Abstract
Theoretical predictions for sample observables of three-nucleon and four-nucleon reactions are reviewed. The focus is on Coulomb force effects. The calculations are based on the Alt–Grassberger–Sandhas version of the Faddeev equations. The calculations are done in momentum space. The calculational technique used to include the Coulomb repulsion between protons screens the infinite Coulomb tail, renormalizes the results and thereby corrects them for screening. The competition between three-nucleon force and Coulomb force effects as well as the Coulomb domination in special kinematic situations of reactions are discussed. Reactions connected by charge symmetry are reviewed. Special reaction observables are studied, in search for the hadronic violation of charge symmetry in the nuclear interaction and for its competition with the charge-asymmetric Coulomb force.
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References
A. Kievsky, M. Viviani, S. Rosati, Polarization observables in p–d scattering below 30 MeV. Phys. Rev. C 64, 024002 (2001)
L.D. Faddeev, Mathematical Aspects of the Three-Body Problem in the Quantum Scattering Theory. Academy of Sciences of the USSR Works of the Steklov Mathematical Institute Vol.69, Israel Program for Scientific Translations, Jerusalem (1965)
A. Deltuva, A.C. Fonseca, P.U. Sauer, Nuclear many-body scattering calculations with the Coulomb interaction. Annu. Rev. Nucl. Part. Sci. 58, 27 (2008)
S.P. Merkuriev, C. Gignoux, A. Laverne, Three-body scattering in configuration space. Ann. Phys. 99, 30 (1976)
R. Lazauskas, Elastic proton scattering on tritium below the \(n\)-\({}^3\rm He\) threshold. Phys. Rev. C 79, 054007 (2009)
E.O. Alt, P. Grassberger, W. Sandhas, Reduction of the three-particle collision problem to multi-channel two-particle Lippmann–Schwinger equations. Nucl. Phys. B 2, 167 (1967)
E.O. Alt, W. Sandhas, H. Ziegelmann, Coulomb effects in three-body reactions with two charged particles. Phys. Rev. C 17, 1981 (1978)
E.O. Alt, W. Sandhas, Coulomb effects in three-body reactions with two charged particles. Phys. Rev. C 21, 1733 (1980)
R. Machleidt, High-precision, charge-dependent Bonn nucleon–nucleon potential. Phys. Rev. C 63, 024001 (2001)
A. Deltuva, R. Machleidt, P.U. Sauer, Realistic two-baryon potential coupling two-nucleon and nucleon-\(\Delta \)-isobar states: fit and applications to three-nucleon system. Phys. Rev. C 68, 024005 (2003)
K. Hatanaka, Y. Shimizu, D. Hirooka, J. Kamiya, Y. Kitamura, Y. Maeda, T. Noro, E. Obayashi, K. Sagara, T. Saito, H. Sakai, Y. Sakemi, K. Sekiguchi, A. Tamii, T. Wakasa, T. Yagita, K. Yako, H.P. Yoshida, V.P. Ladygin, H. Kamada, W. Glöckle, J. Golak, A. Nogga, H. Witała, Cross section and complete set of proton spin observables in \(\vec{p}d\) elastic scattering at 250 MeV. Phys. Rev. C 66, 044002 (2002)
D.G. McDonald, W. Haeberli, L.W. Morrow, Polarization and cross section of protons scattered by \(He^{3}\) from 4 to 13 MeV. Phys. Rev. 133, B1178 (1964)
M .T. Alley, L .D. Knutson, Spin correlation measurements for p\({}^{3}\)He elastic scattering between 4.0 and 10.0 MeV. Phys. Rev. C 48, 1890 (1993)
S. Kistryn, E. Stephan, B. Klos, A. Biegun, K. Bodek, I. Ciepal, A. Deltuva, A. Fonseca, N. Kalantar-Nayestanaki, M. Kis, A. Kozela, M. Mahjour-Shafiei, A. Micherdzinska, P. Sauer, R. Sworst, J. Zejma, W. Zipper, Evidence of the Coulomb-force effects in the cross-sections of the deuteron proton breakup at 130 MeV. Phys. Lett. B 641, 23 (2006)
P.U. Sauer, Can the charge symmetry of nuclear forces be confirmed by nucleon–nucleon scattering experiments? Phys. Rev. Lett. 32, 626 (1974)
R.A. Brandenburg, S.A. Coon, P.U. Sauer, Nuclear charge asymmetry in the A = 3 nuclei. Nucl. Phys. A 294, 305 (1978)
K. Sagara, H. Oguri, S. Shimizu, K. Maeda, H. Nakamura, T. Nakashima, S. Morinobu, Energy dependence of analyzing power \(A_y\) and cross section for \(p+d\) scattering below 18 MeV. Phys. Rev. C 50, 576 (1994)
C.R. Howell, W. Tornow, K. Murphy, H.G. Pfützner, M.L. Roberts, A. Li, P.D. Felsher, R.L. Walter, I. Šlaus, P.A. Treado, Y. Koike, Comparison of vector analyzing-power data and calculations for neutron–deuteron elastic scattering from 10 to 14 MeV. Few Body Syst. 2, 19 (1987)
W. Glöckle, H. Witała, D. Hüber, H. Kamada, J. Golak, The three-nucleon continuum: achievements, challenges and applications. Phys. Rep. 274, 107 (1996)
J. Strate, K. Geissdörfer, R. Lin, W. Bielmeier, J. Cub, A. Ebneth, E. Finckh, H. Friess, G. Fuchs, K. Gebhardt, S. Schindler, Differential cross section of the 2H(n, nnp)-reaction at \(E_n = 13\) MeV. Nucl. Phys. A 501, 51 (1989)
H .R. Setze, C .R. Howell, W. Tornow, R .T. Braun, D .E. González Trotter, A .H. Hussein, R .S. Pedroni, C .D. Roper, F. Salinas, I. Šlaus, B. Vlahovic, R .L. Walter, G. Mertens, J .M. Lambert, H. Witała, W. Glöckle, Cross-section measurements of neutron–deuteron breakup at 13.0 MeV. Phys. Rev. C 71, 034006 (2005)
G. Rauprich, S. Lemaitre, P. Niessen, K.R. Nyga, R. Reckenfelderbäumer, L. Sydow, H. Paetz gen. Schieck, H. Witała, W. Glöckle, Study of the kinematically complete breakup reaction 2H(p, pp)n at \(E_p = 13\) MeV with polarized protons. Nucl. Phys. A 535, 313 (1991)
A.C. Fonseca, A. Deltuva, Numerical exact ab initio four-nucleon scattering calculations: from dream to reality. Few-Body Syst. 58, 46 (2017)
P. Doleschall, Influence of the short range nonlocal nucleon–nucleon interaction on the elastic n–d scattering: below 30 MeV. Phys. Rev. C 69, 054001 (2004)
W. Grüebler, V. König, P.A. Schmelzbach, B. Jenny, J. Vybiral, New highly excited 4He levels found by the 2H(d, p)3H reaction. Nucl. Phys. A 369, 381 (1981)
J .M. Blair, G. Freier, E. Lampi, W. Sleator, J .H. Williams, The angular distributions of the products of the D–D reaction: 1 to 3.5 Mev. Phys. Rev. 74, 1599 (1948)
W. Grüebler, V. König, P.A. Schmelzbach, R. Risler, R.E. White, P. Marmier, Investigation of excited states of 4He via the 2H(d, p)3H and 2H(d, n)3He reactions using a polarized deuteron beam. Nucl. Phys. A 193, 129 (1972)
V. König, W. Grüebler, R.A. Hardekopf, B. Jenny, R. Risler, H. Bürgi, P. Schmelzbach, R. White, Investigation of charge symmetry violation in the mirror reactions 2H(d, p)3H and 2H(d, n)3He. Nucl. Phys. A 331, 1 (1979)
O.A. Yakubovsky, On the integral equations in the theory of N particle scattering. Sov. J. Nucl. Phys. 5, 937 (1967)
L.S. Fereira, A.C. Fonseca, L. Streit, (eds). Models and Methods in Few-Body Physics. Lecture Notes in Physics, vol. 273 (1987)
M. Viviani, L. Girlanda, A. Kievsky, L.E. Marcucci, Effect of three-nucleon interactions in p-He\(_3\) elastic scattering. Phys. Rev. Lett. 111, 172302 (2013)
H. Pöpping, P.U. Sauer, Z. Xi-Zhen, The two-nucleon system above pion-threshold: a force model with \(\Delta \)-isobar and pion degrees of freedom. Nucl. Phys. A 474, 557 (1987) (Erratum Nucl. Phys. A 550, 563 (1992))
R. Machleidt, D.R. Entem, Chiral effective field theory and nuclear forces. Phys. Rep. 503, 1 (2011)
E. Epelbaum, H. Krebs, U.-G. Meißner, Improved chiral nucleon–nucleon potential up to next-to-next-to-next-to-leading order. Eur. Phys. J. A 51, 53 (2015)
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A.D. acknowledges the support by the Alexander von Humboldt Foundation under Grant No. LTU-1185721-HFST-E.
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Deltuva, A., Fonseca, A.C. & Sauer, P.U. Coulomb Force Effects in Few-Nucleon Systems. Few-Body Syst 60, 29 (2019). https://doi.org/10.1007/s00601-019-1496-x
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DOI: https://doi.org/10.1007/s00601-019-1496-x