N / Z influence on the level density parameter

A completely exclusive experiment was performed by the INDRA collaboration to study the isospin dependence of the level density parameter. Over a large N/Z range, the fusion-evaporation charged products of Ar+Ni reactions were measured and identified both in charge and mass by coupling INDRA and VAMOS spectrometer. Preliminary results obtained by combining data of both detectors are presented for the Ar+Ni at 13.3 AMeV. The analysis method of relevant observables for such an ambitious investigation are discussed and the progress of the data analysis are reviewed.


Introduction
Being able to describe the competition among the various decay modes of excited nuclei has been one of the main goals of research in nuclear physics.Fusion process at low bombarding energy is well suited to produce such nuclei in a controlled way.At low energies the properties of the compound nucleus are well known.However incomplete fusion, linked to the fast emission of nucleons before the composite nucleus reaches thermal equilibrium, already occurs at 6 or 7 A MeV for light systems [1].
The level density parameter is a fundamental quantity in such a study.It is involved in several aspects of nuclear reactions, for instance in statistical models used in nuclear physics, astrophysics and in the search for superheavy elements.It is related to the effective mass, a property of the effective nucleon-nucleon interaction that is sensitive to the neutron and proton content of the nuclei.The level density governs the statistical decay of excited nuclei.Knowledge of the level density is thus highly needed at low and high excitation energies and for the largest possible range of N and Z, from the valley of stability to the drip lines.Indeed in the multifragmentation process observed at Fermi energies, excited neutron deficient fragments are assumed to be formed, and their de-excitation is not well constrained [2].
In the Fermi-gas framework the density of states ρ can be related to the excitation energy E and the level density parameter a by This expression is obtained within a single particle model and used in most statistical model calculations.Collective effects (many body and effective mass) can be included by using an effective a which depends on excitation energy [3].
The effective nucleon mass is expected to decrease with increasing temperature T while T ≤2 MeV.This implies a decrease of the level density parameter but also an increase of the kinetic symmetry energy contribution to the nuclear binding energy E sym (T ) = b sym (T ) × (N − Z) 2 /A as T increases.These effects would experimentally appear as a change in the particle multiplicity and in the relative yields of the exit channels [4].While a cannot be directly measured at high energy, the temperature T and 1/T = d ln ρ/dE * can be extracted from the exponential slope of kinetic energy spectra of evaporated particles.Multichance emission is taken into account by comparison with statistical model calculations such as GEMINI [5].Comparison with calculations [6] constrains the dependence of a with E * and T and verifies the consistency with other data for known isotopes.a was shown to evolve from A/8.5 MeV −1 at low temperature to A/15 MeV −1 around T =4-5 MeV [7].
The predicted isospin dependence of level density within the Fermi gas model is a decrease with increasing (N − Z).In this framework the level density parameter exhibits a small variation with isospin: . A significantly larger dependence would have important implications for other fields (r-process).Different extrapolations starting from stable nuclei lead to empirical parametrisations of the form [8] Those parametrisations lead to quite important variation of the estimated values of the level density parameter.The availability of stable and radioactive beams at new nuclear facilities offers a great chance to perform precise measurements on a large range of isotopes.
Experimental data far from the valley of stability are very scarce.Up to now, as only stable beams were available, level densities were studied for nuclei close to the valley of stability, on the neutron-poor side.Moreover, experiments consisted in inclusive measurements, determining either mass (charge) distribution of evaporation residues, and eventually fission products, or multiplicities of light charged particles associated with fusion.At the dawn of this century, some experiments measured evaporation residues (ER) in coincidence with one or two light charged particles [5,9].A first completely exclusive experiment was performed recently by the INDRA collaboration who studied the 78,82 Kr+ 40 Ca at 5.5 AMeV.The fission channel is 25% higher for the neutron deficient system, including very asymmetric fission configurations [10] while the extrapolated evaporation residue crosssection for both systems are similar within the error bars.
In the present very ambitious project we aimed at obtaining highly exclusive data by detecting and identifying event by event the residue and all the accompanying charged particles.The fundamental goal is to explore the variation of de-excitation properties and thus level density parameters with the N/Z of the compound nucleus when going from the proton-drip line to stable nuclei.Indeed the advent of radioactive beams, coupled to judiciously chosen targets, allows for the very first time to explore the properties of a large number of isotopes of compound nuclei of a given Z. Finally we can test the influence of the mass asymmetry of the entrance channel on the different components of the fusion cross section (ER, fission . . .).

The studied systems
The experiment was performed at Ganil/SPIRAL.In order to search for any evidence of a N/Z dependence of the level-density parameter from the Ni.In order to reach a compromise between reduced preequilibrium effects and a sufficient recoil energy for nuclear charge identification of residues, as well as to get the same excitation energy per nucleon of compound nuclei (∼2.9A MeV) and very similar angular momentum ranges, the incident energy for each beam was chosen around 13 A MeV. Five Pd isotopes were thus sampled with N/Z ranging from 1.00 ( 92 Pd) to 1.26 ( 104 Pd).The 92 Pd formed with exotic 34 Ar allows to touch the p-drip line [11].In this case special de-excitation properties might be observed as for the semi-magic nucleus 96 Pd.

Experimental set-up
The INDRA multidetector [12] was coupled to the large acceptance mass spectrometer VAMOS [13] allowing a 4π coverage.INDRA is made of 17 rings centered on the beam axis.Each one of these contains multi-stage telescopes composed of Ionisation Chambers, Silicon and Caesium Iodide detectors (for this experiment, the first 3 rings were removed to allow coupling to VAMOS).INDRA is dedicated to detecting the emitted light charged particles (LCP).
VAMOS provides the charge, mass and velocity of the evaporation residues (ER).Its focal plane detection system was composed of two emissive foils (SeD) coupled with an ionization chamber (IC) and a silicon detector wall (Si) providing ΔE, E, Z and position measurements.The scattering angle at the target (θ) and the magnetic rigidity (Bρ) are obtained by software trajectory reconstruction.The time-of-flight (ToF) of evaporation residues is measured between the target and the SeDs (or Si) using the high frequency signal of the cyclotron as reference.With such long flight distances, mass (A) and charge state (Q) identifications are achieved.We set different angular positions of the spectrometer to cover the residue angular distribution (∼ 0 • − 12 • ) to avoid any bias of the relative weights of the different exit channels.We placed a carbon foil of 70 μg/cm 2 at a distance of about 50 cm from the target in order to reach the equilibrium charge state distribution [5], independently of the compound nucleus production position within the target.
This experimental setup is crucial as it allows direct measurement of both the evaporation residue in VAMOS and the associated light charged particles in INDRA.

Analysis plan
The detection efficiency was maximized to obtain a large number of complete events of fusion (detection of the total charge of the compound system).The 4π angular acceptance allows to differentiate more easily fusion reactions from deep inelastic collisions or incomplete fusion thanks to recoil energy criteria [1].In fusion-evaporation events, the multiplicity of the undetected neutrons will be derived by the difference between the compound nucleus mass and those of all detected de-excitation charged products.
All decay chains will be precisely characterized: isotopic composition of emitted particles and their multiplicity added to the residue characteristics (A, Z) and their kinetic energies event by event.Moreover, we will obtain the percentage with which different chains lead to the same residue.The energy spectra (slope) of all de-excitation products will provide information on apparent temperature for all decay chains.For example, in this experiment, the Ni(Ar,αxn)Ru channel can be disentangled from the Ni(Ar,2p(x+2)n)Ru and Ni(Ar,pd(x+1)n)Ru channels and correctly weighed.
The detection of complete events will put additional strong constraints on the values of a for nuclei along the de-excitation chain for theoretical models; this has never been done up to now.

Present status of the project
Before the data can be analysed for physics, it is necessary to have a good calibration for both INDRA and VAMOS detectors.Presently identifications and calibrations of the INDRA array are nearly ready for all the systems.The Z and A identification of LCPs is achieved.
The data reduction of the VAMOS part is more delicate.We are in the final process of getting the mass and charge of the evaporation residues, after reconstruction of the trajectories in the spectrometer and the calibration of ToFs.The obtained mass separation in VAMOS for the ERs in the where the probabilities of the ten most likely deexcitation chains of 94 Pd leading to the 67 Se residue are plotted.These very accurate and selective information will bring new strong constraints for the study of the evolution of the level density parameter from the deexcitation of compound nucleus.

Conclusion
In summary, the E494S INDRA-VAMOS experiment represents a great opportunity to explore the isospin dependence of the level density parameter by coupling a 4π charged particle multi-detector to a high resolution magnetic spectrometer.At present, both INDRA and VAMOS data sets are being combined to give the full information about each decay channel of evaporation residues and the current physics analysis is on the threshold of releasing the new expected constraints on the level density parameter.

36Figure 1 :Figure 2 :
Figure 1: Mass separation (A) of evaporation residues produced in 36 Ar+ 58 Ni reaction and measured within VAMOS at Bρ 0 = 0.638 T.m and θ V AMOS = 0 • .Left: distribution of charge state (Q) versus A/Q deduced from ToF, reconstructed Bρ and/or energy measured in all silicon detectors.Right: Distribution of measured atomic charge (real Z) versus mass (A).The mass (A) is obtained by multiplying the reconstructed A/Q ratio by the integer value of Q for 16≤Q≤27.