~（16）O的4α结构低激发态波函数及P-~（16）O非弹性散射
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摘要
在α粒子模型下,将~(16)O原子核看成由四个独立α粒子构成(即看成四粒子系统),每个α粒子被看成无自旋无结构的点粒子,并在其他α粒子的平均场中运动(即平均场近似和独立粒子运动近似)。在平均场和独立粒子运动近似下~(16)O原子核的基态波函数写成四个α粒子基态波函数的乘积,~(16)O原子核的激发归因于核内α粒子的激发,核的激发态波函数对应α粒子激发态波函数得出。
~(16)O原子核内α粒子跃迁密度由~(16)O原子核内α粒子结构下的基态波函数和激发态波函数得出。在球平均场近似下波函数可以分解为径向部分和球谐部分,其径向部分又可以按谐振子径向波函数展开。文中对每个激发态波函数径向部分分别以两项和三项谐振子径向波函数展开。其参数利用最佳平方拟合程序拟合电子散射~(16)O跃迁形状因子确定。对拟合所得的不同的激发态波函数~(16)O原子核的跃迁密度是不同的。
给出的一组参数化的~(16)O原子核内α粒子的跃迁密度,这一跃迁密度对于利用中能质子、π子、α粒子、~(12)C核、~(16)O核对~(16)O原子核散射来研究~(16)O原子核的α粒子结构问题是必要的输入量。
Based on theα-particle model,~(16)O core can be regarded as being made up ofαclusters(i.e.a four-αparticle system).Theαclusters are considered to be spinless point particles without any internal structure,and eachα-particle is viewed as moving in an external field created by the remainingαparticles(i.e,the mean-field approximation and independent-particle motion).In the mean-field approximation and independent-particle motion the wave-function of the ground state of ~(16)O core is thus a product of single-α-particle wave functions.Excitation of ~(16)O core is attributed to excitation ofα-particle in ~(16)O core.The excited state wave-function of ~(16)O core can be obtained by means of the corresponding excited state wave-function ofα-particle in the core.
Theα-particle transition density in the ~(16)O core can be obtained by the wave-function of the ground state and excited state of ~(16)O core based on theα-particle model.In the mean-field approximation the wave function can be separated into radial part and sphere-humorous part,and the radial part can be expended according to the radial resonance wave-functions.The radial part of each excited state wave-function is expanded in two or three term radial resonance wave-functions whose parameters are decided by fitting to ~(16)O transition-shape-factor electron scattering experimental data.In this way the ~(16)O transition densities are different corresponding different excited state wave-functions.
The parameterizedα-particle transition density in the ~(16)O core are obtained.This amplitude is useful as input for studying theα-particle structure of ~(16)O core by means of intermediate energy proton、pion、alpha particle and ~(12)C、~(16)O core.
~(16)O原子核内α粒子跃迁密度由~(16)O原子核内α粒子结构下的基态波函数和激发态波函数得出。在球平均场近似下波函数可以分解为径向部分和球谐部分,其径向部分又可以按谐振子径向波函数展开。文中对每个激发态波函数径向部分分别以两项和三项谐振子径向波函数展开。其参数利用最佳平方拟合程序拟合电子散射~(16)O跃迁形状因子确定。对拟合所得的不同的激发态波函数~(16)O原子核的跃迁密度是不同的。
给出的一组参数化的~(16)O原子核内α粒子的跃迁密度,这一跃迁密度对于利用中能质子、π子、α粒子、~(12)C核、~(16)O核对~(16)O原子核散射来研究~(16)O原子核的α粒子结构问题是必要的输入量。
Based on theα-particle model,~(16)O core can be regarded as being made up ofαclusters(i.e.a four-αparticle system).Theαclusters are considered to be spinless point particles without any internal structure,and eachα-particle is viewed as moving in an external field created by the remainingαparticles(i.e,the mean-field approximation and independent-particle motion).In the mean-field approximation and independent-particle motion the wave-function of the ground state of ~(16)O core is thus a product of single-α-particle wave functions.Excitation of ~(16)O core is attributed to excitation ofα-particle in ~(16)O core.The excited state wave-function of ~(16)O core can be obtained by means of the corresponding excited state wave-function ofα-particle in the core.
Theα-particle transition density in the ~(16)O core can be obtained by the wave-function of the ground state and excited state of ~(16)O core based on theα-particle model.In the mean-field approximation the wave function can be separated into radial part and sphere-humorous part,and the radial part can be expended according to the radial resonance wave-functions.The radial part of each excited state wave-function is expanded in two or three term radial resonance wave-functions whose parameters are decided by fitting to ~(16)O transition-shape-factor electron scattering experimental data.In this way the ~(16)O transition densities are different corresponding different excited state wave-functions.
The parameterizedα-particle transition density in the ~(16)O core are obtained.This amplitude is useful as input for studying theα-particle structure of ~(16)O core by means of intermediate energy proton、pion、alpha particle and ~(12)C、~(16)O core.
引文
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[18]Li Qing-run,Pion-oxygen scattering in the four-α-particle model,[J]Phys.Rev.C,1984,30:1284.
[19]何淦明,李清润,中能p-~(12)C散射截面和自旋量的研究[J]高能物理与核物理,1991,15:623
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[23]郝云荣,杨永栩,低能区的~(16)O-~(12)C散射折叠模型研究[J]广西师范大学学报自然科学版,2008,26:23.
[24]郝云荣,用α粒子折叠模型光学势研究~(16)O-~(12)C散射[D]桂林:广西师范大学,2006.
[25]杨永栩,李清润,124MeV下~(16)O-~(16)O弹性散射的折叠模型[J]高能物理与核物理,1997,21:645-647.
[26]杨永栩,李清润,α粒子结构下的π-~(12)C非弹性散射[J]广西师范大学学报自然科学版,2001,19:13.
[27]熊慧萍,α粒子激发机制下的π-~(12)C非弹性散射[D]桂林:广西师范大学,1999.
[28]张德伟,α粒子结构下p-~(12)C非弹性散射的研究[D]桂林:广西师范大学,2007.
[29]K.Amos,M.Bauhoff,I.Morrison,S.F.Collins,R.S.Henderson,B.M.Spicer,G.G.Shute,V.C.Officer,D.W.Dvins,D.L.Friesel,and W.P.Jons,Nucl.Phys.A413,255(1984).
[30]T.Erikon,Nucl.Phys.A170,513(1971).
[31]T.Erikon,Nucl.Phys.A211,105(1973).
[32]V.Horsfjord,Nucl.Phys.A209,493(1973).
[33]李清润,周金礼,中能区质子与He原子核散射的唯象全振幅[J]高能物理与核物理,1993,17:918.
[34]曾谨言,量子力学(卷一)[M].中国北京:科学出版社,2000:314.
[35]曾谨言,量子力学(卷一)[M].中国北京:科学出版社,2000:739.
[36]S.L.Kameny,α-particle model ~(16)O[J].Phys.Rev.1956,103:358.
[37]Willem H Dickhoff,Dimitri Van Neck,Manny-body theory explosed[M]USA:World Scientific Publishing Co.Pte.Ltd.
[38]J.F.Germond and C.Wilkin,Pio-carbon scattering in the α-particle model[J]Nucl.Phys.A,1975,237(3):477-492.
[39]Gillet.V.Melkanoff MA.,Role of particle-hole correlations in the inelastic scattering of electron from ~(12)C, ~(16)O, and ~(40)Ca [J] Phys. Rev. 1964,133(5B):1190-1199.
[40] R. F. Frossch, et al. , Structure of the He nucleus from elastic electron scattering [J] Phys. Rev. , 1967, 160(4): 874.
[41]R. H. Landau, S.C. Phatak, Improved theoretical pion-nucleus optical potentials [J] Ann. Phys. 1973,78 (2):874-879.
[2] E. M. Lyman, A. O. Hanson and M. B. Scott, Scattering of 15. 7MeV electrons by nuclei [J] Phys. Rev. 1951,84:626.
[3] Beat Hahn, D. G. Ravenhall and Robert Hofstadter, High-Energy Electron scattering and the change Distributions of selected nuclei [J] Phys. Rev., 1956, 101:1131.
[4] T. N. Buti, J.Kelly, W. Bertozzi, J. M. Finn et al. Electroexcitation of isoscalar states in ~(16)O [J] Phys. Rev. C, 1986, 33:755.
[5] H. L. Crannell and T. Griffy, Role of particle-hole correlations in the inelastic scattering of electrons from ~(12)C, ~(16)O and ~(40)Ca [J] Phys. Rev. , 1961,136:1580-1584
[6] H. L. Crannell, Elastic and inelastic electron scattering from ~(12)C and ~(16)O [J]Phys. Rev. , 1966, 148:1107-1118.
[7] E. Blesz Ynski et al. Energy dependence of relativistic effects in the elastic scattering of polarized protons from ~(16)O and ~(40)Ca [J] Phys. Rev. C, 1988, 37:1527-1536.
[8] G. S. Adams, Th. S. Bauer et al. , Microscopic description of 800-MeV polarized-proton scattering from ~(16)O [J] Phys. Rev. Lett. , 1979, 43:421.
[9] H. Seifert, J.J.Kelly et al. , Effective interaction for ~(16)O(p-p )and Ca (p-p' ) at Ep=200MeV, Phys. Rev. C, 1993, 47:1615.
[10] J. J. Kelly, A. E. Feldman et al. , Effective interaction for ~(16)O(p-p ) at Ep=318MeV, [J] Phys. Rev. C, 1991, 43:1272
[11]Terence J. Gooding and George Igo, Scattering of 915MeV a particles from carbon and helium:Direct evidence for α-particle cluster in nuclei [J] Phys. Rev. Lett. , 1961, 7:28.
[12]G. Igo, L. F. Hansen and T. J. Gooding, Evidence for "alpha-particle" cluster in several nuclei from the (a, 2a) rection at 0.91BeV [J] Phys. Rev. , 1963, 131:337.
[13]D. S. Delion, A. Sandulescu, and W. Greiner, Evidence for a clustering in heavy and superheavy nuclei [J] Phys. Rev. C, 2004, 69:044318. D. Robson, Evidence for the tetrahedral nature of ~(16)O [J] Phys. Rev. Lett, 1979,42:876.
[14]R. B. Raphael and M. Rosen, Effect of dynamical deformation in elastic electron scattering on the charge distributions the calcium isotopes [J]Phys.Rev.C,1972,2:1040-1047.
[15]E.V.Inopin and B.I.Tishchenko,Soviet phys.JETP,11(1960),840.
[16]李清润、陈生中、赵恩广,独立α粒子模型下的电子散射[J]高能物理与核物理,5(1981)531.
[17]李清润、陈生忠、赵恩广,α粒子模型下的π~- -~(12)C散射[J]高能物理与核物理,5(1981)641.
[18]Li Qing-run,Pion-oxygen scattering in the four-α-particle model,[J]Phys.Rev.C,1984,30:1284.
[19]何淦明,李清润,中能p-~(12)C散射截面和自旋量的研究[J]高能物理与核物理,1991,15:623
[20]张荣,α粒子结构下p-~(12)C,p-~(16)O散射截面及极化量的研究[D]桂林:广西师范大学,2004.
[21]Yang Yong-Xu,Lu Xiao,and Li Qing-Run,4.2GeV α-~(12)C elastic scattering based on α-particle model,2008,49:1587-1590.
[22]李清润,杨永栩,通过~(12)C-~(12)C散射对两种不同模型的一个比较[J]高能物理与核物理,1994,18:1115.
[23]郝云荣,杨永栩,低能区的~(16)O-~(12)C散射折叠模型研究[J]广西师范大学学报自然科学版,2008,26:23.
[24]郝云荣,用α粒子折叠模型光学势研究~(16)O-~(12)C散射[D]桂林:广西师范大学,2006.
[25]杨永栩,李清润,124MeV下~(16)O-~(16)O弹性散射的折叠模型[J]高能物理与核物理,1997,21:645-647.
[26]杨永栩,李清润,α粒子结构下的π-~(12)C非弹性散射[J]广西师范大学学报自然科学版,2001,19:13.
[27]熊慧萍,α粒子激发机制下的π-~(12)C非弹性散射[D]桂林:广西师范大学,1999.
[28]张德伟,α粒子结构下p-~(12)C非弹性散射的研究[D]桂林:广西师范大学,2007.
[29]K.Amos,M.Bauhoff,I.Morrison,S.F.Collins,R.S.Henderson,B.M.Spicer,G.G.Shute,V.C.Officer,D.W.Dvins,D.L.Friesel,and W.P.Jons,Nucl.Phys.A413,255(1984).
[30]T.Erikon,Nucl.Phys.A170,513(1971).
[31]T.Erikon,Nucl.Phys.A211,105(1973).
[32]V.Horsfjord,Nucl.Phys.A209,493(1973).
[33]李清润,周金礼,中能区质子与He原子核散射的唯象全振幅[J]高能物理与核物理,1993,17:918.
[34]曾谨言,量子力学(卷一)[M].中国北京:科学出版社,2000:314.
[35]曾谨言,量子力学(卷一)[M].中国北京:科学出版社,2000:739.
[36]S.L.Kameny,α-particle model ~(16)O[J].Phys.Rev.1956,103:358.
[37]Willem H Dickhoff,Dimitri Van Neck,Manny-body theory explosed[M]USA:World Scientific Publishing Co.Pte.Ltd.
[38]J.F.Germond and C.Wilkin,Pio-carbon scattering in the α-particle model[J]Nucl.Phys.A,1975,237(3):477-492.
[39]Gillet.V.Melkanoff MA.,Role of particle-hole correlations in the inelastic scattering of electron from ~(12)C, ~(16)O, and ~(40)Ca [J] Phys. Rev. 1964,133(5B):1190-1199.
[40] R. F. Frossch, et al. , Structure of the He nucleus from elastic electron scattering [J] Phys. Rev. , 1967, 160(4): 874.
[41]R. H. Landau, S.C. Phatak, Improved theoretical pion-nucleus optical potentials [J] Ann. Phys. 1973,78 (2):874-879.