Dynamical effects of spin-dependent interactions in low- and intermediate-energy heavy-ion reactions

Abstract

It is well known that noncentral nuclear forces, such as the spin–orbital coupling and the tensor force, play important roles in understanding many interesting features of nuclear structures. However, their dynamical effects in nuclear reactions are poorly known because only the spin-averaged observables are normally studied both experimentally and theoretically. Realizing that spin-sensitive observables in nuclear reactions may convey useful information about the in-medium properties of noncentral nuclear interactions, besides earlier studies using the time-dependent Hartree–Fock approach to understand the effects of spin–orbital coupling on the threshold energy and spin polarization in fusion reactions, some efforts have been made recently to explore the dynamical effects of noncentral nuclear forces in intermediate-energy heavy-ion collisions using transport models. The focus of these studies has been on investigating signatures of the density and isospin dependence of the form factor in the spin-dependent single-nucleon potential. Interestingly, some useful probes were identified in the model studies but so far there are still no data to compare with. In this brief review, we summarize the main physics motivations as well as the recent progress in understanding the spin dynamics and identifying spin-sensitive observables in heavy-ion reactions at intermediate energies. We hope the interesting, important, and new physics potentials identified in the spin dynamics of heavy-ion collisions will stimulate more experimental work in this direction.

Keywords

heavy-ion collisions / transport model / spin–orbit interaction / tensor force / polarization

References

[1] P. Danielewicz, R. Lacey, and W. G. Lynch, Determination of the equation of state of dense matter, Science298(5598), 1592 (2002)

[2] V. Baran, M.Colonna, V. Greco, and M. Di Toro, Reaction dynamics with exotic nuclei, Phys. Rep.410(5–6), 335 (2005)

[3] B. A. Li, L. W.Chen, and C. M. Ko, Recent progress and new challenges in isospin physics with heavy-ion reactions, Phys. Rep.464(4–6), 113 (2008)

[4] H.Liang, J. Meng, and S. G. Zhou, Hidden pseudospin and spin symmetries and their origins in atomic nuclei, Phys. Rep.570, 1 (2015)

[5] J. E. Hirsch, Spin Hall effect, Phys. Rev. Lett.83(9), 1834 (1999)

[6] M. I. Dyakonov and V. I.Perel, Possibility of orientating electron spins with current, Sov. Phys. JETP Lett.13, 467 (1971)

[7] M. I. Dyakonov, and V. I.Perel, Current-induced spin orientation of electrons in semiconductors, Phys. Lett. A35(6), 459 (1971)

[8] Lecture Notes of R. Machleidt, CNS Summer School, University of Tokyo, <Date>Aug. 18-23</Date>, 2005

[9] M. G. Mayer, On closed shells in nuclei, Phys. Rev.74(3), 235 (1948);M. G.Mayer, On closed shells in nuclei (II), Phys. Rev.75(12), 1969 (1949)

[10] O.Haxel, J. H. D. Jensen, and H. E. Suess, On the “magic numbers” in nuclear structure, Phys. Rev.75(11), 1766 (1949)

[11] D.Vautherin and D. M. Brink, Hartree–Fock calculations with Skyrme’s interaction (I): Spherical nuclei, Phys. Rev. C 5(3), 626 (1972)

[12] P.Ring, Relativistic mean field theory in finite nuclei, Prog. Part. Nucl. Phys.37, 193 (1996)

[13] M. Bender, P. Heenen, and P.-G Reinhard, Self-consistent mean-field models for nuclear structure, Rev. Mod. Phys. 75, 121 (2003)

[14] P. G. Reinhard, The relativistic mean-field description of nuclei and nuclear dynamics, Rep. Prog. Phys.52(4), 439 (1989)

[15] A. Sulaksono, T. B�rvenich, J. A. Maruhn, P. G. Reinhard, and W. Greiner, The nonrelativistic limit of the relativistic point coupling model, Ann. Phys. 308(1), 354 (2003)

[16] J. M. Pearson and M.Farine, Relativistic mean-field theory and a density-dependent spin–orbit Skyrme force, Phys. Rev. C 50(1), 185 (1994)

[17] B. G. Todd-Rutel, J. Piekarewicz, and P. D. Cottle, Spin–orbit splitting in low-j neutron orbits and proton densities in the nuclear interior, Phys. Rev. C69, 021301 (2004)

[18] M.Grasso, L. Gaudefroy, E. Khan, T.Nikšić, J. Piekarewicz, O. Sorlin, N. V.Giai, and D. Vretenar, Nuclear “bubble” structure in Si³⁴, Phys. Rev. C 79(3), 034318 (2009)

[19] O.Sorlin and M. G. Porquet, Evolution of the N = 28 shell closure: A test bench for nuclear forces, Phys. Scr. T152, 014003 (2013)

[20] P. G. Reinhard and H.Flocard, Nuclear effective forces and isotope shifts, Nucl. Phys. A584(3), 467 (1995)

[21] M. M. Sharma, G.Lalazissis, J. König, and P. Ring, Isospin dependence of the spin–orbit force and effective nuclear potentials, Phys. Rev. Lett.74(19), 3744 (1995)

[22] M.Onsi, R. C. Nayak, J. M. Pearson, H.Freyer, and W. Stocker, Skyrme representation of a relativistic spin–orbit field, Phys. Rev. C 55(6), 3166 (1997)

[23] J. M. Pearson, Skyrme Hartree–Fock method and the spin–orbit term of the relativistic mean field, Phys. Lett. B513(3–4), 319 (2001)

[24] G. A. Lalazissis, D.Vretenar, W. Pöschl, and P. Ring, Reduction of the spin–orbit potential in light drip-line nuclei, Phys. Lett. B418(1-2), 7 (1998)

[25] B. S. Pudliner., A.Smerzi, J. Carlson, V. R. Pandharipande, S. C.Pieper, and D. G. Ravenhall, Neutron drops and Skyrme energy-density functionals, Phys. Rev. Lett.76(14), 2416 (1996)

[26] J. P. Schiffer, S. J. Freeman, J. A. Caggiano, C. Deibel, A. Heinz, C.L. Jiang, R. Lewis, A. Parikh, P. D. Parker, K. E. Rehm, S. Sinha, and J. S. Thomas, Is the nuclear spin-orbit interaction changing with neutron excess?Phys. Rev. Lett.92(16), 162501 (2004) [Erratum, Phys. Rev. Lett.,110, 169901 (2013)]

[27] T.Lesinski, M. Bender, K. Bennaceur, T.Duguet, and J. Meyer, Tensor part of the Skyrme energy density functional: Spherical nuclei, Phys. Rev. C 76(1), 014312 (2007)

[28] M.Zalewski, J. Dobaczewski, W. Satuła, and T. R.Werner, Spin–orbit and tensor mean-field effects on spin–orbit splitting including self-consistent core polarizations, Phys. Rev. C 77(2), 024316 (2008)

[29] M.Bender, K. Bennaceur, T. Duguet, P.H.Heenen, T. Lesinski, and J. Meyer, Tensor part of the Skyrme energy density functional (II): Deformation properties of magic and semi-magic nuclei, Phys. Rev. C 80(6), 064302 (2009)

[30] Y. M. Engel, D. M.Brink, K. Goeke, S. J.Krieger, and D. Vautherin, Time-dependent Hartree–Fock theory with Skyrme’s interaction, Nucl. Phys. A249(2), 215 (1975)

[31] T. H. R. Skyrme, The effective nuclear potential, Nucl. Phys.9(4), 615 (1958)

[32] T.Otsuka, T. Suzuki, R. Fujimoto, H.Grawe, and Y. Akaishi, Evolution of nuclear shells due to the tensor force, Phys. Rev. Lett.95(23), 232502 (2005)

[33] T.Otsuka, T. Matsuo, and D. Abe, Mean field with tensor force and shell structure of exotic nuclei, Phys. Rev. Lett.97(16), 162501 (2006)

[34] T.Otsuka, T. Suzuki, M. Honma, Y.Utsuno, N. Tsunoda, K. Tsukiyama, and M.Hjorth-Jensen, Novel features of nuclear forces and shell evolution in exotic nuclei, Phys. Rev. Lett.104(1), 012501 (2010)

[35] L.Gaudefroy, O. Sorlin, D. Beaumel, Y.Blumenfeld, Z. Dombrádi, S. Fortier, S.Franchoo, M. Gélin, J. Gibelin, S.Grévy, F. Hammache, F.Ibrahim, K. W. Kemper, K.L. Kratz, S. M.Lukyanov, C. Monrozeau, L. Nalpas, F.Nowacki, A. N. Ostrowski, T. Otsuka, Y.E.Penionzhkevich, J.Piekarewicz , E. C. Pollacco, P.Roussel-Chomaz, E. Rich, J. A. Scarpaci, M. G.St. Laurent, D. Sohler, M.Stanoiu , T.Suzuki, E. Tryggestad, and D. Verney, Reduction of the spin–orbit splittings at the N = 28 shell closure, Phys. Rev. Lett.97(9), 092501 (2006)

[36] G.Colò, H. Sagawa, S. Fracasso, and P. F.Bortignon, Spin–orbit splitting and the tensor component of the Skyrme interaction, Phys. Lett. B646(5–6), 227 (2007) [Erratum, Phys. Lett. B, 668, 457(2008)].

[37] L. G. Cao, G.Colò, H. Sagawa, P. F.Bortignon, and L. Sciacchitano, Effects of the tensor force on the multipole response in finite nuclei, Phys. Rev. C 80(6), 064304 (2009)

[38] C. L. Bai, H. Q.Zhang, H. Sagawa, X. Z.Zhang, G. Coló, and F. R. Xu, Effect of the tensor force on the charge exchange spin-dipole excitations of Pb²⁰⁸, Phys. Rev. Lett.105(7), 072501 (2010)

[39] C. L. Bai, H. Q.Zhang, H. Sagawa, X. Z.Zhang, G. Coló, and F. R. Xu, Spin–isospin excitations as quantitative constraints for the tensor force, Phys. Rev. C 83(5), 054316 (2011)

[40] E. B. Suckling and P. D.Stevenson, The effect of the tensor force on the predicted stability of superheavy nuclei, Eur. Phys. Lett.90(1), 12001 (2010)

[41] H. A. Bethe, Theory of nuclear matter, Annu. Rev. Nucl. Part. Sci.21(1), 93 (1971)

[42] V. R. Pandharipande, Variational calculation of nuclear matter, Nucl. Phys. A181(1), 33 (1972)

[43] S.Fantoni and V. R. Pandharipande, Momentum distribution of nucleons in nuclear matter, Nucl. Phys. A427(3), 473 (1984)

[44] S. C. Pieper, R. B.Wiringa, and V. R. Pandharipande, Variational calculation of the ground state of O¹⁶, Phys. Rev. C 46(5), 1741 (1992)

[45] C.Ciofi degli Atti and S.Simula, Realistic model of the nucleon spectral function in few- and many-nucleon systems, Phys. Rev. C 53(4), 1689 (1996)

[46] A.Tang, J. W. Watson, J. Aclander, J.Alster, G. Asryan, Y. Averichev, D.Barton, V. Baturin, N.Bukhtoyarova , A.Carroll, S. Gushue, S. Heppelmann, A.Leksanov, Y. Makdisi, A. Malki, E.Minina, I. Navon, H. Nicholson, A.Ogawa, Y. Panebratsev, E. Piasetzky, A.Schetkovsky, S. Shimanskiy, and D. Zhalov, n-p short-range correlations from (p, 2p+n) measurements, Phys. Rev. Lett.90(4), 042301 (2003)

[47] K. S. Egiyan, CLAS Collaboration), Measurement of two- and three-nucleon short-range correlation probabilities in nuclei, Phys. Rev. Lett.96(8), 082501 (2006)

[48] E.Piasetzky, M. Sargsian, L. Frankfurt, M.Strikman, and J. W. Watson, Evidence for strong dominance of proton–neutron correlations in nuclei, Phys. Rev. Lett.97(16), 162504 (2006)

[49] R.Subedi, R. Shneor, P. Monaghan, B. D.Anderson, K. Aniol, J. Annand, J.Arrington, H. Benaoum, F. Benmokhtar, W.Boeglin, , Probing cold dense nuclear matter, Science320(5882), 1476(2008)

[50] O.Hen, . (Jefferson Lab CLAS Collaboration), Momentum sharing in imbalanced Fermi systems, Science346(6209), 614 (2014)

[51] R.Schiavilla, R. B. Wiringa, S. C. Pieper, and J.Carlson, Tensor forces and the ground-state structure of nuclei, Phys. Rev. Lett.98(13), 132501 (2007)

[52] M.Alvioli, C. Ciofi degli Atti, and H. Morita, Proton–neutron and proton–proton correlations in medium-weight nuclei and the role of the tensor force, Phys. Rev. Lett.100(16), 162503 (2008)

[53] J.Arrington, D. W. Higinbotham, G. Rosner, and M.Sargsian, Hard probes of short-range nucleon–nucleon correlations, Prog. Part. Nucl. Phys.67(4), 898 (2012)

[54] I. Vidaña, A. Polls, and C. Providencia, Nuclear symmetry energy and the role of the tensor force, Phys. Rev. C84, 062801(R) (2011)

[55] A.Carbone, A. Polls, and A. Rios, High-momentum components in the nuclear symmetry energy, Eur. Phys. Lett.97(2), 22001 (2012)

[56] C.Xu, A. Li, and B. A. Li, Delineating effects of tensor force on the density dependence of nuclear symmetry energy, J. Phys.: Conf. Ser.420, 012090 (2013)

[57] K.Pomorski and J. Dudek, Nuclear liquid-drop model and surface-curvature effects, Phys. Rev. C 67(4), 044316 (2003)

[58] O.Hen, B. A. Li, W. J. Guo, L. B.Weinstein, and E. Piasetzky, Symmetry energy of nucleonic matter with tensor correlations, Phys. Rev. C 91(2), 025803 (2015)

[59] B. A. Li, W. J.Guo, and Z. Z. Shi, Effects of the kinetic symmetry energy reduced by short-range correlations in heavy-ion collisions at intermediate energies, Phys. Rev. C 91(4), 044601 (2015)

[60] P.Hoodbhoy and J. W. Negele, Solution of Hartree-Fock equations in coordinate space for axially symmetric nuclei, Nucl. Phys. A.288(1), 23 (1977)

[61] K. T. R. Davies and S. E.Koonin, Skyrme-force time-dependent Hartree–Fock calculations with axial symmetry, Phys. Rev. C 23(5), 2042 (1981) (Erratum, Phys. Rev. C, 24, 1820 (1981) )

[62] A. S. Umar, M. R.Strayer, and P. G. Reinhard, Resolution of the fusion window anomaly in heavy-ion collisions, Phys. Rev. Lett.56(26), 2793 (1986)

[63] P. G. Reinhard, A. S.Umar, K. T. R. Davies, M. R. Strayer, and S.J.Lee, Dissipation and forces in time-dependent Hartree–Fock calculations, Phys. Rev. C 37(3), 1026 (1988)

[64] A. S. Umar, M. R.Strayer, P.G. Reinhard, K. T. R. Davies, and S.J.Lee, Spin-orbit force in time-dependent Hartree–Fock calculations of heavy-ion collisions, Phys. Rev. C 40(2), 706 (1989)

[65] J. A. Maruhn, P.G.Reinhard, P. D. Stevenson, and M. R. Strayer, Spin-excitation mechanisms in Skyrme-force time-dependent Hartree–Fock calculations, Phys. Rev. C 74(2), 027601 (2006)

[66] A. S. Umar and V. E.Oberacker, Three-dimensional unrestricted time-dependent Hartree–Fock fusion calculations using the full Skyrme interaction, Phys. Rev. C 73(5), 054607 (2006)

[67] G. F. Dai, L.Guo, E. G. Zhao, and S. G.Zhou, Dissipation dynamics and spin-orbit force in time-dependent Hartree–Fock theory, Phys. Rev. C 90(4), 044609 (2014)

[68] Y.Iwata and J. A. Maruhn, Enhanced spin-current tensor contribution in collision dynamics, Phys. Rev. C 84(1), 014616 (2011)

[69] G. F. Dai,L.Guo, E. G. Zhao, and S. G.Zhou, Effect of tensor force on dissipation dynamics in time-dependent Hartree-Fock theory, Science China- Physics, Mechanics & Astronomy57(9), 1618 (2014)

[70] P. D. Stevenson., E. B.Suckling, S. Fracasso, M. C. Barton, and A. S. Umar, The Skyrme tensor force in heavy ion collisions, arXiv: 1507.00645[nucl-th]

[71] C. Y. Wong, Dynamics of nuclear fluid. VIII. Time-dependent Hartree–Fock approximation from a classical point of view, Phys. Rev. C 25(3), 1460 (1982)

[72] G. F. Bertsch and S. Das Gupta, A guide to microscopic models for intermediate energy heavy ion collisions, Phys. Rep.160(4), 189 (1988)

[73] J. Xu and B. A. Li, Probing in-medium spin–orbit interaction with intermediate-energy heavy-ion collisions, Phys. Lett. B724(4-5), 346 (2013)

[74] Y. Xia, J. Xu, B. A. Li, and W. Q. Shen, Spin–orbit coupling and the up-down differential transverse flow in intermediate-energy heavy-ion collisions, Phys. Rev. C 89(6), 064606 (2014)

[75] Y. Xia, J. Xu, B. A. Li, and W. Q. Shen, The spin-splitting of collective flows in intermediate-energy heavy-ion collisions, arXiv: 1411.3057[nucl-th]

[76] J. Xu, B. A. Li, Y. Xia, and W. Q. Shen, Spin effects in intermediate-energy heavy-ion collisions, Nucl. Phys. Rev.31, 306 (2014)

[77] J. Xu, Y. Xia, B. A. Li, and W. Q. Shen, Spin-orbit coupling in intermediate-energy heavy-ion collisions, Nucl. Technol.37, 100513 (2014) (in Chinese)

[78] G. G. Ohlsen, Polarization transfer and spin correlation experiments in nuclear physics, Rep. Prog. Phys.35(2), 717 (1972)

[79] W. G. Love and M. A. Franey, Effective nucleon–nucleon interaction for scattering at intermediate energies, Phys. Rev. C 24(3), 1073 (1981) W. G. Love and M. A. Franey, Erratum: Effective nucleon–nucleon interaction for scattering at intermediate energies, Phys. Rev. C 27(1), 438 (1983)

[80] P. Danielewicz and G. Odyniec, Transverse momentum analysis of collective motion in relativistic nuclear collisions, Phys. Lett. B157(2–3), 146 (1985)

[81] V. Greco, C. M. Ko, and P. Lévai, Parton coalescence and the antiproton/pion anomaly at RHIC, Phys. Rev. Lett.90(20), 202302 (2003)

[82] V. Greco, C. M. Ko, and P. Lévai, Partonic coalescence in relativistic heavy ion collisions, Phys. Rev. C 68(3), 034904 (2003)

[83] L. W. Chen, C. M. Ko, and B. A. Li, Light cluster production in intermediate energy heavy-ion collisions induced by neutron-rich nuclei, Nucl. Phys. A729(2–4), 809 (2003)

[84] L. W. Chen, C. M. Ko, and B. A. Li, Light clusters production as a probe to nuclear symmetry energy, Phys. Rev. C 68(1), 017601 (2003)

[85] Y. Xia, J. Xu, B. A. Li, and W. Q. Shen, in preparation

[86] L. W. Chen, C. M. Ko, B. A. Li, and J. Xu, Density slope of the nuclear symmetry energy from the neutron skin thickness of heavy nuclei, Phys. Rev. C 82(2), 024321 (2010)

[87] C. Hartnack, L. Zhuxia, L. Neise, G. Peilert, A. Rosenhauer, H. Sorge, J. Aichelin, H. Stöcker, and W. Greiner, Quantum molecular dynamics a microscopic model from UNILAC to CERN energies, Nucl. Phys. A.495(1–2), 303 (1989)

[88] J. Aichelin, “Quantum” molecular dynamics — a dynamical microscopic n-body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions, Phys. Rep.202(5–6), 233 (1991)

[89] C. C. Guo, Y. J. Wang, Q. F. Li, and F. S. Zhang, Effect of the spin–orbit interaction on flows in heavy-ion collisions at intermediate energies, Phys. Rev. C 90(3), 034606 (2014)

[90] K. Asahi, M. Ishihara, N. Inabe, T. Ichihara, T. Kubo, M. Adachi, H. Takanashi, M. Kouguchi, M. Fukuda, D. Mikolas, D. J. Morrissey, D. Beaumel, T. Shimoda, H. Miyatake, and N. Takahashi, New aspect of intermediate energy heavy ion reactions: Large spin polarization of fragments, Phys. Lett. B251(4), 488 (1990)

[91] H. Okuno, K. Asahi, H. Sato, H. Ueno, J. Kura, M. Adachi, T. Nakamura, T. Kubo, N. Inabe, A. Yoshida, T. Ichihara, Y. Kobayashi, Y. Ohkubo, M. Iwamoto, F. Ambe, T. Shimoda, H. Miyatake, N. Takahashi, J. Nakamura, D. Beaumel, D. J. Morrissey, W.D. Schmidt-Ott, and M. Ishihara, Systematic behavior of ejectile spin polarization in the projectile fragmentation reaction, Phys. Lett. B335(1), 29 (1994)

[92] W. -D. Schmidt-Ott, K. Asahi, Y. Fujita, H. Geissel, K. -D. Gross, T. Hild, H. Irnich, M. Ishihara, K. Krumbholz, V. Kunze, A. Magel, F. Meissner, K. Muto, F. Nickel, H. Okuno, M. Pfützner, C. Scheidenberger, K. Suzuki, M. Weber, C. Wennemann, Spin alignment of ⁴³Sc produced in the fragmentation of 500 MeV/u ⁴⁶Ti, Z. Phys. A 350(3), 215 (1994)

[93] D. E. Groh, P. F. Mantica, A. E. Stuchbery, A. Stolz, T. J. Mertzimekis, W. F. Rogers, A. D. Davies, S. N. Liddick, and B. E. Tomlin, Spin polarization of K³⁷ produced in a Single-proton pickup reaction at intermediate energies, Phys. Rev. Lett.90(20), 202502 (2003)

[94] K. Asahi, M. Ishihara, T. Ichihara, M. Fukuda, T. Kubo, Y. Gono, A. C. Mueller, R. Anne, D. Bazin, D. Guillemaud-Mueller, R. Bimbot, W. D. Schmidt-Ott, and J. Kasagi, Observation of spin-aligned secondary fragment beams of B¹⁴, Phys. Rev. C 43(2), 456 (1991)

[95] D. Borremans, J. M. Daugas, S. Teughels, D. L. Balabanski, N. Coulier, F. de Oliveira Santos, G.Georgiev, M. Hass, G. GeorgievM. Lewitowicz, I. Matea, Y. E. Penionzhkevich, W.D. Schmidt-Ott, Y. E. Sobolev, M. Stanoiu, K. Vyvey, and G. Neyens, Spin polarization of ²⁷Na and ³¹Al in intermediate energy projectile fragmentation of ³⁶S, Phys. Rev. C 66(5), 054601 (2002)

[96] K. Turzó, P. Himpe, D. L. Balabanski, G. Bélier, D. Borremans, J. M. Daugas, G. Georgiev, F. O. Santos, S. Mallion, I. Matea, G. Neyens, Y. E. Penionzhkevich, C. Stodel, N. Vermeulen, and D. Yordanov, Spin polarization of Al³⁴ fragments produced by nucleon pickup at intermediate energies, Phys. Rev. C 73(4), 044313 (2006)

[97] Y. Ichikawa, H. Ueno, Y. Ishii, T. Furukawa, A. Yoshimi, D. Kameda, H. Watanabe, N. Aoi, K. Asahi, D. L. Balabanski, R. Chevrier, J.M. Daugas, N. Fukuda, G. Georgiev, H. Hayashi, H. Iijima, N. Inabe, T. Inoue, M. Ishihara, T. Kubo, T. Nanao, T. Ohnishi, K. Suzuki, M. Tsuchiya, H. Takeda, and M. M. Rajabali, Production of spin-controlled rare isotope beams, Nat. Phys.8(12), 918 (2012)

[98] N. H. Buttimore, E. Gotsman, and E. Leader, Spin-dependent phenomena induced by electromagnetic–hadronic interference at high energies, Phys. Rev. D 18(3), 694 (1978)

[99] A. Zelenski, G. Atoian, A. Bogdanov, D. Raparia, M. Runtso, and E. Stephenson, Precision, absolute proton polarization measurements at 200 MeV beam energy, J. Phys.: Conf. Ser.295, 012132 (2011)

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg