Radial and angular correlation effects in (e,3e) processes

G. GASANEO, S. OTRANTO, K. V. RODRIGUEZ

Rosario, Argentina

Conferencia; XXIV International conference on Photonic Electronic and Atomic collisions (ICPEAC); 2005

G. Gasaneo1,2, S. Otranto1, and K. V Rodríguez 1,21,2, S. Otranto1, and K. V Rodríguez 1,2 1) Departamento de Física - Universidad Nacional del Sur,8000 Bahía Blanca, Argentina 2) Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina This work is focused on the initial state dependence of the five fold differential cross section (FDCS) for the double ionization of He by electron impact [1]. The energies and angles considered for the scattered and emitted electrons are those shown in the work of Lahmam-Bennani [2]. The FDCS for the (e,3e) process is defined [1] in terms of the transition amplitude Tfi   Tfi=áYf-|Vi|Yiñ Here, the initial state Ψi is represented by a two-electron ground state wave function times a plane wave for the projectile. In this Born approximation, the potential Vi is given by the sum of the nucleus-projectile and bound electronsprojectile Coulomb interactions. All the interparticles Coulomb interactions are included inTfi   Tfi=áYf-|Vi|Yiñ Here, the initial state Ψi is represented by a two-electron ground state wave function times a plane wave for the projectile. In this Born approximation, the potential Vi is given by the sum of the nucleus-projectile and bound electronsprojectile Coulomb interactions. All the interparticles Coulomb interactions are included inTfi=áYf-|Vi|Yiñ Here, the initial state Ψi is represented by a two-electron ground state wave function times a plane wave for the projectile. In this Born approximation, the potential Vi is given by the sum of the nucleus-projectile and bound electronsprojectile Coulomb interactions. All the interparticles Coulomb interactions are included inΨi is represented by a two-electron ground state wave function times a plane wave for the projectile. In this Born approximation, the potential Vi is given by the sum of the nucleus-projectile and bound electronsprojectile Coulomb interactions. All the interparticles Coulomb interactions are included inVi is given by the sum of the nucleus-projectile and bound electronsprojectile Coulomb interactions. All the interparticles Coulomb interactions are included in Ψf through a set of screened charges. Four different variational wave functions are used to represent the He ground state. These wave functions contain different information on the radial and angular correlations and three of them exactly satisfy the three Kato cusp conditions. In Fig. 1, we represent with dashed-line the results obtained with GRI as given by the function jGRI =f[2b+1+e-2br23     ]/2b which only has angular correlation. Here, f=eZ(r2+ r3)  and mean binding energy EGRI=- 2.8773 a.u.. On the function GRII (dotted-line) we improved the angular correlation by adding more variational parameters and obtained the energy EGRII=-2.87933 a.u. (close to the angular correlation limit). With GRII we obtain the best agreement with the experimental data of Ref. [2]. If only radial correlation is included as done by the function GRIII jGRIII =f[1+aIII (r22+ r32) ] the results obtained (dotted-dashed-line) are a factor 1.8 when compared with the experimental data. GRIII has only radial correlation and it gives an energy EGRIII=-2.8721 a.u. close to the radial limit. When the radial correlation of GRIII is combined with the angular correlation of the function GRI we obtain the function GRIV (shortdashed- line). The mean energy of GRIV is EGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. Af through a set of screened charges. Four different variational wave functions are used to represent the He ground state. These wave functions contain different information on the radial and angular correlations and three of them exactly satisfy the three Kato cusp conditions. In Fig. 1, we represent with dashed-line the results obtained with GRI as given by the function jGRI =f[2b+1+e-2br23     ]/2b which only has angular correlation. Here, f=eZ(r2+ r3)  and mean binding energy EGRI=- 2.8773 a.u.. On the function GRII (dotted-line) we improved the angular correlation by adding more variational parameters and obtained the energy EGRII=-2.87933 a.u. (close to the angular correlation limit). With GRII we obtain the best agreement with the experimental data of Ref. [2]. If only radial correlation is included as done by the function GRIII jGRIII =f[1+aIII (r22+ r32) ] the results obtained (dotted-dashed-line) are a factor 1.8 when compared with the experimental data. GRIII has only radial correlation and it gives an energy EGRIII=-2.8721 a.u. close to the radial limit. When the radial correlation of GRIII is combined with the angular correlation of the function GRI we obtain the function GRIV (shortdashed- line). The mean energy of GRIV is EGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. A jGRI =f[2b+1+e-2br23     ]/2b which only has angular correlation. Here, f=eZ(r2+ r3)  and mean binding energy EGRI=- 2.8773 a.u.. On the function GRII (dotted-line) we improved the angular correlation by adding more variational parameters and obtained the energy EGRII=-2.87933 a.u. (close to the angular correlation limit). With GRII we obtain the best agreement with the experimental data of Ref. [2]. If only radial correlation is included as done by the function GRIII jGRIII =f[1+aIII (r22+ r32) ] the results obtained (dotted-dashed-line) are a factor 1.8 when compared with the experimental data. GRIII has only radial correlation and it gives an energy EGRIII=-2.8721 a.u. close to the radial limit. When the radial correlation of GRIII is combined with the angular correlation of the function GRI we obtain the function GRIV (shortdashed- line). The mean energy of GRIV is EGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. A which only has angular correlation. Here, f=eZ(r2+ r3)  and mean binding energy EGRI=- 2.8773 a.u.. On the function GRII (dotted-line) we improved the angular correlation by adding more variational parameters and obtained the energy EGRII=-2.87933 a.u. (close to the angular correlation limit). With GRII we obtain the best agreement with the experimental data of Ref. [2]. If only radial correlation is included as done by the function GRIII jGRIII =f[1+aIII (r22+ r32) ] the results obtained (dotted-dashed-line) are a factor 1.8 when compared with the experimental data. GRIII has only radial correlation and it gives an energy EGRIII=-2.8721 a.u. close to the radial limit. When the radial correlation of GRIII is combined with the angular correlation of the function GRI we obtain the function GRIV (shortdashed- line). The mean energy of GRIV is EGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. A and mean binding energy EGRI=- 2.8773 a.u.. On the function GRII (dotted-line) we improved the angular correlation by adding more variational parameters and obtained the energy EGRII=-2.87933 a.u. (close to the angular correlation limit). With GRII we obtain the best agreement with the experimental data of Ref. [2]. If only radial correlation is included as done by the function GRIII jGRIII =f[1+aIII (r22+ r32) ] the results obtained (dotted-dashed-line) are a factor 1.8 when compared with the experimental data. GRIII has only radial correlation and it gives an energy EGRIII=-2.8721 a.u. close to the radial limit. When the radial correlation of GRIII is combined with the angular correlation of the function GRI we obtain the function GRIV (shortdashed- line). The mean energy of GRIV is EGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. AGRII=-2.87933 a.u. (close to the angular correlation limit). With GRII we obtain the best agreement with the experimental data of Ref. [2]. If only radial correlation is included as done by the function GRIII jGRIII =f[1+aIII (r22+ r32) ] the results obtained (dotted-dashed-line) are a factor 1.8 when compared with the experimental data. GRIII has only radial correlation and it gives an energy EGRIII=-2.8721 a.u. close to the radial limit. When the radial correlation of GRIII is combined with the angular correlation of the function GRI we obtain the function GRIV (shortdashed- line). The mean energy of GRIV is EGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. A jGRIII =f[1+aIII (r22+ r32) ] the results obtained (dotted-dashed-line) are a factor 1.8 when compared with the experimental data. GRIII has only radial correlation and it gives an energy EGRIII=-2.8721 a.u. close to the radial limit. When the radial correlation of GRIII is combined with the angular correlation of the function GRI we obtain the function GRIV (shortdashed- line). The mean energy of GRIV is EGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. Athe results obtained (dotted-dashed-line) are a factor 1.8 when compared with the experimental data. GRIII has only radial correlation and it gives an energy EGRIII=-2.8721 a.u. close to the radial limit. When the radial correlation of GRIII is combined with the angular correlation of the function GRI we obtain the function GRIV (shortdashed- line). The mean energy of GRIV is EGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. AGRIII=-2.8721 a.u. close to the radial limit. When the radial correlation of GRIII is combined with the angular correlation of the function GRI we obtain the function GRIV (shortdashed- line). The mean energy of GRIV is EGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. AGRIV=- 2.90127 a.u.. Similar behavior is observed when the other angular configurations considered in [2] are studied. Figure 1: FFDCS for the (e,3e) process. We plot one of the angles given on Ref. [2] We find puzzling that as the quality of the function is improved, the results tend to disagree with the experimental data. New experimental data for different emission energies would be helpful in order to clarify on this point and give a deeper insight on the final state wave function role for this process. References [1] J. Berakdar, A. Lahmam-Bennani and C. Dal Capello, Phys. Rep. 374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. A374, 91 (2003) [2] A. Lahmam-Bennani et al., Phys. Rev. A 59, 3548 (1999), 3548 (1999)