SCIENCE CHINA Physics, Mechanics & Astronomy

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*Corresponding author (email: zhushj@mail.tsinghua.edu.cn)

• Research Paper • August 2011 Vol.54 Suppl. 1: s44–s48

Radioactive Nuclear Beam Physics and Nuclear Astrophysics doi: 10.1007/s11433-011-4417-7

New multi-phonon gamma vibrational bands in A~110 neutron-rich nuclei

ZHU ShengJiang1*, WANG JianGuo1, GU Long1, HAMILTON J H2, RAMAYYA A V2, LUO YiXiao2,3, RASMUSSEN J O3, HWANG J K2, DING HuaiBo1, LI Ke2, LIU ShaoHua2, YEOH E Y1, XU Qiang1 & XIAO ZhiGang1

1 Department of Physics, Tsinghua University, Beijing 100084, China; 2 Department of Physics, Vanderbilt University, Nashville TN 37235, USA;

3 Lawrence Berkeley National Laboratory, Berkeley CA 94720, USA

Received January 6, 2011; accepted March 15, 2011; published online July 18, 2011

The high spin states of neutron-rich 103Nb, 107Tc and 109Tc nuclei in A~110 region have been investigated by measuring prompt -- coincident measurements populated with the spontaneous fission of 252Cf with the Gammasphere detector array. In 103Nb, one-phonon K = 9/2 and two-phonon K = 13/2 -vibrational bands have been identified. In 107Tc and 109Tc, one-phonon K = 11/2 and two-phonon K = 15/2 -vibrational bands, in which the zero-phonon bands are based on K=7/2 excited states, have also been identified. The two-phonon bands are first observed in odd-Z nuclei. The characteristics for these band structures have been discussed.

high spin states, neutron-rich nucleus, -vibrational bands

PACS: 21.10.Re, 23.20.Lv, 27.60.+j, 25.85.Ca

1 Introduction

In the study of nuclear structure, the multi-phonon -vibrational bands are very important subjects. The multi- phonon excitations in deformed nuclei can provide valu- able information of the nuclear vibrational collectivity. However, to experimentally observe the multi-phonon bands is difficult. So far, considerable efforts have been made to search for the multi-phonon bands in even-even nuclei. Several low lying K = 4+ two-phonon (2) bands have been identified, such as in 166,168Er [13], 164Dy [4] and 232Th [5]. In A=110 neutron-rich nuclear region, the one-phonon (1)- and 2 bands have been observed in even-even 104,106,108Mo [611] and 108,110,112Ru [1214]. For the odd-A nuclei, the study of the 2 bands is scarce.

Piepenbring and Durand [15,16] made some predications using the extended multi-phonon method (MPM). They indicate that in the odd-A nuclei, if the K is a band-head quantum number of a quasiparticle band, there exist two 1 states with K+2 and K2. For the 2 states, there may exist three states with K4, K and K+4. It is also expected that the K+2 1 state and the K+4 2 state may be easy to be observed, and others may be difficult. Recently, in A~110 neutron-rich region, a first 2 band in an odd-N nucleus has been observed in 105Mo by our cooperators [17], but no 2 band has been observed in odd-Z nuclei. To search for information of the 2 bands in odd-Z nuclei, the high spin states of 103Nb, 107Tc and 109Tc are reinvestigated in the present work. In previous publications, some high spin state structures in 103Nb [18,19], 107Tc and 109Tc [20,21] have been reported. Here, we report the new results of the 1- and 2 bands in these nuclei.

Zhu S J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 Suppl. 1 s45

2 Experimental methods

To study the high spin states of the neutron-rich nuclei is difficult as it can not be formed by usual heavy-ion induced fusion-evaporation reactions. A practical method is to measure the prompt -rays of spontaneous fission or in-duced fission from heavy nuclei [22]. Following the devel-opment of the large detector array, great progress in re-search in the high spin states in neutron-rich nuclei around A~110 and 140 regions has been made. In this work, the high spin states in 103Nb, 107Tc and 109Tc were studied by measuring the prompt -rays emitted from the fragments produced in the spontaneous fission of 252Cf. The experi-ment was carried out at the Lawrence Berkeley National Laboratory. The Gammasphere detector array which, for this experiment, consisted of 102 Compton- suppressed Ge detectors, was employed to detect -rays. A total of 5.71011 triple- and higher-fold -coincidence events were collected. The RADWARE software package [23] was used for the coincidence analysis.

3 Results and discussion

The partial level schemes of 103Nb, 107Tc and 109Tc in the

present work are shown in Figures 1 and 2. The collective bands observed are labeled on the tops of the schemes. The bands (1) in 103Nb, 107Tc and 109Tc and the partial levels in bands (2) in 107Tc and 109Tc have been observed in the pre-vious work [1821]. Here we confirmed or expanded them. The bands (2)–(4) in 103Nb, and bands (3) in 107Tc and 109Tc are newly observed in the present work.

The bands (1) in 103Nb have been assigned as 5/2+[422] with K = 5/2+ [19]，and the bands (1) in 107Tc and 109Tc built on 137.5 and 69.6 keV excited state levels respectively, were assigned as 7/2+[413] with K = 7/2+ [21]. Compar-ing bands (2) and (3) with band (1) in each nucleus, one can see that they have similar regular level spacings. Bands (2) are built on the higher excited states at 716.8 keV in 103Nb, 766.2 keV in 107Tc and 633.4 keV in 109Tc. It is not likely for the single-quasiparticle states to be built with such high excitation energies, compared with the other single-qua- siparticle bands in 103Nb [18,19] and 107Tc [21]. The ob-served strong linking transitions between bands (1) and (2) suggest that bands (2) most probably have the same paritie with bands (1) in these nuclei. Comparison of bands (2) in 103Nb, 107Tc and 109Tc with the 1 bands in 104,106,108Mo [611] shows that they have similar characteristics. So we assign bands (2) in 103Nb, 107Tc and 109Tc as 1 bands with K = 9/2+, 11/2+ and 11/2+, respectively. Bands (3) are based on the

Figure 1 Partial level scheme in 103Nb.

s46 Zhu S J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 Suppl. 1

Figure 2 Partial level schemes in 107Tc and 109Tc.

1282.1 keV level in 103Nb, 1499.5 keV one in 107Tc and 1383.2 keV one in 107Tc. With the excitation energies of the band-head levels much less than the neutron pairing-gap energy 2n~2.1 MeV and the proton pairing-gap energy 2p~1.7 MeV [6], bands (3) in these nuclei should not be three-quasiparticle bands. They should be 2 bands. Thus, the bands (1)–(3) in odd-Z 103Nb, 107Tc and 109Tc nuclei are proposed as the zero- phonon (0)-, 1- and 2 bands, re-spectively.

The comparisons of the band-head energies of 0-, 1- and 2 bands along with the ratios of (E2E0)/(E1E0) in

103Nb, 107Tc and 109Tc with those in 104106Mo [610,17] are shown in Table 1. One can see that the energies and ratios in different nuclei show similar values. This gives evidence for the 1- and 2 band assignments in 103Nb, 107Tc and 109Tc. On the other hand, the energy ratios (E2E0)/(E1 E0) are ~1.8 for 103Nb and 105Mo, ~2.2 for 107Tc and ~2.3 for 109Tc, but the harmonic ratios for the even-even 104,106Mo are around 2.0 in the A=110 nuclear region. The ratios in odd-A nuclei somewhat deviate from the harmonic ratio 2 in the even-even nuclei in this region. This may be caused by the anharmonic characteristics of the -vibrational bands in

Table 1 The systematic comparison of band-head energies of 0-, 1- and 2 bands and the ratios of (E2E0)/(E1E0) in 103Nb, 107Tc and 109Tc with those in 104106Mo

Nucleus E0 (keV) E1 (keV) E2 (keV) 2 0

2 0

E E

E E

103Nb 0 716.8 1282.1 1.79 107Tc 137.5 766.2 1499.5 2.17 109Tc 69.6 633.4 1384.2 2.33

104Mo 0 812.1 1583.3 1.95 105Mo 0 870.5 1534.6 1.76 106Mo 0 710.4 1434.6 2.02

Zhu S J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 Suppl. 1 s47

the odd-A nuclei. The anharmonic values also are reported with 2.62.8 in the A = 160 region [1–3].

The 1- and 2 bands in a nucleus are expected to exhibit similar inertia parameters [24]. The inertia parameter A can be obtained from the second-order rotational energy for-mula:

22 2, 1 1 . KE I K E A I I K B I I K (1)

The values of the parameters A obtained in the present work are 18.2, 18.0, 18.2 in 103Nb, 18.1, 18.6, ~17 in 107Tc, and 17.0, 18.7, ~16 in 109Tc for the 0-, 1- and 2 bands respectively, which support our assignments.

In order to understand the multi-phonon bands deeply, here we discuss other characteristics of 103Nb.

The g factors in the vibrational bands of a nucleus should have the same values [25]. The (gK–gR)/Q0 values can be calculated from the -ray transition branching ratios [26]:

1/ 210/ 0.934 1 1 1 ,

K Rg g Q E I I I I

(2)

where E is the energy of -transition (in MeV), and is E2/M1 mix ratio which can be obtained from the branching ratio:

5

int 2 2

int

1

112 2 1 1

2 2

1 1 1 ,

E I II I IK I

I I I E I I

I I K I K (3)

where the Iint is the intensity of the corresponding -transition. The branching ratios of -transitions are ob-tained from the present work. Calculated (gK –gR)/Q0 values for 103Nb are 0.39(2) b1 for band (2) and 0.34(2) b1 for band (3). The values in both -vibrational bands are with the same magnitude as expected by theoretical prediction.

Another characteristic for 2 band is that the transitions from 2 band to 1 band should be collective. This collec-tivity can be obtained from absolute reduced transition rates B(E2) values of the transitions [2]. In our data, we can not obtain B(E2) values directly. But we can use the experi-mental transition branching ratios R to calculate the B(E2) ratio between the two E2 transitions, and to obtain the relative collectivity between 1- and 2 bands, as done in ref. [6]. The ratio can be obtained in the experiment as fol-lows:

12 g2

1 21 1

1 21 2

1 2g 1

53[ 2 ]1

13 5

2 [ 1 ] [ 2 ]

[ 1; 1 ] [ 1; 1 ]

[ 2; 2 ] [ 2; 2 ]

,

I II I

I I I I

B M I I B M I I

B E I I B E I I

EER

R E E

(4)

where R1 and R2 are the -transition branching ratios with

1 1 1 g

2 2 2 1

1 int[ ( 1) ] int[ ( 1) ]

2 int[ ( 1) ] int[ ( 2) ]

,

.

I I I I

I I I I

R I I

R I I

The values of B(M1) for K>1/2 can be written as [31]:

22

1 2 1

21 2

3 e1; , 14 2

10 .

K RB M KI K I I g g K

Mc

I K I K

(5)

The (gK gR) factors have been obtained from the above

(gK gR)/Q0 values. Here, 20 0 2(3 / 5 ) [1 (7 / 2) Q ZR

25 / ] and R0=1.2×A1/3 fm. From total-Routhian- sur-

faces (TRS) calculations based on the cranked shell model with universal Woods-Saxon potential and Strutinsky shell correction formalism [27], the value of 2 obtained in 103Nb is 0.31. So the ratio of the reduced transition rate B(E2) for the connecting transitions among bands (1)(3) in 103Nb can be obtained using eqs. (4) and (5), where the transition branching ratios are taken from the present work. The re-sults obtained are:

2 1 1 g( 2;15 / 2 11/ 2 ) ( 2;11/ 2 7 / 2 ) 1.53(16), B E B E

2 1 1 g2;15 / 2 11/ 2 2;13 / 2 9 / 2 3.45(37). B E B E

Here, we assume the transitions of I I1 inside the band are pure M1 transitions. From the ratios, one can find that the B(E2) value of the 646.4 keV transition connecting the 2 band to the 1 band has the same order as those of the 788.7 and 873.7 keV transitions connecting the 1 band to the ground band. So the transitions between the 2- and 1 bands also keep the collective character. On the other hand, the theoretical values of harmonic vibration for the B(E2) ratios have been discussed in ref. [6]. The values in 103Nb are calculated as:

2 1 1 g2;15 / 2 11/ 2 2;11/ 2 7 / 2 2.59, B E B E

2 1 1 g2,15 / 2 11/ 2 2;13 / 2 9 / 2 3.34, B E B E

which are close to the above experimental results. So these results also support our assignment of band (3) as a two- phonon -vibrational band in 103Nb.

Band (4) in 103Nb may be a three-phonon -vibrational band. The characteristics of this band need further research.

4 Conclusions

In summary, the high spin states of 103Nb, 107Tc and 109Tc nuclei have been re-investigated from the study of the prompt -rays. New collective bands have been identified. The one-phonon and two-phonon -vibrational bands in these nuclei have been identified. The evidence supporting these -vibrational bands has been discussed. This is the

s48 Zhu S J, et al. Sci China Phys Mech Astron August (2011) Vol. 54 Suppl. 1

first identification of such two-phonon -vibrational band structures in odd-Z nuclei. And also for 107Tc, 109Tc, it is the first identification of the -vibrational bands based on the excited state instead of the ground state.

The work at Tsinghua University was supported by the Major State Basic Research Development Program (Grant No. 2007CB815005), and the National Natural Science Foundation of China (Grant No. 10775078). The work at Vanderbilt University, Lawrence Berkeley National Laboratory, was supported by U. S. Department of Energy (Grant Nos. DE-FG05-88ER40407 and DEAC03-76SF00098).

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