Structural effects in the nuclide distributions of the residues of highly excited systems
P. Napolitani, F. Rejmund, L. Tassan-Got, M.V. Ricciardi, A. Kelic, K.-H. Schmidt, O. Yordanov, A.V. ignatyuk, C. villagrasa
aa r X i v : . [ nu c l - e x ] M a y STRUCTURAL EFFECTS IN THE NUCLIDEDISTRIBUTIONS OF THE RESIDUES OF HIGHLYEXCITED SYSTEMS
P. NAPOLITANI, F. REJMUND and L. TASSAN-GOTIPN Orsay, IN2P3, 91406 Orsay, FranceM. V. RICCIARDI, A. KELIC, K.-H. SCHMIDT and O. YORDANOVGSI, Planckstr. 1, 64291 Darmstadt, GermanyA. V. IGNATYUKIPPE, Bondarenko Squ. 1, 249020 Obninsk, RussiaC. VILLAGRASADAPNIA/SPhN, CEA/Saclay, 91191 Gif sur Yvette, France
New data from GSI on the production-cross-section forfragmentation of the systems Fe+ p and Fe+ nat
Ti at1 A GeV revealed the appearance of even-odd staggeringin the cross-section distribution for chains of isotopeswith given N − Z . The staggering is strongly enhancedfor the chain N = Z , it reduces as the production movesaway from the N = Z chain, and it reverses for themost neutron-rich odd- A residues. These phenomena,observed in the residues of rather violent reactions, arerelated to structural effects in the level-densities belowthe particle-emission threshold. Nuclear structure is extensively studied in relation to mean-field properties, by analyzingnuclear masses, binding energy, shell effects or deformation. Additional insight on nuclearstructure is carried by other frequently investigated observables; among these are the yieldsof the residues in low energy fission. In this case, the fragment distribution reveals an en-hanced production of the even elements, which gradually vanishes with increasing reactionenergy. The disappearence of this staggering with the excitation energy seemed to constrainthe study of nuclear structure to systems with low excitation energies. Though, some ex-periments dedicated to different and more violent reactions, like spallation or fragmentation,revealed similar structures in the yields of the residues [1]. A very complete systematics ofstructural effects in the isotopic distributions of highly excited systems is the result of a recent
Introduction 2 σ / m b σ / m b Fe+p Fe+Ti Fe+p Fe+Ti
Figure 1: Experimantal cross sections of Fe+ p (top) and Fe+ nat
Ti (bottom) for even-massresidues (left) and odd-mass residues (right), respectively. The cross sections are ordered inchains according to given N − Z values. The values of N − Z are marked in the figure, nextto the corresponding chains.experiment: the residue cross-sections of the reaction Fe+p and Fe+ nat
Ti at 1 A GeV weremeasured in inverse kinematics with the FRagment Separator at GSI (Darmstadt). In fig. (1)the cross sections are presented ordered according to different chains of isotopes with given N − Z , for even (left) and odd (right) masses, respectively. Even-mass isotopes manifestan enhanced production of even elements all along the different chains. The staggering ismaximum for symmetric nuclei ( N = Z ), and it gradually smooths down for more asym-metric isotopes. The case of odd masses is more complex: proton-rich isotopes (the chain N − Z = − ) show an enhanced production of even elements, while the staggering reversesin favour of an enhanced production of odd elements for neutron-rich nuclei. The Fe+ nat
Tisystem, introducing appreciably higher excitation energy than the Fe+ p system on the av-erage, shows higher cross sections, but identical features in the staggering along the chains ofgiven N − Z . From this comparison, and from the extension to other measured highly excitedsystems [1], we conclude that the observed structure effect does not depend on the increaseof excitation energy, and it reveals to be a general property of spallation and fragmentationresidues. A schematic explanation 3
A simple statistical evaporation model, where the nuclear level densities are calculated ac-cording to the Fermi-gas model [3] would be sufficient to reproduce all the features observed inthe yields, in first order [1]. This could seem to be in contradiction with the counterbalancingof the pairing gap in the nuclear masses and in the level densities. On the contrary, in eachevaporation step, the probability of the possible decay channels do not only reflect the leveldensities of the daughter nucleus, but they also depend on the number of excited levels of themother nucleus that could decay into the daughter. The excited levels available for the decayextend from the separation energy of the daughter nucleus down to the separation energy ofthe mother nucleus, increased of the Coulomb barrier in the case of charged particle emission.The separation energy of the mother nucleus corresponds to the ground state of the daughternucleus. This is sketched in fig. (2), where the levels of some isotopes are distributed ontheir mass-excess parabolae. Let us consider the case of an odd-mass nucleus decaying intoan even-mass nucleus. A series of even-mass isotopes ( Al, Si, P, S) show a smoothvariation of the separation energies as a function of the element, once shifted by the pairinggap δ P. The absence of staggering in the separation energies is reflected in a smooth variationof the level density for the even-mass nuclei as a function of the element. Nevertheless, due tothe pairing gap, odd-mass nuclei decaying into even-even daughters ( Si or S) have more O dd m a ss E v e n m a ss O dd m a ss Mg Al Al Al Si Si Si P P P S S
10 5 13 14 15 16 E / M e V ZE - δ P S n E + E - δ P S P CoulombA = 31 A = 30
10 5 13 14 15 16 np np np npnp npnp npnp np E / M e V np np Figure 2: Evaporation scheme. The experimental levels of a set of nuclei are ordered on theirmass-excess parabolae. proton and neutron separation energies are marked with "p" and "n",respectively. On the right, the proton ( S p ) and neutron ( S n ) separation energies, shifted bythe pairing gap δ P, are presented for A =30 and A =31. Conclusions and open questions 4 excited levels available for the decay with respect to odd-mass nuclei decaying into odd-odddaughters ( Al or P). At the very end of the evaporation process, the decay in the groundstate of the daughter nucleus becomes so relevant to determine the overproduction of even-even nuclei compared to odd-odd ones. A slightly different discussion should be dedicated tothe formation of odd-mass residues ( Mg, Al, Si, P). As the ground states of odd-massnuclei are all ordered along the same mass parabola, the restoring of the structure in theproduction yields should be determined by the separation energy that shows up as an even-odd staggering in both, proton and neutron separation energies, however with different signs,depending on the neutron excess. In odd-mass neutron-rich nuclei ( Mg, Al) the neutronseparation energy, that is lower than the proton separation energy, determines the choice ofthe most probable evaporation channel. Thus, the residues will reflect the structure of theneutron separation energy favouring the production of odd elements. Contrarely, the yields ofodd-mass proton-rich nuclei ( Si, P) reflect the structure of the proton separation energyfavouring the production of even elements.
We demonstrated qualitatively that the structure observed in the nuclide cross section ofspallation and fragmentation residues is a result of the very last steps of the evaporationprocess. It should be pointed out that the strength of the staggering is remarkably high. A study based on Tracy’s analysis [2] would reveal a strenght higher than 50% for the even-oddstaggering of the N = Z chain, and up to 20% for the odd-even staggering of the odd-massneutron rich nuclei. This is to be compared to the even-odd staggering that characterizesthe low-energy fission yields, measured to reach a strength of around 40% at maximum [4].Another interesting aspect is the much higher production of alpha-multiple nuclei (i.e. thehuge staggering along the N = Z chain). This could be understood as an effect of the lowerbinding of odd-odd symmetric nuclei due to the effect of the Wigner term. Nevertheless, ifwe add the remark that the hot fragments of the reaction Fe+ p or Fe+ nat
Ti could havespent a considerable part of their excitation energy undergoing a multifragmentation-like orbreak-up process [5], we might also consider alpha-cluster emission as an additional channelresponsible of the restoring of the structural effects in the production yields.
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Phys. Rev C5 , 222 (1972).[3] V. M. Strutinski, in Int. Conf. on Nuclear Physics , p. 617 (Paris, Italy, 1958).[4] Steinhaeuser et Al,
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