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Negative ion formation by charge exchange between hydrogen and cesium
Volume 6 8A, number 2
PHYSICS LETTERS
2 October 1978
NEGATIVE ION FORMATION BY CHARGE EXCHANGE BETWEEN HYDROGEN AND CESIUM* J.R. HISKES, A.M. KARO and P.A. WILLMANN Lawrence Livermore Laboratory, Livermore, CA, USA and
W.J. STEVENS NBS, Washington,DC, USA Received 27 June 1978
The close coupled equations provide low-energy cross sections which are in good agreement with the experimental values.
The charge exchange of hydrogen in Cs vapor has attracted considerable attention in recent years as a means for generating beams of negative hydrogen ions [ 11. In general, for protons incident upon thick cesiurn targets, the equilibrium ratio of negative ions per incident proton is determined by six formation-destruction processes [2,3] ; in practice however, this ratio is dominated by the charge exchange reaction, H+Cs-+H-
+Cs+,
1
H + Cs +
T
H- + Cs+
(1)
and by the process of single electron detachment following H- collisions on Cs. Experimental values for reaction (1) at low energies are given in refs. [2,3] and summarized in fig. 1. The theoretical description for this process at the low energies where the cross section and equilibrium ratio are large requires the solution of a set of closecoupled equations [4]. The calculation of the cross section for transitions to a particular electronic state i of the system reduces to a set of first order equations for the expansion coefficients of the molecular electronic states [5] :
(2) * Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore Laboratory under contract number W-7405.ENG-48.
OL 0
I
I
I
I
I
0.4
0.8
1.2
1.6
2.0
I
2.4
Hydrogen energy, keV
Fig. 1. Charge exchange cross section plotted as a function of incident hydrogen energy. Flagged experimental points SBLAH: ref. [ 21; experimental curve CABR: ref. [ 31; theoretical curve OSB: ref. [6] ; theoretical curve HKWS, this work.
with
Wij= l/flu S (Ej - Ei) dZ, _-oo
(3)
rij = (ZfR)Mij + (b/R)Nij ,
(4)
Mii = <~~ Ia/aR I‘ki>,
(5) 221
Volume 68A, number 2
N
/
=
PHYSICS LETTERS
“I”i ‘1’R’~’~O ‘I’’ ‘. I J I .,
‘6’ ‘. I
~
The coordinate z is measured along the straight-line trajectory of the H atom; v is the relative velocity; ~1’~ is the molecular fixed-nuclei electronic function, and E~the molecular energy. The coupling terms M11 and IVi! have a simple physical interpretation: the former arises from the compression and tension of the dec. tronic motions along the internuclear axis, R, as the H atom approaches and recedes from the target Cs; the latter from the continuous readjustment of the electronic motions due to the changing orientation of the internuclear axis as 0 turns through an angle of 180°during the course of the collision. The coupling terms have the property M1, = —Mfl, and N~1= JV~the second equality follows from the hermitian property of the matrix elements of angular momentum. Integrating over a range of impact parameters b, the cross section for transitions to the state i becomes a.1 = 2ir JtbIC.(z 1
=
+oo~I2 db /
~ “
‘
0
The electronic configuration of H~implies a singlet state on the right hand side of reaction (1). The H atom however, can approach the Cs in either a singlet or a triplet configuration; implicit in eq. (7) is a spin statistical factor equal to one-fourth which accounts for the fact that only singlet transitions can lead to negative ions. Eqs. (2) through (7) for reaction (1) have been solved by Olson et a!. [6] ; these authors have generated the energy levels and coupling terms using a set of ab initio functions, ‘I’~,derived from a one-electron model. Their calculation utilized four electronic states including the lowest singlet ir state, and full rotational coupling. A comparison of their cross section with the experimental data is included in fig. 1; the calculated cross section falls below the experimental curve at low energies and lies above the experimental points at the higher energies. We have recalculated the cross section given by eqs. (2)—(7) using some new experimental data for CsH together with a new calculation of the CsH ground state. In a recent paper [7] potential energy curves for the ground and first excited electronic states of CsH have been derived spectroscopically over an intermediate range of internuclear separations; these data ,
222
2 October 1978
include the energy difference between the minima of the X ~ and A ~ states. A pseudo-potential calculation of the CsH ground state [8] shOws a potential minimum of —1.90 eV, which compares with an earlier spectroscopic value [9] equal to —1.96 eV. At large I
internuclear separations we have relied upon the p0tential shapes from refs. [8—10]. For the two upper states we have taken the energy curves of ref. [7] excepting that at small internuclear separations and for all four states we have used the energy differences of the Ba united-atom limit. The only coupling terms extant in the literature are those given in ref. [6] which we have adopted here. As shown in fig. 1, our cross section plotted as a function of energy agrees qualitatively with the experimental data. At high energies the cross section falls between the data of refs. [2] and [3] ; at the lowest energy our cross section compares favorably with ref. [31. Increasing the potential minimum of the ground state to —1.96 eV (cf. ref. [9]) increased the 300eV peak ,
by four per cent. The minimum 500 eV approximately is the only apparent discrepancy; notice thatatthe statistical uncertainties in the experimental data are sufficiently large to accommodate a similar variation in the cross section. In summaly, the use of the close-coupled equations together with the molecular energy levels and coupling matrix elements available in the literature provides for qualitative agreement with the experimental cross sections, and for good quantitative agreement over most of the energy range from 200 to 2000 eV. [1] E.B. Hooper Jr., O.A. Anderson, T.J. Orzechowski and P. Poulson, Proc. Symp. on the Production and neutralization of negative hydrogen ions and beams (Brookhaven National Lab., 1977). [2] A.S. Schlachter, P.J. Bjorkholm, D.H. Loyd, L.W. Anderson and W. Haeberli, Phys. Rev. 177 (1969)
[31 C. Cisneros,
I. Alvarez, C.F. Barnett and J.A. Ray, Phys. Rev. A14 (1976) 76. [41 D.R. Bates, H.S.W. Massey and A.L. Stewart, Proc. Roy. Soc. London 216A (1953) 437. [5] C.F. Melius and W.A. Goddard III, Chem. Phys. Lett. 15 [6] ~ E.J. Shipsey and J.C. Browne, Phys. Rev. A13 (1976) 180. [7] Y.K. Hsieh, S.C. Yang, A.C. Tam and W.C. Stwalley, J. Chem. Phys. 68 (1978) 1448. [8] w.J. Stevens, A.M. Karo and J.R. Hiskes, to be published. [9] G.M. Aliny and M. Rassweiler, Phys. Rev. 53 (1938) 890. [10] A.M. Karo, M.A. Gardner and J.R. Hiskes, J. Chem. Phys. 68(1978) 1942.
PHYSICS LETTERS
2 October 1978
NEGATIVE ION FORMATION BY CHARGE EXCHANGE BETWEEN HYDROGEN AND CESIUM* J.R. HISKES, A.M. KARO and P.A. WILLMANN Lawrence Livermore Laboratory, Livermore, CA, USA and
W.J. STEVENS NBS, Washington,DC, USA Received 27 June 1978
The close coupled equations provide low-energy cross sections which are in good agreement with the experimental values.
The charge exchange of hydrogen in Cs vapor has attracted considerable attention in recent years as a means for generating beams of negative hydrogen ions [ 11. In general, for protons incident upon thick cesiurn targets, the equilibrium ratio of negative ions per incident proton is determined by six formation-destruction processes [2,3] ; in practice however, this ratio is dominated by the charge exchange reaction, H+Cs-+H-
+Cs+,
1
H + Cs +
T
H- + Cs+
(1)
and by the process of single electron detachment following H- collisions on Cs. Experimental values for reaction (1) at low energies are given in refs. [2,3] and summarized in fig. 1. The theoretical description for this process at the low energies where the cross section and equilibrium ratio are large requires the solution of a set of closecoupled equations [4]. The calculation of the cross section for transitions to a particular electronic state i of the system reduces to a set of first order equations for the expansion coefficients of the molecular electronic states [5] :
(2) * Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore Laboratory under contract number W-7405.ENG-48.
OL 0
I
I
I
I
I
0.4
0.8
1.2
1.6
2.0
I
2.4
Hydrogen energy, keV
Fig. 1. Charge exchange cross section plotted as a function of incident hydrogen energy. Flagged experimental points SBLAH: ref. [ 21; experimental curve CABR: ref. [ 31; theoretical curve OSB: ref. [6] ; theoretical curve HKWS, this work.
with
Wij= l/flu S (Ej - Ei) dZ, _-oo
(3)
rij = (ZfR)Mij + (b/R)Nij ,
(4)
Mii = <~~ Ia/aR I‘ki>,
(5) 221
Volume 68A, number 2
N
/
=
PHYSICS LETTERS
“I”i ‘1’R’~’~O ‘I’’ ‘. I J I .,
‘6’ ‘. I
~
The coordinate z is measured along the straight-line trajectory of the H atom; v is the relative velocity; ~1’~ is the molecular fixed-nuclei electronic function, and E~the molecular energy. The coupling terms M11 and IVi! have a simple physical interpretation: the former arises from the compression and tension of the dec. tronic motions along the internuclear axis, R, as the H atom approaches and recedes from the target Cs; the latter from the continuous readjustment of the electronic motions due to the changing orientation of the internuclear axis as 0 turns through an angle of 180°during the course of the collision. The coupling terms have the property M1, = —Mfl, and N~1= JV~the second equality follows from the hermitian property of the matrix elements of angular momentum. Integrating over a range of impact parameters b, the cross section for transitions to the state i becomes a.1 = 2ir JtbIC.(z 1
=
+oo~I2 db /
~ “
‘
0
The electronic configuration of H~implies a singlet state on the right hand side of reaction (1). The H atom however, can approach the Cs in either a singlet or a triplet configuration; implicit in eq. (7) is a spin statistical factor equal to one-fourth which accounts for the fact that only singlet transitions can lead to negative ions. Eqs. (2) through (7) for reaction (1) have been solved by Olson et a!. [6] ; these authors have generated the energy levels and coupling terms using a set of ab initio functions, ‘I’~,derived from a one-electron model. Their calculation utilized four electronic states including the lowest singlet ir state, and full rotational coupling. A comparison of their cross section with the experimental data is included in fig. 1; the calculated cross section falls below the experimental curve at low energies and lies above the experimental points at the higher energies. We have recalculated the cross section given by eqs. (2)—(7) using some new experimental data for CsH together with a new calculation of the CsH ground state. In a recent paper [7] potential energy curves for the ground and first excited electronic states of CsH have been derived spectroscopically over an intermediate range of internuclear separations; these data ,
222
2 October 1978
include the energy difference between the minima of the X ~ and A ~ states. A pseudo-potential calculation of the CsH ground state [8] shOws a potential minimum of —1.90 eV, which compares with an earlier spectroscopic value [9] equal to —1.96 eV. At large I
internuclear separations we have relied upon the p0tential shapes from refs. [8—10]. For the two upper states we have taken the energy curves of ref. [7] excepting that at small internuclear separations and for all four states we have used the energy differences of the Ba united-atom limit. The only coupling terms extant in the literature are those given in ref. [6] which we have adopted here. As shown in fig. 1, our cross section plotted as a function of energy agrees qualitatively with the experimental data. At high energies the cross section falls between the data of refs. [2] and [3] ; at the lowest energy our cross section compares favorably with ref. [31. Increasing the potential minimum of the ground state to —1.96 eV (cf. ref. [9]) increased the 300eV peak ,
by four per cent. The minimum 500 eV approximately is the only apparent discrepancy; notice thatatthe statistical uncertainties in the experimental data are sufficiently large to accommodate a similar variation in the cross section. In summaly, the use of the close-coupled equations together with the molecular energy levels and coupling matrix elements available in the literature provides for qualitative agreement with the experimental cross sections, and for good quantitative agreement over most of the energy range from 200 to 2000 eV. [1] E.B. Hooper Jr., O.A. Anderson, T.J. Orzechowski and P. Poulson, Proc. Symp. on the Production and neutralization of negative hydrogen ions and beams (Brookhaven National Lab., 1977). [2] A.S. Schlachter, P.J. Bjorkholm, D.H. Loyd, L.W. Anderson and W. Haeberli, Phys. Rev. 177 (1969)
[31 C. Cisneros,
I. Alvarez, C.F. Barnett and J.A. Ray, Phys. Rev. A14 (1976) 76. [41 D.R. Bates, H.S.W. Massey and A.L. Stewart, Proc. Roy. Soc. London 216A (1953) 437. [5] C.F. Melius and W.A. Goddard III, Chem. Phys. Lett. 15 [6] ~ E.J. Shipsey and J.C. Browne, Phys. Rev. A13 (1976) 180. [7] Y.K. Hsieh, S.C. Yang, A.C. Tam and W.C. Stwalley, J. Chem. Phys. 68 (1978) 1448. [8] w.J. Stevens, A.M. Karo and J.R. Hiskes, to be published. [9] G.M. Aliny and M. Rassweiler, Phys. Rev. 53 (1938) 890. [10] A.M. Karo, M.A. Gardner and J.R. Hiskes, J. Chem. Phys. 68(1978) 1942.