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1
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0033204050
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See the review by A. Caneschi et al., J. Magn. Magn. Mater. 200, 182 (1999), and the references therein, for a detailed discussion of the experimental basis for this description.
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J. Magn. Magn. Mater.
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Caneschi, A.1
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K. Wieghardt, K. Pohl, I. Jibril, and G. Huttner, Angew. Chem. Int. Ed. Engl. 23, 77 (1984).
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A.-L. Barra, P. Debrunner, D. Gatteschi, Ch.E. Schultz, and R. Sessoli, Europhys. Lett. 35, 133 (1996)
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A.-L. Barra, P. Debrunner, D. Gatteschi, Ch.E. Schultz, and R. Sessoli, Europhys. Lett. 35, 133 (1996).
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5
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C. Sangregorio, T. Ohm, C. Paulsen, R. Sessoli, and D. Gatteschi, Phys. Rev. Lett. 78, 4645 (1997).
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Sangregorio, C.1
Ohm, T.2
Paulsen, C.3
Sessoli, R.4
Gatteschi, D.5
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6
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0000042337
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R. Caciuffo, G. Amoretti, A. Murani, R. Sessoli, A. Caneschi, and D. Gatteschi, Phys. Rev. Lett. 81, 4744 (1998).
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Phys. Rev. Lett.
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Caciuffo, R.1
Amoretti, G.2
Murani, A.3
Sessoli, R.4
Caneschi, A.5
Gatteschi, D.6
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8
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85038920533
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We have omitted fourth-order anisotropy terms that are necessary for a quantitative fit to the data in Ref. 7, but which do not change the essential concepts. Inclusion of these terms is possible, but it makes an already complex analysis even more complicated, and so we do not undertake it here. We also note that Eq. (1.1) differs from Eq. (1) of Ref. 7 by an additive term proportional to (Formula presented), which is a constant as it commutes with (Formula presented)
-
We have omitted fourth-order anisotropy terms that are necessary for a quantitative fit to the data in Ref. 7, but which do not change the essential concepts. Inclusion of these terms is possible, but it makes an already complex analysis even more complicated, and so we do not undertake it here. We also note that Eq. (1.1) differs from Eq. (1) of Ref. 7 by an additive term proportional to (Formula presented), which is a constant as it commutes with (Formula presented).
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13
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2642512023
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J. Friedman, M.P. Sarachik, J. Tejada, and R. Ziolo, Phys. Rev. Lett. 76, 3830 (1996).
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Friedman, J.1
Sarachik, M.P.2
Tejada, J.3
Ziolo, R.4
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15
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0001667689
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J.A.A.J. Perenboom, J.S. Brooks, S. Hill, T. Hathaway, and N.S. Dalal, Phys. Rev. B 58, 330 (1998).
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Phys. Rev. B
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Perenboom, J.A.A.J.1
Brooks, J.S.2
Hill, S.3
Hathaway, T.4
Dalal, N.S.5
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17
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5244325951
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W. Wernsdorfer, R. Sessoli, A. Caneschi, D. Gatteschi, and A. Cornia, J. Appl. Phys. 87, 5481 (2000).
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J. Appl. Phys.
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Wernsdorfer, W.1
Sessoli, R.2
Caneschi, A.3
Gatteschi, D.4
Cornia, A.5
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18
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85038927045
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cond-mat/0009478 (unpublished);
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Thus, in collaboration with C. S. Park [cond-mat/0009478 (unpublished);
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Park, C.S.1
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19
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85038917379
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cond-mat/0010373(unpublished)], we have used our approach to develop analytic approximations for the quenching points in (Formula presented) which have not yet been seen. We invite readers to develop similar formulas from numerical diagonalization of the relevant Hamiltonian. Similarly, with E. Keçecioğlu (in preparation), we have found approximate formulas for (Formula presented) when the higher order terms are included. As part of our analysis, we understand, e.g., why with these terms the number of diabolical points for the lowest two levels when (Formula presented) is even (Wernsdorfer and Sessoli see four for (Formula presented) and not odd
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C. S. Parkcond-mat/0010373(unpublished)], we have used our approach to develop analytic approximations for the quenching points in (Formula presented) which have not yet been seen. We invite readers to develop similar formulas from numerical diagonalization of the relevant Hamiltonian. Similarly, with E. Keçecioğlu (in preparation), we have found approximate formulas for (Formula presented) when the higher order terms are included. As part of our analysis, we understand, e.g., why with these terms the number of diabolical points for the lowest two levels when (Formula presented) is even (Wernsdorfer and Sessoli see four for (Formula presented) and not odd.
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Park, C.S.1
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27
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85038966692
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Note, however, that when viewed in the larger (Formula presented) plane, or the full three-dimensional space of magnetic fields (Formula presented), all points of degeneracy are diabolical
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Note, however, that when viewed in the larger (Formula presented) plane, or the full three-dimensional space of magnetic fields (Formula presented), all points of degeneracy are diabolical.
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31
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15744369090
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P.A. Braun, Rev. Mod. Phys. 65, 115 (1993). See the opening part of Sec. II, and Appendix C for references to many other problems solved by the DPI method.
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(1993)
Rev. Mod. Phys.
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, pp. 115
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Braun, P.A.1
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34
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0003692706
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L. Gunther and B. Barbara Kluwer, Dordecht
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in Quantum Tunneling of Magnetization—QTM’94, edited by L. Gunther and B. Barbara (Kluwer, Dordecht, 1995).
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(1995)
Quantum Tunneling of Magnetization—QTM’94
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35
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85038913852
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math-ph/0003005 (unpublished)
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A. Garg, math-ph/0003005 (unpublished).
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Garg, A.1
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36
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85038926928
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We note that recursion relations with arbitrary numbers of terms are considered in Sec. 7 of Ref. 26(b), but, using the tight-binding terminology, with restrictions on the further neighbor hopping elements that rule out the possibility of nonclassical turning points. In addition, it is assumed that the farthest neighbor hopping dominates all others, so that the q vs m relation is essentially that of a nearest-neighbor or three-term recursion relation problem [see Eq. (7.11) there]. Even when (Formula presented) is pure imaginary throughout the tunneling region, the approximate formula for the tunnel splitting, Eq. (7.13), is inapplicable in many situations, for instance, the (Formula presented) problem that we would get with (Formula presented), but without neglecting the fourth-order terms
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We note that recursion relations with arbitrary numbers of terms are considered in Sec. 7 of Ref. 26(b), but, using the tight-binding terminology, with restrictions on the further neighbor hopping elements that rule out the possibility of nonclassical turning points. In addition, it is assumed that the farthest neighbor hopping dominates all others, so that the q vs m relation is essentially that of a nearest-neighbor or three-term recursion relation problem [see Eq. (7.11) there]. Even when (Formula presented) is pure imaginary throughout the tunneling region, the approximate formula for the tunnel splitting, Eq. (7.13), is inapplicable in many situations, for instance, the (Formula presented) problem that we would get with (Formula presented), but without neglecting the fourth-order terms.
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37
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0033901203
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Proceedings of the XXII International Conference on Low Temperature Physics, Espoo and Helsinki, Finland, Aug. 4–11, 1999
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A. Garg, Proceedings of the XXII International Conference on Low Temperature Physics, Espoo and Helsinki, Finland, Aug. 4–11, 1999 Physica B 280, 269 (2000).
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(2000)
Physica B
, vol.280
, pp. 269
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Garg, A.1
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38
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85038955947
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See Eqs. (3) and (4) in Ref. 29, or Eqs. (5) and (6) of Ref. 19(e)
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See Eqs. (3) and (4) in Ref. 29, or Eqs. (5) and (6) of Ref. 19(e).
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39
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4243843874
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Ersin Keçecioğlu and A. Garg, Phys. Rev. B 63, 064422 (2001)
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Ersin Keçecioğlu and A. Garg, Phys. Rev. B 63, 064422 (2001).
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40
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85038967939
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L.D. Landau and E.M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1977), 3rd ed. See Sec. 50, Problem 3. The final answer here is our Eq. (1.6) minus the curvature correction factor (Formula presented) [Eq. (1.7)]
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L.D. Landau and E.M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1977), 3rd ed. See Sec. 50, Problem 3. The final answer here is our Eq. (1.6) minus the curvature correction factor (Formula presented) [Eq. (1.7)].
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41
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36149026938
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Conyers Herring, Rev. Mod. Phys. 34, 631 (1962)
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Conyers Herring, Rev. Mod. Phys. 34, 631 (1962).
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42
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0007123069
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Dokl. Akad. Nauk (SSSR) 151, 822 (1963)
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L.P. Gor’kov and L.P. Pitaevski, Dokl. Akad. Nauk (SSSR) 151, 822 (1963) [Sov. Phys. Dokl. 8, 788 (1964)].
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Sov. Phys. Dokl.
, vol.8
, pp. 788
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Gor’kov, L.P.1
Pitaevski, L.P.2
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45
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85038889033
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We do not know a reference where these formulas, especially the integral form (1.10) for (Formula presented) have appeared before, although it seems almost certain that many earlier workers must be aware of them
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We do not know a reference where these formulas, especially the integral form (1.10) for (Formula presented) have appeared before, although it seems almost certain that many earlier workers must be aware of them.
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46
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0000630713
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S.P. Kou, J.Q. Liang, Y.B. Zhang, and F.C. Pu, Phys. Rev. B 59, 11 792 (1999).
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(1999)
Phys. Rev. B
, vol.59
, pp. 11 792
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Kou, S.P.1
Liang, J.Q.2
Zhang, Y.B.3
Pu, F.C.4
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47
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0001707057
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J.-Q. Liang, H. J. W. Müller-Kirsten, D. K. Park, and F.-C. Pu, Phys. Rev. B 61, 8856 (2000)
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J.-Q. Liang, H. J. W. Müller-Kirsten, D. K. Park, and F.-C. Pu, Phys. Rev. B 61, 8856 (2000).
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48
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85038911517
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One must instead resort to the coordinate-free methods of symplectic mechanics. This point is further explained by B. Simons in his webnotes, Concepts in Theoretical Physics, Sec. 3.2.4, at www.tcm.phy.cam.ac.uk/̃bds10
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One must instead resort to the coordinate-free methods of symplectic mechanics. This point is further explained by B. Simons in his webnotes, Concepts in Theoretical Physics, Sec. 3.2.4, at www.tcm.phy.cam.ac.uk/̃bds10.
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49
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0000582036
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See also M. Stone, Nuc. Phys. B 314, 557 (1989), Sec. 3.
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(1989)
Nuc. Phys. B
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, pp. 557
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Stone, M.1
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54
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45949130769
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M. Wilkinson, Physica D 21, 341 (1986) (see final paragraph of Sec. 6).
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Physica D
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, pp. 341
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Wilkinson, M.1
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57
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1642278713
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Tosio Kato, J. Phys. Soc. Jpn. 4, 334 (1949)
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Tosio Kato, J. Phys. Soc. Jpn. 4, 334 (1949).
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59
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85038903352
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S. Creagh, in Tunneling in Complex Systems, edited by Steven Tomsovic (World Scientific, Singapore, 1998)
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S. Creagh, in Tunneling in Complex Systems, edited by Steven Tomsovic (World Scientific, Singapore, 1998).
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60
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33744584849
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In fact, because of the two nearly coincident turning points, it would be necessary to use quadratic connection formulas, given, e.g., by Eqs. (3.63) and (4.21) in M.V. Berry and K.E. Mount, Rep. Prog. Phys. 35, 315 (1972). Use of a linear connection formula, as in Ref. 32, leads to a splitting that lacks the curvature correction factor (Formula presented) [Eq. (1.7)].
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(1972)
Rep. Prog. Phys.
, vol.35
, pp. 315
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Berry, M.V.1
Mount, K.E.2
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61
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85038947310
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Since the eikonal equation (2.6) has four solutions, there are four DPI solutions, all of which break down at the turning point at (Formula presented). In Ref. 27 we derive connection formulas for all four solutions, of which, the one used here is the case there designated by (Formula presented)
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Since the eikonal equation (2.6) has four solutions, there are four DPI solutions, all of which break down at the turning point at (Formula presented). In Ref. 27 we derive connection formulas for all four solutions, of which, the one used here is the case there designated by (Formula presented).
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