Staggering in S + Ni collisions

Odd-even effects in fragment production have been studied since a long time and never quantitatively understood. The odd-even anomaly was reported in the literature [1,2] to be more pronounced in reactions involving Ni projectile and targets, in particular in n-poor systems. In some experiments [1, 2] the magnitude of the odd-even effect is found to be related to the isospin of the projectile and/or the target. From a theoretical point of view, odd-even effects in fragmentation reactions are clearly linked to the pairing residual interaction and its dependence on temperature. 1 Experiment and data selection The measurements were performed at the Legnaro National Laboratory. A pulsed beam was used to bombard self-supporting 58Ni and 64Ni targets, 150 μg/cm2 thick. The bombarding energy was 463 MeV. The detecting device is composed by the GARFIELD detector [3] and an annular three-stage detector (Ring Counter) [3] covering laboratory forward angles from 5.3o to 17.5o. GARFIELD is made by a drift chamber, filled with CF4 gas at low EPJ Web of Conferences DOI: 10.1051/ , epjconf 2012 / 00042 (2012) 31 3100042 This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. C © Owned by the authors, published by EDP Sciences , 2012 SIF Article available at http://www.epj-conferences.org or http://dx.doi.org/10.1051/epjconf/20123100042 Figure 1: (Color online) Total detected charge and charge of the largest fragment as a function of the cosinus of the flow angle for S+Ni under the condition: Pz/Pbeam ≥ 0.5. pressure (53 mbar), azimuthally divided into 24 sectors, each one consisting of 8 ΔE−E telescopes, for a total of 96 telescopes. The CsI(Tl) scintillation detectors, lodged in the same gas volume, are used to get information on the residual energy. The Ring Counter [3] is an array of three-stage telescopes realized in a truncated cone shape. The first stage is an ionization chamber (IC), the second a 300μm strip silicon detector (Si) and the last stage a CsI(Tl) scintillator. To sort the measured events as a function of the centrality, we adopted the method of the “shape analysis” [4], common to other intermediate and high energy experiments performed with 4π detectors [5]. In Fig. 1 we examine the behavior of the total detected charge as a function of the “flow angle” [4] for the n-poor system. The flow angle was calculated for events where at least a fragment (Z ≥ 3) and an α-particle have been detected. We observe of fig. 1) that peripheral events, characterized by a total detected charge close to the projectile charge, keep a strong memory of the entrance channel and are therefore restricted to low value of the flow angle. Higher values of the total charge are distributed over the whole range of θflow with nearly constant statistics, which implies a nearly flat distribution of cos(θflow), as expected for spherical events. From now on, “central” events will be defined by the additional condition of a total detected charge Ztot ≥ 70% · ZS+Ni, and “peripheral“ events by Ztot ≤ 25 and θflow ≤ 40o.


Experiment and data selection
The measurements were performed at the Legnaro National Laboratory.A pulsed beam was used to bombard self-supporting 58 Ni and 64 Ni targets, 150 μg/cm 2 thick.The bombarding energy was 463 MeV.The detecting device is composed by the GARFIELD detector [3] and an annular three-stage detector (Ring Counter) [3] covering laboratory forward angles from 5.3 o to 17.5 o .GARFIELD is made by a drift chamber, filled with CF 4 gas at low pressure (53 mbar), azimuthally divided into 24 sectors, each one consisting of 8 ΔE −E telescopes, for a total of 96 telescopes.The CsI(Tl) scintillation detectors, lodged in the same gas volume, are used to get information on the residual energy.The Ring Counter [3] is an array of three-stage telescopes realized in a truncated cone shape.The first stage is an ionization chamber (IC), the second a 300μm strip silicon detector (Si) and the last stage a CsI(Tl) scintillator.To sort the measured events as a function of the centrality, we adopted the method of the "shape analysis" [4], common to other intermediate and high energy experiments performed with 4π detectors [5].In Fig. 1 we examine the behavior of the total detected charge as a function of the "flow angle" [4] for the n-poor system.The flow angle was calculated for events where at least a fragment (Z ≥ 3) and an α-particle have been detected.We observe of fig. 1) that peripheral events, characterized by a total detected charge close to the projectile charge, keep a strong memory of the entrance channel and are therefore restricted to low value of the flow angle.Higher values of the total charge are distributed over the whole range of θ flow with nearly constant statistics, which implies a nearly flat distribution of cos(θ flow ), as expected for spherical events.From now on, "central" events will be defined by the additional condition of a total detected charge Z tot ≥ 70% • Z S+Ni , and "peripheral" events by Z tot ≤ 25 and θ flow ≤ 40 o .

Results
Figure 2 displays the fragment (Z ≥ 3) charge distribution measured for the two reactions in central (left) and peripheral (right) events.The superposition of the two peripheral data sets shows that our selection of peripheral events is effective in isolating the contribution of the quasi-projectile.A  different behavior is observed in central collision, where the charge distribution does not scale with the size of the system and a clear isospin effect can be seen, similar to other experimental results [6] .As far as staggering is concerned, we can see that for both reactions a well pronounced odd-even effect is seen in the charge distribution of peripheral collisions, while almost no staggering is apparent neither in the IMF yield nor in the residue region for central collisions, where only an extra-production of carbon fragments is evident.The difference observed between central and peripheral collisions could be ascribed to the isotopic ratio of the evaporating source, which is sensibly more neutron rich for the fused sources than for the quasi-projectile.However another important difference between the two samples concerns the excitation energy, which corresponds to 3 A.MeV in average in the central sample and less than half of this value for the peripheral sample.Such an important difference in the deposited energy could lead to different mechanisms for fragment production.To reinforce this conclusion, we show in Fig. 3 the ratio between the elemental charge distribution of the whole central sample and a smoothed distribution obtained by a parabolic interpolation of the measured yields over 5 consecutive points.By looking at fig. 3 it is evident that the staggering is present also in central collisions with amplitudes similar to the peripheral ones.Some extra differences between the two samples appear in this representation: the extra-production of carbon with respect to oscillations of neighboring charges is larger in central collisions and the amplitude of the staggering decreases for increasing fragment charge, at difference with peripheral events, where it remains almost constant.For the two centrality selections the different isospin of the entrance channel plays a minor role, enforcing the idea that a different mechanism of decay is at the origin of the observed differences between central and peripheral collisions.Concluding, only if the production yield as a function of the fragment size is reasonably constant a clear visual staggering can be observed.
To investigate in more detail the influence of the excitation energy of the fragment source in central collisions, a possible way would be to analyze data in excitation energy bins, but the statistics of the present data-set is not sufficient.The staggering effects appears to be a universal feature of fragment production, slightly enhanced when the emission source is neutron poor.A closer look at the behavior of isotopic chains reveals that odd-even effects cannot be explained by pairing effects in the nuclear mass alone, but depend in a more complex way on the de-excitation chain.

Figure 1 :
Figure 1: (Color online) Total detected charge and charge of the largest fragment as a function of the cosinus of the flow angle for 32 S+ 58 Ni under the condition: P z /P beam ≥ 0.5.

Figure 3 :
Figure 3: Ratio of the elemental fragment (Z ≥ 3) distribution of Fig.2 for 32 S+ 58 Ni (full symbols connected by dashed lines) and 32 S+ 64 Ni (open symbols connected by full lines) by smoothed distributions obtained by a parabolic interpolation over 5 consecutive points.Left: central events.Right: peripheral collisions.