Coulomb-nuclear interference in the inelastic scattering of 6Li on 76Ge

Angular distribution for the inelastic scattering of 28 MeV 6Li on 76Ge was measured using the Sao Paulo PelletronEngeSplit-pole Spectrograph facility. The coulomb-nuclear interference (CNI) analysis was applied to the first quadrupole state transition. The values of CL = δCL/δNL, the ratio of charge to isoscalardeformation lengths, and of (δNL02 were extracted through the comparison of experimental and DWBA-DOMP predicted cross section. The ratio of reduced charge to isoscalartransition probabilities, B(EL) to B(ISL) respectively, are related to the square of the parameter CL and were thus obtained with the advantage of scale uncertainties cancellation. The value of C2 = 1.10(2) obtained indicate a slight predominance of the protons relative to the neutrons for 76Ge.


Introduction
The characteristics of excited states 2 + 1 are widely used as indicators of nuclear structure, particularly the electric reduced transition probability B(E2) is used as a measure of the collectivity of these transitions. The B(E2) is in principle sensitive only to the contribution of the charge and to quantify the contributions of neutrons is also an important ingredient to characterize the collectivity. This aim is achieved through the isoscalar (mass) reduced transition probability B(IS2) obtained from the inelastic scattering. Particularly suitable are the measurements in an incident energy that enhances coulomb-nuclear interference (CNI) and allows simultaneous extractions of B(IS2) and the ratio between electric and isoscalar reduced transition probabilities B(E2)/B(IS2) [1][2][3]. The ratio B(E2)/B(IS2) is related to the square of the parameter C2. The previous CNI work, in the A~ 70 transitional mass region, considering the germanium isotopic chain [3] demonstrate an abrupt change for 74 Ge with C2 = 0.775(8): although for 70,72 Ge, values of the order of 1.0 or slightly higher were obtained. In particular, the present work pursues the study of CNI in the inelastic scattering of 6 Li on 76 Ge, in order to determine the relative contributions of protons and neutrons in the transition to the first quadrupole state.

Experimental setup
Measurements of the inelastic scattering of 6 Li on 76 Ge were obtained using the Pelletron Enge Split-pole Spectrograph facility. A solid-state position sensitive detector (PSD) of 500 m thickness, and 47 x 8 mm 2 area was positioned on the focal plane. The 28.0 MeV energy 6 Li beam was focused after passing defining slits of 1.0 x 2.0 mm 2 on an enriched target of 76 Ge with 510.5 10 15 particles/cm 2 thickness. A solid angle of 0.65 msr was used in the spectrometer entrance. Twenty-six spectra were measured at carefully chosen scattering angles in a range of 10 o ≤ Lab ≤ 55 o , in order to characterize CNI in the angular distribution corresponding to the first quadrupole excitation. A surface barrier detector, with 10 mm diameter and 1000 m thickness, was placed inside the scattering chamber at an angle of 30 o relative to the ion beam. Relative normalization of the data for the various scattering angles was obtained through the total charges collected by the Faraday cup and the elastic scattering measurements from the monitor detector.
The digital pulse processing (DPP) acquisition system used in the measurement was composed by the board PCI-6133 from National Instrument with a sample of analogic inputs up to 2.5 MS/s. The analysis of the pulse shape and the use of electronic noise filters provide an important resolution improvement, which is the advantage of this acquisition system. Figure 1 shows the position spectrum along the focal plane at the scattering angle θLab = 31 o . The three peaks observed on figure are associated with the elastic peak on 76 Ge, the 2 + 1 state inelastic peak and the elastic peak on the silicon contaminant. The energy resolution achieved was about 37 keV.

Data analysis and Results
The distorted wave Born approximation (DWBA) prediction using the deformed optical potential model (DOMP) approach with global optical parameters was applied. The value of the ratio between charge (L C ) and mass (L N ) deformation lengths CL is obtained from the angular distribution shape. The square of mass deformation length, (L N ) 2 , is also extracted, as a scale factor. The procedure applied for the  2 minimization was the iterative method of Gauss [4], extracting the correlated parameters 2 N and C2. Figure 2 illustrates the preliminary results obtained from the angular distribution of 76 Ge( 6 Li, 6 Li') 76 Ge to the first quadrupole excited state 2 + 1 in comparison with DWBA-DOMP prediction obtained in the fit (red solid curve). In order to illustrate the sensitivity of the method, two predictions corresponding to C = 0.78 (green dash curve) and C = 1.00 (blue dash curve) are also shown.
The results for the two correlated parameters in a preliminary data analysis are C2 = 1.10(2) and 2 N = 1.08(2) fm. The C2 value obtained is slightly higher than 1.0, indicating a homogeneous excitation with a small predominant contribution of protons in the first quadrupole excited state 2 + 1 of 76 Ge.