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Experimental and Theoretical Study of Quasi-Particle Alignment in 82Sr
Nuclear Physics A 834 (2010) 107c–109c www.elsevier.com/locate/nuclphysa
Experimental and Theoretical Study of Quasi-Particle Alignment in 82 Sr Ping Fan, Daqing Yuan, Yongnan Zheng, Yi Zuo, Dongmei Zhou, Xiaoguang Wu, Guangsheng Li, Lihua Zhu, Guoji Xu, Qiwen Fan, Xizhen Zhang and Shengyun Zhu China Institute of Atomic Energy, P.O. Box 275-50, Beijing 102413, China
∗
†
The g factors of the rotational states with spin up to 8+ of the ground state band in Sr have been measured by the Transient-Magnetic-Field Ion Implantation Perturbed Angular Distribution method following the 58 Ni(28 Si,4p)82 Sr reaction. The measured g factors rapidly increase with the increasing of the spin from spin 6+ to 8+ , showing the proton aligment. The present results can be well interpreted in the framework of the particle-rotor model. 82
1. Introduction One of the interesting features in mass A=80 region is interplay between the collective rotation and the quasi-particle alignment[1]. It is attractive to know whether nuclei gain their spins through collective motion or quasi-particle alignment. Nuclear magnetic dipole moments are closely connected and sensitive to nuclear structure. Hence measurements of magnetic moments can provide valuable information on nuclear structure of nuclei. Since the magnitude and sign of magnetic moments or g factors are dramatically affected by the quasi-particle alignment, g factor or magnetic moment is a very sensitive probe to investigate the quasi-particle alignment. The level scheme and the lifetimes of the rotational states in 82 Sr have been investigated by a number of groups [2–4]. So far, the pairing breaking and alignment of quasi-particles have not been studied directly by the g factor measurement. The present work was motivated to experimentally and theoretically determine the g factors of the ground state rotational band states in 82 Sr in order to study the quasi-particle alignment. 2. Experiment and Calculation g factors of rotational states of the ground state band (GSB) in 82 Sr were determined by the transient-magnetic-field ion implantation perturbed angular distribution(TMFIMPAD) method. The rotational states in 82 Sr were populated by the fusion-evaporation reaction 58 Ni(28 Si,4p)82 Sr with a 110 MeV Si beam from the HI-13 tandem accelerator at China Institute of Atomic Energy. The TMF-IMPAD set-up used in the experiment is mainly composed of a target chamber housing a 58 Ni-Fe-Cu three layer target, a polarizing ∗ The present work was supported by the National Natural Science Foundation of China under Grant No. 10435010 † corresponding author [email protected]
0375-9474/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2010.01.032
108c
P. Fan et al. / Nuclear Physics A 834 (2010) 107c–109c
magnet and γ-ray detector system. The details of the experiment can be found in Ref. [5]. In connection with the experimental work the g factors of the GSB in 82 Sr have been studied in the framework of the particle rotor model based on the Nilsson potential[6– 8]. On the basis of the model for one neutron and one proton in Ref.[6], the present model here is formulated for two identical protons outside the 80 36 kr44 core. The Nilsson parameters κ(N ) and μ(N ) are taken from Ref.[9], and the axial deformation parameter β2 is 0.33 deduced from experimental Qt value[3]. The rotational g factor, gR is 0.36, which is obtained after taking into account the factor that the pairing force acting between protons is larger than between neutrons[10]. And the orbital and spin g factors of the f ree valence protons are gl = 1 and gs = 0.6 × gs,proton respectively. 3. Results and Discussion The measured and calculated g factors for the rotational states up to spin 8+ of the positive parity ground state in 82 Sr are shown in Fig 1. It can be seen that the measured g factors rapidly increase with the increasing of the spin from spin 6+ . The averaged value of g factors for 2+ , 4+ and 6+ states is 0.51(13) that is consistent with the value of 0.50 (2) measured by A. I. Kucharskats et al [2]. In their paper the respective g factors of the 2+ , 4+ and 6+ states were not given.
Figure 1. Measured and calculated g factors of rotational states of ground state band in 82 Sr Since the fraction of un-paired protons determines the variation of g factor with spin, the rapid rising of g factors at spins 6+ and 8+ can be interpreted by the increase of the unpaired proton alignment. Table 1 shows our calculated percentages of un-paired protons in the positive parity states in 82 Sr together with the percentages calculated by S. Cacciamani et al [11], in terms of the interacting boson model. Though the results given by S. Cacciamani et al show the breaking of the paired protons, the percentages of un-paired protons do not significantly change with spin. Their results could not be employed to explain our experimental values of g factors. The present calculation yields
P. Fan et al. / Nuclear Physics A 834 (2010) 107c–109c
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very small percentages of un-paired quasi-protons at the spins of 0+ , 2+ and 4+ , exhibiting the collective motion for which the g factor values are close to the collective value of Z/A. The calculated percentages are 11% and 65% at spin 6+ and 8+ , respectively, illustrating that the alignment of protons appears, which brings in an increase of g factor from spin 6+ . The quasi-particle excitation or alignment plays more important role at the spin 8+ and the g factor is greatly increased. This is in good agreement with our experimental results. Table 1 Percentage of broken-pair component in the wave function of positive-parity states in 82 Sr I 0+ 2+ 4+ 6+ 8+ 10+ Present results (%) 0.4 1 3 11 65 74 Result in Ref [11] (%) 15 18 19 21 22 23
4. Conclusion The g factors of the rotational states of the positive parity ground state band up to spin I=8 in even-even nucleus 82 Sr have been measured by a TMF-IMPAD method and calculated by a two quasi-particle plus a rotor model. The experimentally measured and calculated g factors are in good agreement. The low-lying states of 2+ and 4+ mainly exhibit collective motion and their g factors take a collective value of Z/A. At the higher states of 6+ and 8+ the g9/2 proton pair breaks and the un-paired protons are aligned. Therefore, the g factors at 6+ and 8+ are explicitly larger than the collective value and increase with the spin increasing. The present results clearly demonstrate the g9/2 proton alignment in ground state band of 82 Sr, which starts at spin I=6 and increases with spin. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
J.A. Sheikh, N. Rowley, M. A.Nagarajan et al., Phys. Rev. Lett. 64 (1990) 376 A.I.Kucharska, J.Billowes, C.J.Lister, J.Phys. G15 (1989) 1039 S. L. Tabor et al., Phys. Rev. C 49 (1994) 730 G. D. Johns et al., Phys. Rev. C53 (1996) 1541 Daqing Yuan, Chin. Phys. Lett., vol. 25, no. 10(2008) 3617 I. Ragnarsson and P. B. Semmes, Hyp. Int. 43(1988) 425 S.E. Larsson, G. Leander and I. Ragnarsson, Nucl. Phys A 307 (1978) 189 B. G. Carlsson and I. Ragnarsson, Phys. Rev. C 74 (2006) 044310 Tord Bengtsson And Ingemar Ragnarsson, Nucl. Phys A 436 (1985) 14 WALTER GREINER, Nucl. Phys. 80 (1966) 417-433 S. Cacciamani and G. Bonsignori, Phys. Rev. C 53 (1996) 1618
Experimental and Theoretical Study of Quasi-Particle Alignment in 82 Sr Ping Fan, Daqing Yuan, Yongnan Zheng, Yi Zuo, Dongmei Zhou, Xiaoguang Wu, Guangsheng Li, Lihua Zhu, Guoji Xu, Qiwen Fan, Xizhen Zhang and Shengyun Zhu China Institute of Atomic Energy, P.O. Box 275-50, Beijing 102413, China
∗
†
The g factors of the rotational states with spin up to 8+ of the ground state band in Sr have been measured by the Transient-Magnetic-Field Ion Implantation Perturbed Angular Distribution method following the 58 Ni(28 Si,4p)82 Sr reaction. The measured g factors rapidly increase with the increasing of the spin from spin 6+ to 8+ , showing the proton aligment. The present results can be well interpreted in the framework of the particle-rotor model. 82
1. Introduction One of the interesting features in mass A=80 region is interplay between the collective rotation and the quasi-particle alignment[1]. It is attractive to know whether nuclei gain their spins through collective motion or quasi-particle alignment. Nuclear magnetic dipole moments are closely connected and sensitive to nuclear structure. Hence measurements of magnetic moments can provide valuable information on nuclear structure of nuclei. Since the magnitude and sign of magnetic moments or g factors are dramatically affected by the quasi-particle alignment, g factor or magnetic moment is a very sensitive probe to investigate the quasi-particle alignment. The level scheme and the lifetimes of the rotational states in 82 Sr have been investigated by a number of groups [2–4]. So far, the pairing breaking and alignment of quasi-particles have not been studied directly by the g factor measurement. The present work was motivated to experimentally and theoretically determine the g factors of the ground state rotational band states in 82 Sr in order to study the quasi-particle alignment. 2. Experiment and Calculation g factors of rotational states of the ground state band (GSB) in 82 Sr were determined by the transient-magnetic-field ion implantation perturbed angular distribution(TMFIMPAD) method. The rotational states in 82 Sr were populated by the fusion-evaporation reaction 58 Ni(28 Si,4p)82 Sr with a 110 MeV Si beam from the HI-13 tandem accelerator at China Institute of Atomic Energy. The TMF-IMPAD set-up used in the experiment is mainly composed of a target chamber housing a 58 Ni-Fe-Cu three layer target, a polarizing ∗ The present work was supported by the National Natural Science Foundation of China under Grant No. 10435010 † corresponding author [email protected]
0375-9474/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2010.01.032
108c
P. Fan et al. / Nuclear Physics A 834 (2010) 107c–109c
magnet and γ-ray detector system. The details of the experiment can be found in Ref. [5]. In connection with the experimental work the g factors of the GSB in 82 Sr have been studied in the framework of the particle rotor model based on the Nilsson potential[6– 8]. On the basis of the model for one neutron and one proton in Ref.[6], the present model here is formulated for two identical protons outside the 80 36 kr44 core. The Nilsson parameters κ(N ) and μ(N ) are taken from Ref.[9], and the axial deformation parameter β2 is 0.33 deduced from experimental Qt value[3]. The rotational g factor, gR is 0.36, which is obtained after taking into account the factor that the pairing force acting between protons is larger than between neutrons[10]. And the orbital and spin g factors of the f ree valence protons are gl = 1 and gs = 0.6 × gs,proton respectively. 3. Results and Discussion The measured and calculated g factors for the rotational states up to spin 8+ of the positive parity ground state in 82 Sr are shown in Fig 1. It can be seen that the measured g factors rapidly increase with the increasing of the spin from spin 6+ . The averaged value of g factors for 2+ , 4+ and 6+ states is 0.51(13) that is consistent with the value of 0.50 (2) measured by A. I. Kucharskats et al [2]. In their paper the respective g factors of the 2+ , 4+ and 6+ states were not given.
Figure 1. Measured and calculated g factors of rotational states of ground state band in 82 Sr Since the fraction of un-paired protons determines the variation of g factor with spin, the rapid rising of g factors at spins 6+ and 8+ can be interpreted by the increase of the unpaired proton alignment. Table 1 shows our calculated percentages of un-paired protons in the positive parity states in 82 Sr together with the percentages calculated by S. Cacciamani et al [11], in terms of the interacting boson model. Though the results given by S. Cacciamani et al show the breaking of the paired protons, the percentages of un-paired protons do not significantly change with spin. Their results could not be employed to explain our experimental values of g factors. The present calculation yields
P. Fan et al. / Nuclear Physics A 834 (2010) 107c–109c
109c
very small percentages of un-paired quasi-protons at the spins of 0+ , 2+ and 4+ , exhibiting the collective motion for which the g factor values are close to the collective value of Z/A. The calculated percentages are 11% and 65% at spin 6+ and 8+ , respectively, illustrating that the alignment of protons appears, which brings in an increase of g factor from spin 6+ . The quasi-particle excitation or alignment plays more important role at the spin 8+ and the g factor is greatly increased. This is in good agreement with our experimental results. Table 1 Percentage of broken-pair component in the wave function of positive-parity states in 82 Sr I 0+ 2+ 4+ 6+ 8+ 10+ Present results (%) 0.4 1 3 11 65 74 Result in Ref [11] (%) 15 18 19 21 22 23
4. Conclusion The g factors of the rotational states of the positive parity ground state band up to spin I=8 in even-even nucleus 82 Sr have been measured by a TMF-IMPAD method and calculated by a two quasi-particle plus a rotor model. The experimentally measured and calculated g factors are in good agreement. The low-lying states of 2+ and 4+ mainly exhibit collective motion and their g factors take a collective value of Z/A. At the higher states of 6+ and 8+ the g9/2 proton pair breaks and the un-paired protons are aligned. Therefore, the g factors at 6+ and 8+ are explicitly larger than the collective value and increase with the spin increasing. The present results clearly demonstrate the g9/2 proton alignment in ground state band of 82 Sr, which starts at spin I=6 and increases with spin. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
J.A. Sheikh, N. Rowley, M. A.Nagarajan et al., Phys. Rev. Lett. 64 (1990) 376 A.I.Kucharska, J.Billowes, C.J.Lister, J.Phys. G15 (1989) 1039 S. L. Tabor et al., Phys. Rev. C 49 (1994) 730 G. D. Johns et al., Phys. Rev. C53 (1996) 1541 Daqing Yuan, Chin. Phys. Lett., vol. 25, no. 10(2008) 3617 I. Ragnarsson and P. B. Semmes, Hyp. Int. 43(1988) 425 S.E. Larsson, G. Leander and I. Ragnarsson, Nucl. Phys A 307 (1978) 189 B. G. Carlsson and I. Ragnarsson, Phys. Rev. C 74 (2006) 044310 Tord Bengtsson And Ingemar Ragnarsson, Nucl. Phys A 436 (1985) 14 WALTER GREINER, Nucl. Phys. 80 (1966) 417-433 S. Cacciamani and G. Bonsignori, Phys. Rev. C 53 (1996) 1618