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Hot spot effect in subatomic physics

October 24, 2023

Hot spots in subatomic physics are regions of high energy density or temperature in hadronic or nuclear matter.

Finite size effects Edit

Hot spots are a manifestation of the finite size of the system: in subatomic physics this refers both to atomic nuclei, which consist of nucleons, as well as to nucleons themselves, which are made of quarks and gluons, Other manifestations of finite sizes of these systems are seen in scattering of electrons on nuclei and nucleons. For nuclei in particular finite size effects manifest themselves also in the isomeric shift and isotopic shift.

Statistical methods in subatomic physics Edit

The formation of hot spots assumes the establishment of local equilibrium, which in its turn occurs if the thermal conductivity in the medium is sufficiently small. The notions of equilibrium and heat are statistical. The use of statistical methods assumes a large number of degrees of freedom. In macroscopic physics this number usually refers to the number of atoms or molecules, while in nuclear and particle physics it refers to the energy level density.[1]

Hot spots in nucleons Edit

Local equilibrium is the precursor of global equilibrium and the hot spot effect can be used to determine how fast, if at all, the transition from local to global equilibrium takes place. That this transition does not always happen follows from the fact that the duration of a strong interaction reaction is quite short (of the order of 10−22–10−23 seconds) and the propagation of "heat", i.e. of the excitation, through the finite sized body of the system takes a finite time, which is determined by the thermal conductivity of the matter the system is made of. Indications of the transition between local and global equilibrium in strong interaction particle physics started to emerge in the 1960s and early 1970s. In high-energy strong interactions equilibrium is usually not complete. In these reactions, with the increase of laboratory energy one observes that the transverse momenta of produced particles have a tail, which deviates from the single exponential Boltzmann spectrum, characteristic for global equilibrium. The slope or the effective temperature of this transverse momentum tail increases with increasing energy. These large transverse momenta were interpreted as being due to particles, which "leak" out before equilibrium is reached. Similar observations had been made in nuclear reactions and were also attributed to pre-equilibrium effects. This interpretation suggested that the equilibrium is neither instantaneous, nor global, but rather local in space and time. By predicting a specific asymmetry in peripheral high-energy hadron reactions based on the hot spot effect Richard M. Weiner[2] proposed a direct test of this hypothesis as well as of the assumption that the heat conductivity in hadronic matter is relatively small. The theoretical analysis of the hot spot effect in terms of propagation of heat was performed in Ref.[3]

In high-energy hadron reactions one distinguishes peripheral reactions with low multiplicity and central collisions with high multiplicity. Peripheral reactions are also characterized by the existence of a leading particle which retains a large proportion of the incoming energy. By taking the notion of peripheral literally Ref.2 suggested that in this kind of reaction the surface of the colliding hadrons is locally excited giving rise to a hot spot, which is de-excited by two processes: 1) emission of particles into the vacuum 2) propagation of “heat” into the body of the target (projectile) wherefrom it is eventually also emitted through particle production. Particles produced in process 1) will have higher energies than those due to process 2), because in the latter process the excitation energy is in part degraded. This gives rise to an asymmetry with respect to the leading particle, which should be detectable in an experimental event by event analysis. This effect was confirmed by Jacques Goldberg[4] in K− p→ K− p π+ π− reactions at 14 GEV/c. This experiment represents the first observation of local equilibrium in hadronic interactions, allowing in principle a quantitative determination of heat conductivity in hadronic matter along the lines of Ref.3. This observation came as a surprise,[5] because, although the electron proton scattering experiments had shown beyond any doubt that the nucleon had a finite size, it was a-priori not clear whether this size was sufficiently big for the hot spot effect to be observable, i. e. whether heat conductivity in hadronic matters was sufficiently small. Experiment4 suggests that this is the case.

Hot spots in nuclei Edit

In atomic nuclei, because of their larger dimensions as compared with nucleons, statistical and thermodynamical concepts have been used already in the 1930s. Hans Bethe[6] had suggested that propagation of heat in nuclear matter could be studied in central collisions and Sin-Itiro Tomonaga[7] had calculated the corresponding heat conductivity. The interest in this phenomenon was resurrected in the 1970s by the work of Weiner and Weström[8][9] who established the link between the hot spot model and the pre-equilibrium approach used in low-energy heavy-ion reactions.[10][11] Experimentally the hot spot model in nuclear reactions was confirmed in a series of investigations[12][13][14][15] some of which of rather sophisticated nature including polarization measurements of protons[16] and gamma rays.[17] Subsequently on the theoretical side the link between hot spots and limiting fragmentation[18] and transparency[19] in high-energy heavy ion reactions was analyzed and “drifting hot spots” for central collisions were studied.[20][21] With the advent of heavy ion accelerators experimental studies of hot spots in nuclear matter became a subject of current interest and a series of special meetings[22][23][24][25] was dedicated to the topic of local equilibrium in strong interactions. The phenomena of hot spots, heat conduction and preequilibrium play also an important part in high-energy heavy ion reactions and in the search for the phase transition to quark matter.[26]

Hot spots and solitons Edit

Solitary waves (solitons) are a possible physical mechanism for the creation of hot spots in nuclear interactions. Solitons are a solution of the hydrodynamic equations characterized by a stable localized high density region and small spatial volume. They were predicted[27][28] to appear in low-energy heavy ion collisions at velocities of the projectile slightly exceeding the velocity of sound (E/A ~ 10-20 MeV; here E is the incoming energy and A the atomic number). Possible evidence[29] for this phenomenon is provided by the experimental observation[30] that the linear momentum transfer in 12C induced heavy-ion reactions is limited.

References Edit

  1. ^ Cf. e.g. Richard M. Weiner, Analogies in Physics and Life, World Scientific 2008, p. 123.
  2. ^ Weiner, Richard M. (18 March 1974). "Asymmetry in Peripheral Production Processes". Physical Review Letters. American Physical Society (APS). 32 (11): 630–633. doi:10.1103/physrevlett.32.630. ISSN 0031-9007.
  3. ^ Weiner, Richard M. (1 February 1976). "Propagation of "heat" in hadronic matter". Physical Review D. American Physical Society (APS). 13 (5): 1363–1375. doi:10.1103/physrevd.13.1363. ISSN 0556-2821.
  4. ^ Goldberg, Jacques (23 July 1979). "Observation of Preequilibrium Pion Evaporation from Excited Hadrons?". Physical Review Letters. American Physical Society (APS). 43 (4): 250–252. doi:10.1103/physrevlett.43.250. ISSN 0031-9007.
  5. ^ "Hot spots discussed at Bonn". CERN Courier. Vol. 19, no. 1. 1979. p. 24-25.
  6. ^ Bethe, H. (1938). "Proceedings of the American Physical Society, Minutes of the New York Meeting February 25-26 1938. Abstract 3: Possible Deviations from the Evaporation Model of Nuclear Reactions". Physical Review. 53 (8): 675. In this short abstract a forward-backward asymmetry in central collisions is considered.
  7. ^ Tomonaga, S. (1938). "Innere Reibung und Wärmeleitfähigkeit der Kernmaterie". Zeitschrift für Physik (in German). Springer Science and Business Media LLC. 110 (9–10): 573–604. doi:10.1007/bf01340217. ISSN 1434-6001. S2CID 123148301.
  8. ^ Weiner, R.; Weström, M. (16 June 1975). "Pre-equilibrium and Heat Conduction in Nuclear Matter". Physical Review Letters. American Physical Society (APS). 34 (24): 1523–1527. doi:10.1103/physrevlett.34.1523. ISSN 0031-9007.
  9. ^ Weiner, R.; Weström, M. (1977). "Diffusion of heat in nuclear matter and preequilibrium phenomena". Nuclear Physics A. Elsevier BV. 286 (2): 282–296. doi:10.1016/0375-9474(77)90408-0. ISSN 0375-9474.
  10. ^ Blann, M (1975). "Preequilibrium Decay". Annual Review of Nuclear Science. Annual Reviews. 25 (1): 123–166. doi:10.1146/annurev.ns.25.120175.001011. ISSN 0066-4243.
  11. ^ J. M. Miller, in Proc lnt. Conf. on nuclear physics, voL 2, ed. J. de Boer and H. J. Mang (North-Holland, Amsterdam, 1973) p. 398.
  12. ^ Ho, H.; Albrecht, R.; Dünnweber, W.; Graw, G.; Steadman, S. G.; Wurm, J. P.; Disdier, D.; Rauch, V.; Scheibling, F. (1977). "Pre-equilibrium alpha emission accompanying deep-inelastic 16O+58Ni collisions". Zeitschrift für Physik A. Springer Science and Business Media LLC. 283 (3): 235–245. doi:10.1007/bf01407203. ISSN 0340-2193. S2CID 119380693.
  13. ^ Nomura, T.; Utsunomiya, H.; Motobayashi, T.; Inamura, T.; Yanokura, M. (13 March 1978). "Statistical Analysis of Preequilibriumα-Particle Spectra and Possible Local Heating". Physical Review Letters. American Physical Society (APS). 40 (11): 694–697. doi:10.1103/physrevlett.40.694. ISSN 0031-9007.
  14. ^ Westerberg, L.; Sarantites, D. G.; Hensley, D. C.; Dayras, R. A.; Halbert, M. L.; Barker, J. H. (1 July 1978). "Pre-equilibrium particle emission from fusion of 12C+158Gd and 20Ne+150Nd". Physical Review C. American Physical Society (APS). 18 (2): 796–814. doi:10.1103/physrevc.18.796. ISSN 0556-2813.
  15. ^ Utsunomiya, H.; Nomura, T.; Inamura, T.; Sugitate, T.; Motobayashi, T. (1980). "Preequilibrium α-particle emission in heavy-ion reactions". Nuclear Physics A. Elsevier BV. 334 (1): 127–143. doi:10.1016/0375-9474(80)90144-x. ISSN 0375-9474.
  16. ^ Sugitate, T.; Nomura, T.; Ishihara, M.; Gono, Y.; Utsunomiya, H.; Ieki, K.; Kohmoto, S. (1982). "Polarization of preequilibrium proton emission in the 93Nb + 14N reaction". Nuclear Physics A. Elsevier BV. 388 (2): 402–420. doi:10.1016/0375-9474(82)90422-5. ISSN 0375-9474.
  17. ^ Trautmann, W.; Hansen, Ole; Tricoire, H.; Hering, W.; Ritzka, R.; Trombik, W. (22 October 1984). "Dynamics of Incomplete Fusion Reactions fromγ-Ray Circular-Polarization Measurements". Physical Review Letters. American Physical Society (APS). 53 (17): 1630–1633. doi:10.1103/physrevlett.53.1630. ISSN 0031-9007.
  18. ^ Beckmann, R.; Raha, S.; Stelte, N.; Weiner, R.M. (1981). "Limiting fragmentation in high-energy heavy-ion reactions and preequilibrium". Physics Letters B. Elsevier BV. 105 (6): 411–416. doi:10.1016/0370-2693(81)91194-1. ISSN 0370-2693.
  19. ^ Beckmann, R; Raha, S; Stelte, N; Weiner, R M (1 February 1984). "Limiting Fragmentation and Transparency in High Energy Heavy Ion Collisions". Physica Scripta. IOP Publishing. 29 (3): 197–201. doi:10.1088/0031-8949/29/3/002. ISSN 0031-8949.
  20. ^ Stelte, N.; Weiner, R. (1981). "Cumulative effect and hot spots". Physics Letters B. Elsevier BV. 103 (4–5): 275–280. doi:10.1016/0370-2693(81)90223-9. ISSN 0370-2693.
  21. ^ Stelte, N.; Weström, M.; Weiner, R.M. (1982). "Drifting hot spots". Nuclear Physics A. Elsevier BV. 384 (1–2): 190–210. doi:10.1016/0375-9474(82)90313-x. ISSN 0375-9474.
  22. ^ “Local Equilibrium in Strong Interactions Physics” (LESIP I), Eds. D. K. Scott and R. M. Weiner, World Scientific 1985
  23. ^ Hadronic Matter in Collision” (LESIP II) Eds. P. Carruthers and D. Strottman, World Scientific 1986
  24. ^ “Hadronic Matter in Collision 1988” (LESIP III), Eds. P. Carruthers and J. Rafelski, World Scientific 1988
  25. ^ “Correlations and Multiparticle Production” (LESI IV), Eds. M. Plümer, S. Raha and R. M. Weiner, World Scientific 1991.
  26. ^ Gyulassy, Miklos; Rischke, Dirk H.; Zhang, Bin (1997). "Hot spots and turbulent initial conditions of quark-gluon plasmas in nuclear collisions". Nuclear Physics A. 613 (4): 397–434. arXiv:nucl-th/9609030. doi:10.1016/s0375-9474(96)00416-2. ISSN 0375-9474. S2CID 1301930.
  27. ^ Fowler, G.N.; Raha, S.; Stelte, N.; Weiner, R.M. (1982). "Solitons in nucleus-nucleus collisions near the speed of sound". Physics Letters B. Elsevier BV. 115 (4): 286–290. doi:10.1016/0370-2693(82)90371-9. ISSN 0370-2693.
  28. ^ Raha, S.; Wehrberger, K.; Weiner, R.M. (1985). "Stability of density solitons formed in nuclear collisions". Nuclear Physics A. Elsevier BV. 433 (3): 427–440. doi:10.1016/0375-9474(85)90274-x. ISSN 0375-9474.
  29. ^ Raha, S.; Weiner, R. M. (7 February 1983). "Are Solitons Already Seen in Heavy-Ion Reactions?". Physical Review Letters. American Physical Society (APS). 50 (6): 407–408. doi:10.1103/physrevlett.50.407. ISSN 0031-9007.
  30. ^ Galin, J.; Oeschler, H.; Song, S.; Borderie, B.; Rivet, M. F.; et al. (28 June 1982). "Evidence for a Limitation of the Linear Momentum Transfer in 12C-Induced Reactions between 30 and 84 MeV/u". Physical Review Letters. American Physical Society (APS). 48 (26): 1787–1790. doi:10.1103/physrevlett.48.1787. ISSN 0031-9007.

October 24, 2023
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This article may be confusing or unclear to readers Please help clarify the article There is a discussion about this on Talk Hot spot effect in subatomic physics Largely incomprehensible April 2018 Learn how and when to remove this template message Hot spots in subatomic physics are regions of high energy density or temperature in hadronic or nuclear matter Contents 1 Finite size effects 2 Statistical methods in subatomic physics 3 Hot spots in nucleons 3 1 Hot spots in nuclei 4 Hot spots and solitons 5 ReferencesFinite size effects EditHot spots are a manifestation of the finite size of the system in subatomic physics this refers both to atomic nuclei which consist of nucleons as well as to nucleons themselves which are made of quarks and gluons Other manifestations of finite sizes of these systems are seen in scattering of electrons on nuclei and nucleons For nuclei in particular finite size effects manifest themselves also in the isomeric shift and isotopic shift Statistical methods in subatomic physics EditThe formation of hot spots assumes the establishment of local equilibrium which in its turn occurs if the thermal conductivity in the medium is sufficiently small The notions of equilibrium and heat are statistical The use of statistical methods assumes a large number of degrees of freedom In macroscopic physics this number usually refers to the number of atoms or molecules while in nuclear and particle physics it refers to the energy level density 1 Hot spots in nucleons EditLocal equilibrium is the precursor of global equilibrium and the hot spot effect can be used to determine how fast if at all the transition from local to global equilibrium takes place That this transition does not always happen follows from the fact that the duration of a strong interaction reaction is quite short of the order of 10 22 10 23 seconds and the propagation of heat i e of the excitation through the finite sized body of the system takes a finite time which is determined by the thermal conductivity of the matter the system is made of Indications of the transition between local and global equilibrium in strong interaction particle physics started to emerge in the 1960s and early 1970s In high energy strong interactions equilibrium is usually not complete In these reactions with the increase of laboratory energy one observes that the transverse momenta of produced particles have a tail which deviates from the single exponential Boltzmann spectrum characteristic for global equilibrium The slope or the effective temperature of this transverse momentum tail increases with increasing energy These large transverse momenta were interpreted as being due to particles which leak out before equilibrium is reached Similar observations had been made in nuclear reactions and were also attributed to pre equilibrium effects This interpretation suggested that the equilibrium is neither instantaneous nor global but rather local in space and time By predicting a specific asymmetry in peripheral high energy hadron reactions based on the hot spot effect Richard M Weiner 2 proposed a direct test of this hypothesis as well as of the assumption that the heat conductivity in hadronic matter is relatively small The theoretical analysis of the hot spot effect in terms of propagation of heat was performed in Ref 3 In high energy hadron reactions one distinguishes peripheral reactions with low multiplicity and central collisions with high multiplicity Peripheral reactions are also characterized by the existence of a leading particle which retains a large proportion of the incoming energy By taking the notion of peripheral literally Ref 2 suggested that in this kind of reaction the surface of the colliding hadrons is locally excited giving rise to a hot spot which is de excited by two processes 1 emission of particles into the vacuum 2 propagation of heat into the body of the target projectile wherefrom it is eventually also emitted through particle production Particles produced in process 1 will have higher energies than those due to process 2 because in the latter process the excitation energy is in part degraded This gives rise to an asymmetry with respect to the leading particle which should be detectable in an experimental event by event analysis This effect was confirmed by Jacques Goldberg 4 in K p K p p p reactions at 14 GEV c This experiment represents the first observation of local equilibrium in hadronic interactions allowing in principle a quantitative determination of heat conductivity in hadronic matter along the lines of Ref 3 This observation came as a surprise 5 because although the electron proton scattering experiments had shown beyond any doubt that the nucleon had a finite size it was a priori not clear whether this size was sufficiently big for the hot spot effect to be observable i e whether heat conductivity in hadronic matters was sufficiently small Experiment4 suggests that this is the case Hot spots in nuclei Edit In atomic nuclei because of their larger dimensions as compared with nucleons statistical and thermodynamical concepts have been used already in the 1930s Hans Bethe 6 had suggested that propagation of heat in nuclear matter could be studied in central collisions and Sin Itiro Tomonaga 7 had calculated the corresponding heat conductivity The interest in this phenomenon was resurrected in the 1970s by the work of Weiner and Westrom 8 9 who established the link between the hot spot model and the pre equilibrium approach used in low energy heavy ion reactions 10 11 Experimentally the hot spot model in nuclear reactions was confirmed in a series of investigations 12 13 14 15 some of which of rather sophisticated nature including polarization measurements of protons 16 and gamma rays 17 Subsequently on the theoretical side the link between hot spots and limiting fragmentation 18 and transparency 19 in high energy heavy ion reactions was analyzed and drifting hot spots for central collisions were studied 20 21 With the advent of heavy ion accelerators experimental studies of hot spots in nuclear matter became a subject of current interest and a series of special meetings 22 23 24 25 was dedicated to the topic of local equilibrium in strong interactions The phenomena of hot spots heat conduction and preequilibrium play also an important part in high energy heavy ion reactions and in the search for the phase transition to quark matter 26 Hot spots and solitons EditSolitary waves solitons are a possible physical mechanism for the creation of hot spots in nuclear interactions Solitons are a solution of the hydrodynamic equations characterized by a stable localized high density region and small spatial volume They were predicted 27 28 to appear in low energy heavy ion collisions at velocities of the projectile slightly exceeding the velocity of sound E A 10 20 MeV here E is the incoming energy and A the atomic number Possible evidence 29 for this phenomenon is provided by the experimental observation 30 that the linear momentum transfer in 12C induced heavy ion reactions is limited References Edit Cf e g Richard M Weiner Analogies in Physics and Life World Scientific 2008 p 123 Weiner Richard M 18 March 1974 Asymmetry in Peripheral Production Processes Physical Review Letters American Physical Society APS 32 11 630 633 doi 10 1103 physrevlett 32 630 ISSN 0031 9007 Weiner Richard M 1 February 1976 Propagation of heat in hadronic matter Physical Review D American Physical Society APS 13 5 1363 1375 doi 10 1103 physrevd 13 1363 ISSN 0556 2821 Goldberg Jacques 23 July 1979 Observation of Preequilibrium Pion Evaporation from Excited Hadrons Physical Review Letters American Physical Society APS 43 4 250 252 doi 10 1103 physrevlett 43 250 ISSN 0031 9007 Hot spots discussed at Bonn CERN Courier Vol 19 no 1 1979 p 24 25 Bethe H 1938 Proceedings of the American Physical Society Minutes of the New York Meeting February 25 26 1938 Abstract 3 Possible Deviations from the Evaporation Model of Nuclear Reactions Physical Review 53 8 675 In this short abstract a forward backward asymmetry in central collisions is considered Tomonaga S 1938 Innere Reibung und Warmeleitfahigkeit der Kernmaterie Zeitschrift fur Physik in German Springer Science and Business Media LLC 110 9 10 573 604 doi 10 1007 bf01340217 ISSN 1434 6001 S2CID 123148301 Weiner R Westrom M 16 June 1975 Pre equilibrium and Heat Conduction in Nuclear Matter Physical Review Letters American Physical Society APS 34 24 1523 1527 doi 10 1103 physrevlett 34 1523 ISSN 0031 9007 Weiner R Westrom M 1977 Diffusion of heat in nuclear matter and preequilibrium phenomena Nuclear Physics A Elsevier BV 286 2 282 296 doi 10 1016 0375 9474 77 90408 0 ISSN 0375 9474 Blann M 1975 Preequilibrium Decay Annual Review of Nuclear Science Annual Reviews 25 1 123 166 doi 10 1146 annurev ns 25 120175 001011 ISSN 0066 4243 J M Miller in Proc lnt Conf on nuclear physics voL 2 ed J de Boer and H J Mang North Holland Amsterdam 1973 p 398 Ho H Albrecht R Dunnweber W Graw G Steadman S G Wurm J P Disdier D Rauch V Scheibling F 1977 Pre equilibrium alpha emission accompanying deep inelastic 16O 58Ni collisions Zeitschrift fur Physik A Springer Science and Business Media LLC 283 3 235 245 doi 10 1007 bf01407203 ISSN 0340 2193 S2CID 119380693 Nomura T Utsunomiya H Motobayashi T Inamura T Yanokura M 13 March 1978 Statistical Analysis of Preequilibriuma Particle Spectra and Possible Local Heating Physical Review Letters American Physical Society APS 40 11 694 697 doi 10 1103 physrevlett 40 694 ISSN 0031 9007 Westerberg L Sarantites D G Hensley D C Dayras R A Halbert M L Barker J H 1 July 1978 Pre equilibrium particle emission from fusion of 12C 158Gd and 20Ne 150Nd Physical Review C American Physical Society APS 18 2 796 814 doi 10 1103 physrevc 18 796 ISSN 0556 2813 Utsunomiya H Nomura T Inamura T Sugitate T Motobayashi T 1980 Preequilibrium a particle emission in heavy ion reactions Nuclear Physics A Elsevier BV 334 1 127 143 doi 10 1016 0375 9474 80 90144 x ISSN 0375 9474 Sugitate T Nomura T Ishihara M Gono Y Utsunomiya H Ieki K Kohmoto S 1982 Polarization of preequilibrium proton emission in the 93Nb 14N reaction Nuclear Physics A Elsevier BV 388 2 402 420 doi 10 1016 0375 9474 82 90422 5 ISSN 0375 9474 Trautmann W Hansen Ole Tricoire H Hering W Ritzka R Trombik W 22 October 1984 Dynamics of Incomplete Fusion Reactions fromg Ray Circular Polarization Measurements Physical Review Letters American Physical Society APS 53 17 1630 1633 doi 10 1103 physrevlett 53 1630 ISSN 0031 9007 Beckmann R Raha S Stelte N Weiner R M 1981 Limiting fragmentation in high energy heavy ion reactions and preequilibrium Physics Letters B Elsevier BV 105 6 411 416 doi 10 1016 0370 2693 81 91194 1 ISSN 0370 2693 Beckmann R Raha S Stelte N Weiner R M 1 February 1984 Limiting Fragmentation and Transparency in High Energy Heavy Ion Collisions Physica Scripta IOP Publishing 29 3 197 201 doi 10 1088 0031 8949 29 3 002 ISSN 0031 8949 Stelte N Weiner R 1981 Cumulative effect and hot spots Physics Letters B Elsevier BV 103 4 5 275 280 doi 10 1016 0370 2693 81 90223 9 ISSN 0370 2693 Stelte N Westrom M Weiner R M 1982 Drifting hot spots Nuclear Physics A Elsevier BV 384 1 2 190 210 doi 10 1016 0375 9474 82 90313 x ISSN 0375 9474 Local Equilibrium in Strong Interactions Physics LESIP I Eds D K Scott and R M Weiner World Scientific 1985 Hadronic Matter in Collision LESIP II Eds P Carruthers and D Strottman World Scientific 1986 Hadronic Matter in Collision 1988 LESIP III Eds P Carruthers and J Rafelski World Scientific 1988 Correlations and Multiparticle Production LESI IV Eds M Plumer S Raha and R M Weiner World Scientific 1991 Gyulassy Miklos Rischke Dirk H Zhang Bin 1997 Hot spots and turbulent initial conditions of quark gluon plasmas in nuclear collisions Nuclear Physics A 613 4 397 434 arXiv nucl th 9609030 doi 10 1016 s0375 9474 96 00416 2 ISSN 0375 9474 S2CID 1301930 Fowler G N Raha S Stelte N Weiner R M 1982 Solitons in nucleus nucleus collisions near the speed of sound Physics Letters B Elsevier BV 115 4 286 290 doi 10 1016 0370 2693 82 90371 9 ISSN 0370 2693 Raha S Wehrberger K Weiner R M 1985 Stability of density solitons formed in nuclear collisions Nuclear Physics A Elsevier BV 433 3 427 440 doi 10 1016 0375 9474 85 90274 x ISSN 0375 9474 Raha S Weiner R M 7 February 1983 Are Solitons Already Seen in Heavy Ion Reactions Physical Review Letters American Physical Society APS 50 6 407 408 doi 10 1103 physrevlett 50 407 ISSN 0031 9007 Galin J Oeschler H Song S Borderie B Rivet M F et al 28 June 1982 Evidence for a Limitation of the Linear Momentum Transfer in 12C Induced Reactions between 30 and 84 MeV u Physical Review Letters American Physical Society APS 48 26 1787 1790 doi 10 1103 physrevlett 48 1787 ISSN 0031 9007 Retrieved from https en wikipedia org w index php title Hot spot effect in subatomic physics amp oldid 1171067633, wikipedia, wiki, book, books, 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