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Systematic study of the surface diffuseness of nuclear potential with high precision large-angle quasi-elastic scattering
Nuclear Physics A 834 (2010) 189c–191c www.elsevier.com/locate/nuclphysa
Systematic study of the surface diffuseness of nuclear potential with high precision large-angle quasi-elastic scattering H.M. Jiaa∗ , C.J. Lina , H.Q. Zhanga , F. Yanga , Z.H. Liua , F. Jiaa , X.X. Xua , S.T. Zhanga , and K. Haginob a
China Institute of Atomic Energy, P. O. Box 275(10), Beijing 102413, P. R. China
b
Department of Physics, Tohoku University, Sendai 980-8578, Japan
The excitation functions of quasi-elastic scattering at a backward angle have been measured for the systems of 16 O + 208 Pb, 196 Pt, 184 W, and 154,152 Sm at energies well below the Coulomb barrier. The surface diffuseness parameters of the nuclear potentials have been extracted from both single-channel and coupled-channels calculations. Considering the coupling effects, the extracted diffuseness parameters are a = 0.64 – 0.69 fm, which are close to the values extracted from the systematic analysis of elastic and inelastic scattering data. On the other hand, single-channel calculations give somewhat larger values in the range from 0.68 to 0.77 fm, especially for systems with deformed targets. 1. INTRODUCTION Recently, Newton et al. [1] found that the diffuseness parameters extracted from the fusion excitation functions above the barrier energies are obviously greater than the commonly accepted value of 0.63 fm. The reason for the large discrepancies in the diffuseness parameter extracted from scattering and fusion analyses remains unknown. Recently, large-angle quasi-elastic scattering has also been used to study this subject [2–5]. Additionally, Hinde et al. [6] have used the oscillatory quasi-elastic Mott scattering at nearbarrier energies to determine the surface diffuseness parameter for a symmetric system. In this contribution, we would like to present some of our experimental analysis of the diffuseness parameters extracted from the spherical and deformed reaction systems, and discuss the coupling effects on the quasi-elastic scattering at deep subbarrier energies. 2. EXPERIMENTAL DATA AND ANALYSIS The experiment was performed at the HI-13 tandem accelerator of the China Institute of Atomic Energy. More details can be found in Ref. [7]. The single-channel and coupledchannels calculations were preformed with a modified version of CCFULL code [8] for quasi-elastic scattering by using a nuclear potential of Woods-Saxon form. Following the procedure of Ref. [5], an imaginary potential with W = 30 MeV, aw = 0.1 fm, and rw = 0.8 fm, which was well kept inside the Coulomb barrier, was chosen to represent the ∗
Corresponding author, Email address: [email protected]
0375-9474/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2009.12.036
190c
H.M. Jia et al. / Nuclear Physics A 834 (2010) 189c–191c
Table 1 The fusion barrier height energies used to determine the real part of the nuclear potential in the calculations. Reaction VB (MeV) Method of determination 16 O + 208 Pb 74.52 Ref. [1] 16 O + 196 Pt 71.37 Scaled from the 16 O+194 Pt data of Ref. [1] 16 O + 184 W 69.04 Scaled from the 16 O+186 W data of Ref. [1] 16 154 O + Sm 59.35 Ref. [1] 16 O + 152 Sm 59.53 Scaled from the16 O+154 Sm data of Ref. [1] Table 2 Diffuseness parameters extracted from the single-channel (SC) and coupled-channels (CC) calculations for all the studied systems. N is the number of the experimental data points. Reaction aSC (fm) χ2 /N aCC (fm) χ2 /N 16 208 O + Pb 0.69(0.02) 1.38 0.69(0.02) 1.21 16 O + 196 Pt 0.68(0.02) 0.63 0.65(0.02) 0.56 16 O + 184 W 0.75(0.03) 0.63 0.65(0.02) 0.58 16 O + 154 Sm 0.75(0.03) 1.91 0.64(0.02) 1.21 16 O + 152 Sm 0.77(0.02) 1.38 0.64(0.02) 1.50 rather small absorption from barrier penetration in the calculations. The parameters of the WS real potential were searched for the optimal fitting to the quasi-elastic data. At the same time, they had to reproduce the expected average fusion barrier height energy. The fusion barriers, obtained from Ref. [1], or determined using the Coulomb 1/3 scaling parameter Zp Zt /(Ap1/3 + At ) from the neighboring reaction systems, are listed in Table 1. For consistency, V0 = 100 MeV for both single-channel and coupled-channels calculations was taken for all the reactions. For a fixed V0 , the r0 and a of the real part were searched for the best data fits. The coupling to the first 3− state in 16 O was not included in the coupled-channels calculations. The experimental excitation functions of quasi-elastic scattering at θlab = 175 ◦ for all the reactions are shown in Fig. 1. The dashed and solid lines are the results of CCFULL calculations with and without coupling to the low inelastic excitation states of the targets, respectively. The main result is shown in Table 2. This result indicates that both singlechannel and coupled-channels calculations give the similar diffuseness parameter values and they are consistent with the values of the elastic scattering for the spherical systems. While for the deformed systems, the coupling effect is important even at deep subbarrier energies. The coupled-channels calculations give the diffuseness parameters similar as elastic scattering. But the single-channel calculations obtain larger values in the range of 0.68-0.77 fm. 3. CONCLUSION The excitation functions of quasi-elastic scattering at a backward angle have been measured for the systems of 16 O + 208 Pb, 196 Pt, 184 W, and 154,152 Sm at deep subbarrier energies. Single-channel fits to quasi-elastic scattering data give values for the diffuseness
H.M. Jia et al. / Nuclear Physics A 834 (2010) 189c–191c
191c
Figure 1. The ratio of the quasi-elastic to the Rutherford cross sections for the reactions. The dashed and solid lines represent the results of CCFULL calculations with and without coupling to the low inelastic excitation states of the targets, respectively. parameter a ranging between 0.68 and 0.77 fm. While the weighted value reduces to a = 0.65 ± 0.01 fm considering the coupling effects to the low excited states of the targets. Similar to the result of Ref. [5], the value of diffuseness parameter is consistent with the result of elastic scattering taking the coupled-channels effect into account in large-angle quasi-elastic scattering at deep subbarrier energies. So further theoretical work should be performed to research the reaction mechanism in the processes of the fusion reaction. 4. ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China under Grant Nos. 10575134, 10675169, 10735100, the Major State Basic Research Developing Program under Grant No. 2007CB815003, and the Japanese Ministry of Education, Culture, Sports, Science and Technology by Grant-in-Aid for Scientific Research under the program number 19740115. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
J.O. Newton et al., Phys. Rev. C 70, 024605 (2004). K. Hagino et al., Phys. Rev. C 71, 044612 (2005). K. Washiyama, K. Hagino, M. Dasgupta, Phys. Rev. C 73, 034607 (2006). L.R. Gasques et al., Phys. Rev. C 76, 024612 (2007). M. Evers et al., Phys. Rev. C 78, 034614 (2008). D.J. Hinde et al., Phys. Rev. C 76, 014617 (2007). C.J. Lin et al., Phys. Rev. C 79, 064603 (2009). K. Hagino, N. Rowley and A.T. Kruppa, Comput. Phys. Commun. 123, 143 (1999).
Systematic study of the surface diffuseness of nuclear potential with high precision large-angle quasi-elastic scattering H.M. Jiaa∗ , C.J. Lina , H.Q. Zhanga , F. Yanga , Z.H. Liua , F. Jiaa , X.X. Xua , S.T. Zhanga , and K. Haginob a
China Institute of Atomic Energy, P. O. Box 275(10), Beijing 102413, P. R. China
b
Department of Physics, Tohoku University, Sendai 980-8578, Japan
The excitation functions of quasi-elastic scattering at a backward angle have been measured for the systems of 16 O + 208 Pb, 196 Pt, 184 W, and 154,152 Sm at energies well below the Coulomb barrier. The surface diffuseness parameters of the nuclear potentials have been extracted from both single-channel and coupled-channels calculations. Considering the coupling effects, the extracted diffuseness parameters are a = 0.64 – 0.69 fm, which are close to the values extracted from the systematic analysis of elastic and inelastic scattering data. On the other hand, single-channel calculations give somewhat larger values in the range from 0.68 to 0.77 fm, especially for systems with deformed targets. 1. INTRODUCTION Recently, Newton et al. [1] found that the diffuseness parameters extracted from the fusion excitation functions above the barrier energies are obviously greater than the commonly accepted value of 0.63 fm. The reason for the large discrepancies in the diffuseness parameter extracted from scattering and fusion analyses remains unknown. Recently, large-angle quasi-elastic scattering has also been used to study this subject [2–5]. Additionally, Hinde et al. [6] have used the oscillatory quasi-elastic Mott scattering at nearbarrier energies to determine the surface diffuseness parameter for a symmetric system. In this contribution, we would like to present some of our experimental analysis of the diffuseness parameters extracted from the spherical and deformed reaction systems, and discuss the coupling effects on the quasi-elastic scattering at deep subbarrier energies. 2. EXPERIMENTAL DATA AND ANALYSIS The experiment was performed at the HI-13 tandem accelerator of the China Institute of Atomic Energy. More details can be found in Ref. [7]. The single-channel and coupledchannels calculations were preformed with a modified version of CCFULL code [8] for quasi-elastic scattering by using a nuclear potential of Woods-Saxon form. Following the procedure of Ref. [5], an imaginary potential with W = 30 MeV, aw = 0.1 fm, and rw = 0.8 fm, which was well kept inside the Coulomb barrier, was chosen to represent the ∗
Corresponding author, Email address: [email protected]
0375-9474/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2009.12.036
190c
H.M. Jia et al. / Nuclear Physics A 834 (2010) 189c–191c
Table 1 The fusion barrier height energies used to determine the real part of the nuclear potential in the calculations. Reaction VB (MeV) Method of determination 16 O + 208 Pb 74.52 Ref. [1] 16 O + 196 Pt 71.37 Scaled from the 16 O+194 Pt data of Ref. [1] 16 O + 184 W 69.04 Scaled from the 16 O+186 W data of Ref. [1] 16 154 O + Sm 59.35 Ref. [1] 16 O + 152 Sm 59.53 Scaled from the16 O+154 Sm data of Ref. [1] Table 2 Diffuseness parameters extracted from the single-channel (SC) and coupled-channels (CC) calculations for all the studied systems. N is the number of the experimental data points. Reaction aSC (fm) χ2 /N aCC (fm) χ2 /N 16 208 O + Pb 0.69(0.02) 1.38 0.69(0.02) 1.21 16 O + 196 Pt 0.68(0.02) 0.63 0.65(0.02) 0.56 16 O + 184 W 0.75(0.03) 0.63 0.65(0.02) 0.58 16 O + 154 Sm 0.75(0.03) 1.91 0.64(0.02) 1.21 16 O + 152 Sm 0.77(0.02) 1.38 0.64(0.02) 1.50 rather small absorption from barrier penetration in the calculations. The parameters of the WS real potential were searched for the optimal fitting to the quasi-elastic data. At the same time, they had to reproduce the expected average fusion barrier height energy. The fusion barriers, obtained from Ref. [1], or determined using the Coulomb 1/3 scaling parameter Zp Zt /(Ap1/3 + At ) from the neighboring reaction systems, are listed in Table 1. For consistency, V0 = 100 MeV for both single-channel and coupled-channels calculations was taken for all the reactions. For a fixed V0 , the r0 and a of the real part were searched for the best data fits. The coupling to the first 3− state in 16 O was not included in the coupled-channels calculations. The experimental excitation functions of quasi-elastic scattering at θlab = 175 ◦ for all the reactions are shown in Fig. 1. The dashed and solid lines are the results of CCFULL calculations with and without coupling to the low inelastic excitation states of the targets, respectively. The main result is shown in Table 2. This result indicates that both singlechannel and coupled-channels calculations give the similar diffuseness parameter values and they are consistent with the values of the elastic scattering for the spherical systems. While for the deformed systems, the coupling effect is important even at deep subbarrier energies. The coupled-channels calculations give the diffuseness parameters similar as elastic scattering. But the single-channel calculations obtain larger values in the range of 0.68-0.77 fm. 3. CONCLUSION The excitation functions of quasi-elastic scattering at a backward angle have been measured for the systems of 16 O + 208 Pb, 196 Pt, 184 W, and 154,152 Sm at deep subbarrier energies. Single-channel fits to quasi-elastic scattering data give values for the diffuseness
H.M. Jia et al. / Nuclear Physics A 834 (2010) 189c–191c
191c
Figure 1. The ratio of the quasi-elastic to the Rutherford cross sections for the reactions. The dashed and solid lines represent the results of CCFULL calculations with and without coupling to the low inelastic excitation states of the targets, respectively. parameter a ranging between 0.68 and 0.77 fm. While the weighted value reduces to a = 0.65 ± 0.01 fm considering the coupling effects to the low excited states of the targets. Similar to the result of Ref. [5], the value of diffuseness parameter is consistent with the result of elastic scattering taking the coupled-channels effect into account in large-angle quasi-elastic scattering at deep subbarrier energies. So further theoretical work should be performed to research the reaction mechanism in the processes of the fusion reaction. 4. ACKNOWLEDGEMENTS This work was supported by the National Natural Science Foundation of China under Grant Nos. 10575134, 10675169, 10735100, the Major State Basic Research Developing Program under Grant No. 2007CB815003, and the Japanese Ministry of Education, Culture, Sports, Science and Technology by Grant-in-Aid for Scientific Research under the program number 19740115. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
J.O. Newton et al., Phys. Rev. C 70, 024605 (2004). K. Hagino et al., Phys. Rev. C 71, 044612 (2005). K. Washiyama, K. Hagino, M. Dasgupta, Phys. Rev. C 73, 034607 (2006). L.R. Gasques et al., Phys. Rev. C 76, 024612 (2007). M. Evers et al., Phys. Rev. C 78, 034614 (2008). D.J. Hinde et al., Phys. Rev. C 76, 014617 (2007). C.J. Lin et al., Phys. Rev. C 79, 064603 (2009). K. Hagino, N. Rowley and A.T. Kruppa, Comput. Phys. Commun. 123, 143 (1999).