# Staggering in S+Ni collisions

L. MORELLI¹, M. D'AGOSTINO¹, M. BRUNO¹, F. GULMINELLI²,
G. BAIOCCO¹, S. BARLINI³, G. CASINI³, F. GRAMEGNA⁴,
V. L. KRAVCHUK⁴, T. MARCHI⁴, AD. R. RADUTA⁵

¹ Dipartimento di Fisica dell'Università and INFN, Bologna, Italy

² LPC (IN2P3-CNRS/ENSICAEN et Université, F-14076 Caen cedex,
France

³ INFN, Firenze, Italy

⁴ INFN, Laboratori Nazionali di Legnaro, Italy

⁵ NIPNE, Bucharest-Măgurele, POB-MG6, Romania

## Abstract

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 5.3° to 17.5°. GARFIELD is made by a drift chamber, filled with CF₄ gas at low

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.
<figure><img src="image_1.png" /><figcaption>Figure 1: (Color online) Total detected charge and charge of the largest fragment as a function of the cosine of the flow angle for $^{32}$S+$^{58}$Ni under the condition: $P_z/P_{beam} \ge 0.5$.</figcaption></figure>

pressure (53 mbar), azimuthally divided into 24 sectors, each one consisting
of 8 $\Delta E - E$ 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 tele-
scopes realized in a truncated cone shape. The first stage is an ionization
chamber (IC), the second a 300$\mu$m 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 $\simeq 4\pi$ detec-
tors [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 cal-
culated for events where at least a fragment ($Z \ge 3$) and an $\alpha$-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 $\theta_{flow}$ with nearly constant statistics, which implies a nearly flat distribu-
tion of $\cos(\theta_{flow})$, as expected for spherical events. From now on, “central”
events will be defined by the additional condition of a total detected charge
$Z_{tot} \ge 70\% \cdot Z_{S+Ni}$, and “peripheral” events by $Z_{tot} \le 25$ and $\theta_{flow} \le 40^\circ$.

## 2 Results

Figure 2 displays the fragment ($Z \ge 3$) 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
<figure><img src="image_2.png" /><figcaption>Figure 2: Elemental fragment ($Z \ge 3$) distribution for $^{32}S + ^{58}Ni$ (full symbols, dashed line) and $^{32}S + ^{64}Ni$ (open symbols, full line) in peripheral sample.</figcaption></figure>

different behavior is observed in central collision, where the charge distribu-
tion 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 im-
portant 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 sim-
ilar 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 dif-
ference 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
<figure><img src="image_3.png" /><figcaption>Figure 3: Ratio of the elemental fragment ($Z \ge 3$) 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.</figcaption></figure>

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 appear 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.

## References

[1] Yang L. B. et al., *Phys. Rev.* C60 (1999) 041602.

[2] Ricciardi M. V. et al., *Nucl. Phys.* A733 (2004) 299; arXiv:1007.0386v1.

[3] Moroni A. et al., *Nucl. Instr. And Meth.* A556 (2006) 516, Gramegna F. et al., *Nucl. Instr. And Meth.* A389 (1997) 474;

[4] Cugnon J. and L'Hôte D., *Nucl. Phys.* A397 (1983) 519.

[5] D'Agostino M. et al., *Phys. Lett.* 368 (1996) 259.

[6] Amorini F. et al., *Phys. Rev. Lett.* 102 (2009) 112701.