-
2
-
-
0033248656
-
-
The three-nucleon forces from the chiral seagulls of Ref. [10] are rederived here in the context of another type of off-shell behavior arising from field redefinitions. These terms should be added to the "Born-term" results of Ref. [5] to obtain complete two-pion-exchange three-nucleon forces of subleading order (corresponding to an energy-independent OPEP)
-
[2] J. L. Friar, D. Hüber, and U. van Kolck, Phys. Rev. C 59, 53 (1999). The three-nucleon forces from the chiral seagulls of Ref. [10] are rederived here in the context of another type of off-shell behavior arising from field redefinitions. These terms should be added to the "Born-term" results of Ref. [5] to obtain complete two-pion-exchange three-nucleon forces of subleading order (corresponding to an energy-independent OPEP).
-
(1999)
Phys. Rev. C
, vol.59
, pp. 53
-
-
Friar, J.L.1
Hüber, D.2
Van Kolck, U.3
-
3
-
-
25544443177
-
-
A great number of quasipotential equations exist and several of these are treated in this reference. Others not treated are cited
-
[3] J. L. Friar, Phys. Rev. C 22, 796 (1980). A great number of quasipotential equations exist and several of these are treated in this reference. Others not treated are cited. Some interesting and more recent treatments are D. R. Phillips and S. J. Wallace, ibid. 54, 507 (1996); A. Stadler and F. Gross, Phys. Rev. Lett. 78, 26 (1997); V. Pascalutsa and J. A. Tjon, Phys. Lett. B 435, 245 (1998).
-
(1980)
Phys. Rev. C
, vol.22
, pp. 796
-
-
Friar, J.L.1
-
4
-
-
0030508743
-
-
[3] J. L. Friar, Phys. Rev. C 22, 796 (1980). A great number of quasipotential equations exist and several of these are treated in this reference. Others not treated are cited. Some interesting and more recent treatments are D. R. Phillips and S. J. Wallace, ibid. 54, 507 (1996); A. Stadler and F. Gross, Phys. Rev. Lett. 78, 26 (1997); V. Pascalutsa and J. A. Tjon, Phys. Lett. B 435, 245 (1998).
-
(1996)
Phys. Rev. C
, vol.54
, pp. 507
-
-
Phillips, D.R.1
Wallace, S.J.2
-
5
-
-
0002240579
-
-
[3] J. L. Friar, Phys. Rev. C 22, 796 (1980). A great number of quasipotential equations exist and several of these are treated in this reference. Others not treated are cited. Some interesting and more recent treatments are D. R. Phillips and S. J. Wallace, ibid. 54, 507 (1996); A. Stadler and F. Gross, Phys. Rev. Lett. 78, 26 (1997); V. Pascalutsa and J. A. Tjon, Phys. Lett. B 435, 245 (1998).
-
(1997)
Phys. Rev. Lett.
, vol.78
, pp. 26
-
-
Stadler, A.1
Gross, F.2
-
6
-
-
0346943110
-
-
[3] J. L. Friar, Phys. Rev. C 22, 796 (1980). A great number of quasipotential equations exist and several of these are treated in this reference. Others not treated are cited. Some interesting and more recent treatments are D. R. Phillips and S. J. Wallace, ibid. 54, 507 (1996); A. Stadler and F. Gross, Phys. Rev. Lett. 78, 26 (1997); V. Pascalutsa and J. A. Tjon, Phys. Lett. B 435, 245 (1998).
-
(1998)
Phys. Lett. B
, vol.435
, pp. 245
-
-
Pascalutsa, V.1
Tjon, J.A.2
-
7
-
-
0000975341
-
-
[4] J. L. Friar, Ann. Phys. (N.Y.) 104, 380 (1977); this is the seminal article for our approach. Energy-dependent terms in the pion-exchange potential were noted here (and removed) as part of a pion-exchange-current calculation. J. Adam, Jr., H. GoØller, and H. Arenhövel, Phys. Rev. C 48, 370 (1993) is a modern version of this work containing numerical results.
-
(1977)
Ann. Phys. (N.Y.)
, vol.104
, pp. 380
-
-
Friar, J.L.1
-
8
-
-
85188706592
-
-
is a modern version of this work containing numerical results
-
[4] J. L. Friar, Ann. Phys. (N.Y.) 104, 380 (1977); this is the seminal article for our approach. Energy-dependent terms in the pion-exchange potential were noted here (and removed) as part of a pion-exchange-current calculation. J. Adam, Jr., H. GoØller, and H. Arenhövel, Phys. Rev. C 48, 370 (1993) is a modern version of this work containing numerical results.
-
(1993)
Phys. Rev. C
, vol.48
, pp. 370
-
-
Adam J., Jr.1
Goøller, H.2
Arenhövel, H.3
-
9
-
-
0000070416
-
-
Equation (33b) should equal Eq. (27b), but contains a typographical error: the indices i and j should be interchanged in Eq. (33b) [J. Adam (private communication)]. Consistency of potential models under Lorentz boosts was discussed in this work, as well as in Refs. [4, 3]. The dependence of our 2π-exchange interaction on the overall nuclear momentum (not listed in the present paper, but arising from the spin-orbit interaction) is constrained by Eqs. (36a) and (A21) of Ref. [5], and can be shown to be satisfied
-
[5] S. A. Coon and J. L. Friar, Phys. Rev. C 34, 1060 (1986). Equation (33b) should equal Eq. (27b), but contains a typographical error: the indices i and j should be interchanged in Eq. (33b) [J. Adam (private communication)]. Consistency of potential models under Lorentz boosts was discussed in this work, as well as in Refs. [4, 3]. The dependence of our 2π-exchange interaction on the overall nuclear momentum (not listed in the present paper, but arising from the spin-orbit interaction) is constrained by Eqs. (36a) and (A21) of Ref. [5], and can be shown to be satisfied.
-
(1986)
Phys. Rev. C
, vol.34
, pp. 1060
-
-
Coon, S.A.1
Friar, J.L.2
-
12
-
-
0002306116
-
-
[8] M. Taketani, S. Machida, and S. Ohnuma, Prog. Theor. Phys. 7, 45 (1952). There are typographical errors in TMO that are corrected in, S. Machida, Prog. Theor. Phys. Suppl. 39, 91 (1967).
-
(1952)
Prog. Theor. Phys.
, vol.7
, pp. 45
-
-
Taketani, M.1
Machida, S.2
Ohnuma, S.3
-
13
-
-
0002556330
-
-
[8] M. Taketani, S. Machida, and S. Ohnuma, Prog. Theor. Phys. 7, 45 (1952). There are typographical errors in TMO that are corrected in, S. Machida, Prog. Theor. Phys. Suppl. 39, 91 (1967).
-
(1967)
Prog. Theor. Phys. Suppl.
, vol.39
, pp. 91
-
-
Machida, S.1
-
15
-
-
0001053259
-
-
[10] C. Ordóñez and U. van Kolck, Phys. Lett. B 291, 459 (1992); C. Ordóñez, L. Ray, and U. van Kolck, Phys. Rev. Lett. 72, 1982 (1994); U. van Kolck, Phys. Rev. C 49, 2932 (1994); C. Ordóñez, L. Ray, and U. van Kolck, ibid. 53, 2086 (1996).
-
(1992)
Phys. Lett. B
, vol.291
, pp. 459
-
-
Ordóñez, C.1
Van Kolck, U.2
-
16
-
-
4243643135
-
-
[10] C. Ordóñez and U. van Kolck, Phys. Lett. B 291, 459 (1992); C. Ordóñez, L. Ray, and U. van Kolck, Phys. Rev. Lett. 72, 1982 (1994); U. van Kolck, Phys. Rev. C 49, 2932 (1994); C. Ordóñez, L. Ray, and U. van Kolck, ibid. 53, 2086 (1996).
-
(1994)
Phys. Rev. Lett.
, vol.72
, pp. 1982
-
-
Ordóñez, C.1
Ray, L.2
Van Kolck, U.3
-
17
-
-
0000310355
-
-
[10] C. Ordóñez and U. van Kolck, Phys. Lett. B 291, 459 (1992); C. Ordóñez, L. Ray, and U. van Kolck, Phys. Rev. Lett. 72, 1982 (1994); U. van Kolck, Phys. Rev. C 49, 2932 (1994); C. Ordóñez, L. Ray, and U. van Kolck, ibid. 53, 2086 (1996).
-
(1994)
Phys. Rev. C
, vol.49
, pp. 2932
-
-
Van Kolck, U.1
-
18
-
-
0000961638
-
-
[10] C. Ordóñez and U. van Kolck, Phys. Lett. B 291, 459 (1992); C. Ordóñez, L. Ray, and U. van Kolck, Phys. Rev. Lett. 72, 1982 (1994); U. van Kolck, Phys. Rev. C 49, 2932 (1994); C. Ordóñez, L. Ray, and U. van Kolck, ibid. 53, 2086 (1996).
-
(1996)
Phys. Rev. C
, vol.53
, pp. 2086
-
-
Ordóñez, C.1
Ray, L.2
Van Kolck, U.3
-
19
-
-
0000532153
-
-
[11] M. Sugawara and S. Okubo, Phys. Rev. 117, 605 (1960); 117, 611 (1960). The first reference treats PS coupling and the second PV.
-
(1960)
Phys. Rev.
, vol.117
, pp. 605
-
-
Sugawara, M.1
Okubo, S.2
-
20
-
-
0007230577
-
-
The first reference treats PS coupling and the second PV
-
[11] M. Sugawara and S. Okubo, Phys. Rev. 117, 605 (1960); 117, 611 (1960). The first reference treats PS coupling and the second PV.
-
(1960)
Phys. Rev.
, vol.117
, pp. 611
-
-
-
22
-
-
0040986025
-
-
edited by M. Rho and D. Wilkinson North-Holland, Amsterdam. A simple example of how to eliminate energy dependence is worked out two ways, one using algebraic methods identical to those used in Ref. [5] and the second using unitary transformations (the Foldy-Wouthuysen transformation)
-
[13] J. L. Friar, in Mesons in Nuclei, edited by M. Rho and D. Wilkinson (North-Holland, Amsterdam, 1979), p. 597. A simple example of how to eliminate energy dependence is worked out two ways, one using algebraic methods identical to those used in Ref. [5] and the second using unitary transformations (the Foldy-Wouthuysen transformation).
-
(1979)
Mesons in Nuclei
, pp. 597
-
-
Friar, J.L.1
-
23
-
-
0007157912
-
-
The Bonn potentials correspond to μ= - 1. This generates nonlocality that results in a lower deuteron D-state percentage and a higher triton binding energy
-
[14] R. Machleidt, K. Holinde, and C. Elster, Phys. Rep. 149, 1 (1987). The Bonn potentials correspond to μ= - 1. This generates nonlocality that results in a lower deuteron D-state percentage and a higher triton binding energy.
-
(1987)
Phys. Rep.
, vol.149
, pp. 1
-
-
Machleidt, R.1
Holinde, K.2
Elster, C.3
-
26
-
-
28844440579
-
-
[17] S. Weinberg, Physica A 96, 327 (1979); Nucl. Phys. B363, 3 (1991); Phys. Lett. B 251, 288 (1990); ibid. 295, 114 (1992).
-
(1979)
Physica A
, vol.96
, pp. 327
-
-
Weinberg, S.1
-
27
-
-
4243773817
-
-
[17] S. Weinberg, Physica A 96, 327 (1979); Nucl. Phys. B363, 3 (1991); Phys. Lett. B 251, 288 (1990); ibid. 295, 114 (1992).
-
(1991)
Nucl. Phys.
, vol.B363
, pp. 3
-
-
-
28
-
-
0011593017
-
-
[17] S. Weinberg, Physica A 96, 327 (1979); Nucl. Phys. B363, 3 (1991); Phys. Lett. B 251, 288 (1990); ibid. 295, 114 (1992).
-
(1990)
Phys. Lett. B
, vol.251
, pp. 288
-
-
-
29
-
-
0009125631
-
-
[17] S. Weinberg, Physica A 96, 327 (1979); Nucl. Phys. B363, 3 (1991) ; Phys. Lett. B 251, 288 (1990); ibid. 295, 114 (1992).
-
(1992)
Phys. Lett. B
, vol.295
, pp. 114
-
-
-
30
-
-
0000560378
-
-
is a comprehensive current review that is indispensable to the practitioner
-
[18] V. Bernard, N. Kaiser, and U.-G. Meißner, Int. J. Mod. Phys. E 4, 193 (1995) is a comprehensive current review that is indispensable to the practitioner.
-
(1995)
Int. J. Mod. Phys. E
, vol.4
, pp. 193
-
-
Bernard, V.1
Kaiser, N.2
Meißner, U.-G.3
-
32
-
-
0002087360
-
-
This is the earliest use of the squaring trick (of which we are aware) for relating the RSE and Schrödinger-like equations. It was also briefly used in Ref. [4]
-
[20] F. Coester, S. C. Pieper, and F. J. D. Serduke, Phys. Rev. C 11, 1 (1975). This is the earliest use of the squaring trick (of which we are aware) for relating the RSE and Schrödinger-like equations. It was also briefly used in Ref. [4].
-
(1975)
Phys. Rev. C
, vol.11
, pp. 1
-
-
Coester, F.1
Pieper, S.C.2
Serduke, F.J.D.3
-
33
-
-
4243381445
-
-
The procedures of this reference allow V̄ in Eq. (7) to be fit to N-N data. In principle this equation should be inverted to obtain the V required for Eq. (6), but in practice this is not done
-
[21] V. G. J. Stoks, R. A. M. Klomp, M. C. M. Rentmeester, and J. J. de Swart, Phys. Rev. C 48, 792 (1993). The procedures of this reference allow V̄ in Eq. (7) to be fit to N-N data. In principle this equation should be inverted to obtain the V required for Eq. (6), but in practice this is not done.
-
(1993)
Phys. Rev. C
, vol.48
, pp. 792
-
-
Stoks, V.G.J.1
Klomp, R.A.M.2
Rentmeester, M.C.M.3
De Swart, J.J.4
-
35
-
-
26344462267
-
-
[23] A. Manohar and H. Georgi, Nucl. Phys. B234, 189 (1984); H. Georgi, Phys. Lett. B 298, 187 (1993).
-
(1984)
Nucl. Phys.
, vol.B234
, pp. 189
-
-
Manohar, A.1
Georgi, H.2
-
36
-
-
0000705227
-
-
[23] A. Manohar and H. Georgi, Nucl. Phys. B234, 189 (1984); H. Georgi, Phys. Lett. B 298, 187 (1993).
-
(1993)
Phys. Lett. B
, vol.298
, pp. 187
-
-
Georgi, H.1
-
37
-
-
0040308626
-
-
There are too many calculations to list them all. We find this recent one particularly useful, and it contains many references to older work
-
[24] Th. A. Rijken, Ann. Phys. (N.Y.) 208, 253 (1991). There are too many calculations to list them all. We find this recent one particularly useful, and it contains many references to older work.
-
(1991)
Ann. Phys. (N.Y.)
, vol.208
, pp. 253
-
-
Rijken, Th.A.1
-
38
-
-
0005574754
-
-
[25] S. Weinberg, Phys. Rev. Lett. 17, 616 (1966); Y. Tomozawa, Nuovo Cimento A 46, 707 (1966).
-
(1966)
Phys. Rev. Lett.
, vol.17
, pp. 616
-
-
Weinberg, S.1
-
39
-
-
51849177657
-
-
[25] S. Weinberg, Phys. Rev. Lett. 17, 616 (1966); Y. Tomozawa, Nuovo Cimento A 46, 707 (1966).
-
(1966)
Nuovo Cimento A
, vol.46
, pp. 707
-
-
Tomozawa, Y.1
-
41
-
-
4243401801
-
-
[26] M. L. Goldberger and S. B. Treiman, Phys. Rev. 110, 1178 (1958); Y. Nambu, Phys. Rev. Lett. 4, 380 (1960).
-
(1960)
Phys. Rev. Lett.
, vol.4
, pp. 380
-
-
Nambu, Y.1
-
42
-
-
0000372025
-
-
[27] M. C. M. Rentmeester, R. G. E. Timmermans, J. L. Friar, and J. J. de Swart, Phys. Rev. Lett. 82, 4992 (1999).
-
(1999)
Phys. Rev. Lett.
, vol.82
, pp. 4992
-
-
Rentmeester, M.C.M.1
Timmermans, R.G.E.2
Friar, J.L.3
De Swart, J.J.4
-
45
-
-
0032514009
-
-
This recent work discussed some of the problems associated with energy-dependent potentials
-
[30] E. Epelbaoum, W. Glöckle, and Ulf-G. Meißner, Nucl. Phys. A637, 107 (1998). This recent work discussed some of the problems associated with energy-dependent potentials.
-
(1998)
Nucl. Phys.
, vol.A637
, pp. 107
-
-
Epelbaoum, E.1
Glöckle, W.2
Meißner, U.-G.3
-
46
-
-
85188695474
-
-
note
-
2/M. The numerical factor depends on the specific form of the function.
-
-
-
|