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1
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0037787395
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note
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We will refer to the present paper and the following paper [2] as Paper I or II when suitable.
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3
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85088491219
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note
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+ ion is in an excited (ground) state, we call the process single ionization with excitation (without excitation).
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4
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0038802066
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note
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By the spectrum we mean the singly different cross section for one detected electron as a function of energy in double ionization in photoabsorption at given incident photon energy, integrated over both electron angles.
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5
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6144231482
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E.W.B. Dias, H.S. Chakraborty, P.C. Deshmuhk, S.T. Manson, O. Hemmers, P. Glans, D.L. Hansen, H. Wang, S.B. Whitfield, D.W. Lindle, R. Wehlitz, J.C. Levin, I.A. Sellin, and R.C.C. Perera, Phys. Rev. Lett. 78, 4553 (1997).
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Phys. Rev. Lett.
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Dias, E.W.B.1
Chakraborty, H.S.2
Deshmuhk, P.C.3
Manson, S.T.4
Hemmers, O.5
Glans, P.6
Hansen, D.L.7
Wang, H.8
Whitfield, S.B.9
Lindle, D.W.10
Wehlitz, R.11
Levin, J.C.12
Sellin, I.A.13
Perera, R.C.C.14
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6
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0001522906
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D.L. Hansen, O. Hemmers, H. Wang, D.W. Lindle, P. Focke, I.A. Sellin, C. Heske, H. S. Chakraborty, P. C. Deshmukh, and S.T. Manson, Phys. Rev. A 60 R2641 (1999).
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Phys. Rev. A
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Hansen, D.L.1
Hemmers, O.2
Wang, H.3
Lindle, D.W.4
Focke, P.5
Sellin, I.A.6
Heske, C.7
Chakraborty, H.S.8
Deshmukh, P.C.9
Manson, S.T.10
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7
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0001650316
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J.A.R. Samson, W.C. Stolte, Z.-X. He, J.N. Cutler, Y. Lu, and R.J. Bartlett, Phys. Rev. A 57, 1906 (1998).
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Phys. Rev. A
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Samson, J.A.R.1
Stolte, W.C.2
He, Z.-X.3
Cutler, J.N.4
Lu, Y.5
Bartlett, R.J.6
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8
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0000689332
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R. Wehlitz, M.-T. Huang, B.D. DePaola, J.C. Levin, I.A. Sellin, T. Nagata, J.W. Cooper, and Y. Azuma, Phys. Rev. Lett. 81, 1813 (1998).
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Phys. Rev. Lett.
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Wehlitz, R.1
Huang, M.-T.2
DePaola, B.D.3
Levin, J.C.4
Sellin, I.A.5
Nagata, T.6
Cooper, J.W.7
Azuma, Y.8
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9
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0038419343
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R. Dörner, V. Mergel, O. Jagutzki, L. Spielberger, J. Ullrich, R. Moshammer, and H. Schmidt-Böcking, Phys. Rep. 330, 95 (2000).
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(2000)
Phys. Rep.
, vol.330
, pp. 95
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Dörner, R.1
Mergel, V.2
Jagutzki, O.3
Spielberger, L.4
Ullrich, J.5
Moshammer, R.6
Schmidt-Böcking, H.7
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10
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0000491274
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Y. Qiu, Y.Z. Teng, J. Burgdörfer, and Y. Wang, Phys. Rev. A 57, R1489 (1998).
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Phys. Rev. A
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Qiu, Y.1
Teng, Y.Z.2
Burgdörfer, J.3
Wang, Y.4
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13
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0034317645
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M.Ya. Amusia, N.B. Avdonina, E.G. Drukarev, S.T. Manson, and R.H. Pratt, Phys. Rev. Lett. 85, 4703 (2000).
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Phys. Rev. Lett.
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, pp. 4703
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Amusia, M.Ya.1
Avdonina, N.B.2
Drukarev, E.G.3
Manson, S.T.4
Pratt, R.H.5
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15
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0032606904
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M.T. Huang, R. Wehlitz, Y. Azuma, L. Pibida, I.A. Sellin, M. Koide, H. Ishijima, and T. Nagata. Phys. Rev. A 59, 3397 (1999).
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(1999)
Phys. Rev. A
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Huang, M.T.1
Wehlitz, R.2
Azuma, Y.3
Pibida, L.4
Sellin, I.A.5
Koide, M.6
Ishijima, H.7
Nagata, T.8
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17
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0001263102
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R. Dörner, T. Vogt, V. Mergel, H. Khemliche, S. Kravis, C.L. Cocke, J. Ullrich, M. Unverzagt, L. Spielberger, M. Damrau, O. Jagutzki, I. Ali, B. Weaver, K. Ullmann, C.C. Hsu, M. Jung, E.P. Kanter, B. Sonntag, M.H. Prior, E. Rotenberg, J. Denlinger, T. Warwick, S.T. Manson, and H. Schmidt-Böcking, Phys. Rev. Lett. 76, 2654 (1996).
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(1996)
Phys. Rev. Lett.
, vol.76
, pp. 2654
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Dörner, R.1
Vogt, T.2
Mergel, V.3
Khemliche, H.4
Kravis, S.5
Cocke, C.L.6
Ullrich, J.7
Unverzagt, M.8
Spielberger, L.9
Damrau, M.10
Jagutzki, O.11
Ali, I.12
Weaver, B.13
Ullmann, K.14
Hsu, C.C.15
Jung, M.16
Kanter, E.P.17
Sonntag, B.18
Prior, M.H.19
Rotenberg, E.20
Denlinger, J.21
Warwick, T.22
Manson, S.T.23
Schmidt-Böcking, H.24
more..
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18
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85088489296
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B is the binding energy of the state that is ionized), but still ω≪m (to stay with a nonrelativistic description of electrons). We are using a system of units, ℏ = c = 1.
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22
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0003930336
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(North-Holland, Amsterdam)
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Albert Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1967), pp. 472-473.
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(1967)
Quantum Mechanics
, pp. 472-473
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Messiah, A.1
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29
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0037787388
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This example of generalization of FT is of more general validity, since it shows that we can apply the AFT approach to functions that have additional p dependence (after pulling out the plane-wave oscillations). This additional p dependence does not cause any problem (and our Coulombic functions are an example of that) as long as it does not imply oscillations that would cancel the plane-wave oscillations.
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31
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0001406593
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C.R. Myers, C.J. Umrigar, J.P. Sethna, and J.D. Morgan, III Phys. Rev. A 44, 5537 (1991).
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(1991)
Phys. Rev. A
, vol.44
, pp. 5537
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Myers, C.R.1
Umrigar, C.J.2
Sethna, J.P.3
Morgan J.D. III4
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32
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0038464214
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Spherical waves are the continuum state pieces that asymptotically behave as exp(ipr)/r.
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33
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0038802055
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Neglecting retardation means taking the oscillatory e-γ interaction factor exp(ik·r) equal to 1 in the matrix element. In using the full multipole expansion, this approximation corresponds to dipole approximation without retardation (sometimes inaccurately called dipole approximation). When taking any needed contribution beyond this dipole approximation without retardation, we say we are including retardation (although perhaps just to the leading order, as in calculating the quasifree contribution).
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34
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0037787392
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As discussed later in considering ionization of a two-electron atom, the overall factor is generally a function of all the other coordinates describing the atomic system, except the relative coordinate describing the coalescence. In IPA, this factor is just a constant, dependent on screening.
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40
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0038464215
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This is one of the points of difference from a perturbative approach (e.g., Born expansion). The Born expansion gives equal weight to all regions, while the AFT approach tells us that it is the singularity region that is important for high-energy photoabsorption.
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46
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0037787389
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1 = 0. In the fully symmetric form of the matrix element, any leading contribution comes half from one singularity, and the other half from the other singularity; but the result is the same.
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47
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0038125113
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In the Paper II, we will consider ionization from excited states, which is also relevant to ionization from shells outer to the K shell in many-electron atoms.
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51
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0038464218
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This is analogous to the IPA case, where the screening effects on the Coulombic shape of the wave functions in the vicinity of the coalescence were argued to be small.
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52
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0038802056
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Equation (25) is also the dominant term in the expansion of the initial-state wave function in terms of angular momentum l of the electron approaching the nucleus (only the l = 0 term is retained). In the case of the ground state of He, the probability to find an electron approaching the nucleus with l = 0 is dominant, while the probability for higher angular momenta is negligible and is not discussed here for simplicity. These higher angular momenta do not contribute to the order we are interested in this paper. More general partitioning is considered in Paper II in connection with photoabsorption from excited states.
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53
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85088490763
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1, which vanishes.
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55
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0038802058
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The effect has been observed in a modification of the IPA result for single ionization from l ≠ 0 states [5,6], but here we see that it also affects ionization from the l = 0 state with excitations to l ≠ 0 states.
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56
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20444415952
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M. Ya Amusia, E.G. Drukarev, V.G. Gorshkov, and M.P. Kazachkov, J. Phys. B 8, 1248 (1975).
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(1975)
J. Phys. B
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, pp. 1248
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Amusia, M.Y.1
Drukarev, E.G.2
Gorshkov, V.G.3
Kazachkov, M.P.4
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60
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0000894056
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K.I. Hino, T. Ishihara, F. Shimizu, N. Toshima, and J.H. McGuire, Phys. Rev. A 48, 1271 (1993).
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Phys. Rev. A
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Hino, K.I.1
Ishihara, T.2
Shimizu, F.3
Toshima, N.4
McGuire, J.H.5
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61
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0038802060
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note
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These findings that the final-state interaction vanishes with increasing energy in any form suggests that there is a problem in the many-body perturbation calculations of Ref. [57], in which diagrams containing final-state interaction (so called TS1 and SO) are large and interfere destructively with diagrams containing only initial-state correlation (GSC). While the correct high-energy result is obtained, the final state interaction appears to be important. We were unable to fully resolve this issue, since the needed intermediate steps of the numerical calculation of Ref. [57] are no longer available. K. Hino (private communication).
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62
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0037787390
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note
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Terms that cannot be integrated independently arise from logarithmic terms, but these vanish faster than r for decreasing r.
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63
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0038125112
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Y. Wang, J.M. McGuire, J. Burgörfer, Y.Z. Tang, and Y. Qiu, Bull. Am. Phys. Soc. 43, 1356 (1998).
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Bull. Am. Phys. Soc.
, vol.43
, pp. 1356
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Wang, Y.1
McGuire, J.M.2
Burgörfer, J.3
Tang, Y.Z.4
Qiu, Y.5
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65
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85088490462
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note
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1.
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66
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85088489869
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note
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2 ≫ a starting from the SO limit [Eq. (37)].
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68
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0000251340
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L. Spielberger, O. Jagutzki, R. Dörner, J. Ullrich, U. Meyer, V. Mergel, M. Unverzagt, M. Damrau, T. Vogt, I. Ali, Kh. Khayyat, D. Bahr, H.G. Schmidt, R. Frahm, and H. Schmidt-Böcking, Phys. Rev. Lett. 74, 4615 (1995).
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Phys. Rev. Lett.
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Spielberger, L.1
Jagutzki, O.2
Dörner, R.3
Ullrich, J.4
Meyer, U.5
Mergel, V.6
Unverzagt, M.7
Damrau, M.8
Vogt, T.9
Ali, I.10
Khayyat, Kh.11
Bahr, D.12
Schmidt, H.G.13
Frahm, R.14
Schmidt-Böcking, H.15
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69
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0000624053
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R.C. Forrey, H.R. Sadehgpour, J.D. Baker, J.D. Morgan, III, and A. Dalgarno, Phys. Rev. A 51, 2112 (1995).
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Phys. Rev. A
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Forrey, R.C.1
Sadehgpour, H.R.2
Baker, J.D.3
Morgan J.D. III4
Dalgarno, A.5
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