Abstract.
I present a brief summary of the first three decades of studies of pygmy resonances in nuclei and their relation to the symmetry energy of nuclear matter. I discuss the first experiments and theories dedicated to study the electromagnetic response in halo nuclei and how a low energy peak was initially identified as a candidate for the pygmy resonance. This is followed by the description of a collective state in medium heavy and heavy nuclei which was identified as a pygmy resonance. The role of the slope parameter of the symmetry energy in determining the properties of neutron stars is stressed. The theoretical and experimental information collected on pygmy resonances, neutron skins, and the numerous correlations found with the slope parameter is briefly reviewed.
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References
G.C. Baldwin, G.S. Klaiber, Phys. Rev. 73, 1156 (1947)
G.C. Baldwin, G.S. Klaiber, Phys. Rev. 71, 3 (1948)
W. Bothe, W. Gentner, Z. Phys. 106, 236 (1937)
A.B. Migdal, J. Phys. USSR 8, 331 (1944)
P.F. Bortignon, A. Bracco, R.A. Broglia, Giant Resonances, Contemporary Concepts in Physics (Rutledge, 1998)
B.L. Berman, S.C. Fultz, Rev. Mod. Phys. 47, 713 (1975)
R. Bergere, Lect. Notes Phys. 61, 1 (1977)
R. Bergere, Lect. Notes Phys. 108, 138 (1979)
T. Aumann, Eur. Phys. J. A 26, 441 (2005)
T. Aumann, C.A. Bertulani, K. Suemmerer, Phys. Rev. C 51, 416 (1995)
C.A. Bertulani, V. Ponomarev, Phys. Rep. 321, 139 (1999)
G.A. Bartholomew, Annu. Rev. Nucl. Sci. 11, 259 (1961)
J.S. Brzosko et al., Can. J. Phys. 47, 2849 (1969)
Radhe Mohan, M. Danos, L.C. Biedenharn, Phys. Rev. C 3, 1740 (1971)
T. Nomura, S. Kubono, Soft giant resonance - Experimental proposal to the Japanese Hadron project (now J-PARC) (1987)
I. Tanihata et al., Phys. Lett. B 160, 380 (1985)
I. Tanihata et al., Phys. Rev. Lett. 55, 2676 (1985)
I. Tanihata et al., Phys. Lett. B 206, 592 (1988)
A.S. Goldhaber, Phys. Lett. B 53, 306 (1974)
T. Kobayashi et al., Phys. Lett. B 232, 51 (1989)
P.G. Hansen, B. Jonson, Europhys. Lett. 4, 409 (1987)
C.A. Bertulani, G. Baur, Nucl. Phys. A 480, 615 (1988)
R. Serber, Phys. Rev. 72, 1008 (1947)
N.A. Orr et al., Phys. Rev. Lett. 69, 2050 (1992)
T. Aumann et al., Phys. Rev. Lett. 84, 35 (2000)
C.A. Bertulani, P.G. Hansen, Phys. Rev. C 70, 034609 (2004)
C.A. Bertulani, K.W. McVoy, Phys. Rev. C 48, 2534 (1993)
K. Hencken, G. Bertsch, H. Esbensen, Phys. Rev. C 54, 3043 (1996)
F. Barranco, P.G. Hansen, Eur. Phys. J. A 7, 479 (2000)
Jerome Margueron, Angela Bonaccorso, David M. Brink, Nucl. Phys. A 703, 105 (2002)
C.A. Bertulani, L.F. Canto, M.S. Hussein, Phys. Rep. 226, 281 (1993)
K. Ieki et al., Phys. Rev. Lett. 70, 730 (1993)
D. Sackett et al., Phys. Rev. C 48, 118 (1993)
C.A. Bertulani, G. Baur, Phys. Rep. 163, 299 (1988)
C.A. Bertulani, G. Baur, M.S. Hussein, Nucl. Phys. 526, 751 (1991)
C.A. Bertulani, A. Sustich, Phys. Rev. C 46, 2340 (1992)
T. Nakamura et al., Phys. Lett. B 331, 296 (1994)
S. Shimoura et al., Phys. Lett. B 349, 29 (1995)
N. Teruya, C.A. Bertulani, S. Krewald, H. Dias, M.S. Hussein, Phys. Rev. C 43, 2049 (1991)
T. Otsuka, M. Ishihara, N. Fukunishi, T. Nakamura, M. Yokoyama, Phys. Rev. C 49, R2289 (1994)
F. Barranco, P.F. Bortignon, R.A. Broglia, G. Colò, E. Vigezzi, Eur. Phys. J. A 11, 385 (2001)
G. Potel, F. Barranco, E. Vigezzi, R.A. Broglia, Phys. Rev. Lett. 105, 172502 (2010)
F. Barranco, G. Potel, R.A. Broglia, E. Vigezzi, Phys. Rev. Lett. 119, 082501 (2017)
Manju, Jagjit Singh, Shubhchintak, R. Chatterjee, Eur. Phys. J. A 55, 5 (2019)
R.A. Broglia, F. Barranco, A. Idini, G. Potel, E. Vigezzi, arXiv:1806.09409 (2019)
F. Barranco, G. Potel, E. Vigezzi, R.A. Broglia, arXiv:1812.01761 (2018)
C.A. Bertulani, L.F. Canto, Nucl. Phys. A 539, 163 (1992)
G.F. Bertsch, C.A. Bertulani, Nucl. Phys. A 556, 136 (1993)
P. Banerjee, R. Shyam, Nucl. Phys. A 561, 112 (1993)
T. Kido, K. Yabana, Y. Suzuki, Phys. Rev. C 50, R1276 (1994)
P. Banerjee, R. Shyam, J. Phys. G: Nucl. Part. Phys. 22, L79 (1996)
T. Kido, K. Yabana, Y. Suzuki, Phys. Rev. C 53, 2296 (1996)
P. Banerjee, G. Baur, K. Hencken, R. Shyam, D. Trautmann, Phys. Rev. C 65, 064602 (2002)
Jerome Margueron, Angela Bonaccorso, David M. Brink, Nucl. Phys. A 720, 337 (2003)
Awad A. Ibraheem, A. Bonaccorso, Nucl. Phys. A 748, 3 (2005)
C.A. Bertulani, Phys. Rev. Lett. 94, 072701 (2005)
S. Typel, G. Baur, Nucl. Phys. A 759, 247 (2005)
A.M. Moro, F. Perez-Bernal, J.M. Arias, J. Gomez-Camacho, Phys. Rev. C 73, 044612 (2006)
K. Ogata, C.A. Bertulani, Prog. Theor. Phys. 121, 1399 (2009)
K. Ogata, T. Matsumoto, Y. Iseri, M. Yahiro, J. Phys. Soc. Jpn. 78, 084201 (2009)
K. Ogata, C.A. Bertulani, Prog. Theor. Phys. 123, 701 (2010)
Ravinder Kumar, Angela Bonaccorso, Phys. Rev. C 86, 061601 (2012)
K. Hagino, I. Tanihata, H. Sagawa, Exotic Nuclei Far from the Stability Line, in 100 Years of Subatomic Physics, edited by Ernest M. Henley, Stephen D. Ellis (World Scientific, 2013) p. 231--272
Shubhchintak, Neelam, R. Chatterjee, R. Shyam, K. Tsushima, Nucl. Phys. A 939, 101 (2015)
N. Alamanos, C.A. Bertulani, A. Bonaccorso, A. Bracco, D.M. Brink, G. Casini, Eur. Phys. J. Plus 132, 37 (2017)
R.A. Broglia, P.F. Bortignon, F. Barranco, E. Vigezzi, A. Idini, G. Potel, Phys. Scr. 91, 063012 (2016)
P. Capel, D. Phillips, H.-W. Hammer, Phys. Rev. C 98, 034610 (2018)
A. Pushkin, B. Jonson, M.V. Zhukov, J. Phys. G 22, L95 (1996)
M.V. Zhukov et al., Phys. Rep. 231, 151 (1993)
B.V. Danilin, J. Thompson, J.S. Vaagen, M.V. Zhukov, Nucl. Phys. A 632, 383 (1998)
C.A. Bertulani, Phys. Rev. C 75, 024606 (2007)
Y. Suzuki, K. Ikeda, H. Sato, Prog. Theor. Phys. 83, 180 (1990)
P. Van Isacker, M.A. Nagarajan, D.D. Warner, Phys. Rev. C 45, R13 (1992)
M. Goldhaber, E. Teller, Phys. Rev. 74, 1046 (1948)
H. Steinwedel, J.H.D. Jensen, Z. Naturforschung 5A, 413 (1950)
W.D. Myers, W.G. Swiatecki, T. Kodama, L.J. El-Jaick, E.R. Hilf, Phys. Rev. C 15, 2032 (1977)
S. Shlomo, G.F. Bertsch, Nucl. Phys. A 243, 507 (1975)
P. Ring, P. Schuck, The nuclear many-body problem (Springer, 2004)
G. Colo, L. Cao, N.V. Giai, L. Capelli, Comp. Phys. Commun. 184, 142 (2013)
G. Bertsch, J. Foxwell, Phys. Rev. C 41, 1300 (1990)
F. Catara, E.G. Lanza, M.A. Nagarajan, A. Vitturi, Nucl. Phys. A 614, 86 (1997)
F. Catara, E.G. Lanza, M.A. Nagarajan, A. Vitturi, Nucl. Phys. A 624, 449 (1997)
D. Vretenar et al., Nucl. Phys. A 692, 496 (2001)
D. Sarchi, Phys. Lett. B 601, 27 (2004)
J. Piekarewicz, Phys. Rev. C 73, 044325 (2006)
Jun Liang et al., Phys. Rev. C 75, 054320 (2007)
N. Paar, D. Vretenar, E. Khan, G. Colo, Rep. Prog. Phys. 70, 691 (2007)
E. Litvinova, P. Ring, D. Vretenar, Phys. Lett. B 647, 111 (2007)
N. Tsoneva, H. Lenske, Phys. Rev. C 77, 024321 (2008)
C. Barbieri, E. Caurier, K. Langanke, G. Martnez-Pinedo, Phys. Rev. C 77, 024304 (2008)
N. Paar, Y.F. Niu, D. Vretenar, J. Meng, Phys. Rev. Lett. 103, 032502 (2009)
T. Inakura, T. Nakatsukasa, K. Yabana, Phys. Rev. C 80, 044301 (2009)
E.G. Lanza, F. Catara, D. Gambacurta, M.V. Andres, Ph. Chomaz, Phys. Rev. C 79, 054615 (2009)
A. Carbone et al., Phys. Rev. C 81, 041301(R) (2010)
X. Roca-Maza, G. Pozzi, M. Brenna, K. Mizuyama, G. Colo, Phys. Rev. C 85, 024601 (2012)
D. Vretenar, Y.F. Niu, N. Paar, J. Meng, Phys. Rev. C 85, 044317 (2012)
D. Savran et al., Phys. Rev. Lett. 100, 232501 (2008)
D. Savran et al., Phys. Rev. C 84, 024326 (2011)
S. Péru, H. Goutte, J.F. Berger, Phys. Rev. Lett. 105, 022502 (2010)
Elena Litvinova, Peter Ring, Victor Tselyaev, Phys. Rev. Lett. 105, 022502 (2010)
Mitsuru Tohyama, Takashi Nakatsukasa, Phys. Rev. C 85, 031302(R) (2012)
A. Bulgac, K.J. Roche, J. Phys. Conf. Ser. 125, 012064 (2008)
A. Bulgac, Y.-L. Luo, P. Magierski, K.J. Roche, Y. Yu, Science 332, 1288 (2011)
I. Stetcu, A. Bulgac, P. Magierski, K.J. Roche, Phys. Rev. C 84, 051309(R) (2011)
A. Bulgac, Annu. Rev. Nucl. Part. Sci. 63, 97 (2013)
I. Stetcu, C. Bertulani, A. Bulgac, P. Magierski, K.J. Roche, Phys. Rev. Lett. 114, 012701 (2015)
A. Bulgac, P. Magierski, K.J. Roche, I. Stetcu, Phys. Rev. Lett. 116, 122504 (2016)
A. Bulgac, Phys. Status Solidi B 256, 1800592 (2019)
Shuichiro Ebata, Takashi Nakatsukasa, Tsunenori Inakura, Phys. Rev. C 90, 024303 (2014)
A.J.F. Siegert, Phys. Rev. 52, 787 (1937)
R.G. Sachs, N. Austern, Phys. Rev. 81, 705 (1951)
A.N. Antonov et al., Nucl. Instrum. Methods Phys. Res. A 637, 60 (2011)
Toshimi Suda et al., Prog. Theor. Exp. Phys. 1, 03C008 (2012)
V. Ponomarev, D.H. Jakubassa-Amundsen, A. Richter, J. Wambach, arXiv:1904.08772 (2019)
C.A. Bertulani, Phys. Lett. B 585, 35 (2004)
J.M. Lattimer, M. Prakash, Science 304, 536 (2004)
P. Avogadro, C.A. Bertulani, Phys. Rev. C 88, 044319 (2013)
Bao-An Li, A. Ramos, G. Verde, I. Vidaña (Editors), Topical Issue on Nuclear Symmetry Energy, Eur. Phys. J. A, Vol. 50 (Springer, 2014)
X. Roca-Maza, M. Centelles, X. Vinas, M. Warda, Phys. Rev. Lett. 106, 252501 (2011)
X. Roca-Maza, X. Vinas, M. Centelles, B.K. Agrawal, G. Colo, N. Paar, J. Piekarewicz, D. Vretenar, Phys. Rev. C 92, 064304 (2015)
N.K. Glendenning, Compact stars: Nuclear physics, particle physics, and general relativity (Springer, New York, 1997)
F. Weber, Prog. Part. Nucl. Phys. 54, 193 (2005)
P. Haensel, A. Potekhin, D. Yakovlev, Neutron stars 1: Equation of state and structure (Springer, New York, 2007)
J.M. Lattimer, Annu. Rev. Nucl. Part. Sci. 62, 485 (2012)
C.A. Bertulani, J. Pieckarewicz (Editors), Neutron Star Crust (Nova Science Publishers, New York, 2012)
K. Hebeler, J.M. Lattimer, C.J. Pethick, A. Schwenk, Astrophys. J. 773, 11 (2013)
J.M. Lattimer, M. Prakash, Phys. Rev. Lett. 94, 111101 (2005)
G.F. Bertsch, C.A. Bertulani, W. Nazarewicz, N. Schunck, M.V. Stoitsov, Phys. Rev. C 79, 0343306 (2009)
B. Alex Brown, Phys. Rev. Lett. 85, 5296 (2000)
M. Beiner et al., Nucl. Phys. A 238, 29 (1975)
J. Dobaczewski et al., Nucl. Phys. A 422, 103 (1984)
P.-G. Reinhard, H. Flocard, Nucl. Phys. 584, 467 (1995)
B.A. Brown, Phys. Rev. C 58, 220 (1998)
E. Chabanat, P. Bonche, P. Haensel, J. Meyer, R. Schaeffer, Nucl. Phys. A 635, 231 (1998)
P.-G. Reinhard et al., Phys. Rev. C 60, 14316 (1999)
S. Goriely et al., Nucl. Phys. A 750, 425 (2005)
M. Dutra, O. Lourenco, J.S. Sa Martins, A. Delfino, J.R. Stone, P.D. Stevenson, Phys. Rev. C 85, 035201 (2012)
C.A. Bertulani, J. Valencia, arXiv:1904.01078 (2019)
P.-G. Reinhard, W. Nazarewicz, Phys. Rev. C 81, 051303(R) (2010)
A. Tamii et al., Phys. Rev. Lett. 107, 062502 (2011)
P. Adrich et al., Phys. Rev. Lett. 95, 132501 (2005)
O. Wieland et al., Phys. Rev. Lett. 102, 092502 (2009)
R. Schwengner et al., Phys. Rev. C 78, 064314 (2008)
C. Iwamoto et al., Phys. Rev. Lett. 108, 262501 (2012)
T. Chapuran, R. Vodhanel, M.K. Brussel, Phys. Rev. C 22, 1420 (1980)
N. Ryezayeva et al., Phys. Rev. Lett. 89, 272502 (2002)
J. Enders et al., Phys. Lett. B 486, 279 (2000)
J. Enders et al., Nucl. Phys. A 724, 243 (2003)
I. Poltoratska et al., Phys. Rev. C 85, 041304(R) (2012)
R.-D. Herzberg et al., Phys. Lett. B 390, 49 (1997)
R.-D. Herzberg et al., Phys. Rev. C 60, 051307 (1999)
A. Zilges et al., Phys. Lett. B 542, 43 (2002)
A. Zilges, Nucl. Phys. A 731, 249 (2004)
S. Volz et al., Nucl. Phys. A 779, 1 (2006)
D. Savran et al., Phys. Rev. Lett. 97, 172502 (2006)
J. Endres et al., Phys. Rev. C 80, 034302 (2009)
J. Endres et al., Phys. Rev. Lett. 105, 212503 (2010)
A.P. Tonchev et al., Phys. Rev. Lett. 104, 072501 (2010)
G. Hagen et al., Nature Phys. 12, 186 (2016)
J. Birkhan et al., Phys. Rev. Lett. 118, 252501 (2017)
D. Rossi et al., Phys. Rev. Lett. 111, 242503 (2013)
N. Brady, T. Aumann, C.A. Bertulani, J. Thomas, Phys. Lett. B 757, 553 (2016)
J. Piekarewicz, Phys. Rev. C 83, 034319 (2011)
C.J. Horowitz, J. Piekarewicz, Phys. Rev. Lett. 86, 5647 (2011)
S. Typel, B.A. Brown, Phys. Rev. C 64, 027302 (2011)
R.J. Furnstahl, Nucl. Phys. A 706, 85 (2002)
J. Jastrzebski, A. Trzcinska, P. Lubinski, B. Clos, F.J. Hartmann, T. von Egidy, S. Wycech, Int. J. Mod. Phys. E 13, 343 (2004)
T. Aumann, C.A. Bertulani, F. Schindler, S. Typel, Phys. Rev. Lett. 119, 262501 (2017)
Shubchintak, C.A. Bertulani, T. Aumann, Phys. Lett. B 778, 30 (2018)
S. Goriely, Phys. Lett. B 436, 10 (1998)
S. Goriely, E. Khan, Nucl. Phys. A 706, 217 (2002)
Christoper T. Angell, PhD Thesis, University of North Carolina (2008)
Nadia Tsoneva, Horst Lenske, Nature Commun. 6, 7384 (2015)
Nadia Tsoneva, Horst Lenske, EPJ Web of Conferences 93, 01021 (2015)
N. Tsoneva, S. Goriely, H. Lenske, R. Schwengner, Phys. Rev. C 91, 044318 (2015)
Nadia Tsoneva, Horst Lenske, arXiv:1410.2458 (2019)
G. Baur, C.A. Bertulani, H. Rebel, Nucl. Phys. A 458, 188 (1986)
N. Iwasa et al., Phys. Rev. Lett. 83, 2910 (1999)
T. Motobayashi, Eur. Phys. J. A 13, 207 (2002)
F. Fleurot et al., Phys. Lett. B 615, 167 (2005)
A. Horvath et al., Eur. Phys. J. A 27, 217 (2006)
E.G. Adelberger et al., Rev. Mod. Phys. 83, 195 (2011)
S.G. Altstadt et al., Nucl. Data Sheets 120, 197 (2014)
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To the memory of Pier Francesco Bortignon
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Bertulani, C.A. Pygmy resonances and symmetry energy. Eur. Phys. J. A 55, 240 (2019). https://doi.org/10.1140/epja/i2019-12883-2
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DOI: https://doi.org/10.1140/epja/i2019-12883-2