/2,11/2$ include two-neutron and two-proton configurations on the basic one-proton configuration. The excited $K=1/2,5/2,9/2$ resulting from projection of three-quasiprotons and two-quasineutrons are denoted by (1/2, $3\pi 2\nu$), (5/2, $3\pi 2\nu$), (9/2, $3\pi 2\nu$) respectively. Because of large signature splitting, bands are separated into favored signature partner (labelled as $\alpha =-1/2$) and unfavored signature partner (labelled as $\alpha =+1/2$). The solid curves represent the $\alpha =-1/2$ states with same legend symbols and quasiparticle states as that of $\alpha =+1/2$ states plotted in dashed curves. The first crossing at $I=31/2$ is due to $(3/2,3\pi )$ aligned configuration that forms the yrast-band configuration. The second crossing at about $I=43/2$ is due to $(5/2,3\pi 2\nu )$ 5-quasiparticle configuration with $K=5/2$. The energies are plotted relative to the $11/2^{-}$ state of Band 1.

Figure 7

Comparison of experimentally observed level energies of negative-parity Band 1, Band 2, and Band 3 with the values obtained from TPSM calculations. The energies are given relative to the ${\mathrm{11/2}}^{-}$ state of Band 1.

Figure 8

Probability of various projected K configurations in the wave functions of the observed Band 1, Band 2, and Band 3 in ${}^{135}\mathrm{Pm}$. Only the lowest projected K configurations in the wave functions of bands are shown. The solid curves represent the $\alpha =-1/2$ states with same legend symbols and quasiparticle states as that of $\alpha =+1/2$ states plotted in dashed curves. Legends for only $\alpha =+1/2$ states are shown for better visual clarity.

Figure 9

Comparison between experimental and theoretical (TPSM) values of alignment ($i_x$) and dynamic moment of inertia ($J^{\left(2\right)}$) as a function of spin ($\hslash$) for the quadrupole negative-parity bands in ${}^{135}\mathrm{Pm}$. The left panel consists of $i_x$ for (a) Band 1, (b) Band 2, and (c) Band 3 while the right panel contains ($J^{\left(2\right)}$) for (d) Band 1, (e) Band 2, and (f) Band 3.

Figure 10

Experimentally measured values of $B\left(E2\right)$ transition strengths are compared with the theoretical values calculated within TPSM formalism. The filled squares correspond to the experimental $B\left(E2\right)$ values. Previously reported values, shown in open squares, are adapted from Ref. [4].