正电子与基态及激发态氦原子散射的理论研究
摘要
在本论文中,我们对原有的动量空间耦合通道光学势方法作了进一步的发展,将极化势模型扩展到了正电子与复杂原子的碰撞问题,并对正电子与激发态原子的碰撞问题作了初步的研究。我们利用发展了的动量空间耦合通道光学势方法研究了正电子与基态及激发态氦原子的散射过程。首先应用一个复的等价局域近似的光学势来描述在正电子散射过程中非常重要的电子偶素形成过程,计算了低能和中能范围内正电子同基态氦原子碰撞的电子偶素形成截面。在此基础上,在考虑了电子偶素通道的影响后,我们计算了低能和中能范围内正电子同基态氦原子碰撞的总散射截面,弹性散射和各种激发散射截面,并与实验数据和其他的理论计算结果进行了比较。计算结果与实验数据和其他的理论数据符合得都比较好,这证明目前的光学势方法能够有效地处理正电子与复杂原子碰撞问题。在此基础上,我们又对正电子同激发态氦原子的散射过程进行了初步的研究。激发态原子体系的散射问题在近几年引起了很大的关注,一些理论方法已经被用来处理电子与激发态原子的碰撞。我们计算了正电子与激发态氦原子(2 3S)碰撞的400 eV以下的电子偶素形成截面,1000 eV以下的电离截面和200 eV以下的总散射截面。由于没有相应的实验和理论数据可供比较,我们将所得的截面数据与电子和激发态氦原子(2 3S)碰撞的散射截面,以及正电子与基态氦原子碰撞的的相应散射截面进行了比较。
The study of atomic and molecular collision,which is a fundamental topic ofatomic and molecular physics, can offer us more accurate understanding of micro-cosmic structure and basic interactions in many-body systems. In the past decades,the positron collisions with atoms and molecules have attracted much more atten-tion along with the founding of positron and development of experimental technique.Compared with electron scattering, there is no exchange-interaction in the positroncollision, and since the positron received a attractive potential from the target atom ormolecule, it is possible to form positronium bound states when energy is appropriate.The positronium formation process, a two-center problem, presents a new challengeto theoretical treatment for positron scattering besides the ionization continuum andthe long range of Coulomb potential.
In the last century, several theoretical methods have been successfully developedfor positron scattering at low and high energies, while the theoretical calculations atintermediate energies are not satisfied until the latest close-coupling methods are ap-plied. In the positron collisions at medium energies, infinite reaction channels areopen, and the positronium formation and ionization continuum strongly in?uence thewhole scattering process. Based on these facts, theoretical calculations must includemany partial-waves, and the contributions of positronium formation channels and ion-ization continuum should be taken into account. Although the accurate variationalcalculation produced excellent data in low energy region, it can not be used whenenergy is higher since only few partial-waves can be included in calculation. TheDistorted-wave Born-approximation (DWBA) method behaved well for high-energycollisions but omitted the positronium formation channels. The calculation results us-ing the early close-coupling methods are also not satisfactory because the positroniumformation channels and ionization continuum are not included. In the past decades,several new close-coupling methods have been developed and successfully applied for positron collisions at medium energies.
The ionization continuum and positronium formation channels are challengingfor theoretical work for positron scattering. In the CCC method, some pseudo-statesare applied in the basis to include the ionization continuum and positronium formationchannels. By this way, great successes have been achieved in positron and electronscattering with simple atoms. However, since the calculation results depend on thechoice of basis and the number of pseudo-states, there are many difficulties for thismethod to be applied in the intermediate energies. The momentum-space coupled-channel optical (CCO) method is an ab-initial method developed by McCarthy et alfor electron scattering. In this method, the whole space is split into P and Q spacesby the rejection vector P and Q. The P space consists of some discrete channels, andthe rest discrete channels and the ionization continuum are included in the Q space.The coupled equations are solved in the P space and the contribution of Q space is de-scribed by a complex optical potential. This method has been successfully applied inthe electron collisions with atoms and molecules. In the past few yeas, a polarizationpotential has been developed by Zhou et al to extend this method to positron scatter-ing, and the positron collisions with atomic hydrogen and alkali-metal atoms whichcan be described as a hydrogenic structure have been successfully studied using thismodel. In this paper, we have applied a complex equivalent local optical potential toextend the CCO method to the positron collisions with complex atoms in ground andexcited states.
Helium atom is an ideal target for theoretical calculation and experimental mea-surement, since it is the most simple many-electron atom and more stable than atomichydrogen. In this paper,we have applied the CCO method to investigate the positroncollisions with ground and excited helium. In the present calculation,the in?uenceof Q space including ionization continuum and positronium formation channels aredescribed by coupling a special polarization potential to the static potential. Thepositronium formation cross sections,total scattering cross sections,elastic scat-tering cross sections and various excitation cross sections of positron collisions withground helium are given and compared with the experimental measurements of Steinet al. [62],Griffith et al.[63], Kappila et al. [64], Chalton and Laricchia [65], Moriand Sueoka [66], Fromme et al. [67], Jacobsen et al. [68], Moxom et al. [69], Ashleyet al. [70], Murtagh et al.[71], Charlton et al. [72], Fornari et al. [73], Diana et al.[74], and Overton et al. [75], and theoretical calculations of Schultz and Olson [79],Sarkar et al. [80], Mandal et al. [29], Igarashi and Toshima [30], Campeanu et al.[31,32], Hewitt et al. [81], Campbell et al. [82], Wu et al. [83] and Chaudhuriet al [84]. Excellent agreement can be found between present positronium formationcross sections and experimental measurements in the whole energy region, especially,the present results achieved the maximum at the same position (about 50 eV) with experimental data, while most of other theoretical results get their peak at 40-45 eV.The present results also agree well with the variational calculation of Van Reeth andHumberston [22] and the measurement of Murtagh et al.[71] from 17 to 22 eV, whilethe other calculations are all above 20 eV. In the calculations of total scattering crosssection, almost all theoretical results have a similar shape and differ with each otherin the magnitude.The present results agree well with the measurements of Stein etal.[62] and Griffith et al.[63], and a little lower than other theoretical calculations.However, significant disagreement exists in the peak position, which is about 60 eVfor Campbell et al.[82] and Wu et al.[83], 40 eV for present calculation, and 50 eVfor experimental measurements. As for the elastic scattering and various excitationcross sections, only the total excitation cross sections are measured by Chalton andLaricchia [65], and Mori and Sueoka [66], and significant disagreement exists amongdifferent calculations, as well as present results.
In recent years,more and more attention have been concentrated on the scat-tering of excited atoms and molecules,wich can offer a new approach to under-stand the structure and interactions of microcosmic systems. Although some theo-retical calculations and experimental measurements have been performed for electronscattering with excited atoms,there is still no report for positron scattering with ex-cited atoms. In the present work, the CCO method have been applied to study thepositron collisions with excited helium (2 3S). The positronium formation cross sec-tions,ionization cross sections and total scattering cross sections are calculated andcompared with corresponding results of electron scattering with excited helium (2 3S)and positron scattering with ground helium. The present scattering cross section ofpositron scattering with excited helium (2 3S) are much higher than correspondingresults of positron scattering with ground helium,and the present total scatteringcross sections are very similar with electron scattering with excited helium (2 3S)in both shape and magnitude. This is the direct consequence of the low ionizationthreshold,minus positronium formation threshold and much higher dipole polariz-ability,which is 318.7 a03 for excited helium (2 3S) and 1.27 a03 for ground helium(Lamm and Szabo [98]).
In this paper,the momentum-space coupled-channel optical method has beenused to study the positron scattering with ground and excited helium,and the cal-culation results agree well with experimental measurements and other theoretical cal-culations. It is approved that the present polarization potential model for positron-ium formation channels are successful,and the CCO method is an effective tool forpositron scattering with complex atoms. From the present calculation,we can havethe conclusion that the positronium formation channels and ionization continuum areimportant for positron scattering with ground helium at low and intermediate energyregion,and neglectable for positron scattering with excited helium. Meanwhile,due to its unique feature,the positron scattering with excited atoms has very differentfigures and can extend our understanding of interactions in many-body systems. Al-though great success has been achieved in present model,some defects could befound in present calculation,and extensive development would be made in the fu-ture.
The study of atomic and molecular collision,which is a fundamental topic ofatomic and molecular physics, can offer us more accurate understanding of micro-cosmic structure and basic interactions in many-body systems. In the past decades,the positron collisions with atoms and molecules have attracted much more atten-tion along with the founding of positron and development of experimental technique.Compared with electron scattering, there is no exchange-interaction in the positroncollision, and since the positron received a attractive potential from the target atom ormolecule, it is possible to form positronium bound states when energy is appropriate.The positronium formation process, a two-center problem, presents a new challengeto theoretical treatment for positron scattering besides the ionization continuum andthe long range of Coulomb potential.
In the last century, several theoretical methods have been successfully developedfor positron scattering at low and high energies, while the theoretical calculations atintermediate energies are not satisfied until the latest close-coupling methods are ap-plied. In the positron collisions at medium energies, infinite reaction channels areopen, and the positronium formation and ionization continuum strongly in?uence thewhole scattering process. Based on these facts, theoretical calculations must includemany partial-waves, and the contributions of positronium formation channels and ion-ization continuum should be taken into account. Although the accurate variationalcalculation produced excellent data in low energy region, it can not be used whenenergy is higher since only few partial-waves can be included in calculation. TheDistorted-wave Born-approximation (DWBA) method behaved well for high-energycollisions but omitted the positronium formation channels. The calculation results us-ing the early close-coupling methods are also not satisfactory because the positroniumformation channels and ionization continuum are not included. In the past decades,several new close-coupling methods have been developed and successfully applied for positron collisions at medium energies.
The ionization continuum and positronium formation channels are challengingfor theoretical work for positron scattering. In the CCC method, some pseudo-statesare applied in the basis to include the ionization continuum and positronium formationchannels. By this way, great successes have been achieved in positron and electronscattering with simple atoms. However, since the calculation results depend on thechoice of basis and the number of pseudo-states, there are many difficulties for thismethod to be applied in the intermediate energies. The momentum-space coupled-channel optical (CCO) method is an ab-initial method developed by McCarthy et alfor electron scattering. In this method, the whole space is split into P and Q spacesby the rejection vector P and Q. The P space consists of some discrete channels, andthe rest discrete channels and the ionization continuum are included in the Q space.The coupled equations are solved in the P space and the contribution of Q space is de-scribed by a complex optical potential. This method has been successfully applied inthe electron collisions with atoms and molecules. In the past few yeas, a polarizationpotential has been developed by Zhou et al to extend this method to positron scatter-ing, and the positron collisions with atomic hydrogen and alkali-metal atoms whichcan be described as a hydrogenic structure have been successfully studied using thismodel. In this paper, we have applied a complex equivalent local optical potential toextend the CCO method to the positron collisions with complex atoms in ground andexcited states.
Helium atom is an ideal target for theoretical calculation and experimental mea-surement, since it is the most simple many-electron atom and more stable than atomichydrogen. In this paper,we have applied the CCO method to investigate the positroncollisions with ground and excited helium. In the present calculation,the in?uenceof Q space including ionization continuum and positronium formation channels aredescribed by coupling a special polarization potential to the static potential. Thepositronium formation cross sections,total scattering cross sections,elastic scat-tering cross sections and various excitation cross sections of positron collisions withground helium are given and compared with the experimental measurements of Steinet al. [62],Griffith et al.[63], Kappila et al. [64], Chalton and Laricchia [65], Moriand Sueoka [66], Fromme et al. [67], Jacobsen et al. [68], Moxom et al. [69], Ashleyet al. [70], Murtagh et al.[71], Charlton et al. [72], Fornari et al. [73], Diana et al.[74], and Overton et al. [75], and theoretical calculations of Schultz and Olson [79],Sarkar et al. [80], Mandal et al. [29], Igarashi and Toshima [30], Campeanu et al.[31,32], Hewitt et al. [81], Campbell et al. [82], Wu et al. [83] and Chaudhuriet al [84]. Excellent agreement can be found between present positronium formationcross sections and experimental measurements in the whole energy region, especially,the present results achieved the maximum at the same position (about 50 eV) with experimental data, while most of other theoretical results get their peak at 40-45 eV.The present results also agree well with the variational calculation of Van Reeth andHumberston [22] and the measurement of Murtagh et al.[71] from 17 to 22 eV, whilethe other calculations are all above 20 eV. In the calculations of total scattering crosssection, almost all theoretical results have a similar shape and differ with each otherin the magnitude.The present results agree well with the measurements of Stein etal.[62] and Griffith et al.[63], and a little lower than other theoretical calculations.However, significant disagreement exists in the peak position, which is about 60 eVfor Campbell et al.[82] and Wu et al.[83], 40 eV for present calculation, and 50 eVfor experimental measurements. As for the elastic scattering and various excitationcross sections, only the total excitation cross sections are measured by Chalton andLaricchia [65], and Mori and Sueoka [66], and significant disagreement exists amongdifferent calculations, as well as present results.
In recent years,more and more attention have been concentrated on the scat-tering of excited atoms and molecules,wich can offer a new approach to under-stand the structure and interactions of microcosmic systems. Although some theo-retical calculations and experimental measurements have been performed for electronscattering with excited atoms,there is still no report for positron scattering with ex-cited atoms. In the present work, the CCO method have been applied to study thepositron collisions with excited helium (2 3S). The positronium formation cross sec-tions,ionization cross sections and total scattering cross sections are calculated andcompared with corresponding results of electron scattering with excited helium (2 3S)and positron scattering with ground helium. The present scattering cross section ofpositron scattering with excited helium (2 3S) are much higher than correspondingresults of positron scattering with ground helium,and the present total scatteringcross sections are very similar with electron scattering with excited helium (2 3S)in both shape and magnitude. This is the direct consequence of the low ionizationthreshold,minus positronium formation threshold and much higher dipole polariz-ability,which is 318.7 a03 for excited helium (2 3S) and 1.27 a03 for ground helium(Lamm and Szabo [98]).
In this paper,the momentum-space coupled-channel optical method has beenused to study the positron scattering with ground and excited helium,and the cal-culation results agree well with experimental measurements and other theoretical cal-culations. It is approved that the present polarization potential model for positron-ium formation channels are successful,and the CCO method is an effective tool forpositron scattering with complex atoms. From the present calculation,we can havethe conclusion that the positronium formation channels and ionization continuum areimportant for positron scattering with ground helium at low and intermediate energyregion,and neglectable for positron scattering with excited helium. Meanwhile,due to its unique feature,the positron scattering with excited atoms has very differentfigures and can extend our understanding of interactions in many-body systems. Al-though great success has been achieved in present model,some defects could befound in present calculation,and extensive development would be made in the fu-ture.
引文
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