-
The level structure of 92Nb was studied by several researchers [10-14]. The high-spin states of 92Nb were recently studied in the 82Se(14N,4n)92Nb reaction by Wu et al [15]. The projectile used in the present experiment brings lower excitation energy to the compound nucleus, so that the relatively lower excited states of 92Nb can be populated and the middle-low level structure of 92Nb studied. The proposed level scheme of 92Nb is shown in Fig. 2, which is extended up to ~5.4 MeV excitation energy, and 20 new transitions and 8 new levels are added to 92Nb. Sample coincidence spectra, gated on 2287, 387, 328 and 115 keV, are shown in Fig. 3(a)-(d). The relative intensities (Iγ) and the initial and final states (
$ E_{\rm i}^\pi $ and$ E_{\rm f}^\pi $ ) of the observed transitions in 92Nb are summarized in Table 1.Figure 2. Level scheme of 92Nb proposed by the present work. New transitions are denoted with asterisks. The width of arrows indicates relative intensity of γ-rays.
Figure 3. Typical prompt γ-γ coincidence spectra for 92Nb, gated on 2287, 387, 325, and 115 keV, respectively.
Eγ /keV Iγa Eiπ→Efπ RADOc Jiπ→Jfπ 97* 8.79(159) 2213→2116 0.71(13) 9(−)→8(−) 116 15.08(80) 2203→2087 1.40(10) 11−→9− 126* 2.68(23) 2213→2087 1.58(25) 9(−)→9− 142 3.07(27) 2087→1945 1.63(33) 9−→7− 148 53.81(280) 2235→2087 0.94(5) 10−→9− 171* 0.49(18) 2116→1945 — 8(−)→7− 328 27.18(151) 3326→2998 1.52(9) 13+→11+ 344* 0.82(12) 2431→2087 0.96(23) 10→9− 354 * 0.66(8) 4941→4587 1.46(37) 15(−)→(13−) 364* 0.43(7) 4587→4223 0.96(30) (13−)→12(−) 387* 3.03(41) 2600→2213 0.96(13) 10(−)→9(−) 397* 0.92(25) 2600→2203 0.94(36) 10(−)→11− 458* 1.92(18) 2693→2235 0.71(15) 11(−)→10− 471 3.53(25) 3797→3326 0.88(8) (12+)→13+ 501 12.77(180) 501→0 0.80(11) 6+→7+ 606* Wb 2693→2087 — 11(−)→9(−) 711 23.85(126) 2998→2287 1.80(11) 11+→9+ 763 39.35(168) 2998→2235 0.95(6) 11+→10− 790* 0.66(11) 4587→3797 1.00(25) (13−)→(12+) 795 1.78(26) 2998→2235 — 11+→11− 799* 2.07(26) 3797→2998 — (12+)→13+ 897* 1.67(76) 4223→3326 0.91(16) 12−→11+ 907* 2.29(34) 3194→2287 1.78(49) 11(+)→9+ 1144* 0.19(6) 4941→3797 — 15−→(12+) 1225* 1.67(18) 4223→2998 0.95(46) 12(−)→11+ 1261* 4.09(52) 4587→3326 1.51(20) (13−)→13+ 1444 5.05(62) 1945→501 0.94(12) 7−→6+ 1586 3.09(45) 2087→501 — 9−→6+ 1694* Wb 3897→2203 — →11− 1945 2.74(56) 1945→0 1.37(27) 7−→7+ 2087 100 2087→0 1.40(8) 9−→7+ 2116* 12.83(358) 2116→0 0.83(19) 8(−)→7+ 2213* 7.67(170) 2213→0 1.66(67) 9(−)→7+ 2287 61.98(367) 2287→0 1.66(14) 9+→7+ a The errors of the relative intensity include the fitting and efficiency corrections. Wb The intensities of transitions are too weak. c The errors of the ADO ratios include the fitting and efficiency corrections. Table 1. Transition energies (Eγ) of 92Nb, relative intensities of γ-rays (Iγ), initial and final states for γ-rays, ADO ratios, initial and final spins of the transitions.
In order to obtain the multipolarity of the newly observed γ-rays, the angular distributions of each γ-ray from the oriented residues (ADO) were analyzed. Assuming that γ1 and γ2 are the cascading transitions in the same nucleus, the ADO ratio of γ1 is deduced by Iγ1(152°)/Iγ1(90°), where Iγ1(152° or 90°) represents the intensity of γ1-rays collected by the detectors at 152° or 90° , and in coincidence with γ2-rays measured by all detectors. By calculating the ADO ratio of γ-rays with known multipolarity in 92Mo, 91Mo, 92Nb, 93Nb, 90Zr, 89Zr produced in the present experiment, typical ADO ratios Iγ(152°)/Iγ(90°) for quadrupole and dipole transitions are around 1.6 and 0.8, respectively, as shown in Fig. 4(a). The spins of the states of 92Nb are assigned tentatively. For the two lower transitions, 97 and 126 keV, the intensity balance rule is used, which supports to some extent the spin assignment of the levels .
Figure 4. (color online) (a) Representative ADO ratios in 92Mo, 92Nb, 91Mo, 93Nb, 89Zr, 90Zr. Typical RADO is given as around 1.6 indicating stretched quadrupole (or ΔI=0) transition, and around 0.8 indicating stretched dipole transition; (b) RADO of transitions plotted against energies of γ-rays in 92Nb.
Two new transitions, 504 and 572 keV, are added to the level scheme of 93Nb feeding into the 2180 keV state, as shown in Fig. 5. From the summed spectrum of 689 and 541 keV, shown in Fig. 6, the peaks of the new transitions 504 and 572 keV can be clearly seen. The ADO ratios for the two transitions are 1.45 and 0.94, indicating quadrupole and dipole properties, respectively. Therefore, the spins of the 2752 keV and 2684 keV states are assigned as 21/2, and 19/2, respectively. The relative intensities of partial γ-rays from 93Nb are given in Table 2.
Figure 5. Level scheme of 93Nb proposed in the present work. New transitions are marked with asterisks. The width of the arrows indicates the relative intensity of γ-rays.
Figure 6. Typical prompt γ-γ coincidence spectrum for 93Nb with two new transitions marked with asterisks.
Eγ/keV Iγa E iπ→Efπ Jiπ→Jfπ 156 8.1(19) 1491→1335 15/2+→17/2+ 385 58.8(69) 1335→950 17/2+→13/2+ 504 * 2.8(6) 2684→2180 (19/2)→(17/2−) 541 39.9(69) 1491→950 15/2+→13/2+ 572* 1.5(5) 2752→2180 (21/2)→(17/2−) 689 7.1(21) 2180→1491 (17/2−)→15/2+ 845 2.2(3) 2180→1335 (17/2−)→17/2+ 906 10.8(24) 3086→2180 (21/2)→(17/2−) 950 100 950→0 13/2+→9/2+ 1498 25.7(36) 2833→1335 25/2(−)→17/2+ a The errors on the relative intensity include the fitting and efficiency corrections. Table 2. Transition energies (Eγ) of 93Nb, relative intensities of γ-rays (Iγ), initial and final spins of the transitions.
-
The excitation of a nearly spherical nucleus is usually considered to be of two types: single particle excitations inside a major shell, and excitations that cross the shell gap(s) [21]. The core excitation has been previously reported in A~90 neighboring nuclei, e.g., 89Y [22], 91-94Mo [8, 23-25], and 94-96Ru [26], which exhibit the characteristics of several parallel transitions with energy around 2 MeV feeding into the same level. The low-lying states may be dominated by single particle excitations inside one major shell. As it is a nearly spherical nucleus, the states of 92Nb should be amenable to shell model calculations.
In order to study the levels in 92Nb, we performed shell model calculations with the code NushellX. The SNE model space and SNET interaction were adopted, which were previously used for level structures of nearly spherical nuclei 85Br [27], 96Ru [26], 94Mo [8]. The model space includes 8 proton orbitals (1f5/2, 2p3/2, 2p1/2, 1g9/2, 1g7/2, 2d5/2, 2d3/2, 3s1/2) and 9 neutron orbitals (1f5/2, 2p3/2, 2p1/2, 1g9/2, 1g7/2, 2d5/2, 2d3/2, 3s1/2, 1h11/2) relative to the inert 56Ni (Z = 28, N = 28) core.
The low-excited states of 92Nb behave like single particle excitation, and thus we describe the low-excited states of 92Nb as pure configurations, which means that each state corresponds to one proton orbital and one neutron orbital. The pure configuration calculations were also carried out for the low-excited states of 91Zr, 93Mo, 95Ru [28]. Since the Fermi levels of 92Nb lie at the πg9/2 and νd5/2 orbitals, the quasi-magic nucleus 90Zr is taken as the inert core to describe the low-lying states of 92Nb, so that the 1f5/2, 2p3/2, 2p1/2 proton orbitals and the 1f5/2, 2p3/2, 2p1/2, 1g9/2 neutron orbitals are fully occupied. The first six positive parity states of 92Nb (Iπ=2+~7+) have been previously interpreted as the π(1g9/2)
$\otimes $ ν(2d5/2) configuration, and the first two negative parity states of 2- and 3- are dominated by the π(2p1/2)$\otimes $ ν(2d5/2) configuration [11, 13]. As 92Nb has one neutron more than 91Nb, it should have similar level structure for low-excited states, as shown in Fig. 7. Hence, the low-lying levels of 92Nb are described as 91Nb$\otimes $ νd5/2 as shown in Table 3, where the negative parity states Iπ=7-, 8-, 9-(1), 9-(2), 10-(1), 10-(2) are described as a proton excited from the p1/2 orbital to the g9/2 orbital, and the positive parity states 9+, 11+, 12+, 13+ are described as a pair of protons excited from the p1/2 orbital to the g9/2 orbital. The calculation results for the one proton-neutron coupled configuration, πg9/2$ \otimes$ νd5/2, and for the two proton-hole neutron-particle coupled configuration, πp1/2-1(g9/2)2$\otimes $ νd5/2 and π(p1/2)-2 (g9/2)3$\otimes $ νd5/2 , are listed in Table 3. As can be seen from this table, the shell model predictions for the low-excited states agree well with the experimental data, which confirms the assignments of Ref. [13] , where the first six positive parity states Iπ=2+~7+ and the first two negative parity states 2- and 3- are πg9/2$\otimes$ νd5/2 and πp1/2-1(g9/2)2$\otimes $ νd5/2, respectively.I π configuration Eexp/MeV Ecal1/MeV 2+ πg9/2 $ \otimes$ νd5/20.136 0.326 3+ 0.286 0.402 4+ 0.480 0.495 5+ 0.357 0.372 6+ 0.501 0.515 7+ 0 0 2− π(p1/2)-1(g9/2)2 $ \otimes$ νd5/20.227 0.275 3− 0.391 0.314 7− 1.945 1.83 8− 2.116 2.028 9−(1) 2.088 1.900 9−(2) 2.213 2.54 10−(1) 2.235 2.203 10−(2) 2.6 2.643 9+ π(p1/2)-2(g9/2)3 $ \otimes$ νd5/22.287 2.552 11+ 2.998 3.295 12+ 3.797 3.859 13+ 3.326 3.528 1 the result of shell model calculation with pure configurations. Table 3. Dominant configurations of the low-lying excited states of 92Nb proposed by the shell model calculations with a pure configuration and SNET interaction, calculated results and experimental level energies.
For the higher excited states of 92Nb, 90Zr is not an ideal core anymore, which makes the configuration of the high-excited states more complicated, as the pure configurations cannot describe the high-excited states properly. In order to study the high-excited states of 92Nb, a large-basis shell model calculation is necessary.
To obtain a more appropriate description of the observed high-excited states of 92Nb, large-basis shell model calculations are used. 92Nb has 13 valence protons and 23 valence neutrons outside the 56Ni core. Due to the large number of active orbitals, truncation of the model space is necessary. In the calculations of 92Nb, the valance space is restricted to π(1f5/24-6, 2p3/22-4, 2p1/20-2, 1g9/21-6, 1g7/20-0, 2d5/20-0, 2d3/20-0, 3s1/20-0)
$ \otimes$ (1f5/26-6, 2p3/24-4, 2p1/22-2, 1g9/29-10, 1g7/20-1, 2d5/20-2, 2d3/20-0, 3s1/20-0, 1h11/20-1). A comparison between the experimentally determined excitations and the large-basis shell model results is shown in Table 4.I π Eexp /MeV Ecal2/MeV configuration partition(%) 9+ 2.287 2.111 6 4 0 3 $ \otimes$ 6 4 2 10 0 1 0 0 050.24 4 4 2 3 $ \otimes$ 6 4 2 10 0 1 0 0 013.84 11+ 2.998 3.146 6 4 0 3 $ \otimes$ 6 4 2 10 0 1 0 0 058.88 12+ 3.797 3.746 6 4 0 3 $ \otimes$ 6 4 2 10 0 1 0 0 064.89 13+ 3.326 3.325 6 4 0 3 $ \otimes$ 6 4 2 10 0 1 0 0 061.88 8− 2.116 2.320 6 4 0 3 $ \otimes$ 6 4 2 10 0 0 0 0 138.79 6 4 2 1 $ \otimes$ 6 4 2 10 0 0 0 0 121.59 9− 2.088 2.232 6 4 0 3 $ \otimes$ 6 4 2 10 0 0 0 0 130.85 6 4 2 1 $ \otimes$ 6 4 2 10 0 0 0 0 112.36 9−(2) 2.213 2.777 6 4 1 2 $ \otimes$ 6 4 2 10 0 1 0 0 052.03 10− 2.235 1.863 6 4 0 3 $ \otimes$ 6 4 2 10 0 0 0 0 141.57 10−(2) 2.6 2.841 6 4 1 2 $ \otimes$ 6 4 2 10 0 1 0 0 049.4 13− 4.587 4.797 6 4 0 3 $ \otimes$ 6 4 2 10 0 0 0 0 131.97 15− 4.941 5.207 6 4 0 3 $ \otimes$ 6 4 2 10 0 0 0 0 165.92 2 the result of shell model calculation with mixed configurations. Table 4. Main partition of the wave function for high-spin states of 92Nb. Each angular momentum is composed of several different partitions. Each partition is of the form p=π[p(1), p(2), p(3), p(4)]
$ \otimes$ ν[n(1), n(2), n(3), n(4), n(5), n(6), n(7), n(8), n(9), n(10)], where p(i) represents the number of valence protons in the 1 f5/2, 2p3/2, 2p1/2 and 1g9/2 orbitals, and n(j) represents the number of valence neutrons in the 1 f5/2, 2p3/2, 2p1/2, 1g9/2, 1g7/2, 2d5/2 2d3/2 3s1/2 1h11/2 orbitals, respectively. One neutron is excited to the g7/2 and h11/2 orbitals in these calculations.
Low-lying states of 92,93Nb excited in the reactions induced by the weakly-bound nucleus 6Li near the Coulomb barrier
- Received Date: 2019-05-26
- Available Online: 2019-10-01
Abstract: Excited states of odd-odd nucleus 92Nb and odd-A nucleus 93Nb were populated in the 6Li+ 89Y reaction with an incident energy of 34 MeV. The processes that produce 92,93Nb and can be measured by a combination of light charged particle and gamma ray measurements are discussed. Twenty new transitions are observed and eight new levels are constructed in 92Nb, and in addition two new transitions are added to the level scheme of 93Nb. Using shell model calculations, the low-lying structure of 92Nb is investigated and compared with the experimental results.