Observation of multiple doubly degenerate bands in 195Tl

Observation of multiple doubly degenerate bands in 195Tl T. Roy a,b, G. Mukherjee a,b,∗, Md.A. Asgar a,b, S. Bhattacharyya a,b, Soumik Bhattacharya a,b, C. Bhattacharya a,b, S. Bhattacharya a,1, T.K. Ghosh a,b, K. Banerjee a,b,c, Samir Kundu a,b, T.K. Rana a, P. Roy a,b, R. Pandey a,b, J. Meena a, A. Dhal a, R. Palit d, S. Saha d, J. Sethi d, Shital Thakur d, B.S. Naidu d, S.V. Jadav d, R. Dhonti d, H. Pai e, A. Goswami e

The atomic nuclei are considered as the fascinating quantal objects to study various symmetries in nature. Breaking of a particular symmetry in the nuclear medium is manifested in terms of different band structures of nuclear excited states. A new type of symmetry breaking for the triaxial nuclei with the unpaired particle(s) and hole(s) in the high-j orbital, referred as chiral symmetry breaking, was proposed by Frauendorf et al. [1,2]. Such a chiral geometry is manifested in the occurrence of a pair of nearly degenerate I = 1 bands. One of the first experimental evidences of this was reported in the N = 75 isotones [3]. Subsequently, such chiral doublet bands have been observed in several nuclei mostly for 2-and 3-quasiparticle (qp) configurations [4][5][6][7]. Very recently, evidence of chirality has been observed in multi-qp configurations of even-even nucleus 136 Nd [8]. The observation of such band structures provides the clear indication of triaxial shape in a nucleus.
Chiral bands based on different configurations in a nucleus are possible provided the configurations satisfy the underlying con-ditions [2]. Evidence of chiral doublet bands based on different configurations was found in 105 Rh [9,10]. However, the possibility of the occurrence of multiple chiral doublet bands in 106 Rh was predicted from the relativistic mean field (RMF) calculations by J. Meng et al. [11] and they used the acronym Mχ D for such bands. However, until now the experimental observation of such bands has been reported only in a few nuclei, 133 Ce [12], 136 Nd [8] and 78 Br [13]. A different kind of Mχ D band, based on the same configuration, has been reported in 103 Rh [14].
For the nuclei in the A = 190 mass region high-j h 9/2 and i 13/2 orbitals are available near the proton and the neutron Fermi levels and the even-even Hg core nuclei are predicted to be triaxial in nature [15]. Therefore, it was suggested in Ref.  [16][17][18].
In this Letter, we are reporting the observation of two pairs of chiral doublet bands in the odd-even nucleus 195    Prior to the present work, the high spin information for 195 Tl was limited to only two bands [19]: the 1-qp πh 9/2 band and a 3-qp band, known up to spin of 27/2 − and 35/2 + and excitation energy of 3156 and 4394 keV, respectively. These were measured using α induced fusion evaporation reaction with one planar Ge detector and two large volume Ge(Li) detectors. The present experimental condition is a much improved one as we have used heavy-ion induced fusion evaporation reaction and a much efficient germanium clover detector array to detect the γ -rays. These allowed us to populate higher spin states, to observe weakly populated states and to assign the spin and the parity of the states firmly.
The high spin states in 195 Tl were populated via the 185,187 Re( 13 C, xn) 195 Tl fusion evaporation reaction with a 75-MeV 13 C beam from the 14-UD Pelletron LINAC Facility at Tata Institute of Fundamental Research (TIFR), Mumbai, India. The prompt γ rays emitted from the residual nuclei were detected by the Indian National Gamma Array (INGA) facility with 15 Compton suppressed clover HPGe detectors. Two and higher-fold coincidence data with time stamp were recorded in a fast (100 MHz) digital data acquisition system based on the Pixie-16 modules of XIA LLC [20,21]. The experimental set up, the data acquisition conditions and the data analysis procedure have been described in Ref. [22].
A new and improved level scheme of 195 Tl with the placement of 57 new γ -rays, compared to the previous work [19], has been constructed by analyzing the intensity and coincidence relations of the γ -rays in the E γ -E γ matrix and the E γ -E γ -E γ cube. A few of the gated spectra are shown in Fig. 1 and Fig. 2. A partial level scheme of 195 Tl, constructed by analyzing several such spectra, has been shown in Fig. 3. The previously known 1-qp and 3-qp bands B1 and B3 have been extended beyond the band crossing regions through the bands B2, B2a and B4, B4a, respectively. The spin and parity ( J π ) of the states were unambiguously assigned in this work from the complete information on the multipolarity (λ) and the nature (E/M) of the γ rays decaying from a state by the integrated polarization asymmetry ratio ( I P DC O ) [23,24] and the directional correlation of oriented states ratio (R DC O ) [25] measurements as described in Ref. [22].
The configurations of the bands in the level scheme of 195 Tl are assigned by considering the measured gain in the aligned particle angular momentum (i x ), their comparison with the neighboring nuclei and, the available single particle orbitals near the proton and the neutron Fermi levels. The band B1 in 195 Tl and the similar bands in the neighboring odd-A Tl isotopes were known to be the rotational bands of an oblate deformed nucleus based on the odd proton in the h 9/2 orbital [19,[26][27][28][29]. The newly observed 3-qp band B2 in 195 Tl is accompanied by a large gain of about 9h in i x (see Fig. 4) indicating the alignment of a pair of neutrons in the high-j i 13/2 orbital. Therefore, this band has been assigned a configuration of πh 9/2 ⊗ νi −2 13/2 , the negative sign in the neutron configuration indicates the hole states. The value of i x for the band B3 and B4 in 195 Tl closely match with the 5 − band in 194 Hg [30] both before and after the neutron pair alignments (Fig. 4). Hence, the neutron configuration of the band B3 and B4 would be similar to the 5 − band in 194 Hg. Considering the negative parity of the bands and the available orbitals near the proton Fermi level, the suggested configurations for the bands B3 and B4 in 195 Tl are π i 13/2 ⊗ νi −1 13/2 (p 3/2 f 5/2 ) −1 and π i 13/2 ⊗ νi −3 13/2 (p 3/2 f 5/2 ) −1 , respectively. In this letter, the primary focus is on the pair of bands B2 with its side band partner B2a and B4 with its side band partner B4a. These are identified as the closely degenerate pairs of bands as can be seen from their spin (I ) vs. E − E ref (E is the excitation energy and E ref = A * I * (I + 1) is a rigid-rotor reference with A is the moment of inertia parameter) plots in Fig. 5(a). The i x values (Fig. 5(b)) of the bands in a pair (B2 with B2a and B4 with B4a) are close to each other, indicating that the side bands have the same configuration as the main bands. Other parameters, like staggering (S(I)) and kinetic moment of inertia J (1) , shown in Fig. 5(c) and (d), are also very similar. The B(M1)/B(E2) ratios for the bands B2-B2a and B4-B4a in 195 Tl match quite well too (Fig. 5(e)). These types of degenerate pair of bands, which have been interpreted as originated due to the chiral symmetry breaking in the angular momentum space in a triaxial nucleus [1,2], are comparable to those observed for the 4-qp configuration in 194 Tl [16,17] and the 2-qp configuration in 198 Tl [18]. The relevant parameters for these bands in 194,198 Tl are also compared in Fig. 5. It is seen that the degeneracies in 195 Tl are either similar or better compared to 194,198 Tl. The average separation of E av ∼ 25 keV (with the maximum value E max = 59 keV) in the excitation energies for the 5-qp bands B4-B4a in 195 Tl is much less than E av ∼ 78 keV (with E max = 110 keV) for the 4-qp bands in 194 Tl. Therefore, it represents one of the best examples of degenerate bands observed so far. The degeneracy in the 3-qp pair B2-B2a, is comparable with that reported for the 2-qp pair in 198 Tl.
The two pairs of doubly degenerate bands identified in 195 Tl is a unique observation in the A = 190 mass region. This is the first time that multiple pairs of candidate chiral partner bands are observed in this region and also identified for the first time for a configuration involving as large as 5 quasiparticles in a nucleus in this mass region. This is a valuable addition to the ones reported for 133 Ce and in 78 Br [12,13] in a different mass region which gives a strong support and general applicability to the recent theoretical prediction of multiple chiral doublet (Mχ D) bands and triaxial shapes involving different configurations in a nucleus [2,11]. The chiral geometry, in this case, is generated with the angular momentum of the valence proton (neutron) particle (hole) aligned along the short (long) nuclear axes and core rotational angular momentum predominantly oriented along the intermediate nuclear axis. For this to happen, the nucleus must be triaxial in shape. A chiral geometry is better realized in a nucleus having stable triaxial shape with triaxiality parameter γ lies between 25 • < |γ | < 40 • [1]. Degenerate chiral doublet bands are most favorable for maximum triaxiality (|γ | = 30 • ). It was also reported that for a γ -soft nucleus, the aplanar solution (which gives chiral side band) disappears and destroys the chirality [31]. In case of 195 Tl, it turns out that the 5-qp configuration seems to have a rather stable triaxial shape than the 3-qp one. This indicates that as the number of unpaired neutron holes increases in the i 13/2 orbital, it drives the nucleus to a more stable triaxial deformation.
In order to estimate the shape of 195 Tl nucleus in the above mentioned configurations, the total Routhian surface (TRS) calculations have been performed. The TRS code of Nazarewicz et al. [32,33] was used in these calculations. The procedure of such calculations has been outlined in Ref. [34,35]. The Routhian surfaces are plotted in the conventional β 2 − γ plane and are shown in Fig. 6. In these plots, γ = 0 0 (γ = −60 0 ) corresponds to prolate (oblate) shape. Triaxial shapes correspond to γ in between these two values with γ = ±30 • represents maximum triaxiality.
The surface calculated for the πh 9/2 configuration corresponding to the band B1 ( Fig. 6(a)) in 195 Tl shows an axially symmetric oblate deformation with β 2 = 0.15 and γ = −58 0 . Whereas, triaxial minimum appears for the 3-qp and the 5-qp configurations corresponding to bands B2 and B4, respectively, with γ ∼ +30 • ( Fig. 6(b) and (c)). Though the surfaces for the 5-qp configuration ( Fig. 6(c)) shows a stable triaxial minimum with γ = 31 • , the surfaces for the 3-qp configuration shows some degree of γ -softness with two close-by minima; the first minimum is at γ = 39 • and the second minimum, lying at about 1 MeV above the first one, is at the oblate deformation with γ = −64 • . It may be noted that although the tilted axis cranking (TAC) calculations give a better estimate for the realization of the chiral geometry in a nucleus [2] with rotation around a tilted axis, but the present TRS calculations using principal axis cranking (PAC) are good to predict the triaxial shapes, a requirement for the realization of the chiral geometry. The stable triaxial minimum for the 5-qp configuration gives the possibility of the nucleus to rotate around its intermediate axis and results in degenerate doublet bands as observed for B4-B4a pair of bands in 195 Tl. In case of 3-qp configuration, the triaxial minimum which lies lower in energy can provide the required chiral condition for the occurrence of doubly degenerate bands in B2 and B2a, however, because of the second co-existing minimum and a small degree of γ -softness, the chiral conditions quickly gets destroyed and hence, the degenerate bands are expected in a limited region as is the case for the B2-B2a pair of bands. The well defined stable triaxial minimum for the 5-qp band in 195 Tl is comparable to some of the best known chiral doublet bands in A = 130 region in which the proton particle and neutron hole lie in the high-j h 11/2 orbitals [3]. Therefore, from the TRS calculations it turns out that likewise for the nuclei in A = 130 region, doubly degenerate band, originated due to the chiral symmetry breaking, is expected for the 5-qp band in 195 Tl. Once the nucleus is triaxial in this A = 190 region, the chiral geometry will be better realized because of the involvement of the higher-j i 13/2 orbital. This is in excellent agreement with the experimental obser- vation in case of bands B4 and B4a in 195 Tl and represents one of the best cases of doubly degenerate band structures. It may however, be noticed that a stable triaxial shape is realized in this case only when several neutron holes are available in the i 13/2 orbital.
In summary, the study of the higher spin states in the nucleus 195 Tl by the heavy-ion induced reaction reveals the evidence for the presence of multiple chiral doublet bands in this nucleus based on 3-qp and 5-qp configurations. This is the first time that Mχ D bands are observed in a nucleus in heavy mass region with A > 150 and only the fourth such evidence in the chart of nuclide. It indicates the presence of triaxial shape coexistence in 195 Tl, which was reproduced well in the microscopic-macroscopic calculations of the TRS. The calculations also give an important conclusion that a stable triaxial shape of 195 Tl is realized only for a configuration with large number of neutron holes (four in case of 195 Tl) in the i 13/2 orbital. Therefore, the predicted chiral geometry in A = 190 region can be realized only for the large quasi-neutron configurations involving the i 13/2 orbital. That may be the reason the experimental observation of chiral geometry was so far almost illusive in this region as it is experimentally difficult to produce and observe the multi-quasiparticle high spin states in this region. The experimental observation of the excellent degeneracy, possibly the best observed so far, between the doubly degenerate chiral partner bands for the 5-qp configuration in 195 Tl in this work, supports the conclusion of the original prediction of Ref. [1] that A = 190 region is one of the best regions to realize chiral geometry in nuclei. Further investigation needs to be carried out in other nuclei in this mass region to establish this fact. Although the PAC calculations give a good account of the triaxial shapes for the two configurations in 195 Tl, but it will be interesting to perform the TAC calculations, particularly for the 3-qp band in order to estimate the shape for tilted axis rotation.