Study of intruder band in 112Sn

Nuclear Physics A 789 (2007) 1–14

Study of intruder band in 112Sn S. Ganguly a , P. Banerjee a,∗ , I. Ray a , R. Kshetri a , R. Raut a , S. Bhattacharya a , M. Saha-Sarkar a , A. Goswami a , S. Mukhopadhyay c , A. Mukherjee a , G. Mukherjee b , S.K. Basu b a Saha Institute of Nuclear Physics, Kolkata 700064, India b Variable Energy Cyclotron Centre, Kolkata 700064, India c UGC-DAE-CSR, Kolkata 700098, India

Received 25 August 2006; received in revised form 9 January 2007; accepted 18 January 2007 Available online 15 February 2007

Abstract Excited states of the positive-parity intruder band in 112 Sn, populated in the 100 Mo(20 Ne, α4n) reaction at a beam energy of 136 MeV, have been studied. The band has been observed up to 11570.0 keV with spin (24+ ). Mean lifetimes have been measured for six states up to the 22+ , 10335.1 keV level and an upper limit of the lifetime has been estimated for the 11570.0 keV (24+ ) state. The B(E2) values, derived from the present lifetime results, correspond to a moderate quadrupole deformation of β2 ∼ 0.18 for states with spin J π  12+ , and the decrease in B(E2) for the 14+ → 12+ transition is consistent with a ν(h11/2 )2 alignment at hω ¯ ∼ 0.35 MeV, predicted by a cranked shell-model calculation. Total Routhian surface calculations predict a triaxial shape following the alignment. © 2007 Elsevier B.V. All rights reserved. PACS: 27.50.+e; 21.10.Re; 21.10.Tg Keywords: N UCLEAR REACTIONS 100 Mo(20 Ne, α4n), E = 136 MeV; measured Eγ , lγ , γ γ -coin, DSA. 112 Sn deduced levels, J , π , configurations, T1/2 , B(E2), deformations.

1. Introduction The tin isotopes with A ∼ 110 have revealed interesting structural features. In most of these nuclei, low-lying moderately deformed intruder rotational states arising from proton two-particle * Corresponding author.

E-mail address: [email protected] (P. Banerjee). 0375-9474/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2007.01.092

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two-hole (2p–2h) excitations across the Z = 50 shell gap have been observed to co-exist with sin2 πg −2 are reported gle particle states. Rotational bands based on such 2p–2h configuration πg7/2 9/2 in the even-Sn nuclei from 106 Sn to 118 Sn [1–5]. More recently, lifetime studies in 108 Sn have shown that the states with spin up to 26+ , having a similar configuration, possess a moderate quadrupole deformation of β2 ∼ 0.20 [6]. The higher spin states are reported to show a nearly smooth decline in the B(E2) values. This has been interpreted as due to a gradual change in the shape of the nucleus from collective prolate at low spins to non-collective oblate at high spins, associated with the alignment of the angular momentum vectors of the valance nucleons with the rotational axis. This phenomenon of smooth band termination, where the dynamic moment of inertia (J (2) ) decreases uniformly with spin to about a third of the rigid body moment of inertia near the terminating spin, has also been experimentally established in 109 Sb [6]. It has recently been suggested [7] that a positive-parity J = 2 band in 110 Sn is an example of an unsmoothly terminating band, as the J (2) was observed to be an irregular function of rotational frequency near the terminating spins. In 112 Sn, intruder states with spins up to (22+ ) have been previously reported [3]. The sequence 6+ –8+ –10+ –12+ in 112 Sn was considered to correspond to the ground state (g.s.) bands in 108 Pd and 116 Xe, based on the similarity in the level spacings, and was termed the intruder g.s. band. The higher spin members were identified as forming an intruder aligned band following the alignment of a pair of h11/2 neutrons. A negative-parity sequence up to a (21− ) state was also assigned to 112 Sn. However, lifetime results are not known for any of these states except for the 8− and 9− levels [8]. In the present work, a study of the structure of the positive-parity intruder band in 112 Sn is attempted in view of the interesting findings reported in the neighbouring even-A isotopes 108,110,114 Sn. The knowledge of the lifetimes of the states of the intruder band is expected to provide important information on their structure. 2. Experimental methods Excited states of 112 Sn were populated in the 100 Mo(20 Ne, α4n) reaction at a beam energy of 136 MeV at the Variable Energy Cyclotron Centre, Kolkata. The target consisted of isotopically enriched (99.54%) 100 Mo, 4.7 mg/cm2 thick, evaporated on an aluminium backing. About 900 million two and higher fold coincident events were collected using an array of six Compton-suppressed Clover detectors belonging to the Indian National Gamma Array (INGA). The detectors, at approximately 22 cm from the target, were arranged in three groups of two detectors each, at angles of 40◦ , 90◦ and 125◦ with respect to the beam-direction. The raw data were sorted into different 4096 × 4096 matrices after gain matching of all the detectors to a dispersion of 1.0 keV per channel. The matrix with data from all six detectors was used for assignment of γ -rays in the level scheme. The directional correlation of oriented nuclei (DCO) ratios for spin assignments were determined from a matrix with events recorded at 90◦ along one axis and those at 125◦ along the other. For polarizational directional correlation orientation (PDCO) ratios, two matrices, one with coincidence events between the segments of the 90◦ clover detector in the direction perpendicular to the emission plane, and the other parallel to it, along one axis and the events recorded at the 40◦ and 125◦ detectors on the other axis, were used. Spectra for lifetime analysis using the Doppler shift attenuation (DSA) technique were generated from matrices formed from coincidences between either the forward or the backward angle events with those in the remaining detectors. The data were analyzed using the computer code INGASORT [9].

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The DCO ratios (RDCO ), determined from RDCO =

Iγ at 125◦ gated by γG at 90◦ Iγ at 90◦ gated by γG at 125◦

with Iγ being the intensity of the γ -ray of interest in coincidence with γG , were compared with the theoretical DCO ratios for assignment of γ -ray multipolarity and the mixing ratios δ using the computer code ANGCOR [10]. A width of σ = 0.3J (J being the level spin) was used for a presumed Gaussian distribution of the magnetic substate population. Gates were set on known E2 transitions. Gates on stretched E2 transitions yield RDCO values close to unity for quadrupole transitions and a value ranging from 0 to 2 for J = 1 transitions, depending on the value of the E2/M1 multipole mixing ratio δ. For transitions with δ close to zero, the RDCO values are expected to be near 0.5. The definition of the PDCO ratio and the details of the measurements are given in Ref. [11]. The correction due to the asymmetry in the response of the clover segments, estimated using a 152 Eu source, was found to be small. Spin and parity assignments were made on the basis of the RDCO and PDCO results. For transitions where only a DCO analysis was possible, parity assignment was based on the systematics of the lower-lying inband transitions. Lifetimes of the excited states were determined from the DSA data using the centroid shift method [12–14]. Experimentally, the average energy shift of a γ -ray of energy Eγ is expressed as E¯ γ = F (τ )Eγ β cos θ , where F (τ ) is an attenuation factor, dependent on the level lifetime τ and the stopping process, β is the initial recoil velocity and θ is the detector angle with respect to the beam direction. A comparison of this attenuation factor (F (τ )obs in Table 2), extracted from the data recorded at 90◦ and 125◦ to the beam, with the theoretical F (τ ) yielded the level lifetimes, uncorrected for the effects of the feedings from the higher-lying discrete levels and from the continuum (side-feeding). These lifetime results were then corrected for the feeding effects, as outlined below, to give the actual level lifetimes. The theoretical attenuation factors were obtained following a modification of the method described by Warburton et al. [12] in order to include the energy loss of recoils in both the target (100 Mo) and the backing (27 Al). The stopping powers were estimated using the computer code SRIM2006, based on Ziegler’s work [15]. The initial recoil velocity was estimated (β = v/c = 0.0201) from the DSA spectra. The energy distribution of the recoils in the backing due to their production at different depths in the target was estimated. The effect of the 10% energy loss of the projectiles in the target was considered. The theoretical F (τ ) was obtained by summing up the contributions from the two media, derived for each of the 50 narrow energy windows set on the energy distribution [14]. The uncertainty in the theoretical F (τ ) was assumed to be ±10% based on the errors in the SRIM2006 stopping power results [16]. In order to incorporate the corrections due to the feedings from the higher lying discrete levels and from the continuum, the centroid shift analysis was started with the highest observed transition with adequate statistics (in this case the 1234.9 keV transition from the 11570.0 keV state (Fig. 1)). As large uncertainties are involved in the feeding times to this state (owing to a lack of information on the next higher-lying discrete transition), only an upper limit of mean life is assigned. This limit also provides an effective lifetime for the observed feeding delay to the 10335.1 keV state (Fig. 1). The mean lifetime (τ in Table 2) of this 10335.1 keV state, de-exciting by the 1149.1 keV transition, is then estimated by accounting for the effects of the observed feeding (by the 1234.9 keV transition) as well as the unobserved feedings from the continuum using the formalism reported in Ref. [17]. The delay due to the feedings from the continuum is accounted for by using the side-feeding times (τsf ) given in Table 2 (discussed below). The procedure is then repeated for each of the successively lower-lying levels. The errors assigned to

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Fig. 1. Level scheme of 112 Sn obtained in the present work. Bands 1 and 2 are described in the text. The level and γ -ray energies are given in keV. The widths of the arrows, representing the transitions, are proportional to their relative intensities.

the lifetime results include the uncertainties in both the observed (see F (τ )obs in Table 2) and the theoretical F (τ ) values, and the effects of the uncertainties in the τsf values. It was ascertained that even a large assumed error of 50% in τsf (see below) leads to an error of only 12.5% in the lifetime result for the 10335.1 keV state where the contribution from side-feeding is the highest (38.8% of the total population of the level). For the other states, where the side-feeding intensities are less, the large uncertainties in τsf were found to have a still smaller effect on the errors of the lifetime result. In the present work, the side-feeding times (τsf ) were measured for the 6362.3 and 8146.5 keV states from spectra obtained by gating from above and below the transition of interest as described earlier [14,18] (see Table 2). These feeding times, used in the lifetime analyses as described earlier, were found to be significantly smaller than the corresponding level lifetimes. The τsf for

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the other states, where measurements were not possible, were estimated using the assumption that the side-feeding time to the highest observed state is 0.1 ps and increases by 0.05 ps per MeV of de-excitation. This assumption is consistent with the two τsf values measured in this work. A 50% uncertainty was assumed for these estimated τsf values (where measurements were not made) while assigning the errors to the level lifetimes. The method adopted for the analysis of the DSA data, reproduces within the error bars the known lifetime of the 1906.6 keV state in 113 Sn [19], also populated in the present experiment. The γ -ray relative intensities were measured from the coincidence data at 125◦ to the beam direction. Relative intensities of transitions belonging to band 1 were mostly determined from the spectrum gated by the 663.6 keV γ -ray while those for the other γ -rays were obtained from the 1256.6 keV gate. These were then normalized relative to each other using the intensities of transitions common to both the gates. The singles spectrum at 125◦ to the beam direction was used to determine the intensity of 1256.6 keV γ -ray relative to 990.5 keV transition. 3. Experimental results The level scheme of 112 Sn, based on the present work and Ref. [3], is shown in Fig. 1. Sequences of states resembling a rotational pattern are labelled by band numbers. The sequence of positive-parity states, identified as the intruder band, is labelled band 1 while the negative-parity states, built on the 13− state at 6397.7 keV, is labelled band 2. The experimental results on the γ -ray energies, their relative intensities, the DCO and PDCO ratios and the spin assignments are presented in Table 1. Table 2 summarises the results on the level lifetimes (τ ), the B(E2) rates, the transition quadrupole moments (Qt ) and the quadrupole deformations (β2 ). The Qt and β2 have been derived using expressions given in Ref. [20]. Most of the results and discussions that follow are related to band 1 only. Results relating to other bands and states populated in the present work are summarised in Table 1 only. The present work confirms the placement of all γ -rays in the level scheme previously reported by Harada et al. [3]. In addition, four new transitions have been placed. Band 1, previously reported up to the 22+ state at 10335.1 keV [3], has been extended with the addition of the new 1234.9 and 1395 keV transitions, the latter tentatively, leading to the 11570.0 keV and the tentative 12965 keV levels, respectively (Fig. 1). Fig. 2 shows the sum of the spectra, recorded at 90◦ to the beam direction, gated by the 663.6, 741.7 and 744.6 keV transitions, in support of the placement of the 1234.9 keV transition in band 1. The gate on the 1234.9 keV transition (inset (a) in Fig. 2) shows all the lower-lying transitions up to 932.9 keV in the band. The higher energy inband transitions are not observed due to their large Doppler shifts. The gate on the 1395 keV γ -ray (inset (b) in Fig. 2) however, shows transitions only up to 798.6 keV, as the 1395 keV γ -ray is relatively weaker compared to the 1234.9 keV transition. Nevertheless, lack of sufficient supportive evidence in the sum gate (Fig. 2) leads to a tentative assignment of the 1395 keV transition in the level scheme. The other new transitions placed in the level scheme are the 868.8, 345.9 and 603.1 keV γ -rays, de-exciting the 8082.4 keV (17− ), 4928.3 keV (11− ) and 4680.5 keV (10+ ) levels, respectively. Beside these, a tentative 844 keV transition is proposed to connect the 15− and 14+ states. Relative γ -ray intensities were measured, as described in Section 2, for all but the last transition depopulating the highest observed states in bands 1 and 2. The present γ -ray branching ratios for the transitions from the 6+ , 3413.8 keV state agree within errors with those reported in Ref. [21].

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Table 1 Level and γ -ray energies, γ -ray relative intensities, DCO and PDCO ratios, multipolarities and spin assignments in 112 Sn Ex a (keV)

Multipolarity/ δ(E2/M1)

Jiπ → Jfπ e

E2b E2b E2b E2 E2 E2 E2 E2d E2d E2 E2 E2 E2 E2 (E2) (E2)

6+ → 4+ 6+ → 4+ 6+ → 4+ 6 + → 4+ 8 + → 6+ 10+ → 8+ 12+ → 10+ 12+ → 10+ 1 14+ → 12+ 2 + 14 → 12+ 16+ → 14+ 18+ → 16+ 20+ → 18+ 22+ → 20+ (24+ ) → 22+ (26+ ) → (24+ )

E2 E2 E2

2 + → 0+ 4 + → 2+ 6 + → 4+

9.5 ± 1.9 7.7 ± 2.3 2.6±1.0 6.8 ± 1.8 4.4 ± 1.5 –

E2d E2d E1d E2d E2d (E2)d

13− → 11− 15− → 13− 17− → 16+ 17− → 15− 19− → 17− (21− ) → 19−

5.9 ± 1.6 11.9 ± 2.3 5.1 ± 1.1 2.7 ± 1.0 2.3 ± 1.1 36.9 ± 4.6 25.3 ± 2.5 5.7 ± 2.2 2.8 ± 1.2 11.1 ± 2.4 <1 11.7 ± 2.8 8.8 ± 2.4

E2b E2b E2d M1b E1b E1 0.12 ± 0.16 E2b E2d E1d (E2/M1) E2b E2b

4+ → 2+ 4+ → 2+ 4+ → 2+ 6+ → 6+ 7− → 6+ 7 − → 6+ 9 − → 8− 10− → 8− 10+ → 8+ 10+ → 9− 11− → 10− 11− → 9− 12+ → 10+

Eγ (keV)

Irel

468.2 ± 0.2 630.2 893.7 ± 0.3 1166.7 ± 0.1 663.6 ± 0.1 741.7 ± 0.1 744.6 ± 0.1 883.2 ± 0.3 678.1 ± 0.8 798.6 ± 0.1 851.3 ± 0.1 932.9 ± 0.2 1039.5 ± 0.2 1149.1 ± 0.3 1234.9 ± 0.5 1395 ± 1.0

6.2 ± 1.2 10.2 ± 0.7 6.4 ± 2.1 16.8 ± 1.7 37.2 ± 2.0 33.1 ± 3.8 20.8 ± 3.7 8.6 ± 2.3 <1 24.6 ± 3.7 21.1 ± 2.2 16.2 ± 3.9 13.8 ± 1.8 10.8 ± 2.1 6.6 ± 1.5 –

g.s. band 1256.6 1256.6 ± 0.1 2247.1 990.5 ± 0.1 2548.8 301.7 ± 0.1

100 ± 3.0 70.8 ± 7.1 42.1 ± 2.5

Band 1 3413.8

4077.4 4819.1 5563.7 6362.3 7213.6 8146.5 9186.0 10335.1 11570.0 12965

Band 2 6397.7 7206.5 8082.4 9044.6 10075.6

1469.4 ± 0.4 808.8 ± 0.3 868.8 ± 0.4 875.9 ± 0.3 962.2 ± 0.4 1031 ± 1.0

Other states 2520.1 1263.5 ± 0.2 2783.6 1527.0 ± 0.2 2945.6 1689.0 ± 0.6 2926.0 377.2 ± 0.3 3353.9 427.8 ± 0.3 805.1 ± 0.1 3693.2 263.0 ± 0.1 4582.4 1152.2 ± 0.4 4680.5 603.1 ± 0.5 987.4 ± 0.3 4928.3 345.9 ± 0.8 1235.1 ± 0.2 5684.4 865.3 ± 0.2

RDCO

Gate (keV)

PDCO

0.96 ± 0.09 0.93 ± 0.09 1.04 ± 0.10c 1.04 ± 0.10c

1256.6 + 990.5 741.7 + 744.6 663.6 663.6

0.99 ± 0.12 1.05 ± 0.13 1.06 ± 0.19 1.00 ± 0.21 1.13 ± 0.23

741.7 + 744.6 741.7 + 744.6 663.6 + 741.7 + 744.6 663.6 + 741.7 + 744.6 663.6 + 741.7 + 744.6

0.08 ± 0.03 0.24 ± 0.14 0.22 ± 0.14

1.01 ± 0.06 1.03 ± 0.05 1.11 ± 0.06

990.5 1256.6 990.5

0.05 ± 0.02 0.07 ± 0.03 0.06 ± 0.03

0.71 ± 0.13 0.78 ± 0.11

301.7 301.7

0.11 ± 0.04 0.25 ± 0.11 0.27 ± 0.11

0.06 ± 0.03

a Uncertainties in E are  0.5 keV for states up to 10335.1 keV and within 1 keV for the two higher-lying states. b Previous x work [21]. c RDCO for 741.7 and 744.6 keV transitions combined. d Multipolarity from J π of the initial and final states. e J π values are from present work wherever the RDCO was measured; otherwise, J π values are taken from Ref. [21].

The DCO ratios (Table 1) confirm the stretched quadrupole nature of all de-exciting transitions in band 1 up to the 10335.1 keV state. Firm spin assignments of 20+ and 22+ are proposed for the 9186.0 and the 10335.1 keV states, respectively. In the absence of a DCO analysis, tentative spins of (24+ ) and (26+ ) are assigned to the 11570.0 and 12965 keV states, respectively, based on the observed regularity of a rotational band. The positive values of the PDCO ratios,

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Table 2 Experimental results on mean lifetime (τ ), B(E2), transition quadrupole moments (Qt ) and quadrupole deformation (β2 ) for band 1 in 112 Sn Ex (keV) Eγ (keV) Jiπ → Jfπ Band 1 5563.7

6362.3

7213.6 8146.5 9186.0 10335.1 11570.0

744.6 12+ → 10+ 883.2 12+ → 10+ 1 798.6 14+ → 12+ 678.1 14+ → 12+ 2 851.3 + 16 → 14+ 932.9 18+ → 16+ 1039.5 20+ → 18+ 1149.1 22+ → 20+ 1234.9 (24+ ) → 22+

F (τ )obs

τuncorr a (ps) τsf (ps)

0.167 ± 0.020 6.71

0.47b

τ d (ps)

B(E2) (W.u.) Qt (eb)

0.95 ± 0.20 83+22 −15

β2

2.79+0.35 −0.25

0.20 ± 0.02

2.04+0.28 −0.20

0.14+0.02 −0.01

15+4 −3 0.184 ± 0.018 5.95

0.43 ± 0.12c

1.75 ± 0.40 45+13 −8 <4

0.314 ± 0.021 2.82

0.38b

0.79 ± 0.15 72+17 −12

2.57+0.29 −0.20

0.18+0.02 −0.01

0.419 ± 0.034 1.65

0.35 ± 0.11c

0.49+0.11 −0.14

74+30 −14

2.59+0.48 −0.25

0.18+0.03 −0.01

0.519 ± 0.035 0.96

0.30b

0.32 ± 0.08 66+22 −13

2.44+0.38 −0.26

0.17+0.03 −0.01

0.607 ± 0.044 0.58

0.20b

0.20 ± 0.06 64+27 −15

2.39+0.47 −0.29

0.17+0.03 −0.02

0.649 ± 0.059 0.45

–

< 0.5

> 1.3

> 0.1

> 18

a Uncorrected lifetime inferred directly from a comparison of the observed F (τ ) with the theoretical F (τ ) (see text). b Calculated as explained in Section 2 of text. c Side-feeding times measured in the present work. d Mean lifetimes corrected for the effects of unobserved side-feeding from the continuum and direct feeding from the higher-lying level(s).

determined for transitions de-exciting states up to 8146.5 keV, are consistent with the spin and parity assignments. Mean lifetimes of 0.95 ± 0.20, 1.75 ± 0.40, 0.79 ± 0.15, 0.49+0.11 −0.14 , 0.32 ± 0.08 and 0.20 ± 0.06 ps have been determined for the six states at 5563.7, 6362.3, 7213.6, 8146.5, 9186.0 and 10335.1 keV, respectively, in band 1 from the DSA data. The results are summarised in Table 2. No information is available on the lifetimes of these states in the literature. In addition, an upper limit of mean life of 0.5 ps has been assigned to the 11570.0 keV state, based on the observed centroid-shift for the 1234.9 keV transition de-exciting this state. Lifetimes for states below 5563.7 keV could not be measured from the data due to the absence of an observable Doppler shift. Fig. 3 shows representative gated spectra, used in the DSA analysis, for the 851.3, 932.9, 1039.5 and 1149.1 keV γ -rays depopulating the 7213.6, 8146.5, 9186.0 and 10335.1 keV states, respectively, observed at 90◦ and 125◦ to the beam direction. Gates on transitions were specifically selected for each spectrum (see Fig. 3) in order to eliminate interference from γ -rays having an energy overlap. Data recorded in the detectors at 40◦ to the beam were not used in the DSA analysis since these effects could not be eliminated. It is to be noted that the gate on the 1256.6 keV 2+ → 0− transition has been included for the upper spectrum in Fig. 3(d) in order to improve the statistics without causing an interference. Inclusion of this gate for the lower spectrum in Fig. 3(d) would lead to interference from the 1152.2 keV (10− → 8− ) transition and is therefore avoided. Since the lifetimes of the states belonging to the weakly populated band 2 could not be measured due to lack of statistics, the effect of the 868.8 keV discrete feeding from the 17− state in band 2 to the 7213.6 keV state in band 1 was accounted for by assuming that the effective feeding

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Fig. 2. Partial γ -ray spectra at 90◦ to the beam direction gated by the 663.6 + 741.7 + 744.6 keV transitions. Only the γ -rays belonging to 112 Sn are marked by their energy. The insets (a) and (b) show the partial spectra gated by the 1234.9 and 1395 keV transitions, respectively (see text).

time for this transition (868.8 keV) is same as that for the 932.9 keV inband transition from the 18+ , 8146.5 keV level. 4. Discussion The intruder band in 112 Sn (band 1) is built on the 3413.8 keV, 6+ state. States up to 12+ in this −2 2 ) [3]. )(g7/2 band have been previously suggested to have the proton 2p–2h configuration π(g9/2 States with spin less than 6+ are not observed as the 6+ state decays out to the spherical 4+ states that arise from the presence of neutron g7/2 , d5/2 and h11/2 orbitals near the Fermi level. A study of the systematics of the intruder bands in 108–114 Sn shows that bandhead spin decreases with increase in neutron number. This is discussed in [4]. A cranked shell model analysis of the experimental data has been done. As seen from Fig. 4, the dynamic moment of inertia J (2) shows a sharp peak at h¯ ω ∼ 0.37 MeV, indicating a change in shape associated with the alignment of a particle-pair. The corresponding aligned spin is about 7h¯ . The sharp peak also indicates a weak interaction between the ground-state and the

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Fig. 3. DSA spectra for the (a) 851.3, (b) 932.9, (c) 1039.5 and (d) 1149.1 keV transitions in band 1, gated by lower-lying transitions in the band. The spectra in the lower (upper) panels correspond to data recorded at 90◦ (125◦ ) to the beam direction. The centroid shifts E¯ γ , the observed attenuation factors F (τ )obs and the level lifetimes (τ ) are shown. The continuous lines provide a guide to the eye.

aligned configurations. Cranked shell model calculations, performed in the present work using a modified harmonic oscillator potential [22], show that the alignment of a pair of h11/2 neutrons is

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Fig. 4. Dynamic moments of inertia (J (2) ) as a function of rotational frequency for bands 1 and 2 in 112 Sn. The inset shows the results for 108 Sn taken from Ref. [23].

expected to occur at a rotational frequency of about 0.35 MeV h¯ −1 . This favours the interpretation −2 2 )ν(h2 of the high spin states above spin 12+ in 112 Sn as belonging to the aligned π(g9/2 )(g7/2 11/2 ) configuration following the alignment of a pair of h11/2 neutrons. Similar low frequency alignments have also been reported in other tin isotopes. The inset of Fig. 4 shows the J (2) plots for two bands in 108 Sn [23], identified as intruder bands. It is seen that both bands show a low-frequency (ω ∼ 0.40 MeV h¯ −1 ) bandcrossing. These have also been interpreted as arising due to the alignment of a h11/2 neutron pair in 108 Sn [23]. Furthermore, the broad peak at the higher frequency of ∼ 0.55 MeV in the positive-parity band in 108 Sn (inset, Fig. 4) was attributed to the π(g7/2 ) alignment [23]. For 112 Sn, there is an indication of a similar broad peak at hω ¯ ∼ 0.60 MeV (Fig. 4). It is possible that this bump corresponds to a π(g7/2 ) alignment as in 108 Sn. The reduced transition probabilities, B(E2), derived from the present lifetime results and the γ -ray branching ratios, suggest that the states with J π  12+ in band 1 are moderately deformed with β2 ∼ 0.18 (Table 2). Experimentally, the deformations for intruder bands have been reported for 108,114 Sn [6,24] among the tin isotopes. A comparison of the results shows that the quadrupole deformations for the states of the positive-parity intruder band in 112 Sn are similar to those for 108 Sn but less than those in 114 Sn. Total Routhian Surface (TRS) calculations, using a deformed Woods–Saxon potential and monopole pairing [25,26], have been performed for band 1. The total energy, calculated for different rotational frequencies, was minimised for each (β2 , γ ) with respect to the hexadecapole deformation β4 . Fig. 5, showing the total Routhian surfaces for the two rotational frequencies

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Fig. 5. Total Routhian surface plots in the β2 –γ plane for band 1 in 112 Sn for the two rotational frequencies h¯ ω = 0.31 and 0.41 MeV. The interval between the successive contours is 0.25 MeV.

0.31 and 0.41 MeV, suggests an almost constant quadrupole deformation of β2 ∼ 0.2. The calculated transition quadrupole moments obtained from Qt (β2 , γ )cal = 6(15π)−1/2 ZR2 β2 (1 + 0.16β2 ) cos(γ + 30◦ ) for (β2 , γ ) values suggested from the TRS, are found to be in good agreement with the Qt values derived from the experimental B(E2) results. These calculations also suggest that at small rotational frequencies, the states have a near prolate shape. At the higher frequency of 0.41 MeV, the shape becomes triaxial with β2 = 0.21, γ = 26◦ and β4 = 0.01. This change in shape may be associated with the ν(h211/2 ) alignment. The reduction in the B(E2) rate for the 14+ → 12+ transition compared to the 12+ → 10+ transition (Table 2 and Fig. 6) is possibly related to this alignment. A similar reduction in the transition probabilities in the region of the bandcrossing, observed in 114 Sn [24], is explained as arising due to a crossing of the ground and aligned intruder bands as well as due to the mixing of the states of the intruder band with the lower-lying spherical states. Although such mixing of deformed and spherical states is also observed in 112 Sn as reflected by the B(E2) rates for the 883.2 and 678.1 keV transitions (Table 2), it is relatively small for the 14+ state in 112 Sn. The observation of the 868.8 keV interband transition from the 17− state of the negative-parity sequence (band 2) to the 16+ state in band 1 indicates an overlap in the configurations of the two −1 )(h11/2 ) configuration [5], also possibly undergoes a bands. Band 2, corresponding to the π(g9/2 2 − ν(h11/2 ) alignment before the 17 state. It is interesting to note that there is an overall decrease in the dynamic moment of inertia J (2) with rotational frequency (Fig. 4) in 112 Sn. The J (2) decreases to 25h¯ 2 MeV−1 , a value considerably less than the rigid body moment of inertia (∼ 38h¯ 2 MeV−1 ), at the frequency h¯ ω = 0.66 MeV. This behaviour, suggestive of band termination, is similar to what is observed for 108 Sn but different from that reported in 110 Sn [7]. Further, the B(E2) rates first increase, as expected, following an alignment, and then tend to decrease somewhat for the 20+ → 18+

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Fig. 6. Plot of B(E2) versus spin for band 1 in 112 Sn. The continuous line provides a guide to the eye.

and 22+ → 20+ transitions (Fig. 6). The upper limit, proposed for the (24+ ) → 22+ transition (Table 2), is consistent with this trend. Although this limited evidence, related to the behaviour of the B(E2) rates, and the decrease of the dynamic moment of inertia J (2) with rotational frequency (Fig. 4), is indicative of the band termination phenomenon, band 1 needs to be extended to close to the terminating spin of 36+ for being conclusively interpreted as a terminating band. 5. Conclusion The intruder 2p–2h band (band 1), built on the 3413.8 keV, 6+ state has been studied. The band has been extended up to 11570.0 keV and spin (24+ ) with the addition of the new 1234.9 keV transition. Firm spin assignments of 20+ and 22+ are suggested for the 9186.0 and 10335.1 keV states, respectively. Mean lifetimes of six states with spins up to 22+ and an upper limit for the lifetime of the (24+ ) state belonging to band 1 have been determined from the DSA data. The B(E2) rates, deduced from the present lifetime results and γ -ray branching ratios, indicate a moderate quadrupole deformation of β2 ∼ 0.18 for these states. The experimental Qt values are consistent with those predicted by TRS calculations performed in this work. The decrease in the B(E2) value for the 14+ → 12+ transition may be related to the low frequency alignment at h¯ ω ∼ 0.37 MeV suggested by the dynamic moment of inertia (J (2) ) plot. CSM calculations that predict the h11/2 neutron alignment to occur at a similar frequency −2 2 )ν(h2 of 0.35 MeV, therefore, favor the configuration π(g9/2 )(g7/2 11/2 ) for the aligned intruder + + band. Although the decrease in the B(E2) rates for the 20 → 18 and 22+ → 20+ transitions

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and that of J (2) with frequency are suggestive of band termination, a definite inference can be drawn only if the band is extended to higher spins. Acknowledgement The authors thank the members of the INGA Collaboration group for setting up the array at the VECC, Kolkata. The contributions of Dr. Ambar Chatterjee (NPD, BARC) and the members of the Electronics Division, BARC, Mumbai is gratefully acknowledged for the multi-parameter data acquisition system. The authors are thankful to Dr. R.K. Bhowmik, S. Venkataramanan and the members of the Electronics group at the Inter University Accelerator Centre (IUAC), New Delhi, for providing the electronics module for the Clover detectors. Thanks are also due to the staff of the Cyclotron and the Target Laboratory at the VECC, Kolkata, for their co-operation. References [1] R. Wadsworth, H.R. Andrews, C.W. Beausang, R.M. Clark, J. DeGraaf, D.B. Fossan, A. Galindo-Uribarri, I.M. Hibbert, K. Hauschild, J.R. Hughes, V.P. Janzen, D.R. LaFosse, S.M. Mullins, E.S. Paul, L. Persson, S. Pilotte, D.C. Radford, H. Schnare, P. Vaska, D. Ward, J.N. Wilson, I. Ragnarsson, Phys. Rev. C 50 (1994) 483. [2] R. Wadsworth, H.R. Andrews, R.M. Clark, D.B. Fossan, A. Galindo-Uribarri, J.R. Hughes, V.P. Janzen, D.R. Lafosse, S.M. Mullins, E.S. Paul, D.C. Radford, H. Schnare, P. Vaska, D. Ward, J.N. Wilson, R. Wyss, Nucl. Phys. A 559 (1993) 461. [3] H. Harada, T. Murakami, K. Yoshida, J. Kasagi, T. Inamura, T. Kubo, Phys. Lett. B 207 (1988) 17. [4] J. Bron, W.H.A. Hesselink, A. Vanpoelgest, J.J.A. Zalmstra, M.J. Uitzinger, H. Verheul, K. Heyde, M. Waroquier, H. Vincx, P. Van Isacker, Nucl. Phys. A 318 (1979) 335. [5] M. Schimmer, S. Albers, A. Dewald, A. Gelberg, R. Wirowski, P. von Brentano, Nucl. Phys. A 539 (1992) 527. [6] R. Wadsworth, R.M. Clark, J.A. Cameron, D.B. Fossan, I.M. Hibbert, V.P. Janzen, R. Krücken, G.J. Lane, I.Y. Lee, A.O. Macchiavelli, C.M. Parry, J.M. Sears, J.F. Smith, A.V. Afanasjev, I. Ragnarsson, Phys. Rev. Lett. 80 (1998) 1174. [7] M. Woli´nska-Cichoka, J. Kownacki, W. Urban, E. Ruchowska, W.A. Plóciennik, B. Bekman, Ch. Droste, W. Gast, R. Lieder, W. Meczy´nski, A. Kordyasz, P. Kownika, J. Iwanicki, T. Morek, J. Perkowski, J. Serbrny, A. Stolarz, J. Stycze´n, Eur. Phys. J. A 24 (2005) 259. [8] J. Kasagi, H. Harada, T. Murakami, K. Yoshida, H. Tachibanaki, T. Inamura, Phys. Lett. B 176 (1986) 307. [9] R.K. Bhowmik, INGASORT manual, private communication, 2003. [10] E.S. Macias, W.D. Ruther, D.C. Camp, R.G. Lanier, Comput. Phys. Commun. 11 (1976) 75. [11] Ch. Droste, S.G. Rohozinski, K. Starosta, T. Morek, J. Srebrny, P. Magierski, Nucl. Instrum. Methods A 378 (1996) 518. [12] E.K. Warburton, J.W. Olness, A.R. Poletti, Phys. Rev. 160 (1967) 938. [13] G. Gürdal, H. Amro, C.W. Beausang, D.S. Brenner, M.P. Carpenter, R.F. Casten, D.J. Hartley, B. Herskind, H. Hübel, T.L. Khoo, T. Lauritsen, W.C. Ma, D.A. Meyer, E.F. Moore, A. Neusser, P. Bringel, D.G. Roux, G. Slatten, R.B. Yadav, Y. Zhang, J. Phys. G: Nucl. Part. Phys. 31 (2005) S1873. [14] I. Ray, P. Banerjee, S. Bhattacharya, M. Saha-Sarkar, B. Sethi, J.M. Chatterjee, S. Chattopadhyay, A. Goswami, S. Muralithar, R.P. Singh, R.K. Bhowmik, Nucl. Phys. A 646 (1999) 141. [15] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, vol. 1, Pergamon, New York, 1985. [16] http://www.srim.org/SRIM/SRIM2006.htm. [17] P. Banerjee, B. Sethi, J.M. Chatterjee, P. Bhattacharya, A.K. Sengupta, Nuovo Cimento A 85 (1985) 54. [18] S. Ganguly, P. Banerjee, I. Ray, R. Kshetri, S. Bhattacharya, M. Saha-Sarkar, A. Goswami, S. Muralithar, R.P. Singh, R. Kumar, R.K. Bhowmik, Nucl. Phys. A 768 (2006) 43. [19] L. Käubler, Yu.N. Lobach, V.V. Trishin, A.A. Pasternak, M.F. Kudojarov, H. Prade, J. Reif, R. Schwengner, G. Winter, J. Blomqvist, J. Döring, Z. Phys. A 358 (1997) 303. [20] A. Dewald, R. Peusquens, B. Saha, P. von Brentano, A. Fitzler, T. Klug, I. Wiedelhöver, M.P. Carpenter, A. Heinz, R.V.F. Janssens, F.G. Kondev, C.J. Lister, D. Seweryniak, K. Abu Saleem, R. Krücken, J.R. Cooper, C.J. Barton, K. Zyromski, C.W. Beausang, Z. Wang, P. Petkov, A.M. Oros-Peusquens, U. Garg, S. Zhu, Phys. Rev. C 68 (2003) 034314.

14

S. Ganguly et al. / Nuclear Physics A 789 (2007) 1–14

[21] D. De Frenne, E. Jacobs, Nucl. Data Sheets 79 (1996) 639. [22] R. Bengtsson, S. Frauendorf, Nucl. Phys. A 327 (1979) 139. [23] R. Wadsworth, C.W. Beausang, M. Cromaz, J. DeGraaf, T.E. Drake, D.B. Fossan, S. Flibotte, A. Galindo-Uribarri, K. Hauschild, I.M. Hibbert, G. Hackman, J.R. Hughes, V.P. Janzen, D.R. LaFosse, S.M. Mullins, E.S. Paul, D.C. Radford, H. Schnare, P. Vaska, D. Ward, J.N. Wilson, I. Ragnarsson, Phys. Rev. C 53 (1996) 2763. [24] J. Gableske, A. Dewald, H. Tiesler, M. Wilhelm, T. Klemme, O. Vogel, I. Schneider, R. Peusquens, S. Kasemann, K.O. Zell, P. von Brentano, P. Petkov, D. Bazzacco, C. Rossi Alvarez, S. Lunardi, G. de Angelis, M. de Poli, C. Fahlander, Nucl. Phys. A 691 (2001) 551. [25] W. Nazarewicz, R. Wyss, A. Johnson, Nucl. Phys. A 503 (1989) 285. [26] G. Mukherjee, H.C. Jain, R. Palit, P.K. Joshi, S.D. Paul, S. Nagaraj, Phys. Rev. C 64 (2001) 034316.