Identification of multi-phonon $\gamma$-vibrational bands in odd-$Z$ ${}^{105}$Nb

Background: The odd-$Z$ ${}^{105}$Nb nucleus is located in the $A=100$ neutron-rich region. The study of multi-phonon vibrational band structures is important for understanding nuclear structure in this region.

Purpose: To search for multi-phonon $\gamma$-vibrational bands in ${}^{105}$Nb.

Methods: The high spin states of ${}^{105}$Nb have been studied by measuring the prompt $\gamma$ rays emitted in the spontaneous fission of ${}^{252}$Cf. The data analysis is carried out using triple- and four-fold $\gamma$ coincidence methods.

Results: A new level scheme of ${}^{105}$Nb is established. The yrast band has been confirmed, and three new collective bands have been identified. Compared with previous results, a total of 14 new levels and 36 new $\gamma$ transitions are observed. Two bands built on 625.9 keV and 1231.9 keV levels are proposed as one-phonon- and two-phonon $\gamma$-vibrational bands, respectively. The evidences for supporting assignments of the multi-phonon $\gamma$-vibrational bands have been discussed. Triaxial projected shell model calculations for the $\gamma$-vibrational band structures are found in good agreement with the experimental data, thus further supporting the $\gamma$-vibrational interpretations for the experimental results in ${}^{105}$Nb.

Conclusions: The one-phonon- and two-phonon $\gamma$-vibrational bands have been identified in ${}^{105}$Nb. Our results provide new data to systematically understand the characteristics of the multi-phonon $\gamma$-vibrational bands in the $A=100$ neutron-rich region.

Figure 1

The level scheme of ${}^{105}$Nb identified in the present paper.

Figure 2

Portion of the $\gamma$ ray spectrum obtained by summing double gates on the 128.1 and 162.5 keV $\gamma$ transitions, and 128.1 and 220.8 keV $\gamma$ transitions in ${}^{105}$Nb. The range of the energy is (a) from 157 to 523 keV, and (b) from 523 to 863 keV.

Figure 3

Portion of the $\gamma$ ray spectrum obtained by summing double gates on the 128.1 and 700.6 keV $\gamma$ transitions, and 128.1 and 538.1 keV $\gamma$ transitions in ${}^{105}$Nb. The range of the energy is (a) from 155 to 415 keV, and (b) from 415 to 700 keV.

Figure 4

Portion of the $\gamma$ ray spectra of ${}^{105}$Nb obtained by (a) double gates on the 128.1 and 606.0 keV $\gamma$ transitions, and (b) triple gates on the 128.1, 497.8, and 606.0 keV $\gamma$ transitions.

Figure 5

Calculated polar coordinate plots of the total Routhian surface for ${}^{105}$Nb at $\hslash \omega =0.0$ MeV. The minimum point corresponds to ${\beta }_2=0.339,{\beta }_4=0.007$, and $\gamma =12.3^{\circ }$.

Figure 6

The plots of the total angular momentum alignments $I_x$ vs the rotational frequency $\hslash \omega$ for the ground state band, and bands (2)-(4) in ${}^{105}$Nb.

Figure 7

The systematic comparisons for the ground-state band, 1$\gamma$ band, and 2$\gamma$ band of ${}^{105}$Nb with those in ${}^{103}$Nb [12] and ${}^{106}$Mo [1].

Figure 8

Comparison of the calculated energy levels for ${}^{105}$Nb with the experimental data.