激发态晕核寻找及晕核性质研究
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摘要
实验测量了11B(d,p)和12C(d，p)反应中12B和13C几个感兴趣的核态角分布，
分别用DWBA方法和ANC方法从角分布数据中抽取了各核态外层中子的密度
分布、RMS半径以及外层核子的贡献等，对这两种方法作了比较。由于ANC方
法的模型近似无关性，采用该方法给出的值作为最终结果：13C基态、第一和第
三激发态ANC系数分别为1． 93±0． 17 fm-1/2、 1． 84±0． 16 fm-1/2和0． 15±0． 01 fm-1/2；
RMS半径分别为3． 39±0． 31 fm、5． 04±0． 75 fm和3． 68±0． 40 fm；相应的外层中子
处于势阱外几率分别为14． 3％、50． 3％和25． 2％。结果证实13C的第一激发态为单
中子晕核态，首次从实验上证实在B稳定线上存在激发的晕核态。同时得到12B
基态、第二和第三激发态ANC系数分别为1． 16±0． 10 fm-1/2、 1． 34±0． 12 fm-1/2和
0． 94±0． 08fm-1/2;RMS半径分别为3． 16±0． 32fm、4． 01±0． 61fm和5． 64±0． 90fm；
相应的外层中子处于势阱外几率分别为19． 9％、53． 6％和66． 8%。结果显示12B第
二、三激发态为单中子晕核态，这是在B稳定线附近找到的第二个核新的晕核
态。
利用(d，p)反应得到的2s1／2激发态ANC系数，计算了核天体物理中感兴趣
的11B(n，γ)12B和12C(n，γ)13C的辐射俘获截面。对12C(n，γ)13C的计算结果与实验
值很好地符合，证明这种ANC方法行之有效。由于直接测量上的困难，间接用
ANC方法计算它们的截面显得尤为重要。这些辐射俘获截面的大小，直接影响
到A>12以上元素合成的途径。
通过论文的实验工作，我们深入了解并改进了单粒子势模型。利用该模型，
计算了一些轻核外层核子的分布，预言了一些尚未发现的晕、皮核态。对49Ca
和209pb各单粒子激发态外层中子的计算表明：在中重和重核区存在中子晕、皮
核。从实验上证实这些核态的存在是我们今后的主要工作之一。此外，根据单粒
子势模型计算结果，给出了更合理的Woods-Saxon势下晕结构形成的必要条件，
比目前所知的条件宽松。首次给出质子晕形成的必要条件和可能存在的区域。这
对寻找新的晕、皮核态有现实的指导意义。
此外，论文中还讨论了一些令人感兴趣的问题，如核子能级组态对密度分布
的影响、中子晕存在时2s1/2与1d5／2能级次序的翻转、质子晕核的存在以及弱束
缚条件下新幻数N=16的出现等等。
Dedicated to my wife and daughter
for freeing me to pursue my dream.
Angular distributions for some interesting states of 12B and 13C have been experimentally measured in HB(d,p) and 12C(d,p) reactions. The density distributions,RMS (Root Mean Square) radii,contributions of outside nucleon,etc.,of the valence neutrons in these states are extracted by DWBA (Distorted Wave Born Approximation) method and ANC (Asymptotic Normalization Coefficient) method,respectively. Additionally,the comparison between these two methods is made. Due to the approximate model-independence of ANC method,the final results are adopt the values given by the ANC method. The ANCs are 1.93+0.17 fin-1/2,1.84+0.16 fm-1/2 and 0.15+0.01 fm-1/2;RMS radii are 3.39+0.31 fin,5.04+0.75 fin and 3.68+0.40 fin;and the probabilities of valence neutrons outside the potentials are 14.3%,50.3% and 25.2% for the ground state,the first and third excited states of 13C,respectively. The results make sure that the first excited state of 13C is the one-neutron halo state. This is the first time to experimentally confirm that
the excited halo state can exist on the p stable line. Meanwhile,the ANCs are 1.16+0.10 fin-1/2,1.34+0.12 fm-1/2 and 0.94+0.08 fm-1/2;RMS radii are 3.16+0.32 fm,4.01+0.61 fin and 5.64+0.90 fin;and the probabilities of valence neutrons outside the potentials are 19.9%,53.6% and 66.8% for the ground state,the second and third excited states of 12B,respectively. The results show that the second and third excited states of 12B are one-neutron halo states. It is the second nucleus to be found with new halo states near the p stable line.
Using the ANCs of the 2s 1/2 states given by the (d,p) reactions,the radioactive capture cross sections of uB(n,Y)'2B and 12C(n,y)'3C,of which are interesting in the astrophysics are calculated. The calculation results are good in agreement with the experimental ones for the 12C(n,y)13C reaction. It is proved that such ANC method works perfectly. Due to the difficulty in the direct measurement,it is important to calculate these cross sections by the indirect ANC method. The values of these cross sections affect the path to synthesize the A > 12 elements.
Through the experimental work of this thesis,the single-particle potential model is comprehended and some improvements are made. Utilizing this model,the distributions of valence nucleons are calculated for some light nuclei. Some new halo or skin states are predicted. Moreover,the calculations of the valence neutrons for the single-particle states of 49Ca and 209Pb show that the neutron halos or skins can exist in the region of heavy nuclei. Search for these nuclear states is one of our tasks in the
future. Furthermore,according to the results of the single-particle potential model,the more natural necessary condition for the formation of the halo structure is given with the Woods-Saxon potential. This condition is more loser than the current one. The necessary condition of proton halo occurrence is first time given out and the existence region is pointed out. All of these have realistic meaning for searching the new halo or skin nuclear states.
In addition,some interesting questions are discussed in this thesis,for example,the effect of the configuration of nucleon on the density distributions,the sequence overturn between the 2s1/2 and 1d5/2 energy levels when the neutron halo exists,the existence of the proton halo nucleus,and the appearance of new magic number (N=16) under the weak bounded condition,etc..
Anyway,halo is a charming phenomenon,waiting for us to discover it.
分别用DWBA方法和ANC方法从角分布数据中抽取了各核态外层中子的密度
分布、RMS半径以及外层核子的贡献等，对这两种方法作了比较。由于ANC方
法的模型近似无关性，采用该方法给出的值作为最终结果：13C基态、第一和第
三激发态ANC系数分别为1． 93±0． 17 fm-1/2、 1． 84±0． 16 fm-1/2和0． 15±0． 01 fm-1/2；
RMS半径分别为3． 39±0． 31 fm、5． 04±0． 75 fm和3． 68±0． 40 fm；相应的外层中子
处于势阱外几率分别为14． 3％、50． 3％和25． 2％。结果证实13C的第一激发态为单
中子晕核态，首次从实验上证实在B稳定线上存在激发的晕核态。同时得到12B
基态、第二和第三激发态ANC系数分别为1． 16±0． 10 fm-1/2、 1． 34±0． 12 fm-1/2和
0． 94±0． 08fm-1/2;RMS半径分别为3． 16±0． 32fm、4． 01±0． 61fm和5． 64±0． 90fm；
相应的外层中子处于势阱外几率分别为19． 9％、53． 6％和66． 8%。结果显示12B第
二、三激发态为单中子晕核态，这是在B稳定线附近找到的第二个核新的晕核
态。
利用(d，p)反应得到的2s1／2激发态ANC系数，计算了核天体物理中感兴趣
的11B(n，γ)12B和12C(n，γ)13C的辐射俘获截面。对12C(n，γ)13C的计算结果与实验
值很好地符合，证明这种ANC方法行之有效。由于直接测量上的困难，间接用
ANC方法计算它们的截面显得尤为重要。这些辐射俘获截面的大小，直接影响
到A>12以上元素合成的途径。
通过论文的实验工作，我们深入了解并改进了单粒子势模型。利用该模型，
计算了一些轻核外层核子的分布，预言了一些尚未发现的晕、皮核态。对49Ca
和209pb各单粒子激发态外层中子的计算表明：在中重和重核区存在中子晕、皮
核。从实验上证实这些核态的存在是我们今后的主要工作之一。此外，根据单粒
子势模型计算结果，给出了更合理的Woods-Saxon势下晕结构形成的必要条件，
比目前所知的条件宽松。首次给出质子晕形成的必要条件和可能存在的区域。这
对寻找新的晕、皮核态有现实的指导意义。
此外，论文中还讨论了一些令人感兴趣的问题，如核子能级组态对密度分布
的影响、中子晕存在时2s1/2与1d5／2能级次序的翻转、质子晕核的存在以及弱束
缚条件下新幻数N=16的出现等等。
Dedicated to my wife and daughter
for freeing me to pursue my dream.
Angular distributions for some interesting states of 12B and 13C have been experimentally measured in HB(d,p) and 12C(d,p) reactions. The density distributions,RMS (Root Mean Square) radii,contributions of outside nucleon,etc.,of the valence neutrons in these states are extracted by DWBA (Distorted Wave Born Approximation) method and ANC (Asymptotic Normalization Coefficient) method,respectively. Additionally,the comparison between these two methods is made. Due to the approximate model-independence of ANC method,the final results are adopt the values given by the ANC method. The ANCs are 1.93+0.17 fin-1/2,1.84+0.16 fm-1/2 and 0.15+0.01 fm-1/2;RMS radii are 3.39+0.31 fin,5.04+0.75 fin and 3.68+0.40 fin;and the probabilities of valence neutrons outside the potentials are 14.3%,50.3% and 25.2% for the ground state,the first and third excited states of 13C,respectively. The results make sure that the first excited state of 13C is the one-neutron halo state. This is the first time to experimentally confirm that
the excited halo state can exist on the p stable line. Meanwhile,the ANCs are 1.16+0.10 fin-1/2,1.34+0.12 fm-1/2 and 0.94+0.08 fm-1/2;RMS radii are 3.16+0.32 fm,4.01+0.61 fin and 5.64+0.90 fin;and the probabilities of valence neutrons outside the potentials are 19.9%,53.6% and 66.8% for the ground state,the second and third excited states of 12B,respectively. The results show that the second and third excited states of 12B are one-neutron halo states. It is the second nucleus to be found with new halo states near the p stable line.
Using the ANCs of the 2s 1/2 states given by the (d,p) reactions,the radioactive capture cross sections of uB(n,Y)'2B and 12C(n,y)'3C,of which are interesting in the astrophysics are calculated. The calculation results are good in agreement with the experimental ones for the 12C(n,y)13C reaction. It is proved that such ANC method works perfectly. Due to the difficulty in the direct measurement,it is important to calculate these cross sections by the indirect ANC method. The values of these cross sections affect the path to synthesize the A > 12 elements.
Through the experimental work of this thesis,the single-particle potential model is comprehended and some improvements are made. Utilizing this model,the distributions of valence nucleons are calculated for some light nuclei. Some new halo or skin states are predicted. Moreover,the calculations of the valence neutrons for the single-particle states of 49Ca and 209Pb show that the neutron halos or skins can exist in the region of heavy nuclei. Search for these nuclear states is one of our tasks in the
future. Furthermore,according to the results of the single-particle potential model,the more natural necessary condition for the formation of the halo structure is given with the Woods-Saxon potential. This condition is more loser than the current one. The necessary condition of proton halo occurrence is first time given out and the existence region is pointed out. All of these have realistic meaning for searching the new halo or skin nuclear states.
In addition,some interesting questions are discussed in this thesis,for example,the effect of the configuration of nucleon on the density distributions,the sequence overturn between the 2s1/2 and 1d5/2 energy levels when the neutron halo exists,the existence of the proton halo nucleus,and the appearance of new magic number (N=16) under the weak bounded condition,etc..
Anyway,halo is a charming phenomenon,waiting for us to discover it.
引文
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[3] R．J．Glauber，Lectures in Theoretical Physics(Interscience，New York)1，315 (1959) ．
[4] 胡济民等编，原子核理论(第一卷)，P.10-14，原子能出版社，1993。
[5] M. Fukuda, T. Ichihara, N. Inabeet et al., Phys. Lett. B268, 339 (1991) .
[6] D. Bazin, B.A. Brown, J. Brown et al., Phys. Rev. Lett. 74, 3569 (1995) .
[7] I. Tanihata, T. Kobayashi, T. Suzuki et al., Phys. Lett. B287, 307 (1992) .
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[9] T. Suzuki, R. Kanungo, O. Bochkarev et al., Nucl. Phys. A658, 313 (1999) .
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[13] V. Guimaraes, J.J. Kolata, D. Peterson et al., Phys. Rev. Lett. 84, 1862 (2000) .
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[18] K. Riisager, Rev. Mod. Phys. 66, 1105 (1994) .
[19] P.G. Hansen, A.S. Jensen, and B. Jonson, Annu. Rev. Nucl. Part. Sci. 45, 591 (1995) .
[20] I. Tanihata, J. Phys. G22,157 (1996) .
[21] D.V. Fedorov, A.S. Jensen, and K. Riisager, Phys. Rev. C49, 201 (1994) ; Phys. Rev. C50,2372 (1994) ; Phys. Lett. B312,1 (1993) .
[22] A.S. Jensen, K. Riisager, Phys. Lett. B480,39 (2000) .
[23] T. Otsuka, N. Fukunishi, and H. Sagawa, Phys. Rev. Lett. 70,1385 (1993) .
[24] Y. Nagai, M. Igashira, N. Mukai et al., Astrophys. J. 381,444 (1991) .
[25] T. Ohsaki, Y. Nagai, M. Igashira et al., Astrophys. J. 422,912 (1994) .
[26] J.M. Blatt and V.F. Weisskopf, Theoretical Nuclear Physics, Wiley, New York, 1952．
[27] T. Otsuka, M. Ishihara, N. Fukunishi et al., Phys. Rev. C49, R2289 (1994) .
[28] A. Mengoni, T. Otsuka, and M. Ishihara, Phys. Rev. C52, R2334 (1995) .
[29] M. Dufour and P. Descouvemont, Phys. Rev. C56,1831(1997) .
[30] R. Anne, S.E. Arnell, R. Bimbot et al., Phys. Lett. B304, 55 (1993) .
[31] T. Minamisono, T. Ohtsubo, I. Minami et al., Phys. Rev. Lett. 69,2058 (1992) .
[32] R．Lewis and A．C．Hayes，Phys．Rev．C59，1211(1999) ．
[33] R．Morlock，R．Kung，A．Mayer et al．，Phys．Rev．Lett．79，3837(1997) ．
[34] 林承键等人，国家自然科学基金申请书，2001。(注：该基金已获批准。)
[35] R.A. Malaney and W.A. Fowler, Astrophys. J. 133, 14 (1988) .
[36] J.H. Applegate and C.J. Hogan, Phys. Rev. D31,3037 (1985) .
[37] T. Kajino, G.J. Mathews, and G.M. Fuller, Astrophys. J. 364, 7 (1990) .
[38] R.L. Mackin, Astrophys. J. 357,649 (1990) .
[39] Y. Nagai, M. Igashira, K. Takeda et al., Astrophys. J. 372, 683 (1991) .
[40] H.M. Xu, C.A. Gagliardi, R.E. Tribble et al., Phys. Rev. Lett. 73, 2027 (1994) .
[41] J. Lang, J. Liechti, R. Muller et al., Nucl. Phys. A477, 77 (1988) .
[42] J.A.R. Griffith, M. Irshad, O. Karban et al., Nucl. Phys. A167, 87 (1971) .
[43] S.A. Goncharov, I.R. Gulamov, E.A. Romanovsky et al., J. Phys. G15, 1431 (1989) .
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