The relative isobaric yields of fragments produced in a series of heavy-ion-induced multifragmentation reactions have been analyzed in the framework of a modified Fisher model, primarily to determine the ratio of the symmetry energy coefficient to the temperature, a(sym)/T, as a function of fragment mass A. The extracted values increase from 5 to similar to 16 as A increases from 9 to 37. These values have been compared to the results of calculations using the antisymmetrized molecular dynamics (AMD) model together with the statistical decay code GEMINI. The calculated ratios are in good agreement with those extracted from the experiment. In contrast, the values extracted from the ratios of the primary isobars from the AMD model calculation are similar to 4 to 5 and show little variation with A. This observation indicates that the value of the symmetry energy coefficient derived from final fragment observables may be significantly different than the actual value at the time of fragment formation. The experimentally observed pairing effect is also studied within the same simulations. The Coulomb coefficient is also discussed.
Minich R.W., Agarwal S., Bujak A., Chuang J., Finn J.E., Gutay L.J., Hirsch A.S., Porile N.T., Scharenberg R.P., Stringfellow B.C., Turkot F., Critical phenomena in hadronic matter and experimental isotopic yields in high energy proton-nucleus collisions, 10.1016/0370-2693(82)90224-6
Hirsch A.S., Bujak A., Finn J.E., Gutay L.J., Minich R.W., Porile N.T., Scharenberg R.P., Stringfellow B.C., Turkot F., The description of fragmentation as a critical phenomenon in high energy P-nucleus collisions, 10.1016/0375-9474(84)90553-0
Kowalski S., Natowitz J. B., Shlomo S., Wada R., Hagel K., Wang J., Materna T., Chen Z., Ma Y. G., Qin L., Botvina A. S., Fabris D., Lunardon M., Moretto S., Nebbia G., Pesente S., Rizzi V., Viesti G., Cinausero M., Prete G., Keutgen T., Masri Y. El, Majka Z., Ono A., Experimental determination of the symmetry energy of a low density nuclear gas, 10.1103/physrevc.75.014601
Li Bao-An, Isospin dependence of theπ−/π+ratio and density dependence of the nuclear symmetry energy, 10.1103/physrevc.67.017601
Bonasera A., Chen Z., Wada R., Hagel K., Natowitz J., Sahu P., Qin L., Kowalski S., Keutgen Th., Materna T., Nakagawa T., Quantum Nature of a Nuclear Phase Transition, 10.1103/physrevlett.101.122702
Xu H. S., Tsang M. B., Liu T. X., Liu X. D., Lynch W. G., Tan W. P., Vander Molen A., Verde G., Wagner A., Xi H. F., Gelbke C. K., Beaulieu L., Davin B., Larochelle Y., Lefort T., de Souza R. T., Yanez R., Viola V. E., Charity R. J., Sobotka L. G., Isospin Fractionation in Nuclear Multifragmentation, 10.1103/physrevlett.85.716
Tsang M. B., Gelbke C. K., Liu X. D., Lynch W. G., Tan W. P., Verde G., Xu H. S., Friedman W. A., Donangelo R., Souza S. R., Das C. B., Das Gupta S., Zhabinsky D., Isoscaling in statistical models, 10.1103/physrevc.64.054615
Botvina A. S., Lozhkin O. V., Trautmann W., Isoscaling in light-ion induced reactions and its statistical interpretation, 10.1103/physrevc.65.044610
Ono Akira, Danielewicz P., Friedman W. A., Lynch W. G., Tsang M. B., Isospin fractionation and isoscaling in dynamical simulations of nuclear collisions, 10.1103/physrevc.68.051601
Marie N., Chbihi A., Natowitz J. B., Le Fèvre A., Salou S., Wieleczko J. P., Gingras L., Assenard M., Auger G., Bacri Ch. O., Bocage F., Borderie B., Bougault R., Brou R., Buchet P., Charvet J. L., Cibor J., Colin J., Cussol D., Dayras R., Demeyer A., Doré D., Durand D., Eudes P., Frankland J. D., Galichet E., Genouin-Duhamel E., Gerlic E., Germain M., Gourio D., Guinet D., Hagel K., Lautesse P., Laville J. L., Lecolley J. F., Lefort T., Legrain R., Le Neindre N., Lopez O., Louvel M., Majka Z., Maskay A. M., Nalpas L., Nguyen A. D., Parlog M., Péter J., Plagnol E., Rahmani A., Reposeur T., Rivet M. F., Rosato E., Saint-Laurent F., Steckmeyer J. C., Stern M., Tabacaru G., Tamain B., Tirel O., Vient E., Volant C., Wada R., Experimental determination of fragment excitation energies in multifragmentation events, 10.1103/physrevc.58.256
Hudan S., Chbihi A., Frankland J. D., Mignon A., Wieleczko J. P., Auger G., Bellaize N., Borderie B., Botvina A., Bougault R., Bouriquet B., Buta A. M., Colin J., Cussol D., Dayras R., Durand D., Galichet E., Guinet D., Guiot B., Lanzalone G., Lautesse, Lavaud F., Lecolley, Legrain R., Le Neindre, Lopez O., Manduci L., Marie J., Nalpas L., Normand J., Pârlog M., Pawłowski P., Pichon M., Plagnol E., Rivet M. F., Rosato E., Roy R., Steckmeyer J.C., Tăbăcaru G., Tamain B., van Lauwe A., Vient E., Vigilante M., Volant C., Characteristics of the fragments produced in central collisions of129Xe+natSnfrom 32Ato 50AMeV, 10.1103/physrevc.67.064613
Moretto L. G., Dorso C. O., Elliott J. B., Phair L., Symmetry entropy and isoscaling, 10.1103/physrevc.77.037603
Albergo S., Costa S., Costanzo E., Rubbino A., Temperature and free-nucleon densities of nuclear matter exploding into light clusters in heavy-ion collisions, 10.1007/bf02773614
Ono Akira, Horiuchi Hisashi, Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of the Vlasov equation, 10.1103/physrevc.53.2958
Ono Akira, Antisymmetrized molecular dynamics with quantum branching processes for collisions of heavy nuclei, 10.1103/physrevc.59.853
Charity R.J., McMahan M.A., Wozniak G.J., McDonald R.J., Moretto L.G., Sarantites D.G., Sobotka L.G., Guarino G., Pantaleo A., Fiore L., Gobbi A., Hildenbrand K.D., Systematics of complex fragment emission in niobium-induced reactions, 10.1016/0375-9474(88)90542-8
Raduta Ad. R., Gulminelli F., Isospin dependent thermodynamics of fragmentation, 10.1103/physrevc.75.044605
Hubert F., Bimbot R., Gauvin H., Range and stopping-power tables for 2.5–500 MeV/nucleon heavy ions in solids, 10.1016/0092-640x(90)90001-z
Bethe H. A., Bacher R. F., Nuclear Physics A. Stationary States of Nuclei, 10.1103/revmodphys.8.82
Green Alex E. S., Edwards David F., Discontinuities in the Nuclear Mass Surface, 10.1103/physrev.91.46
Preston M. A., Whaling Ward, Physics of the Nucleus, 10.1119/1.1969247
Wang J., Wada R., Keutgen T., Hagel K., Ma Y. G., Murray M., Qin L., Botvina A., Kowalski S., Materna T., Natowitz J. B., Alfarro R., Cibor J., Cinausero M., Masri Y. El, Fabris D., Fioretto E., Keksis A., Lunardon M., Makeev A., Marie N., Martin E., Majka Z., Martinez-Davalos A., Menchaca-Rocha A., Nebbia G., Prete G., Rizzi V., Ruangma A., Shetty D. V., Souliotis G., Staszel P., Veselsky M., Viesti G., Winchester E. M., Yennello S. J., Zipper W., Ono A., Tracing the evolution of temperature in near Fermi energy heavy ion collisions, 10.1103/physrevc.72.024603
Ono Akira, Hudan S., Chbihi A., Frankland J. D., Compatibility of localized wave packets and unrestricted single particle dynamics for cluster formation in nuclear collisions, 10.1103/physrevc.66.014603
Wada R, Hagel K, Cibor J, Li J, Marie N, Shen W.Q, Zhao Y, Natowitz J.B, Ono A, Entrance channel dynamics in 40Ca+40Ca at 35A MeV, 10.1016/s0370-2693(98)00033-1
Wada R., Hagel K., Cibor J., Gonin M., Keutgen Th., Murray M., Natowitz J. B., Ono A., Steckmeyer J. C., Kerambrum A., Angélique J. C., Auger A., Bizard G., Brou R., Cabot C., Crema E., Cussol D., Durand D., El Masri Y., Eudes P., He Z. Y., Jeong S. C., Lebrun C., Patry J. P., Péghaire A., Peter J., Régimbart R., Rosato E., Saint-Laurent F., Tamain B., Vient E., Reaction mechanisms and multifragmentation processes in64Zn+58Niat35A–79A MeV, 10.1103/physrevc.62.034601
Wada R., Keutgen T., Hagel K., Ma Y. G., Wang J., Murray M., Qin L., Smith P., Natowitz J. B., Alfarro R., Cibor J., Cinausero M., Masri Y. El, Fabris D., Fioretto E., Keksis A., Kowalski S., Lunardon M., Makeev A., Marie N., Martin E., Majka Z., Martinez-Davalos A., Menchaca-Rocha A., Nebbia G., Prete G., Rizzi V., Ruangma A., Shetty D. V., Souliotis G., Staszel P., Veselsky M., Viesti G., Winchester E. M., Yennello S. J., Zipper W., Ono A., Reaction dynamics and multifragmentation in Fermi energy heavy ion reactions, 10.1103/physrevc.69.044610
Hudan S., Souza R. T. de, Ono A., Short timescale behavior of colliding heavy nuclei at intermediate energies, 10.1103/physrevc.73.054602
Ono Akira, Horiuchi Hisashi, Maruyama Toshiki, Ohnishi Akira,
Antisymmetrized Version of Molecular Dynamics with Two-Nucleon Collisions and Its Application to Heavy Ion Reactions
, 10.1143/ptp.87.1185
Ricciardi M.V., Ignatyuk A.V., Kelić A., Napolitani P., Rejmund F., Schmidt K.-H., Yordanov O., Complex nuclear-structure phenomena revealed from the nuclide production in fragmentation reactions, 10.1016/j.nuclphysa.2004.01.069
Ricciardi M.V., Ignatyuk A.V., Kelić A., Napolitani P., Rejmund F., Schmidt K.-H., Yordanov O., Complex nuclear-structure phenomena in the cooling down of highly excited nuclear systems, 10.1016/j.nuclphysa.2004.12.019
Liu T. X., van Goethem M. J., Liu X. D., Lynch W. G., Shomin R., Tan W. P., Tsang M. B., Verde G., Wagner A., Xi H. F., Xu H. S., Colonna M., Di Toro M., Zielinska-Pfabe M., Wolter H. H., Beaulieu L., Davin B., Larochelle Y., Lefort T., de Souza R. T., Yanez R., Viola V. E., Charity R. J., Sobotka L. G., Isotope yields from centralSn112,124+Sn112,124collisions: Dynamical emission?, 10.1103/physrevc.69.014603
Bibliographic reference
Huang, M. ; Chen, Z. ; Kowalski, S. ; Ma, Y. G. ; Wada, R. ; et. al. Isobaric yield ratios and the symmetry energy in heavy-ion reactions near the Fermi energy. In: Physical Review C (Nuclear Physics), Vol. 81, no. 4 (2010)