Abstract
The equations of state for symmetric nuclear matter and pure neutron matter are investigated with the tensor-optimized Fermi Sphere method (TOFS) up to the density \(\varvec{\rho =0.5}\) fm\(^{-3}\). This method is based on a linked-cluster expansion theorem, and the energy per particle of nuclear matter (\(\varvec{E/A}\)) is calculated variationally with respect to the correlated nuclear matter wave function. We can study the density dependence of the many-body terms arising from the operator products, which contribute to \(\varvec{E/A}\). In order to clarify the relation between the many-body effects and short-range correlation, we take the spin-isospin dependent central NN interaction with a few GeV repulsion in the inner region. The EOS obtained by the TOFS method is reasonably reproduced, compared with other ab initio many-body methods. We found that the many-body terms (from the 2-body to 6-body ones) give sizable effects on E/A at higher density, and they play an important role in nuclear matter.
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References
J.M. Lattimer, M. Prakash, Phys. Rep. 333–334, 121 (2000)
G. Röpke, A. Schnell, P. Schuck, P. Noziéres, Phys. Rev. Lett. 80, 3177 (1998)
P. Schuck, Y. Funaki, H. Horiuchi, G. Röpke, A. Tohsaki, T. Yamada, Phys. Scr. 91, 123001 (2016)
I. Bombaci, A. Fabrocini, A. Polls, I. Vidaña, Phys. Lett. B 609, 232 (2005)
H.Q. Song, M. Baldo, G. Giansiracusa, U. Lombardo, Phys. Rev. Lett. 81, 1584 (1998)
M. Baldo, A. Polls, A. Rios, H.J. Schulze, I. Vidaña, Phys. Rev. C 86, 064001 (2012)
M. Baldo, A. Fiasconaro, H.Q. Song, G. Giansiracusa, U. Lombardo, Phys. Rev. C 65, 017303 (2001)
V.R. Pandharipande, R.B. Wiringa, Rev. Mod. Phys. 51, 821 (1979)
S. Fantoni, A. Fabrocini, Microscopic Quantum Many Body Theories and Their Applications: Correlated basis function theory for fermion systems, in Lecture Notes in Physics, vol. 510, ed. by J. Navarro, A. Polls (Springer, Berlin, 1998), pp.119–186
A. Lovato, O. Benhar, S. Fantoni, A.Y. Illarionov, K.E. Schmidt, Phys. Rev. C 83, 054003 (2011)
A. Akmal, V.R. Pandharipande, D.G. Ravenhall, Phys. Rev. C 58, 1804 (1998)
W.H. Dickhoff, C. Barbieri, Prog. Part. Nucl. Phys. 52, 377 (2004)
V. Somà, P. Bozėk, Phys. Rev. C 74, 045809 (2006)
A. Rios, A. Polls, I. Vidaña, Phys. Rev. C 79, 025802 (2009)
K.E. Schmidt, S. Fantoni, Phys. Lett. B 446, 99 (1999)
A. Sarsa, S. Fantoni, K.E. Schmidt, F. Pederiva, Phys. Rev. C 68, 024308 (2003)
S. Gandolfi, J. Carlson, S. Reddy, A.W. Steiner, R.B. Wiringa, Eur. Phys. J. A 50, 10 (2014)
G. Baardsen, A. Ekström, G. Hagen, M. Hjorth-Jensen, Phys. Rev. C 88, 054312 (2013)
G. Hagen, T. Papenbrock, A. Ekström, K.A. Wendt, G. Baardsen, S. Gandolfi, M. Hjorth-Jensen, C.J. Horowitz, Phys. Rev. C 89, 014319 (2014)
J. Lietz, S. Novario, G.R. Jansen, G. Hagen, M. Hjorth-Jensen, An Advanced Course in Computational NuclearPhysics: Bridging the Scales from Quarks to Neutron Stars, in Lecture Notes in Physics, vol. 936, ed. by M. Hjorth-Jensen, M.P. Lombardo, U. van Kolck (Springer, Berlin, 2017), pp.293–399
G.H. Bordbar, M. Modarres, J. Phys. G Nucl. Part. Phys. 23, 163 (1997)
G.H. Bordbar, M. Modarres, Phys. Rev. C 57, 714 (1998)
M. Modarres, A. Tafrihi, Prog. Part. Nucl. Phys. 131, 104047 (2023)
R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995)
M. Piarulli, I. Bombaci, D. Logoteta, A. Lovato, R.B. Wiringa, Phys. Rev. C 101, 045801 (2020)
A. Lovato, I. Bombaci, D. Logoteta, M. Piarulli, R.B. Wiringa, Phys. Rev. C 105, 055808 (2022)
E. Hiyama, Y. Kino, M. Kamumura, Prog. Part. Nucl. Phys. 51, 223 (2003)
Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, Phys. Rev. Lett. 101, 082502 (2008)
T. Yamada, Ann. Phys. 403, 1 (2019)
T. Yamada, T. Myo, H. Toki, H. Horiuchi, K. Ikeda, Prog. Theor. Exp. Phys. 2019, 113D03 (2019)
T. Yamada, Eur. Phys. J. A 57, 73 (2021)
T. Myo, H. Toki, K. Ikeda, H. Horiuchi, T. Suhara, Prog. Theor. Exp. Phys. 2015, 073D02 (2015)
T. Myo, H. Toki, K. Ikeda, H. Horiuchi, T. Suhara, Phys. Lett. B 769, 213 (2017)
H. Kümmel, H.K. Lührmann, J.G. Zabolitzky, Phys. Rep. 36, 1 (1978)
R. Barlett, Ann. Rev. Phys. Chem. 32, 359 (1981)
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This work was partially supported by the JSPS KAKENHI Grant numbers JP26400283, JP23K03397.
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Yamada, T. Variational calculations of symmetric nuclear matter and pure neutron matter with the tensor-optimized Fermi Sphere (TOFS) method: many-body effects and short-range correlation. Eur. Phys. J. A 60, 57 (2024). https://doi.org/10.1140/epja/s10050-024-01267-w
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DOI: https://doi.org/10.1140/epja/s10050-024-01267-w