• 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

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)

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

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

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*

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

(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.

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

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

• 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

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*

• 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*

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.

Selection of Experimental data: Eα ≤ 22 MeV (α’s on ridge)

┴114Cd + 92Mo at 50 A.MeV

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.

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.

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.

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).