E. Norbeck at RHIC2000

Odd-even Z Effects in the Abundance of Fragments from Heavy Nuclei

The analysis discussed here was performed by:

E. Norbeck and L.B. Yang at the University of Iowa
W.A. Friedman at the University of Wisconsin
F.D. Ingram at Rock Valley College, Rockford, IL

The data, from the 4p Array at NSCL, Michigan State Uiversity, was obtained by:

G.D. Westfall, A.M. Vander Molen, O. Bjarki, D.J. Magestro, and M.L. Miller at NSCL
R. Pak at the University of Rochester
E. Norbeck and L.B. Yang at the University of Iowa
R.A. Lacey at SUNY, Stony Brook
S.J. Yennello at Texas A & M

Slide 2
Energy spectra for nuclear fragments at forward angles (5.4^o) for 75A Mev ⁵⁸Ni + ⁵⁸Ni and ⁵⁸Fe + ⁵⁸Fe. Beam-velocity fragments have energy 75A MeV (dashed line). A careful examination of the figure shows that nuclear fragments with even atomic number, such as C, O, Ne, and Mg are formed more often than fragments with odd atomic number, such as B, N, F, and Na. The one exception is lithium (Z=3) for which the peak is higher and broader than all of the others. Take special notice of the fact that the nickel peaks are larger than the iron peaks for even Z values but not for odd Z values.

For non-central collisions the unreacted part of the beam is sheared off to continue on almost as if nothing had happened. If the data could be described by a plane-wave Born approximation, the peak for each fragment type would be centered at the beam velocity (the dotted line) with a width reflecting the separation energy. The shift of the peak to somewhat lower energies shows the need to use distorted waves in the input channel. The distortion of the initial wave function is caused by both Coulomb and nuclear forces that reduce the relative beam-target velocity before the main reaction takes place.

The widths of the peaks in the figure are real. The uncertainty in the energy of an individual fragment is less than the size of the points.

Slide 3 Energy spectrua for 5.4^o nitrogen separated into impact parameter bins. (The measure of centrality is the number of light-charged particles (Z=1,2)) Note that for more central events the average nitrogen energy is lower.

It can be expected that larger fragments would be correlated with larger impact parameters. This is confirmed by the data. The peak in plots of number of fragments vs impact parameter goes from b=4 fm for Z=6 to b=5 fm for Z=10.

Slide 4
d(Z) is a measure of the excess of even Z fragments for a set of four Z values, Z to Z+3. (Y is the area under a peak in Slide 2.) An excess of odd-Z fragments gives a negative d. For both reactions there is an excess of even-Z fragments, but the excess is larger for Ni. The negative d for Z=3 is caused by the exceptionally large yield of the odd-Z lithium.

d(Z) = 1/8(-1)^Z+1{ln Y(Z+3)-ln Y(Z) -3[ln Y(Z+2)-ln Y(Z+1)]}

Slide 5
In Slide 2 the Ni peaks are larger than the Fe peaks for even Z. This plot of the ratio of the area under the peaks shows the effect across the entire range from Z=3 to 15.

Slide 6
Statistical model predictions of the data in Slide 5. To better understand the source of the effects that are seen, the features of the model are applied in stages.
Stage 1. Includes the masses of only the ground states and ignores the statistical weights due to non-zero spin
Stage 2. Same as Stage 1 but includes the proper statistical weights.
Stage 3. Adds all bound states with proper statictical weights.
Stage 4. Adds all known resonances and takes into account particle unstable decays.

Slide 7
Stage 3 and Stage 4 in the format shown in Slide 4. This shows that the charge changing decays of unstable states allow the increased binding energy of the even-Z fragments to overcome the greater statistical weight of the ood-Z fragments. One might expect that the larger odd-even effect for Ni is caused by its larger number of protons allowing more charge changing decays. Remarkably, taking into account the unstable states actually narrows the difference between Fe and Ni.

Conclusions

This data show a number of interesting effects that are only poorly understood. In addition to more theory, experiments are needed that resolve individual isotopes and that use beams with a wider range of N/Z
Click here to see the rest of the papers ot RHIC2000, the 16^th Winter Workshop on Nuclear Dynamics at Park City, Utah, March 11-18, 2000.