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Notes
- 1.
The Weinberg power counting scheme is known to be inconsistent. As there is no other viable EFT alternative for the many-body community presently, it is often used in calculations without regard to the issues of renormalization-group invariance.
References
P. Navrátil, S. Quaglioni, I. Stetcu, B.R. Barrett, Recent developments in no-core shell-model calculations. J. Phys. G: Nucl. Part. Phys. 36(8), 083101 (2009)
P. Navrátil, B.R. Barrett, Shell-model calculations for the three-nucleon system. Phys. Rev. C 57, 562–568 (1998)
P. Navrátil, J.P. Vary, B.R. Barrett, Properties of \({}^{12}c\) in the Ab Initio nuclear shell model. Phys. Rev. Lett. 84, 5728–5731 (2000)
P. Navrátil, V.G. Gueorguiev, J.P. Vary, W.E. Ormand, A. Nogga, Structure of \(a=10\breve{}13\) nuclei with two- plus three-nucleon interactions from chiral effective field theory. Phys. Rev. Lett. 99, 042501 (2007)
B. Alex Brown, W.A. Richter, New “USD” hamiltonians for the \(\mathit{sd}\) shell. Phys. Rev. C 74, 034315 (2006)
V.G.J. Stoks, R.A.M. Klomp, C.P.F. Terheggen, J.J. de Swart, Construction of high-quality NN potential models. Phys. Rev. C 49, 2950–2962 (1994)
Hideki Yukawa, On the interaction of elementary particles. i \(^{*}\). Prog. Theoret. Phys. Suppl. 1, 1–10 (1955)
R. Machleidt, High-precision, charge-dependent bonn nucleon-nucleon potential. Phys. Rev. C 63, 024001 (2001)
R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Accurate nucleon-nucleon potential with charge-independence breaking. Phys. Rev. C 51, 38–51 (1995)
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)
P. Doleschall, I. Borbély, Z. Papp, W. Plessas, Nonlocality in the nucleon-nucleon interaction and three-nucleon bound states. Phys. Rev. C 67, 064005 (2003)
J. Gasser, H. Leutwyler, Chiral perturbation theory to one loop. Ann. Phys. 158(1), 142–210 (1984)
J. Gasser, H. Leutwyler, Chiral perturbation theory: expansions in the mass of the strange quark. Nucl. Phys. B 250(1–4), 465–516 (1985)
S. Weinberg, Phenomenological lagrangians. Physica A 96(12), 327–340 (1979)
S. Weinberg, Nuclear forces from chiral lagrangians. Phys. Lett. B 251(2), 288–292 (1990)
S. Weinberg, Effective chiral lagrangians for nucleon-pion interactions and nuclear forces. Nucl. Phys. B 363(1), 3–18 (1991)
U. van Kolck, Few-nucleon forces from chiral lagrangians. Phys. Rev. C 49, 2932–2941 (1994)
C. Ordóñez, L. Ray, U. van Kolck, Nucleon-nucleon potential from an effective chiral lagrangian. Phys. Rev. Lett. 72, 1982–1985 (1994)
C. Ordóñez, L. Ray, U. van Kolck, Two-nucleon potential from chiral lagrangians. Phys. Rev. C 53, 2086–2105 (1996)
D. Gazit, S. Quaglioni, P. Navrátil, Three-nucleon low-energy constants from the consistency of interactions and currents in chiral effective field theory. Phys. Rev. Lett. 103, 102502 (2009)
W. Gloeckle, E. Epelbaum, U.G. Meissner, A. Nogga, H. Kamada, et al., Nuclear forces and few nucleon studies based on chiral perturbation theory (2003)
D.R. Entem, R. Machleidt, Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory. Phys. Rev. C 68, 041001 (2003)
E. Epelbaum, A. Nogga, W. Glöckle, H. Kamada, Ulf-G. Meißner, H. Witała, Three-nucleon forces from chiral effective field theory. Phys. Rev. C 66, 064001 (2002)
S.K. Bogner, T.T.S. Kuo, A. Schwenk, Model-independent low momentum nucleon interaction from phase shift equivalence. Phys. Rep. 386(1), 1–27 (2003)
S.D. Głazek, K.G. Wilson, Renormalization of hamiltonians. Phys. Rev. D 48, 5863–5872 (1993)
S.D. Glazek, K.G. Wilson, Perturbative renormalization group for hamiltonians. Phys. Rev. D 49, 4214–4218 (1994)
F.J. Wegner. Flow equations for hamiltonians. Phys. Rep. 348(1–2), 77–89 (2001) [Renormalization group theory in the new millennium. II]
F. Wegner, Flow-equations for hamiltonians. Ann. Phys. 506(2), 77–91 (1994)
S.K. Bogner, R.J. Furnstahl, R.J. Perry, Similarity renormalization group for nucleon-nucleon interactions. Phys. Rev. C 75, 061001 (2007)
S.K. Bogner, R.J. Furnstahl, R.J. Perry, A. Schwenk, Are low-energy nuclear observables sensitive to high-energy phase shifts? Phys. Lett. B 649(5–6), 488–493 (2007)
E.D. Jurgenson, Applications of the similarity renormalization group to the nuclear interaction. Ph.D. Thesis (Advisor: R.J. Furnstahl) (2009)
E.D. Jurgenson, P. Navrátil, R.J. Furnstahl, Evolution of nuclear many-body forces with the similarity renormalization group. Phys. Rev. Lett. 103, 082501 (2009)
S. Ôkubo, Diagonalization of hamiltonian and tamm-dancoff equation. Progress Theoret. Phys. 12(5), 603–622 (1954)
K. Suzuki, S.Y. Lee, Convergent theory for effective interaction in nuclei. Progress Theoret. Phys. 64(6), 2091–2106 (1980)
H. Kamada, A. Nogga, W. Glöckle, E. Hiyama, M. Kamimura, K. Varga, Y. Suzuki, M. Viviani, A. Kievsky, S. Rosati, J. Carlson, S.C. Pieper, R.B. Wiringa, P. Navrátil, B.R. Barrett, N. Barnea, W. Leidemann, G. Orlandini, Benchmark test calculation of a four-nucleon bound state. Phys. Rev. C 64, 044001 (2001)
E.D. Jurgenson, P. Navrátil, R.J. Furnstahl, Evolving nuclear many-body forces with the similarity renormalization group. Phys. Rev. C 83, 034301 (2011)
A.F. Lisetskiy, B.R. Barrett, M.K.G. Kruse, P. Navratil, I. Stetcu, J.P. Vary, Ab-initio shell model with a core. Phys. Rev. C 78, 044302 (2008)
M. Moshinsky, Transformation brackets for harmonic oscillator functions. Nucl. Phys. 13(1), 104–116 (1959)
P. Navrátil, G.P. Kamuntavičius, B.R. Barrett, Few-nucleon systems in a translationally invariant harmonic oscillator basis. Phys. Rev. C 61, 044001 (2000)
P. Navrátil, B.R. Barrett, Four-nucleon shell-model calculations in a faddeev-like approach. Phys. Rev. C 59, 1906–1918 (1999)
P. Navrátil, B.R. Barrett, W. Glöckle, Spurious states in the faddeev formalism for few-body systems. Phys. Rev. C 59, 611–616 (1999)
L. Trlifaj, Simple formula for the general oscillator brackets. Phys. Rev. C 5, 1534–1539 (1972)
B.J. Cole, R.R. Whitehead, A. Watt, I. Morrison, Computationa methods for shell-model calculations. Adv. Nucl. Phys. 9, 123–176 (1977)
P.K. Rath, A. Faessler, H. Muther, A. Watt, A practical solution to the problem of spurious states in shell-model calculations. J. Phys. G Nucl. Part. Phys. 16(2), 245 (1990)
D.H. Gloeckner, R.D. Lawson, Spurious center-of-mass motion. Phys. Lett. B 53(4), 313–318 (1974)
C. Forssén, J.P. Vary, E. Caurier, P. Navrátil, Converging sequences in the ab initio no-core shell model. Phys. Rev. C 77, 024301 (2008)
P. Navrátil, E. Caurier, Nuclear structure with accurate chiral perturbation theory nucleon-nucleon potential: application to \(^{6}\)Li and \(^{10}\)B. Phys. Rev. C 69, 014311 (2004)
P. Maris, J.P. Vary, A.M. Shirokov, Ab initio no-core full configuration calculations of light nuclei. Phys. Rev. C 79, 014308 (2009)
P. Navrátil. No core slater determinant code. Unpublished (1995)
J.P. Vary, D.C. Zheng, The many-fermion-dynamics shell-model code. Unpublished (1994)
J.P. Vary, The many-fermion-dynamics shell-model code. Iowa State University, Unpublished (1992)
P. Navrátil, Manyeff code. Unpublished (1998)
E. Caurier, F. Nowacki, Present status of shell model techniques. Acta Phys. Pol. B 30(3), 705 (1999)
E. Caurier, G. Martínez-Pinedo, F. Nowacki, A. Poves, A.P. Zuker, The shell model as a unified view of nuclear structure. Rev. Mod. Phys. 77, 427–488 (2005)
P. Maris, M. Sosonkina, J.P. Vary, E. Ng, C. Yang, Scaling of ab-initio nuclear physics calculations on multicore computer architectures. Procedia Comput. Sci. 1(1), 97–106 (2010)
P. Sternberg, E.G. Ng, C. Yang, P. Maris, J.P. Vary, M. Sosonkina, H.V. Le, Accelerating configuration interaction calculations for nuclear structure, in Proceedings of the 2008 ACM/IEEE conference on Supercomputing, SC ’08, Piscataway, NJ, USA (IEEE Press, 2008), pp. 15:1–15:12
P. Maris, A.M. Shirokov, J.P. Vary, Ab initio nuclear structure simulations: the speculative \(^{14}\)F nucleus. Phys. Rev. C 81, 021301 (2010)
P. Maris, J.P. Vary, P. Navrátil, W.E. Ormand, H. Nam, D.J. Dean, Origin of the anomalous long lifetime of \(^{14}\)C. Phys. Rev. Lett. 106, 202502 (2011)
V.Z. Goldberg, B.T. Roeder, G.V. Rogachev, G.G. Chubarian, E.D. Johnson, C. Fu, A.A. Alharbi, M.L. Avila, A. Banu, M. McCleskey, J.P. Mitchell, E. Simmons, G. Tabacaru, L. Trache, R.E. Tribble, First observation of 14f. Phys. Lett. B 692(5), 307–311 (2010)
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Kruse, M.K.G. (2013). The No Core Shell Model. In: Extensions to the No-Core Shell Model. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01393-0_2
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