Reaction dynamics and multifragmentation in Fermi energy heavy ion reactions

R. Wada et al. (NIMROD Collaboration)

Phys. Rev. C 69, 044610 – Published 23 April 2004

Abstract

The reaction systems, ${}^{64}{Zn} + {}^{58}{Ni}$ , ${}^{64}{Zn} + {}^{92}{Mo}$ , ${}^{64}{Zn} + {}^{197}{Au}$ , at 26, 35, and $47 A MeV$ , have been studied both in experiments with a $4 π$ detector array, NIMROD, and with antisymmetrized molecular dynamics model calculations employing effective interactions corresponding to soft and stiff equation of state (EOS). Direct experimental observables, such as multiplicity distributions, charge distributions, energy spectra and velocity spectra, have been compared in detail with those of the calculations and a reasonable agreement is obtained for both EOS’s. No conclusive preference for either EOS has been observed. Neither of the above direct observables nor the strength of the elliptic flow are also sensitive to changes in the in-medium nucleon-nucleon cross sections. A detailed analysis of the central collision events revealed that multifragmentation with cold fragment emission is a common feature predicted for all reactions studied here. A possible multifragmentation scenario is presented; after the preequilibrium emission ceases in the composite system, cold light fragments are formed in a hotter gas of nucleons and stay cold until the composite system underdoes multifragmentation. For reaction with ${}^{197}{Au}$ at $47 A MeV$ a significant radial expansion takes place. For reactions with ${}^{58}{Ni}$ and ${}^{92}{Mo}$ at $47 A MeV$ semitransparency becomes prominent. The differing reaction dynamics drastically change the kinematic characteristics of emitted fragments. This scenario gives consistent explanations for many existing experimental results in the Fermi energy domain.

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Received 29 August 2003

DOI:https://doi.org/10.1103/PhysRevC.69.044610

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Vol. 69, Iss. 4 — April 2004

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Figure 1
(Color online) (a) Calculated in-medium NN cross sections for normal density nuclear matter. The cross sections calculated by the empirical formula Eq. (13) are depicted by a dashed line and those of the Li-Machleidt formulas Eqs. (14) and (15) are given by dots $(n − p)$ and squares $(n − n, p − p)$ . (b) Number of collisions as a function of reaction time for central collisions of ${}^{64}{Zn} + {}^{58}{Ni}$ at $47 A MeV$ . Events with $b ⩽ 3 fm$ are analyzed. Solid symbols indicate the number of attempted collisions and open symbols indicate the number of Pauli-allowed collisions. Circles show the results of the Li-Machleidt formulas and squares show those of the empirical formula.
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Figure 2
(Color online) Calculated parallel velocity distributions of nucleons at $280 fm ∕ c$ are plotted in the center-of-mass system for ${}^{58}{Ni}$ , ${}^{92}{Mo}$ , and ${}^{197}{Au}$ at $47 A MeV$ from top to bottom, respectively. The results for soft $EOS + {NN}_{emp}$ , $stiff + {NN}_{emp}$ , and $stiff + {NN}_{L M}$ are plotted from left to right, respectively. Thick solid and dashed lines indicate the contributions of nucleons from the target and the projectile, respectively. Thin lines show the sum of these two contributions.
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Figure 3
(Color online) Difference of the peak values of the parallel velocity distribution of nucleons from the projectile and from the target. Peak values are obtained by a Gaussian fit around each peak. Dashed lines are the guide to eye.
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Figure 4
Calculated neutron ball efficiency without the charged particle array (a) and with the charged particle array (b). Intrinsic neutron efficiency at a given energy is shown by dots. The contribution of the first detected neutrons is shown by triangles, and that of the second and higher order detected neutrons is shown by squares. The solid line in the left figure shows results from the DENIS code. The open circles in the right figure display the detection efficiency of generated neutrons when a proton of an initial energy, given on $x$ axis, is emitted at the target.
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Figure 5
(Color online) (a) Typical experimental two dimensional plot of fast vs slow components of charge integrated light output from a CsI detector. Insert shows the expanded spectrum for Hydrogen isotopes. Corresponding elements are indicated in the figure. HF stands for heavy fragments with $Z ⩾ 5$ . (b) Distributions of artificially generated double-hit events for $p − p$ , $p − α$ , and $α − α$ . Each particle combination is indicated in the figure. Solid lines correspond to the locus of the ridges of $p, d, t$ , ${}^{3}{He}$ , $α$ , ${}^{6}{Li}$ , and ${}^{7}{Li}$ from (a).
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Figure 6
(Color online) (Left) Number of particles generated by the calculation for ${}^{92}{Mo}$ at $47 A MeV$ . Total number of charged particles is given by a histogram as a function of particle ID. The particle ID is given by $ID = 0$ , 1, 2, 3, 4 for $p, d, t,$ ${}^{3}{He}$ , $α$ , and $ID = Z + 2$ for $Z ⩾ 3$ , respectively. The number of single-hit particles is given by dots and that of double-hit particles is shown by squares. The number of the detected single-hit particle is shown by crosses. (Right) Number of double $α$ hit events is shown as a function of multiplicity for the experiment (dots) and the simulation (histogram). In both cases one million events were analyzed. The calculation is done for the stiff $EOS + {NN}_{L M}$ case. The calculated events have been treated by the experimental filter.
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Figure 7
(Color online) Calculated effects of double hits on the energy spectra of deuterons (left) and $α$ (right) particles at three different detection angles, as indicated in each figure. Reaction for ${}^{92}{Mo}$ at $47 A MeV$ is used. Thick line histograms show the single hit spectra and thin line histograms indicate the spectra of $p − p$ in the deuteron spectra and $p − α$ in the $α$ spectra. The energy of the double hit events is given by the sum of the energy of the two particles.
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Figure 8
(Color online) 2D plots of the experimental (right) and the calculated (left) $M_{L P} ∕ A_{system}$ vs $E_{t}^{L P C} ∕ E_{beam}$ for ${}^{92}{Mo}$ at $47 A MeV$ . $M_{L P}$ is the observed multiplicity of light particles, including neutrons, and $A_{system}$ is the total nucleon number of the reaction system. $E_{t}^{L C P}$ is the sum of transverse energy of the light charged particles with $Z ⩽ 2$ and $E_{beam}$ is the projectile incident energy. Generated events by AMD-V has been filtered through the experimental acceptance. Contours are in logarithmic scale and the scale is set arbitrarily.
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Figure 9
(Color online) Impact parameter distributions for different classes of events for (a) ${}^{58}{Ni}$ (b) ${}^{92}{Mo}$ and (c) ${}^{197}{Au}$ at $47 A MeV$ . Triangles (down), triangles (up), squares and dots indicate the results for violent, semi-violent, semi-peripheral, and peripheral classes, respectively. The area of each distribution is normalized to 1.
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Figure 10
(Color online) Neutron multiplicity distributions for events in the violent class of events of the reactions at $47 A MeV$ for (a) ${}^{58}{Ni}$ , (b) ${}^{92}{Mo}$ , and (c) ${}^{197}{Au}$ . Experimental results are shown by circles and calculated results are shown by different lines. Thin solid, dashed, and thick solid lines indicate the results of $Soft + {NN}_{emp}$ , $Stiff + {NN}_{emp}$ , and $Stiff + {NN}_{L M}$ , respectively. No efficiency and background corrections were applied for the experimental distributions, whereas the calculated results have been treated with the experimental filter. All distributions are normalized to one million events in total.
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Figure 11
(Color online) Multiplicity distributions of light charged particles $(Z ⩽ 2)$ (left) and heavier charged particles $(Z ⩾ 3)$ (right) for events in the violent, semi-violent, and semi-peripheral classes, from top to bottom, respectively, for ${}^{92}{Mo}$ at $47 A MeV$ . Selected classes are indicated in each figure. Experimental results are shown by circles and calculated results are shown by different lines. Thin solid, dashed, and thick solid lines indicate the results of $Soft + {NN}_{emp}$ , $Stiff + {NN}_{emp}$ , and $Stiff + {NN}_{L M}$ , respectively. All calculated results have been treated with the experimental filter. All distributions are normalized to $1 \times 10^{6}$ events in total.
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Figure 12
(Color online) Multiplicity distributions of selected particles for the violent collisions for ${}^{92}{Mo}$ at $47 A MeV$ . Particles are indicated in each figure. See also the caption of Fig. 11.
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Figure 13
(Color online) Proton multiplicity distributions for the violent collisions of all reactions. Figures in the same column show the results from the same reaction system and figures in the same row show those at the same incident energy. The reaction system is indicated at the top of the figure and the incident energy is indicated in each row. Experimentally observed multiplicities are shown by the circles and calculations with soft $EOS + {NN}_{emp}$ and stiff $EOS + {NN}_{L M}$ are shown by thin and thick solid lines, respectively.
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Figure 14
(Color online) Similar plot to Fig. 13 but for $α$ particles.
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Figure 15
(Color online) Summary of mean multiplicities of selected particles for the violent class of events for all reactions. Experimental values are efficiency corrected but calculated ones are nonfiltered values. Reaction systems and incident energies are indicated on the $x$ axis and particle is indicated in each panel. Experimental results are shown by solid dots and calculated results with soft $EOS + {NN}_{emp}$ and stiff $EOS + {NN}_{L M}$ are shown by open squares and triangles, respectively.
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Figure 16
(Color online) Angle integrated charge distributions of events in (a) violent, (b) semi-violent, and (c) semi-peripheral classes are shown for ${}^{92}{Mo}$ at $47 A MeV$ . Experimental results are shown by circles. Dot-dashed, dashed, and solid lines correspond to soft ${EOS + NN}_{emp}$ , stiff $EOS + {NN}_{L M}$ and stiff $EOS + {NN}_{emp}$ , respectively.
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Figure 17
(Color online) Angle integrated charge distributions of events in violent collisions for (a) ${}^{58}{Ni}$ and (b) ${}^{197}{Au}$ at $47 A MeV$ . Dot-dashed and solid lines correspond to soft ${EOS + NN}_{emp}$ and stiff $EOS + {NN}_{L M}$ , respectively.
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Figure 18
(Color online) Efficiency corrected experimental charge distributions for fragments with $3 ⩽ Z ⩽ 20$ . Each group shows results with three different targets at a given incident energy. The incident energy is shown on the right. The differential multiplicity is given in an absolute scale at $47 A MeV$ and premultiplied by factors of 100 and 10, respectively, for results at 26 and $35 A MeV$ .
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Figure 19
(Color online) Proton energy spectra for the violent collisions for ${}^{92}{Mo}$ at three incident energies. The incident energy is indicated at the top of each figure. The spectra in each column correspond to the energy spectra at different angles, indicated in the left column. Experimental results are shown by dots. Thick and thin solid lines correspond to calculated results for $Soft + {NN}_{emp}$ and $Stiff + {NN}_{L M}$ , respectively. For all cases the differential multiplicity is given in absolute units. In order to avoid the overlap of thedata spectra are multiplied by factors of $10^{n}$ $(n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)$ from bottom to top. No experimental filter is used for the calculated events.
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Figure 20
(Color online) Similar plots to Fig. 19, but for $α$ particles.
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Figure 21
(Color online) Similar plots to Fig. 19, but for deuterons.
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Figure 22
(Color online) Similar plots to Fig. 19, but for tritons.
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Figure 23
(Color online) Inclusive energy spectra of IMF with $Z = 8$ at different angles for violent collisions with ${}^{92}{Mo}$ (a) at $35 A MeV$ and (b) at $47 A MeV$ . Experimental spectra are shown by symbols and calculated results with soft $EOS + {NN}_{emp}$ and stiff $EOS + {NN}_{L M}$ are shown by thick and thin solid lines, respectively. The experimental spectra are plotted in an absolute scale, whereas each calculated result is normalized to the experimental spectra at $θ = 4.3 °$ .
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Figure 24
(Color online) Calculated parallel velocity distribution of protons in the center-of-mass system for different reactions at $47 A MeV$ . Each row corresponds to the same reaction which is specified by target as indicated in each panel on the left. The calculated results with soft $EOS + {NN}_{emp}$ are plotted on the left and those with stiff $EOS + {NN}_{L M}$ are on the right. The distributions of all free and bound protons before the afterburner at $280 fm ∕ c$ are displayed by thin lines. The distributions of free protons after the afterburner are shown by thick lines. The normalization for the latter is arbitrary.
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Figure 25
(Color online) Parallel velocity distributions of protons (left) and $α$ particles (right) in the center-of-mass system for different reactions at $47 A MeV$ . Reaction is specified by target as indicated in each panel on the left. Experimental results are shown by dots and the calculated results with the soft $EOS + {NN}_{emp}$ are plotted by histograms of thick lines and those for the stiff $EOS + {NN}_{L M}$ by histograms of thin lines. The calculated results are normalized to the experimental distributions to obtain the same number of protons at $V_{‖} ⩾ 0$ in each case.
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Figure 26
Averaged differential elliptic flow for protons for ${}^{58}{Ni}$ at $47 A MeV$ as a function of the transverse momentum $p_{t}$ . Events in the violent and semi-violent classes are used. Experimental results are shown by dots and calculated results for stiff $EOS + {NN}_{L M}$ , stiff $EOS + {NN}_{emp}$ , and soft $EOS + {NN}_{emp}$ , are shown by open circles, squares, and triangles, respectively. $⟨ v_{2} ⟩$ values are calculated in $50 MeV ∕ c$ steps in $p_{t}$ . Calculated results are plotted around the center value of each $p_{t}$ with a small shift to avoid overlap of results.
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Figure 27
Time evolution of nuclear density distributions, projected on the reaction plane ( $x − z$ plane, $z$ being the beam direction), for a calculated event with $b \sim 2 fm$ at different reaction times for ${}^{197}{Au}$ . Incident energy is indicated at the top of each column. Reaction time is indicated in the unit of fm∕c in each panel. The time zero is set at the time when the projectile and the target touch each other. The $z$ axis is taken as the beam direction and the contour scale is in linear. The smallest circle indicates a nucleon.
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Figure 28
(Color online) Time evolution of mass number, density, and excitation energy of the largest fragment (left) and the second largest fragment with $Z > 2$ (right) from top to bottom, respectively, for ${}^{197}{Au}$ at $35 A MeV$ . See details in the text. Contours are in logarithmic scale.
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Figure 29
(Color online) Nucleon emission rate for ${}^{197}{Au}$ is plotted as a function of time. (a) $47 A MeV$ with ${NN}_{L M}$ (b) $47 A MeV$ with ${NN}_{emp}$ (c) $35 A MeV$ with ${NN}_{L M}$ (d) $26 A MeV$ with ${NN}_{L M}$ . Nucleons emitted as light particles $(Z ⩽ 2)$ are selected. Open circles indicate nucleons from the target and solid dots indicate those from the projectile.
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Figure 30
(Color online) Similar plots to Fig. 29, but for ${}^{92}{Mo}$ (left) and ${}^{58}{Ni}$ (right) at $47 A MeV$ .
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Figure 31
(Color online) (Left) Average kinetic energy of neutrons in the center-of-mass system as a function of time for ${}^{197}{Au}$ at three incident energies. The incident energies are indicated in each panel. Total and transverse energy are shown by open squares and circles, respectively. Energies and times are those when neutrons are identified for the first time. (Right) Ratios of the total to transverse energies of the left figure.
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Figure 32
(Color online) Average kinetic energy of neutrons as a function of time at $47 A MeV$ . Different symbols correspond to different targets, as indicated in the figure. Upper set of results shows the total kinetic energy $E_{t o t}$ and lower set for the transverse energy $(E_{⊥})$ .
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Figure 33
(Color online) (a) Excitation energy and (b) emission time of fragments with $A ⩽ 100$ are plotted as a function of fragment mass number for ${}^{197}{Au}$ at $47 A MeV$ . The largest fragment is excluded in these plots.
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Figure 34
Average excitation energy of fragments with $Z ⩾ 3$ is plotted as a function of the fragment mass number for ${}^{197}{Au}$ at three incident energies. The incident energy is indicated in each panel.
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Figure 35
Similar plots to Fig. 34, but for ${}^{58}{Ni}$ on left and ${}^{92}{Mo}$ on right sides, respectively.
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Figure 36
Isotope distributions of fragments for ${}^{58}{Ni}$ (upper) and ${}^{197}{Au}$ (lower). Lines indicate $N = 2 Z$ .
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Figure 37
(Color online) Average excitation energy distributions of isotopes for ${}^{197}{Au}$ .
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Figure 38
Average internal energy distribution of fragments with $A ⩾ 5$ for ${}^{197}{Au}$ at $47 A MeV$ . The energy is evaluated when the fragments are identified at the first time.
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Figure 39
(Left) Average kinetic energy of fragments in the center of mass system as a function of fragment mass number for ${}^{197}{Au}$ . Incident energy is indicated in each panel. Energy is evaluated at the time when the fragment is identified at the first time. (Right) Subtracted kinetic energy of fragments for $E_{k}$ at $47 A MeV — E_{k}$ at $26 A MeV$ in the upper panel and for $E_{k}$ at $35 A MeV — E_{k}$ at $26 A MeV$ in the lower one.
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Figure 40
Average total and transverse fragment energies as a function of fragment mass number in the center-of-mass system for reactions at $47 A MeV$ with the different targets. The target is indicated in each figure. Dots indicate the total energy and open circles indicate the transverse energy.
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Figure 41
(Color online) Ratio of the excitation energy of the second largest fragment $(F_{2})$ and that of the largest fragment $(F_{\max})$ as a function of time for ${}^{197}{Au}$ . Open circles represent results when all fragments with $Z ⩾ 3$ are taken into account as $F_{2}$ and solid dots indicate results when only fragments with $A ⩾ 30$ are taken into account as $F_{2}$ . Incident energy is indicated in each figure.
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Figure 42
Time evolution of the average root-mean-square radius of 14 nucleons, which end up ${}^{14}C$ at $t = 480 fm ∕ c$ for ${}^{197}{Au}$ . See details in the text.
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