- Email: [email protected]
Cross sections for H− formation from H(2s)+Ar, Kr, and Xe collisions
NUCLEAR
INSTRUMENTS
AND
METHODS
I26
(I975)
467-468;
©
NORTH-HOLLAND
PUBLISHING
CO.
CROSS SECTIONS FOR H - FORMATION FROM H ( 2 s ) + A r , Kr, AND Xe C O L L I S I O N S R O N A L D E. O L S O N *
Service de Physique Atomique, Centre d'Etudes Nacldaires de Saclay, B.P. No 2, 91190 Gif-sur- Yvette, France Received 1 April 1975 Inelastic total cross sections for the reaction H ( 2 s ) + X - + H - + X +, where X ~ A r , 0.1-2.0 keV.
The production of H - or D - by collisions of H(2s) or D(2s) with Ar has been successfully used in the application to polarized-ion sources~'2). In such a device, metastable H(2s) atoms are produced by charge exchange of H + with Cs at a collision energy of approximately 0.5 keV [for D(2s) this energy corresponds to 1.0 keV], where the cross section for H(2s) production is at its maximum3). The H(2s) is then polarized by selective quenching of hyperfine states in magnetic and electric fields. After becoming polarized, the H(2s) is collided with Ar or 12 , capturing an electron and thus producing polarized H - ions. Since the reaction for producing H - ions from H(2s) appears to be the rate-controlling step for an efficient polarizedion source [at 500 eV, the cross section for forming H(2s) from H + + C s collisions is ~ 6 × 10-15cm23), while our calculations show that the cross section for electron capture by H(2s) to form H - on collisions with Ar is ~ 1 x 10 -16 cm2], it is important to examine other reactions producing H - from H(2s), to see if the efficiency can be improved. F r o m this study, it appears that Kr is a more favorable gas for negativeion production. The calculation of the inelastic total cross section for the reaction: H ( 2 s ) + X --* H - + H +, (1) is considerably simplified, because the interaction potentials can be reasonably approximated by a constant interaction for the reactants and an attractive Coulomb potential for the products. Thus, the problem reduces to a curve-crossing process where considerable study has been carried out, especially for the reverse reaction to (1), that of ion-ion mutual neutralization 4"5). A multichannel Landau-Zener calculation can be * On leave of absence from the Molecular Physics G r o u p of the Stanford Research Institute.
467
Kr, and Xe, are calculated in the energy range
used to compute the cross sections for (1), after the coupling matrix elements at the curve crossings are calculated. For one-electron transfer, these matrix elements can be reasonably estimated using a semiempirical formula°), where the degeneracy in the H*(n _> 2 ) + X states has been included in the same manner as Bates and Lewis7). The only additional difficulty in calculating the cross sections for (1) when X = Ar, Kr, or Xe, is that we must work in a framework the total angular momentum J and the core configuration of the X + ion are conserved, For Kr and Xe, these restrictions imply that only X + and excited states X* will be produced with a 2pu2 core. However, for Ar some core mixing is possible, but this problem can be treated in the same manner as done previously S). In the cross-section calculation, it is essential to include the excited states H * + X and H + X * that are populated during the collision, since these states considerably reduce the negative-ion formation. For Ar we have included 18 channels, while 10-15
f
I
'
Kr
E 10-16 w
o~
10-17
i 0
[ I IE (keY)
i
Fig. 1. Inelastic total cross sections for H(2s)+X---~H + X +, where X ~ A r , Kr, and Xe.
468
p,. E. OLSON
the number of excited states of importance reduces to 11 for Kr and 10 for Xe. The calculated cross sections are shown in fig. 1. At 0.5 keV (equivalent to a 1.0 keV collision for D), collisions of H(2s) with Kr are more efficient in H production than either Ar or Xe. Since another requirement for an efficient polarized-ion source is that negative-ion formation from ground-state collisions must be much smaller than for H ( 2 s ) + X collisions, we have also calculated the H ( I s ) + X negative-ionformation cross sections. However, these cross sections are much more uncertain, since the coupling matrix elements and crossing distances are less accurately predicted for the H ( l s ) + X state. These rough calculations indicate that at 0.5 keV the ratios of cross sections R for negative-ion formation from the H(2s) state vs that from the H ( l s ) state are R ( A r ) = 16, R(Kr) = 12, and R ( X e ) = 2 . Thus, it is seen that Xe will be a very poor candidate to use to produce a polarized H - beam for injection into a Tandem accelerator. The effect of the Coulomb scattering on the angular distribution of the H - may also be calculated, to indicate the experimental acceptance angle necessary to collect the H - that is produced. For H ( 2 s ) + X , the majority of the cross section will be obtained for a minimum acceptance angle of z = EO'~ 200 eV deg. However, for H ( l s ) + X , since the particles are on the Coulomb potential for a longer time, the minimum acceptance angle increases to z ~ 5 0 0 eV deg. These minimum acceptance angles are very approximative, since we are not able to estimate the contribution to the total cross section for the scattering off the repulsive walls of the potentials. Hence, to be conservative, the minimum acceptance angles given should be doubled, with the knowledge that the repulsive-wall-scattering correction is more important for the H(ls) than for the H(2s). Thus, we can see that under single-collision conditions, an experimental arrangement can enhance the ratio R by accepting only those H - ions scattered from z ~<400 eV deg.
From the experience gained in calculating ion ion mutual neutralization cross sections, the reverse of reaction (1), the absolute values of the calculated cross sections should be accurate to approximately a factor of 2 at energies where competing processes for electron transfer, such as direct ionization to the continuum, are not important. Because these types of processes require a hard collision, since the interaction will be high on the repulsive wall of the H ( 2 s ) + X potential, we would estimate that an energy of at least 1 keV will be needed before such processes become important. Thus, the result will be that the calculated cross sections will most likely be too large at energies above 1 keV, with the effect increasing with energy. However, at the energy of interest for application to polarizedion sources, E ~ 0 . 5 keV, the cross sections will be unaffected, and the trend at 0.5 keV for Q m - ( K r ) > Q m _ ( A r ) ~ Qm-(Xe) is expected to be valid. Thus, these calculations strongly point out the possible advantage of using Kr, not Ar, in polarized-ion sources. The author wishes helpful conversations Also, he would like to the opportunity to do
to thank Dr Schlachter for his and for suggesting this study. thank Drs Watel and Manus for research at CEN/Saclay.
References 1) B. L. Donnally and W. Sawyer, Phys. Rev. Letters 10 (1965) 439. e) L. D. Knutgon, Phys. Rev. A2 (1970) 1878. 3) p. Pradel, F. goussel, A. S. Schlachter, G. Spiess and A. Valance, Phys. Rev. A10 (1974) 797. 4) R. E. Olson, J. R. Peterson, and J. Moseley, J. Chem. Phys. 9 (1970) 3391. ~) J. T. Moseley, R. E. Olson, and J. R. Peterson, Review: Ion-ion mutual neutralization .for case studies in atomic physics (North-Holland Publ. Co., Amsterdam, 1975).
o) R. E. Olson, F. T. Smith, and E. Bauer, Appl. Opt. 10 (1971) 1848. 7) D. R. Bates and J. T. Lewis, Proc. Phys. Soc. (London) A68 (1955) 173. 8) G. E, Ice and R. E. Olson, Phys. Rev. A l l (1975) I 11.
INSTRUMENTS
AND
METHODS
I26
(I975)
467-468;
©
NORTH-HOLLAND
PUBLISHING
CO.
CROSS SECTIONS FOR H - FORMATION FROM H ( 2 s ) + A r , Kr, AND Xe C O L L I S I O N S R O N A L D E. O L S O N *
Service de Physique Atomique, Centre d'Etudes Nacldaires de Saclay, B.P. No 2, 91190 Gif-sur- Yvette, France Received 1 April 1975 Inelastic total cross sections for the reaction H ( 2 s ) + X - + H - + X +, where X ~ A r , 0.1-2.0 keV.
The production of H - or D - by collisions of H(2s) or D(2s) with Ar has been successfully used in the application to polarized-ion sources~'2). In such a device, metastable H(2s) atoms are produced by charge exchange of H + with Cs at a collision energy of approximately 0.5 keV [for D(2s) this energy corresponds to 1.0 keV], where the cross section for H(2s) production is at its maximum3). The H(2s) is then polarized by selective quenching of hyperfine states in magnetic and electric fields. After becoming polarized, the H(2s) is collided with Ar or 12 , capturing an electron and thus producing polarized H - ions. Since the reaction for producing H - ions from H(2s) appears to be the rate-controlling step for an efficient polarizedion source [at 500 eV, the cross section for forming H(2s) from H + + C s collisions is ~ 6 × 10-15cm23), while our calculations show that the cross section for electron capture by H(2s) to form H - on collisions with Ar is ~ 1 x 10 -16 cm2], it is important to examine other reactions producing H - from H(2s), to see if the efficiency can be improved. F r o m this study, it appears that Kr is a more favorable gas for negativeion production. The calculation of the inelastic total cross section for the reaction: H ( 2 s ) + X --* H - + H +, (1) is considerably simplified, because the interaction potentials can be reasonably approximated by a constant interaction for the reactants and an attractive Coulomb potential for the products. Thus, the problem reduces to a curve-crossing process where considerable study has been carried out, especially for the reverse reaction to (1), that of ion-ion mutual neutralization 4"5). A multichannel Landau-Zener calculation can be * On leave of absence from the Molecular Physics G r o u p of the Stanford Research Institute.
467
Kr, and Xe, are calculated in the energy range
used to compute the cross sections for (1), after the coupling matrix elements at the curve crossings are calculated. For one-electron transfer, these matrix elements can be reasonably estimated using a semiempirical formula°), where the degeneracy in the H*(n _> 2 ) + X states has been included in the same manner as Bates and Lewis7). The only additional difficulty in calculating the cross sections for (1) when X = Ar, Kr, or Xe, is that we must work in a framework the total angular momentum J and the core configuration of the X + ion are conserved, For Kr and Xe, these restrictions imply that only X + and excited states X* will be produced with a 2pu2 core. However, for Ar some core mixing is possible, but this problem can be treated in the same manner as done previously S). In the cross-section calculation, it is essential to include the excited states H * + X and H + X * that are populated during the collision, since these states considerably reduce the negative-ion formation. For Ar we have included 18 channels, while 10-15
f
I
'
Kr
E 10-16 w
o~
10-17
i 0
[ I IE (keY)
i
Fig. 1. Inelastic total cross sections for H(2s)+X---~H + X +, where X ~ A r , Kr, and Xe.
468
p,. E. OLSON
the number of excited states of importance reduces to 11 for Kr and 10 for Xe. The calculated cross sections are shown in fig. 1. At 0.5 keV (equivalent to a 1.0 keV collision for D), collisions of H(2s) with Kr are more efficient in H production than either Ar or Xe. Since another requirement for an efficient polarized-ion source is that negative-ion formation from ground-state collisions must be much smaller than for H ( 2 s ) + X collisions, we have also calculated the H ( I s ) + X negative-ionformation cross sections. However, these cross sections are much more uncertain, since the coupling matrix elements and crossing distances are less accurately predicted for the H ( l s ) + X state. These rough calculations indicate that at 0.5 keV the ratios of cross sections R for negative-ion formation from the H(2s) state vs that from the H ( l s ) state are R ( A r ) = 16, R(Kr) = 12, and R ( X e ) = 2 . Thus, it is seen that Xe will be a very poor candidate to use to produce a polarized H - beam for injection into a Tandem accelerator. The effect of the Coulomb scattering on the angular distribution of the H - may also be calculated, to indicate the experimental acceptance angle necessary to collect the H - that is produced. For H ( 2 s ) + X , the majority of the cross section will be obtained for a minimum acceptance angle of z = EO'~ 200 eV deg. However, for H ( l s ) + X , since the particles are on the Coulomb potential for a longer time, the minimum acceptance angle increases to z ~ 5 0 0 eV deg. These minimum acceptance angles are very approximative, since we are not able to estimate the contribution to the total cross section for the scattering off the repulsive walls of the potentials. Hence, to be conservative, the minimum acceptance angles given should be doubled, with the knowledge that the repulsive-wall-scattering correction is more important for the H(ls) than for the H(2s). Thus, we can see that under single-collision conditions, an experimental arrangement can enhance the ratio R by accepting only those H - ions scattered from z ~<400 eV deg.
From the experience gained in calculating ion ion mutual neutralization cross sections, the reverse of reaction (1), the absolute values of the calculated cross sections should be accurate to approximately a factor of 2 at energies where competing processes for electron transfer, such as direct ionization to the continuum, are not important. Because these types of processes require a hard collision, since the interaction will be high on the repulsive wall of the H ( 2 s ) + X potential, we would estimate that an energy of at least 1 keV will be needed before such processes become important. Thus, the result will be that the calculated cross sections will most likely be too large at energies above 1 keV, with the effect increasing with energy. However, at the energy of interest for application to polarizedion sources, E ~ 0 . 5 keV, the cross sections will be unaffected, and the trend at 0.5 keV for Q m - ( K r ) > Q m _ ( A r ) ~ Qm-(Xe) is expected to be valid. Thus, these calculations strongly point out the possible advantage of using Kr, not Ar, in polarized-ion sources. The author wishes helpful conversations Also, he would like to the opportunity to do
to thank Dr Schlachter for his and for suggesting this study. thank Drs Watel and Manus for research at CEN/Saclay.
References 1) B. L. Donnally and W. Sawyer, Phys. Rev. Letters 10 (1965) 439. e) L. D. Knutgon, Phys. Rev. A2 (1970) 1878. 3) p. Pradel, F. goussel, A. S. Schlachter, G. Spiess and A. Valance, Phys. Rev. A10 (1974) 797. 4) R. E. Olson, J. R. Peterson, and J. Moseley, J. Chem. Phys. 9 (1970) 3391. ~) J. T. Moseley, R. E. Olson, and J. R. Peterson, Review: Ion-ion mutual neutralization .for case studies in atomic physics (North-Holland Publ. Co., Amsterdam, 1975).
o) R. E. Olson, F. T. Smith, and E. Bauer, Appl. Opt. 10 (1971) 1848. 7) D. R. Bates and J. T. Lewis, Proc. Phys. Soc. (London) A68 (1955) 173. 8) G. E, Ice and R. E. Olson, Phys. Rev. A l l (1975) I 11.