1. Ricardo Yanez Indiana University Cyclotron Facility
Characterization of PLF Particle Emission in Peripheral Heavy-ion Collisions
Ricardo Yanez Indiana University Cyclotron Facility
I would like to present recent results concerning the characterization of the emission of particles from excited projectile-like fragments in peripheral heavy-ion collisions. I’m Ricardo Yanez from IUCF.

2. Experiment PLF Telescope: 2.1º    4.2º LASSA: 7º    58º
MB/MW: 7º    168º
We performed experiments at NSCL using a beam of 50 MeV per nucleon 114-Cd on 92-Mo. Our detector set-up consisted of a projectile-like fragment telescope located at forward angles between 2 and 4 degrees. This telescope is able to resolve charges up to the charge of the projectile. Between 7 and 58 degrees and about 20 cm from the target is the Large Acceptance Silicon Strip Array, LASSA for short. LASSA measures light charged particles and intermediate mass fragments up to Z=9 with unit mass resolution. The miniball/miniwall detector arrays covered angles between 7 and 168 degrees and is used for global characterization of events. The total detector setup covered about 80% of 4pi.

3. PLF telescope DE: E: segmented 300 mm Si 4 quadrants 4 pies, 16 rings
for each quadrant E:
2 cm CsI(Tl)
One important ingredient of the present analysis is the PLF telescope. This is a two element telescope with a segmented 300 micron circular Si in the front . It has a hole in the center to allow beam particles thru. The front face is segmented in four quadrants, each quadrant further segmented in 16 concentric rings. The back of the Si is segmented in 16 pies. This detector gives an angular resolution of about .13 degrees in theta and 22.5 degrees in phi. To the Si follows 16 2 cm thick CsI of the shape of the pies.
This is a map of delta E-E. One can clearly see the lines corresponding to different charges and in particular the elastically scattered projectile nuclei. Unit charge resolution is achieved up to the charche of the projectile. From here on we define a projectile-like fragment as a fragment detected in the telescope whose charge is greater than ten and less or equal than 46.

4. LASSA Element: thickness: #/telescope: DESi1 DESi2 CsI
65 mm 500 mm 6 cm
16 1616 4
Dq~0.87
LASSA consists of nine telescopes, each having three elements. The first element is a rather thin 65 micron 5 times 5 cm strip Si. This Si is segmented in 16 vertical strips. A thicker 500 micron double sided Si follows. This Si is also 5 times 5 cm in size and is segmented in 16 strip vertical strips in the front face and 16 horizontal strips in the back face. This gives an angular resolution of about .87 degrees. The last elements giving a measure of E are 4 6cm thick CsI cristals.
A delta E-E map shows that LASSA resolves individual isotopes up to Z=9 fragments.
This is the particle identication for Carbons and Oxigens in the Si-Si and Si-CsI portions of the tepescope.
Further information about LASSA can be found in the paper by Brian Davin and collaborators.
B. Davin et al., Nucl. Inst. Meth. Phys. Res. A 473, 302 (2001).

5. Event selection at least 3 charged particles in MB/MW
1 fragment with 10 < Z  46 in PLF telescope
It is important to explain the event selection that has been made. The first one is the minimum trigger condition during data taking. This is at least 3 detected charge particles in the minibal/miniwall array. Second, we requiere that a PLF is detected in the forward PLF telescope. For these events the total charge particle multiplicity shows a rather strong correlation with the charge of the PLF. Since the total charge particle multiplicity is related to the excitation energy we may say the charge of the PLF is also related to the excitation energy. The velocity of the PLF shows a less obvious correlation. For a given Z of the PLF there is a rather broad distribution of velocity damping. The arrow shows the velocity of the projectile.
We will show later that the velocity damping is indeed related to the excitation energy as one would expect.
To further restrict ourselves to the more peripheral collisions, we have selected the events where the charge of the PLF is between 30 and 46.

6. Galilean invariant velocity maps
Laboratory
frame
Having the mass and energy of the fragments in LASSA we can construct the galilean invariant velocity maps for the selected events. Several features can be distinguished. Centered around the velocity of the projectile one observes a well defined Coulomb ridge produced by the emission of particles from the projectile-like fragments. The coulomb ridge is particularly evident for alpha particles. Also evident is the emission of particles from the midrapidity zone centered around the center of mass velocity. The emission of midrapidity particles is broad and can reach very high transversal velocities. It also contaminates considerably the region of PLF emission. Only in the forward part of the Coulomb ridge can we minimize this contamination. Also less evident is the emission of the target-like fragment, at low velocities. Having a rather clean spot in the velocity maps and a well-defined source, we have set out to characterize the emission from this source.

7. Galilean invariant velocity maps
PLF
frame
A transformation to the frame where the detected PLF is at rest shows even more clearly the coulomb ridge and the Coulomb hole. In order to select the emitted fragmets in the more clean area we have made cuts in angle forward to the PLF as shown by the lines. We expect this region to be fairly free from the emission from other sources. Care must be taken to make the cuts so that regions affected by detector acceptance are left out.

8. Kinetic energy spectra
Lorentz
solid angle
normalize 
d2M /dEdW
We have constructed the kinetic energy spectra en the rest frame of the PLF. In an event by event basis we make a Lorenz transformation, since the velocities forward to the PLF are quite high, we make corrections for the changes in solid angle and normalize to the total number of events that we are considereding. The quantity que construct is the multiplicity double differential, d2M deE dOmega.
These are 2d maps of this quantity as a function of the angle of emission in the PLF frame for the light charged particles. One can clearly see that in the forward direction the emission is fairly free from contamination from the midrapidity emission. So, we have made cuts in angle as shown by the solid lines. The width of these cuts was dictated by the number of particles so that sufficient statistics is accumulated to define a spectrum.

9. The case of alphas is particularly helpful in understanding what we want to accomplish. Here the Coulomb ridge is well evident and between say 50 and 70 degrees the spectra are rather clean from the emission from the midrapidity source. This portion of the spectra should be isotropic.

10. Source fit Maxwell-Boltzmann B  Barrier parameter
T  Temperature parameter
D  Barrier diffuseness parameter
Next we take the kinetc energy spectra in the clean areas and make a source fit using a maxwell-boltzmann type of function. The parametrization contains the basic features of surface emission from an equilibrated source. Three parameters are fit by minimizing chi-squared. “B” is the barrier parameter, related to the emission barrier, “T” is the temperature parameter, related to the emission temperature. The maximum is at “B”+”T” and “T” controls the slope of the high energy part. “D” is the barrier diffuseness parameter and controls the curvature in the lower energy part.
These are examples of the source fitting for several fragments. We see that the one source fit is able to reproduce well the measured spectra. The slope parameter for alpha particles is rather small compared to other fragments.
J.P.Lestone, Phys. Rev. Lett. 67, 1078 (1991).

11. If we take the fit for alphas at 55 degrees and supeninpose it to the spectra a other angles we can see that the emission from the PLF is isotropic. At 50 degrees, 55 and 60 degrees the intensity of the coulomb ridge is constant. Even if we go to 90 degrees we can still recognize the coulomb ridge superimposed on a high energy tail coming from the midrapidity source. The contamination here is about 20% of the PLF emission.
I have to stress here that the red line is not a fit to the spectra. It is the superimposed fit at 55 degrees.
So, by characterizing the spectra at forward angles and assuming the emission there is fairly uncontaminated from other emission sources, and by assuming the emission is isotropic, which is supported by the data. we can in fact extrapolate to contaminated areas.

12. Multiplicities Average multiplicity: Emitted charge:
One of the quantities we can estimate using the fitted fuction at forward angles is the multiplicity of PLF emission. This is simply the double differential integrated over energy and solid angle. We do so for all the species we have sufficient statistics for. We see that protons and alphas exhaust the emission completely. Both have a multiplicity close to 3.
It should be stressed that these are the multiplicities from the PLF. The average PLF multiplicity is close to 7, whereas the average total charged particle multiplicity is around 10. We can also estimate the total average charge emitted from the PLF. This turns out to be close to 11 units of charge.
Emitted charge:

13. Statistical simulation
Average charge
primary PLF:
Average mass 
SIMON
Knowing the average charge of the measured PLF (35) and the average emitted charge(11), we estimate the charge of the primary PLF prior to decay to 46 charge units. Assuming this primary PLF has the same N over Z ratio as the projectile, we estimate it’s mass number to 109. If we use a statistical model like SIMON to deexcite a nucleus of charge 46 and mass 109, we would need about 512 MeVof excitation energy, or about 7.4 MeVof temperature, to end up with a nucleus of charge 35, the average charge of the PLF.
Comparing the average multiplicities with simulation (thick solid lines) shows that the code overestimates the multiplicities of hydrogens an underestimates the multiplicities of alphas.  

14. Fractional yield
If we construct the fractional yields, that is the fraction to the total multiplicity for a given atomic number, we se that the simulation does a fair job.

15. Barrier parameter vs. barrier
If we compare the barrier parameter with the simulated average barrier at the moment of emission we see that the extracted barrier parameters are consistent with what is expected of a barrier given two touching spheres. For carbons the extracted barrier parameter seem a bit to dependent on mass. The disagreement is perhaps due to the inability to fit well at low counting statistics.

16. Slope parameter vs. temperature
The slope parameters and the simulated average temperature at the moment of emission however are not comparable except for hydrogens and alphas. The dotted line is the temperature of the starting nucleus in the simulations.
One possible reason is that the emission of clusters in the simulation come too late, when the nucleus has already cooled off considerably by neutron emission.

17. Velocity damping
Finally, we have futher made cuts on the velocity of the projectile. One expects that the excitation energy of the projectile increases with the velocity damping. This appears indeed to be the case at least for alphas. The highest multiplicity and slopes are attained for the most damped events.

18. Conclusions
PLF* emission in peripheral collisions is well characterized by isotropic emission in the forward direction.
vPLF* provides a measure of E*.
Malpha and Talpha,slope
The <E*> is ~ 500 MeV, T ~ 7.4 MeV
Tslope,frag ~ 7 MeV > Tslope,alpha ~4-5 MeV: fragments probe the highest excitations/early times.
To show this relation we plot the simulated average temperature at the moment of emission versus average emission time. We do see that protons and alphas do come on average late in the cascades. Other clusters, in particular IMFs are perhaps be emitted earlier than predicted by the statistical model.

19. Collaborators Indiana University Cyclotron Facility
B. Davin, R. Alfaro, H. Xu, L. Beaulieu, Y. Larochelle, T. Lefort,
S. Hudan, A.L. Caraley, R.T. de Souza
NSCL, 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,
Washington University, St. Louis
R.J. Charity, and L.G. Sobotka