peripheral collisions as a means of attaining high excitation –velocity dissipation is key...
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• Peripheral collisions as a means of attaining high excitation– Velocity dissipation is key quantity R. Yanez et al, PRC (in press)
• Proximity emission as a clock of the statistical emission time scale
Outline
Thanks to
Indiana University: S. Hudan, R. Yanez, A.S. Botvina, B. Davin, R. Alfaro, H. Xu, Y. Larochelle, L. Beaulieu, T. Lefort, V.E. Viola
Washington University, St. Louis: R.J. Charity, L.G. Sobotka
Michigan State University: T.X. Liu, X.D. Liu, W.G. Lynch, R. Shomin, W.P. Tan, M.B. Tsang, A. Vander Molen, A. Wagner, H.F. Xi, C.K. Gelbke
Decay of highly excited projectile-like fragments produced in dissipative peripheral collisions at intermediate energies.
Thermodynamic properties of nuclear matter (esp. N/Z exotic)
Decay properties of hot nuclei (finite, reaction dynamics, etc.)
R.T. de Souza, Indiana UniversityHIC03, Montreal
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Experimental details
Ring Counter :Si (300 m) – CsI(Tl) (2cm)2.1 lab 4.2δZ/Z ~ 0.25 Mass deduced†
Beam
LASSA : 0.8Mass resolution up to Z=97 lab 58
114Cd + 92Mo at 50 A.MeV
Detection of charged particles in 4
† EPAX K. Sümmerer et al., PRC 42, 2546 (1990) Projectile
48
B. Davin et al., NIM A473, 302 (2001)
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114Cd
92Mo
Overlap zone is highly excited
1. PLF* and TLF* are relatively unexcited.
2. <VPLF*> nearly unchanged from beam velocity.
3. Impact parameter is the key quantity in the reaction.
PLF*
TLF*
Select PLF at very forward angles 2.1 lab 4.2
Participant-Spectator model
L.F. Oliviera et al., PRC 19, 826 (1979)
Zprojectile
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PLF* decay following a peripheral collision
PLF* = good case: (as compared to central collisions)System size (Z,A) is well -defined Normal densityLarge cross-section (high probability process)
0
Circular ridge PLF* emission“Isotropic” component
Projectile velocity
Other emission(mid-rapidity, ...)
Examine emission forward of PLF*
Select 15≤ZPLF≤46 with 2.1 lab 4.2
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With decreasing VPLF*, the kinetic energy spectra have less steep exponentials higher temperatures
Vbeam -VPLF*
D
D
D
DTT/C'
BTD1B'
TBEE/TeBE
TBEB'E/TeB'EC'
B'E0
N(E)
B Barrier parameterT Temperature parameterD Barrier diffuseness parameter
Maxwell-Boltzmann
J.P.Lestone, PRL 67, 1078 (1991).
“pre-equilibrium” component 2%
Forward of the PLF*
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Evaporation and velocity damping
vbeam
IMFs also well characterized by MBD, exhibit larger slope parameters emission earlier in de-excitation cascade
Multiplicities increase with velocity dampingTslope increases with velocity damping “Linear” trend for both observables
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(Linear) dependence of E* with velocity damping High E* is reached (6 MeV/n)
Velocity damping and excitation energyReconstruct excitation of PLF* by doing calorimetry: particle multiplicity, kinetic energies, and binding energies. D. Cussol et al., Nucl. Phys. A 541, 298 (1993)
Good agreement with GEMINI*
Some sensitivity of M to J, level density
*“Statistical model code”R.J. Charity et al., PRC63, 024611 (2001)
Multiplicities, average emitted charge predicted by GEMINI support deduced excitation scale.
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Select PLF* size by selecting residue Z.
Select excitation by selecting VPLF*
Vary N/Z by changing (N/Z)proj.,tgt.
When selected on VPLF*, total excitation is independent of ZPLF.
If ZPLF is related to the overlap of the projectile and target (impact parameter), this result says that <E*> has the same dependence on VPLF*, independent of overlap.
10
20
30
40
50
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Statistical decay in an inhomogeneous external field
vs.
PLF*
TLF*
V
PLF*
TLF*
V
• successive binary decays of PLF* as it moves away from TLF* with velocity V
• modified Weisskopf approach
• consider all binary partitions up to emission of 18O
-- both ground and particle-stable excited states.
• Starting at an initial distance D, the total decay width, Г, is calculated
• τ=ħ/Г and P(t) ~ exp(-t/ τ)
• PLF* Initial distance = 15 fm(Z,A) PLF* = 38, 90 ; based on experimental data
ZTLF* = 42 ; taken as point source
For a fixed PLF*-TLF* distance
VR
ZZV
fj
jfc
CN
CN
f
f
j
j
R
ZZ
R
ZZ
R
ZZV
2
2
2
2
2
2
2
jf2
fj
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• de-excitation of isolated and proximity cases fairly similar as a function of time
• At E*/A = 2 MeV, proximity case de-excites slightly faster
• No difference is observed at E*/A = 4 MeV
• By 250 fm/c, most of rapid de-excitation has occurred.
V=0.2728c
t=250 fm/c D=70 fm
Distinguish:Early emissions: D ≤ 70 fmLate emissions: D > 70 fm
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Distinguish:Early emissions: D ≤ 70 fmLate emissions: D > 70 fm
• Early emissions are backward peaked
• Late emissions have a symmetric angular distribution
Angular distribution is peaked in direction of the TLF* with an enhancement by a factor of 3-7 as compared to cos(θ)=0.
Asymmetry of the angular distribution can provide a “clock” of the statistical emission time scale.
Towards TLF* Away from TLF*
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• As expected, early emissions populate the tail of the kinetic energy distribution.
• Coulomb proximity introduces a correlation between emission angle and time. As they occur on average earlier, backward emissions (towards the TLF*) are “hotter” and forward emissions are “colder”.
Calorimetry based on forward emission that assumes isotropy under-predicts the initial excitation of the PLF*
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Sensitivity of different emitted particles as a “clock”
• d, t, 3He and in particular IMFs exhibit emission time distributions more sharply peaked at short times as compared to p and α.
• These particles are therefore preferentially emitted towards backward angles.
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Selection of Experimental data: Eα ≤ 22 MeV (α’s on ridge)
┴114Cd + 92Mo at 50 A.MeV
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Both the asymmetry of the angular distribution and the kinetic energy spectra of forward emitted alpha particles can be explained by this schematic Coulomb proximity model.
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Sensitivity of the “clock”
0.1cos
92.0cos
0.1cos
92.0cos
)(
)(
Y
Y
Y
Y
forward
backward
• Ybackward/Yforward decreases with increasing initial distance (equivalent to increased pre-saddle time)
• For a fixed distance, Ybackward/Yforward decreases with both increasing E* and J decreased influence of barrier difference caused by external field. Alternatively, increasing the external
field increases the asymmetry.
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Conclusions Highly excited PLF* formed in peripheral heavy-ion collisions at E/A = 50 MeV
• Excitation energy is connected with velocity dissipation
• Different overlaps have the same dependence of <E*> on velocity dissipation
Coulomb proximity decay provides a clock for the statistical emission time scale
• Examine dependence on E*, Ztarget, VPLF* to characterize emission.
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Proximity Coulomb decay: A clock for measuring the statistical emission time scale
Backward enhancement of alpha particles along Coulomb ridge.
IMFs show a larger backward/forward enhancement than alpha particles
IMFs preferentially sample the earlier portion of the de-excitation cascade.
Previous work: D. Durand et al., Phys. Lett. B345, 397 (1995).