We discuss equilibration times and isospin effect for various quantities in
low-energy heavy-ion reactions. These include equilibration of mass, isospin,
and total kinetic energy (TKE) in quasifission and deep-inelastic reactions.
The calculations are performed using the time-dependent Hartree-Fock theory.
The influence of shell effects on the equilibration times are also discussed in
the context of theoretical and experimental results.Comment: 7 pages, 5 figures, proceedings of IWM-EC201

Godbey, K.

Simenel, C.

Umar, A. S.

English

arXiv

We discuss equilibration times and isospin eﬀect for various quantities in low-energy heavy-ion reactions. These include equilibration of mass, isospin, and total kinetic energy (TKE) in quasiﬁssion and deep-inelastic reactions. The calculations are performed using the time-dependent Hartree-Fock theory. The inﬂuence of shell eﬀects on the equilibration times are also discussed in the context of theoretical and experimental results

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DOI 10.1393/ncc/i2018-18173-9Colloquia: IWM-EC 2018IL NUOVO CIMENTO 41 C (2018) 173Equilibration dynamics and isospin effects in nuclear reactionsA. S. Umar(1)(∗), C. Simenel(2) and K. Godbey(1)(1) Department of Physics and Astronomy, Vanderbilt University - Nashville, TN 37235, USA(2) Department of Nuclear Physics, Research School of Physics and Engineering, The AustralianNational University - Canberra ACT 2601, Australiareceived 3 December 2018Summary. — We discuss equilibration times and isospin effect for various quanti-ties in low-energy heavy-ion reactions. These include equilibration of mass, isospin,and total kinetic energy (TKE) in quasifission and deep-inelastic reactions. Thecalculations are performed using the time-dependent Hartree-Fock theory. The in-fluence of shell effects on the equilibration times are also discussed in the context oftheoretical and experimental results.1. – IntroductionLow-energy heavy-ion reactions provide us a rich laboratory to study the equilibrationdynamics of strongly interacting many-body systems. In addition, these reactions probean intriguing interplay between the microscopic single-particle dynamics and collectivemotion at time scales too short for complete equilibration. In order to elucidate trendsand systematics in these reactions both theoretical and experimental studies must be un-dertaken for an assortment of projectile and target combinations. Such studies is expectedto be undertaken at the current and future radioactive ion-beam (RIB) facilities [1].In this manuscript we will discuss the equilibration dynamics and time-scales forvarious quantities that are connected to the experimentally observable entities. Theseinclude the study of mass, isospin, and total kinetic energy (TKE) equilibration time-scales. In most of these studies one is essentially dealing with the transport phenomenaof isospin asymmetric systems. Recently, charge equilibration, driven by the nuclearsymmetry-energy, has been experimentally studied near the Fermi energy [2]. At theseenergies the sticking or contact times of the participating nuclei are sufficiently shortto induce a partial charge equilibration [3]. Charge equilibration has also been studiedwith deep inelastic collisions at lower energies, but with large isospin asymmetry in the(∗) E-mail: umar@compsci.cas.vanderbilt.eduCreative Commons Attribution 4.0 License (http://creativecommons.org/licenses/by/4.0) 12 A. S. UMAR et al.entrance channel [4-6]. In recent years a number of transport models have been employedto investigate the density dependence of the symmetry energy away from the saturationdensity [7-13]. While considerable success has been achieved in obtaining informationabout the EOS from these calculations more refinement of the models are needed to makea deeper connection to fundamental aspects of nuclear many-body physics.For the low-energy heavy-ion collisions the relative motion of the centers of the twonuclei is characterized by a short wavelength and thus allows for a classical treatment,whereas the wavelength for the particle motion is not small compared to nuclear sizesand should be treated quantum mechanically. The mean-field approach such as the time-dependent Hartree-Fock (TDHF) theory [14,15] and its extensions provide a microscopicbasis for describing the heavy-ion reaction mechanism at low bombarding energies. Inthis manuscript we provide studies of a variety of nuclear reactions to address some ofthe issues discussed above.2. – Equilibration dynamicsIn this section we discuss equilibration times for mass, isospin, and TKE in low-energyheavy-ion reactions. Figure 1 shows the general time-scales associated with variousreaction types as a function of increasing inelasticity. It is important to state thatsomewhere in the quasifission time-scale range (slow quasifission) [16, 17] we observea total TKE loss of the reaction products, TKE following the Viola systematics. Inthis sense quasifission reactions are most suitable for the study of time-scales for massequilibration, whereas time-scales for isospin and TKE equilibration can be investigatedin deep-inelastic reactions.2.1. Quasifission. – Quasifission, which occurs typically for systems with product ofthe charges Z1Z2 > 1600, is characterized by two final state fragments that emerge af-ter a long lived composite system (typically longer than 5 zs) and final fragment massesAf = ACN/2 ± 20 or more, and thus occupy the regime between quasielastic and fu-sion/fission. In addition, final TKE’s distinguish quasifission from highly damped deep-inelastic collisions, which have a smaller mass and charge difference between initial andfinal fragments. In TDHF the mass and charge differences between the initial nucleiand the final fragments measure the number of nucleons transferred. In recent years acompelling number of TDHF calculations of quasifission have shown that TDHF is anexcellent predictor for the experimentally measured quantities, such as the mass-angledistributions [18-28]. Due to the long contact times the quasifission process is suitable tostudy mass equilibration. In fig. 2 we plot the ratio of final and initial mass differencesdefined generally by(1a) ΔA(t) = ATLF (t) − APLF (t),Fig. 1. – Time-scales for various reaction types as a function of increasing inelasticity.EQUILIBRATION DYNAMICS AND ISOSPIN EFFECTS IN NUCLEAR REACTIONS 30 2 4 6 8 10 12 14 16 18 20 22 24τ - contact time (zs)0.20.40.60.81β = 0oβ = 90o48Ca + 249BkEc.m.= 234 MeV±20/±30ΔA±30/±40±40/±50±50/±60±60/±70ΔA(ΔA(τ)/)0Fig. 2. – The ratio of the final and initial fragment masses as a function of contact time for the48Ca +249 Bk system at Ec.m. = 234 MeV and for two orientations of the249Bk nucleus. Thedashed line shows one possible fit.as a function of contact time for the 48Ca +249 Bk system at Ec.m. = 234 MeV, andfor two extreme orientations of the deformed 249Bk nucleus indicated by the angle βwhich is the angle between the symmetry axis of the nucleus and the collision axis. Thepoints correspond to the impact parameters used, ranging from head-on collisions tomore peripheral collisions. The horizontal bars on the right side of the figure indicatethe number of particles transferred between the target and the projectile. We observethat more mass transfer happens at larger contact times as expected. The dashed lineshows a typical fit of a function in the form of c0 + c1 exp(−τ/τ0). Depending on thequality of the fit we obtain equilibration times in the range 5–10 zs. In fig. 3 we plot the0 2 4 6 8 10 12 14 16 18 20 22 24τ - contact time (zs)0.20.40.60.81ΔA(ΔA(τ)/)54Cr + 186WEc.m.= 218.6 MeV±20/±30ΔA±30/±40±40/±500Fig. 3. – The ratio of the final and initial fragment masses as a function of contact time for the54Cr+186 W system at Ec.m. = 218.6 MeV and for two orientations of the186W nucleus. Dashedlines show two possible fits.4 A. S. UMAR et al.same fragment mass difference ratio for the 54Cr +186 W system at Ec.m. = 218.6 MeVand for two orientations of the 186W nucleus. On the plot we show two possible fits to thepoints. The obtained equilibration times are in the range 7–12 zs. More calculations areunderway to study the orientation angle dependence of the equilibration times in moredetail. However, based on these and other results obtained from TDHF calculationswe can safely conclude that mass equilibration times are long, and a typical time ofaround 10 zs could be argued. Mass equilibration times can also be influenced by shelleffects. While the preference of Pb isotopes as quasifission product was theoreticallyobserved in TDHF calculations of 48Ca+238U system [20,29-32], it was recently confirmedexperimentally by explicit charge measurement of the quasifission products [27] in the48Ti+238U system. Naturally, influence of shell effects will depend on the target projectilecombinations but it is clear that shell effects do introduce a delay in the equilibrationprocess.2.2. Deep-inelastic reactions. – Study of strongly damped collisions of nuclei or so-called deep-inelastic collisions can play an important role in elucidating the dynamicsof charge and mass exchange, dissipation of energy and angular momentum, degree ofisospin equilibration, and the dependence of these quantities on the properties of thereactants such as the neutron-to-proton ratio (N/Z) [33-35]. Here, we focus on the studyof equilibration times for isospin and TKE. Recently, an experimental study [2] in theFermi energy range have obtained an isospin equilibration time of about 0.3 zs. We haveperformed studies of the 78Kr + 208Pb system at 8.5 MeV/nucleon [36]. In fig. 4 we plotthe (N − Z)/A value of the primary PLF (full circles) and TLF (open squares) formedin 78Kr +208 Pb at E = 8.5 MeV/nucleon as a function of the contact time between thecollision partners. The solid lines show fits to the TDHF results. For this system themean life time of the charge equilibration process, obtained from the final (N − Z)/Avalue of the fragments is ∼ 0.5 zs. This and other studies suggest that for low-energyheavy-ion collisions isospin equilibration occurs in the time-scale range 0.5–1.0 zs.Fig. 4. – The (N −Z)/A value of the primary PLF (full circles) and TLF (open squares) formedin 78Kr +208 Pb at E = 8.5 MeV/nucleon are plotted as a function of the contact time betweenthe collision partners. The solid lines show fits to the TDHF results.EQUILIBRATION DYNAMICS AND ISOSPIN EFFECTS IN NUCLEAR REACTIONS 5Fig. 5. – The exit channel TKE in 78Kr +208 Pb reaction at E = 8.5 MeV/nucleon are plottedas a function of the contact time between the collision partners.In order to study TKE equilibration times in fig. 5 we plot the exit channel TKE forthe 78Kr +208 Pb and 92Kr +208 Pb reactions at E = 8.5 MeV/nucleon as a function ofthe contact time. The calculations are done for two extreme orientations of the deformedKr nuclei. The points correspond to calculations for impact parameters in the range0–10 fm. We observe that for both systems the TKE rapidly falls initially as a functionof contact time but slowly stabilizes around and after the contact times 1.5–2 zs. Fromthis we may conclude that the equilibration time for TKE is in the range of 1.5–2 zs.Similar results have been recently found for the Ni + Ni system [31].3. – SummaryWe have presented a discussion of equilibration times for mass, isospin, and TKEusing the TDHF approach. We find that mass equilibration times are much longer thanthose for isospin and TKE. The fully microscopic TDHF theory has shown itself to be richin nuclear phenomena and continues to stimulate our understanding of nuclear dynamics.The time-dependent mean-field studies seem to show that the dynamic evolution buildsup correlations that are not present in the static theory. Although there is evidence thatone-body dissipation can properly account for the transport phenomena seen in thesereactions, further experiments are needed to test this conclusion. We plan to supplementthe studies mentioned in this manuscript with more TDHF calculations and provide amore detailed analysis of equilibration times in low-energy heavy-ion reactions.∗ ∗ ∗This work has been supported by the U.S. Department of Energy under grant No. DE-SC0013847 with Vanderbilt University and by the Australian Research Council GrantsNo. FT120100760 and DP160101254.6 A. S. UMAR et al.REFERENCES[1] Balantekin A. B., Carlson J., Dean D. J., Fuller G. M., Furnstahl R. J.,Hjorth-Jensen M., Janssens R. V. F., Li B.-A., Nazarewicz W., Nunes F. M.,Ormand W. E., Reddy S. and Sherrill B. M., Mod. Phys. Lett. A, 29 (2014) 1430010.[2] Jedele A., McIntosh A. B., Hagel K., Huang M., Heilborn L., Kohley Z., MayL. W., McCleskey E., Youngs M., Zarrella A. and Yennello S. J., Phys. Rev.Lett., 118 (2017) 062501.[3] Tsang M. B., Liu T. X., Shi L., Danielewicz P., Gelbke C. K., Liu X. D., LynchW. G., Tan W. P., Verde G., Wagner A., Xu H. S., Friedman W. A., Beaulieu L.,Davin B., de Souza R. T., Larochelle Y., Lefort T., Yanez R., Viola V. E.,Charity R. J. and Sobotka L. G., Phys. Rev. Lett., 92 (2004) 062701.[4] Planeta R., Zhou S. H., Kwiatkowski K., Wilson W. G., Viola V. E., Breuer H.,Benton D., Khazaie F., McDonald R. J., Mignerey A. C., Weston-Dawkes A.,de Souza R. T., Huizenga J. R. and Schröder W. U., Phys. Rev. C, 38 (1988) 195.[5] de Souza R. T., Schröder W. U., Huizenga J. R., Planeta R., Kwiatkowski K.,Viola V. E. and Breuer H., Phys. Rev. C, 37 (1988) 1783.[6] Planeta R., Kwiatkowski K., Zhou S. H., Viola V. E., Breuer H., McMahanM. A., Kehoe W. and Mignerey A. C., Phys. Rev. C, 41 (1990) 942.[7] Danielewicz P., Lacey R. and Lynch W. G., Science, 298 (2002) 1592.[8] Rizzo J., Chomaz P. and Colonna M., Nucl. Phys. A, 806 (2008) 40.[9] Colonna M., Di Toro M., Guarnera A., Maccarone S., Zielinska-Pfabé M. andWolter H. H., Nucl. Phys. A, 642 (1998) 449.[10] Di Toro M., Baran V., Colonna M. and Greco V., J. Phys. G, 37 (2010) 083101.[11] Rizzo C., Baran V., Colonna M., Corsi A. and Di Toro M., Phys. Rev. C, 83 (2011)014604.[12] Zhang Y., Coupland D. D. S., Danielewicz P., Li Z., Liu H., Lu F., Lynch W. G.and Tsang M. B., Phys. Rev. C, 85 (2012) 024602.[13] Colonna M., Phys. Rev. Lett., 110 (2013) 042701.[14] Simenel C., Eur. Phys. J. A, 48 (2012) 152.[15] Simenel C. and Umar A. S., Prog. Part. Nucl. Phys., 103 (2018) 19.[16] Khuyagbaatar J., Hinde D. J., Carter I. P., Dasgupta M., Düllmann C. E.,Evers M., Luong D. H., du Rietz R., Wakhle A., Williams E. and Yakushev A.,Phys. Rev. C, 91 (2015) 054608.[17] Khuyagbaatar J., David H. M., Hinde D. J., Carter I. P., Cook K. J.,Dasgupta M., Düllmann C. E., Jeung D. Y., Kindler B., Lommel B., Luong D. H.,Prasad E., Rafferty D. C., Sengupta C., Simenel C., Simpson E. C., Smith J. F.,Vo-Phuoc K., Walshe J., Wakhle A., Williams E. and Yakushev A., Phys. Rev. C,97 (2018) 064618.[18] Cédric Golabek and Cédric Simenel, Phys. Rev. Lett., 103 (2009) 042701.[19] David J. Kedziora and Cédric Simenel, Phys. Rev. C, 81 (2010) 044613.[20] Wakhle A., Simenel C., Hinde D. J., Dasgupta M., Evers M., Luong D. H.,du Rietz R. and Williams E., Phys. Rev. Lett., 113 (2014) 182502.[21] Oberacker V. E., Umar A. S. and Simenel C., Phys. Rev. C, 90 (2014) 054605.[22] Umar A. S., Oberacker V. E. and Simenel C., Phys. Rev. C, 92 (2015) 024621.[23] Hammerton K., Kohley Z., Hinde D. J., Dasgupta M., Wakhle A., Williams E.,Oberacker V. E., Umar A. S., Carter I. P., Cook K. J., Greene J., Jeung D. Y.,Luong D. H., McNeil S. D., Palshetkar C. S., Rafferty D. C., Simenel C. andStiefel K., Phys. Rev. C, 91 (2015) 041602(R).[24] Umar A. S., Oberacker V. E. and Simenel C., Phys. Rev. C, 94 (2016) 024605.[25] Sekizawa K. and Yabana K., Phys. Rev. C, 93 (2016) 054616.[26] Chong Yu and Lu Guo, Sci. China Phys., 60 (2017) 092011.EQUILIBRATION DYNAMICS AND ISOSPIN EFFECTS IN NUCLEAR REACTIONS 7[27] Morjean M., Hinde D. J., Simenel C., Jeung D. Y., Airiau M., Cook K. J.,Dasgupta M., Drouart A., Jacquet D., Kalkal S., Palshetkar C. S., Prasad E.,Rafferty D., Simpson E. C., Tassan-Got L., Vo-Phuoc K. and Williams E., Phys.Rev. Lett., 119 (2017) 222502.[28] Wakhle A., Hammerton K., Kohley Z., Morrissey D. J., Stiefel K., Yurkon J.,Walshe J., Cook K. J., Dasgupta M., Hinde D. J., Jeung D. J., Prasad E.,Rafferty D. C., Simenel C., Simpson E. C., Vo-Phuoc K., King J., Loveland W.and Yanez R., Phys. Rev. C, 97 (2018) 021602.[29] Hinde D. J., du Rietz R., Simenel C., Dasgupta M., Wakhle A., Evers M. andLuong D. H., AIP Conf. Proc., 1423 (2012) 65.[30] du Rietz R., Williams E., Hinde D. J., Dasgupta M., Evers M., Lin C. J., LuongD. H., Simenel C. and Wakhle A., Phys. Rev. C, 88 (2013) 054618.[31] Williams E., Sekizawa K., Hinde D. J., Simenel C., Dasgupta M., Carter I. P.,Cook K. J., Jeung D. Y., McNeil S. D., Palshetkar C. S., Rafferty D. C.,Ramachandran K. and Wakhle A., Phys. Rev. Lett., 120 (2018) 022501.[32] Mohanto G., Hinde D. J., Banerjee K., Dasgupta M., Jeung D. Y., Simenel C.,Simpson E. C., Wakhle A., Williams E., Carter I. P., Cook K. J., Luong D. H.,Palshetkar C. S. and Rafferty D. C., Phys. Rev. C, 97 (2018) 054603.[33] Schröder W. U. and Huizenga J. R., Annu. Rev. Nucl. Part. Sci., 27 (1977) 465.[34] Moretto L. G. and Schmitt R. P., Rep. Prog. Phys., 44 (1981) 533.[35] Tõke J. and Schröder W. U., Annu. Rev. Nucl. Part. Sci., 42 (1992) 401.[36] Umar A. S., Simenel C. and Ye W., Phys. Rev. C, 96 (2017) 024625.

Equilibration dynamics and isospin eﬀects in nuclear reactions

We discuss equilibration times and isospin effect for various quantities in low-energy heavy-ion reactions. These include equilibration of mass, isospin, and total kinetic energy (TKE) in quasifission and deep-inelastic reactions. The calculations are performed using the time-dependent Hartree-Fock theory. The influence of shell effects on the equilibration times are also discussed in the context of theoretical and experimental results.This work has been supported by the U.S. Department of Energy under grant No. DESC0013847 with Vanderbilt University and by the Australian Research Council Grants No. FT120100760 and DP160101254

Equilibration dynamics and isospin effects in nuclear reactions

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