Abstract
We examine the effects of the long range Coulomb force on the three-body contact interaction in a pionless effective theory of 3He. The corresponding interaction in 3H exhibits limit-cycle behavior and we show that this is not altered by the 1/r singularity of the potential.
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References
Weinberg S.: Nuclear forces from chiral lagrangians. Phys. Lett. B 251, 288–292 (1999)
Weinberg S.: Effective chiral lagrangians for nucleon-pion interactions and nuclear forces. Nucl. Phys. B 363, 3–18 (1991)
Epelbaum E., Hammer H.-W., Meißner U.-G.: Modern theory of nuclear forces. Rev. Mod. Phys. 81, 1773–1825 (2009)
Mechleidt R., Entem D.: Chiral effective field theory and nuclear forces. Phys. Rep 503, 1–75 (2011)
Kaplan D.B., Savage M.J., Wise M.B.: A new expansion for nucleon-nucleon interactions. Phys. Lett. B 424, 390–396 (1998)
Kaplan D.B., Savage M.J., Wise M.B.: Two-nucleon systems from effective field theory. Nucl. Phys. B 534, 329–355 (1998)
Bedaque P.F., Hammer H.-W., van Kolck U.: The three-boson system with short-range interactions. Nucl. Phys. A 646, 444–466 (1999)
Birse M.C., McGovern J.A., Richardson K.G.: A renormalisation-group treatment of two-body scattering. Phys. Lett. B 464, 169–176 (1999)
Valderrama M.P.: Perturbative renormalizability of chiral two-pion exchange in nucleon-nucleon scattering: P and D waves. Phys. Rev. C 84, 064002 (2011)
Bethe H.A.: Theory of the effective range in nuclear scattering. Phys. Rev. 76, 38–50 (1949)
Harada K., Inoue K., Kubo H.: Wilsonian RG and redundant operators in nonrelativistic effective field theory. Phys. Lett. B 636, 305–309 (2006)
Efimov V.N.: Weakly-bound states of three resonantly-interacting particles. Sov. J. Nucl. Phys. 12, 589–595 (1971)
Efimov V.N.: Low-energy properties of three resonantly interacting particles. Sov. J. Nucl. Phys. 29, 546–553 (1979)
Ando S.-I., Birse M.C.: Renormalization-group analysis for low-energy scattering of charged particles. Phys. Rev. C 78, 024004 (2008)
Barford T., Birse M.C.: Renormalization group approach to two-body scattering in the presence of long-range forces. Phys. Rev. C 67, 064006 (2003)
Hammer H.-W., Higa R.: A model study of discrete scale invariance and long-range interactions. Eur. Phys. J. A 37, 193–200 (2008)
Ando S.-I., Birse M.C.: Effective field theory of 3He. J. Phys. G: Nucl. Part. Phys. 37, 105108 (2010)
Kaplan D.B.: More effective field theory for non-relativistic scattering. Nucl. Phys. B 494, 471–483 (1997)
Beane S.R., Savage M.J.: Rearranging pionless effective field theory. Nucl. Phys. A 694, 511 (2001)
Ando, S.-I., Hyun, C.H.: Effective field theory of the deuteron with dibaryon fields. Phys. Rev. C 72, 014008 (2005)
Kok, L.P., Sruik, D.J., van Haeringen, H.: On the exact solution of three-particle equations with Coulomb interaction. The driving terms. University of Groningen Internal report 151 (1975)
Kok, L.P., Struik, D.J., Holwerda, J.E., van Haerigen, H.: On the exact solution of three-particle equations with Coulomb interaction II. Bound states. University of Groningen Internal report 170 (1975)
Chen J.C.Y., Chen A.C.: Nonrelativistic off-shell two-body Coulomb amplitudes. Adv. Atom. Mol. Phys. 8, 71 (1972)
Skorniakov G.V., Ter-Martirosian K.A.: Three body problems for short range forces. I. Scattering of low energy neutrons by deuterons. Sov. Phys. JETP 4, 648–661 (1957)
Bedaque P.F., Hammer H.-W., van Kolck U.: Effective field theory of the triton. Nucl. Phys. A 676, 357–370 (2000)
Kong X., Ravndal F.: Proton-proton scattering lengths from effective field theory. Phys. Lett. B 450, 320–324 (1999)
Kong X., Ravndal F.: Proton-proton fusion in effective field theory. Phys. Rev. C 64, 044002 (2001)
Ando S., Shin J.W., Hyun C.H., Hong S.W.: Low energy proton-proton scattering in effective field theory. Phys. Rev C 76, 064001 (2007)
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Ando, SI., Birse, M.C. Effective Field Theory of 3He. Few-Body Syst 54, 235–238 (2013). https://doi.org/10.1007/s00601-012-0350-1
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DOI: https://doi.org/10.1007/s00601-012-0350-1