Lifetime measurements in 138Nd

Jian Zhong· Xiao-Guang Wu · Shi-Peng Hu · Ying-Jun Ma·Yun Zheng · Cong-Bo Li · Guang-Sheng Li · Bao-Ji Zhu · Tian-Xiao Li ·Yan-Jun Jin · Yan-Xiang Gao · Qi-Wen Fan · Ke-Yan Ma · Dong Yang ·Hui-Bin Sun · Hai-Ge Zhao · Lin Gan · Qi Luo · Zheng-Xin Wu

Abstract Lifetimes of the 2+1, 4+1, 7-2, 10+2, 12+2, and 14+1 states in 138Nd populated via the 123Sb(19F, 4n)138Nd fusion-evaporation reaction were measured with the recoil distance Doppler shift technique in combination with the differential decay curve method. The B(E2;2+1 →0+1)value fit well with the systematic trend in the Nd isotope chain and Grodzins rule, which proved that 138Nd is a transitional nucleus.

Keywords Lifetime measurement · Recoil distance Doppler shift technique · Differential decay curve method

1 Introduction

For the N =78 isotonic chain, the shapes of the eveneven rare-earth nuclei ranging from Z =60 to 70 were predicted to have a shape change from prolate to oblate.[1, 2]. The observations of the γ-vibrational bands in132-138Nd [3-6] in this region proved the theoretical trend in some sense. Moreover, electromagnetic transition probabilities provide a sensitive test for understanding the nuclear structure. For the transitional nucleus138Nd,experimental data on electromagnetic transition probabilities are still scarce, and further studies need to be conducted.

In the present work, lifetimes of the 2+1, 4+1, 7-2, 10+2,12+2,and 14+1states were measured with the recoil distance Doppler shift (RDDS) technique. The data were analyzed by using the differential decay curve method(DDCM).The lifetime of the 2+1state has been published in Ref. [7]previously,and the other lifetimes will be presented in this study.

It should be noted that another study also using the RDDS technique and the DDCM to measure lifetimes of several states in138Nd was published by Bello Garrote et al. [8]. Most of the results in the present work are close to the values in Ref. [8], except for the 7-2state. In their work, the experimental results, especially for the two different 10+states, associated with proton and neutron configurations, respectively, have been explained in detail by various theories. Therefore, in the present work, the focus is concentrated on the systemic trend of the low-lying states in the138Nd isotopes and N =78 isotonic chains.

2 Experimental details

The present work was performed at the HI-13 tandem accelerator of the China Institute of Atomic Energy(CIAE)in Beijing.Excited states in138Nd were populated using the123Sb(19F, 4n)138Nd fusion-evaporation reaction at a beam energy of 87 MeV. The reaction was chosen based on a cross section calculation performed using the code PACE4.Lifetimes were measured using the CIAE plunger device,which has been introduced in Ref. [9], and was utilized to set and keep the distance between the target and stopper with a relative precision of 0.3 μm. Eight Compton-suppressed high-purity Ge (HPGe) detectors were used to detect γ rays from the residues. Three of these detectors were placed at 90°, four at 153°, and one at 42°with respect to the beam direction. Thirteen different target-tostopper distances (5, 9, 15, 25, 41, 70, 100, 166, 275, 457,758, 1259, and 2000 μm) were used to record the γ-γ coincidence data.The first five distances were measured for 8 h.The last three distances were measured for 4 h,and the rest were measured for 6 h. In addition to those distances mentioned above,another 3-μm distance,with a measuring time of 2 h, was used in the data analysis of the 4+1state,because the lifetime of this state is quite short. The NAPATAU code [10] was used in the data analysis. The mean recoil velocity of the compound nucleus was ～1%of the light speed c.Owing to the neutron damage and poor statistics of the forward (42°) detector, only backward(153°)detectors were used for data analysis.The backward total projection at a distance of 100 μm is shown in Fig. 1.

3 Data analysis and results

The experimental data were analyzed by using the DDCM, which has been proven to be a precise method for determining the lifetime of excited states [11-13]. For the DDCM,the mean lifetime τiat level i and distance x can be determined as follows (see Fig. 2):

Fig. 1 Backward (153°) total projection at a target-stopper distance of 100 μm. The main γ-ray transitions in 138Nd are marked in the spectrum.

Before being used to determine the lifetime,the intensities of the shifted and unshifted components were normalized for differences in beam intensity and measuring time at different target-to-stopper distances.

However, if the energies of transitions A and B are the same, gating on the shifted component of transition B also gates on the shifted component of transition A.The shifted peak of ‘‘transition’’ in the gating spectrum comprises two parts(see Fig. 3).The first part is the shifted component of transition A obtained by gating on the shifted peak oftransition B, and the second part is the shifted component of transition B,which is obtained from gating on the shifted component of transition A. However, the unshifted component of transition A can be obtained by gating only on the shifted peak of transition B, because the unshifted component of transition B cannot be seen from the gating on the shifted component of transition A. In this special case, the following relationship can be obtained:

3.1 Lifetime of the 7-2 state

The lifetime the of 7-2state cannot be determined easily using Eq. 1, because energies of the strongest populated and depopulated transitions for this level are all close to 557 keV, and other populated and depopulated transitions are much weaker than the strongest one(see Fig. 4)[14].In other words,the 680 keV 9-3→7-2and 470 keV 7-2→5-2transitions are too weak to use for lifetime determination in our data. When we gated on the shifted component of the 557 keV γ peak, the shifted and unshifted components of the 470 keV 7-2→5-2transition can barely be seen in the gating spectra. Therefore, in the present work, the lifetime of the 7-2state could not be extracted as done in Ref. [8]by fitting the shifted and unshifted components of the 470 keV 7-2→5-2transition in the gating spectra, and the 557 keV 7-2→6+1transition is the only choice to fit the differential decay curve. However, when we set a cut on the shifted component of the 9-2→7-2556 keV transition, we will also set a cut on the shifted part of the 7-2→6+1557 keV transition at the same time. Therefore. in the lifetime analysis of the 7-2state, Eq. 7 was used.

Fig. 4 Partial level scheme for 138Nd. Lifetimes measured in the present work are also labeled in the level scheme. The width of the arrows represents the relative intensity of the transitions. Relative intensity information was taken from Ref. [14]. The lifetime of the 3175 keV 10+1 state with an asterisk was taken from Refs. [15, 16].

According to the analysis above, the IAu(x) and IAs(x)trends fitted by the NAPATAU code are shown in the right panels of Fig. 5. Partly backward-shifted and unshifted gating spectra are shown in the left panels of Fig. 6 for the γ peak at 557 keV. The mean value of 9.5(10) ps fits well with the result in Ref. [8] within the experimental uncertainty.The mean lifetime of 19.0(20)ps,which is twice the mean value of 9.5(10)ps,is set as the final result for the 7-2state.

3.2 Lifetimes of other states

In addition to the lifetimes of the 7-2state mentioned above and the lifetime of the 2+1state determined in Ref. [7], the lifetimes of the 4+1, 10+2, 12+2, and 14+1states were measured in the present work. For the 4+1, 10+2, and 14+1states,a direct gating case was used.However,for the 12+2state, an indirect gating case was used because the shifted peak of the 792 keV 14+1→12+2transition will overlap with the unshifted peak of the 787 keV 13+2→12+2transition.Moreover,the shifted and unshifted components of the 453 keV 10+2→9-2transition were fit in the 10+2state lifetime determination, because the energy of the 329 keV 10+2→9-3transition is close to the energy of the 331 keV 7-1→5-1transition. Partly backward-shifted and unshifted gating spectra of the 503 keV 12+2→10+2transitions are shown in the right panels of Fig. 6. The decay curves and τ plots of 4+1, 10+2, 12+2, and 14+1states are shown in the left panels of Figs. 5 and 7.From the resulting decay curves, the deduced mean lifetimes of these states were determined to be 2.0(4), 50.5(41), 11.5(11), and 2.3(3) ps, respectively, and these states are all labeled in Fig. 4. A comparison of the results from the current work to those of Ref. [8] is given in Table 1.

Fig.5 Decay curves and lifetime determination of the 729 keV 4+1 →2+1 transition (left) and 557 keV γ transitions (right) in 138Nd. The middle and lower panels show the Doppler-shifted and stopped intensities versus distance. The mean lifetime at each distance is determined and is shown in the upper panel as a function of distance.The weighted average of these values yields the overall mean lifetime.

4 Discussion

Fig. 6 (Color online) Left: Partial stopped and backward-shifted components for the 557 keV γ transitions in 138Nd from gating on the backward-shifted components of the 557 keV transition.Right:Partly backward-shifted and unshifted components of the 503 keV 12+2 →10+2 transition in 138Nd from gating on the backward-shifted components of the 847 keV 16+2 →14+1 transition.

The lifetime of the 2+1state in the present work yields a reduced transition probability of B(E2;2+1→0+1)=0.19(2)e2b2, or 45(5) W.u. This value lies in the middle of the value of 39(4)W.u.in136Ce[17]and the value 51(4)W.u.in140Sm[18].To identify the variation in the collectivity in the A=130 mass region,the value of B(E2)of the 2+1state in the present work was compared to those values in the neighboring even-even isotopes (see Fig. 8). As can be observed in Fig. 8,when the neutron number increases,the B(E2) values of the 2+1states decrease, which means that collectivity decreases. The B(E2) value usually correlates with the energy of the 2+1state. When the collectivity increases,the B(E2)value increases and the energies of the 2+1state decrease. This conclusion was recognized by Grodzins [19] and is known as Grodzins rule. Within an isobaric chain, Grodzins rule can be described as follows[20]:

Fig. 7 Decay curves and lifetime determination of the 792 keV 1 → (left), 503 keV 1 →1(middle), and 453 keV 1 →9 transitions(right)in 138Nd.The middle and lower panels show the Dopplershifted and stopped intensities versus distance. The mean lifetime at each distance is determined and is shown in the upper panel as a function of distance. The weighted average of these values yields the overall mean lifetime.

Table 1 Comparison of results between the present work and those of Ref. [8]

In Eq. 8,B(E2)↑is given by e2b2and E keV,which is the level energy of the 2+1state; Z, N, and A are the proton number, neutron number, and mass number, respectively;and H1 and H2 are the Habs fit values,which can be found in Ref. [20]. For the Nd isotopic chain, H1=3.38 and H2=0.35. Values obtained from the modified Grodzins formula were compared to the experimental results, as shown in Fig. 8. Except for132Nd [21], the experimental B(E2) values of the 2+1states for the chain of Nd isotopes fit well with the systematic trend of the modified Grodzins rule.This means that the closer the neutron number gets to the N =82 subshell, the weaker is the collectivity.

Fig.8 (Color online)Systematics of B(E2)values for the even-even Nd isotopic chain. The experimental values for 132Nd, 134Nd, 136Nd,138Nd, and 140Nd are taken from Ref. [21], Ref. [22], Ref. [23], this work, and Ref. [24], respectively.

138Nd has been discussed as a transitional nucleus [25].To identify the shape information of the low-lying states in138Nd and the neighboring even-even nuclei,the excitation energy ratio R4/2, defined as E(4+1)/E(2+1), and the ratio B4/2, defined as B(E2;4+1→2+1)/B(E2;2+1→0+1), are proposed (see Fig. 9). For the shell configuration, R4/2＜2 and B4/2～1; for a geometric vibrator, R4/2= 2-2.2 and B4/2～ 2; for the γ-unstable nuclei, R4/2= 2.2-2.4; and R4/2～3.3, B4/2～1.4 for an ideal rotor, respectively. As can be observed in Fig. 9, the R4/2values of both Nd isotopes and N =78 isotone chains show that138Nd should be a γ-soft or transitional nucleus,as discussed in Ref. [6].The potential energy surface calculation in Ref. [8] also supports this conclusion. However, the B4/2value in the present work is close to 1.0. Owing to the lack of B(E2;4+1→2+1) values in136Nd and140Nd, the trend followed by the B4/2value is not clear in the Nd isotope chain.However, the B4/2value in138Nd is smaller than the neighboring results for136Ce and140Sm in the isotone chain. This phenomenon may be caused by the lifetime of the 4+1state in138Nd,because the lifetime of the 4+1state is close to the lower limit of the RDDS used in the present work and in Ref. [8]. The B(E2;4+1→2+1) value is 47(9)W.u.in the current experiment,which is close to the result of 49(7) W.u. in Ref. [8] but smaller than the values of 56(10)W.u.in136Ce and 69(5)W.u.in140Sm,although the B(E2;2+1→0+1)values in the present work and Ref. [8]fit smoothly into the trends of136Ce and140Sm. Moreover, in Ref. [8],the experimental B(E2;4+1→2+1)value is smaller than the theoretical prediction, which means that the lifetime of the 4+1state in138Nd may be shorter than the present result.

Fig. 9 Excitation energy ratio R4/2 (upper panels) and the ratio of B(E2)values B4/2 (lower panels)for the even-even Nd isotopic chain(left) and N =78 isotones (right). Information for 132Nd, 134Nd,134Ba, 136Ce, 138Nd, and 140Sm was obtained from Refs. [21, 26],Refs. [22, 27], Ref. [27], Ref. [17], this work, and Refs. [24, 28],respectively.

5 Summary

In addition to the lifetime of 10.9(11) ps of the 2+1state reported in Ref. [7],lifetimes of the 4+1,7-2,10+2,12+2,and 14+1states in138Nd were measured using the RDDS technique and the DDCM in the present work. Most of the results in this experiment were similar to those in Ref. [8],except for the lifetime of the 7-2state, which is twice that found in Ref. [8].The B(E2;2+1→0+1)value in the present work fits smoothly into the systematics of the even-even Nd isotope chain and the prediction of Grodzins rule. R4/2exhibits a smooth trend in the A=130 mass region,which indicates that138Nd should be a γ-soft nucleus,but the B4/2value deviates from it. This may be due to the lifetime of the 4+1state being too short to be measured using the RDDS method.

AcknowledgementsThe authors would like to thank the staff of the HI-13 tandem accelerator at the China Institute of Atomic Energy for the steady operation of the accelerator.

Author ContributionsAll authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Jian Zhong,Xiao-Guang Wu,Shi-Peng Hu,Ying-Jun Ma,Yun Zheng,Cong-Bo Li,Guang-Sheng Li,Bao-Ji Zhu,Tian-Xiao Li, Yan-Jun Jin, Yan-Xiang Gao, and Qi-Wen Fan. The first draft of the manuscript was written by Jian Zhong, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.