Coulomb-nuclear interference (CNI) results of the collective quadrupolar excitations in odd and even Ru isotopes

Abstract

The study of the odd 99;101Ru nuclei complements the investigation of the collectivity of the first quadrupolar excitations in 100;102;104Ru. Angular distributions for the 99;101Ru(d, d') reactions at 13 MeV were obtained in the Pelletron Laboratory using nuclear emulsion plates on the focal plane of the Enge spectrograph. A Coulomb-Nuclar Interference analysis employing DWBA-DOMP predictions with global optical potential parameters was applied to the excitation of states which could belong to the multiplet built on the first quadrupolar excitation of the core. In the analysis, three states were identified for each of the isotopes and associated, respectively, with adopted levels in the Nuclear Data Sheets Compilation of Jpi= 5=2+, 7=2+ and 9=2+. Through the comparison of experimental and predicted cross section angular distributions, the values of (<IMG SRC="/img/revistas/bjp/v34n3a/a14img01.gif">)² and of the ratio C = <IMG SRC="/img/revistas/bjp/v34n3a/a14img01.gif" >/ <IMG SRC="/img/revistas/bjp/v34n3a/a14img02.gif" >were obtained.

Coulomb-nuclear interference (CNI) results of the collective quadrupolar excitations in odd and even Ru isotopes

C. L. Rodrigues^I; M. R. D. Rodrigues^I; T. Borello-Lewin^I; L. B. Horodynski-Matsushigue^I; J. L. M. Duarte^I; G. M. Ukita^{1, II}; G. N. Hanninger^I

^IInstituto de Física, Universidade de São Paulo, Caixa Postal 66318, CEP 05389-970, São Paulo, SP, Brazil

^IIFaculdade de Psicologia, Universidade de Santo Amaro, Rua Professor Enéas da Siqueira Neto, 340, CEP 04829-300, São Paulo, SP, Brazil

ABSTRACT

The study of the odd ^99;101Ru nuclei complements the investigation of the collectivity of the first quadrupolar excitations in ^100;102;104Ru. Angular distributions for the ^99;101Ru(d, d') reactions at 13 MeV were obtained in the Pelletron Laboratory using nuclear emulsion plates on the focal plane of the Enge spectrograph. A Coulomb-Nuclar Interference analysis employing DWBA-DOMP predictions with global optical potential parameters was applied to the excitation of states which could belong to the multiplet built on the first quadrupolar excitation of the core. In the analysis, three states were identified for each of the isotopes and associated, respectively, with adopted levels in the Nuclear Data Sheets Compilation of J^p= 5=2⁺, 7=2⁺ and 9=2⁺. Through the comparison of experimental and predicted cross section angular distributions, the values of ()² and of the ratio C = / were obtained.

1 Introduction

The São Paulo Nuclear Spectroscopy with Light Ions Group, employing the Pelletron-Magnetic-Spectrograph system, has contributed to the experimental study of the complicated region of A ~ 100 with the investigation of the Coulomb-Nuclear interference (CNI) on even nuclei [1, 2], in the inelastic scattering of isoscalar projectiles (deuterons,alphas and lithium).

The present study of the odd ^99,101Ru nuclei complements the survey of the collectivity of the first quadrupolar excitations in ^100,102,104Ru [1], allowing for the simultaneous extraction of the square of mass deformation length (()²), obtained through the scale factor from the fit of predictions of the distorted wave Born approximation (DWBA), within the deformed optical model potential (DOMP), to the experimental data, and of the ratio C = / , extracted through of the analysis of the angular distribution shape.

Since the cross sections of inelastic scattering on odd nuclei are much smaller than the corresponding ones on even nuclei, due to the fragmentation of the multipolar excitations, there are relatively less studies on odd targets. In particular, no previous study of the odd ruthenium isotopes is available, although one theoretical interpretation [3] of ⁹⁹Ru, linking it to its even neighbour, had aroused an interesting question about the magnitude of the quadrupolar deformation length, therein predicted to be much smaller for the odd isotope.

2 Experimental Procedure

Data for the ⁹⁹Ru(d, d') and ¹⁰¹Ru(d, d') reactions at 13 MeV were obtained in the Pelletron Laboratory, with the beam trimmed to produce a conveniently small object on the ⁹⁹Ru and ¹⁰¹Ru targets (97% enriched).

The products of each reaction were momentum analysed by the Enge split-pole spectrograph and detected in nuclear emulsion plates, positioned on the focal plane of the spectrograph. Thirteen and sixteen inelastic scattering spectra, respectivily for ⁹⁹Ru and ¹⁰¹Ru, with an energy resolution between 6 keV and 12 keV, were measured in the angular range of 16.5^°< q_lab < 64^°. The use of nuclear emulsion and the good energy resolution of the experimental facilities were essential to achieve the aims of this study. Fig. 1 displays part of one spectrum for each reaction.

Through the comparison of the elastic scattering experimental angular distribution (taken at five angles between 30^° and 70^° for each target) with optical model predictions, the normalization of the data was obtained.

3 Analysis

In the analysis, three states were identified and associated, respectively, with adopted levels in the Nuclear Data Sheets Compilation [4, 5] of J^p = 5/2⁺, 7/2⁺ and 9/2⁺. The parameters C and have been extracted in the characterization of the coulomb-nuclear interference. These states, excited by inelastic scattering from the 5/2⁺ G.S. of ⁹⁹Ru and ¹⁰¹Ru, could be members of the multiplet built on the first quadrupolar excitation of the core coupled to the d_5/2 particle.

The analyses of the multiplet states associated with the first quadrupolar excitation in ^99,101Ru were done through the comparison of the experimental angular distributions with DWBA-DOMP predictions employing the DWUCK4 [6] code and the global deuteron optical potential parameters of Perey & Perey [7], with the usual correction for nonlocality effects. The relation between the experimental results and the DWBA-DOMP description of the cross section is written as:

s^exp(q) = a²(q, C),

with C = / = / and proportional to a, where () and () are the charge and mass deformation lengths, respectively. The usual deformation length parameter is related to through:

where J_i and J_f are the spins of the initial and final states.

The fits of the experimental angular distributions are performed by a c² minimization procedure, using the iterative method of Gauss [8], since C and are correlated.

4 Results and Comments

Figure 2 shows the predicted angular distributions, fitted to the experimental data, as well as two other curves, with a variation around the fitted C value. The sensibility of the method is, thus, illustrated.

The results obtained for the more strongly excited 7/2⁺ and 9/2⁺ states are compared with information given in the literature for some of the even nuclei in the chain of Ru, as shown in Table I. The less intense 5/2⁺ excitations are still under analysis and upper limits for the other states which could belong to the multiplet [3] are also being investigated.

Table I

The one particle-rotor model calculations [3], had to resort to a deformation length reduced by about a factor of two with respect to the even neighbour. The 7/2⁺ and 9/2⁺ states in ⁹⁹Ru and 7/2⁺ in ¹⁰¹Ru seem to follow the usual statistical (2J_f + 1) factor in the excitation of the multiplets, but the 9/2⁺ excitation in ¹⁰¹Ru is appreciably weaker than would be predicted by a simple weak coupling model. In fact, as shown in Fig.1, the intensity of this state is fragmented to another 9/2⁺ state of ¹⁰¹Ru, at 928.77(5) keV.

Also shown in Table I are preliminary results associated with this second 9/2⁺ state detected in ¹⁰¹Ru. The sum of the deformation lengths for both 9/2⁺ states reaches the same value, considering the uncertainties, of the deformation length extracted for the 7/2⁺. In the last column of the table the correspondent parameters using the reduced mass radius of 1.16 fm are indicated for a easier comparison with information of the literature for other nuclei.

Acknowledgments

This work was partially supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP).

Received on 9 September, 2003

• [1] L. C. Gomes et al., Phys. Rev. C54, 2296 (1996).
• [2] G. M. Ukita, T. Borello-Lewin, L. B. Horodynski-Matsushigue, J. L. M. Duarte, and L. C. Gomes, Phys. Rev. C64, 014316 (2001).
• [3] C. S. Whisnant et al, Phys. Rev. C34, 443 (1986).
• [4] B. Singh, Nuclear Data Sheets, 81, 1 (1997).
• [5] J. Blachot, Nuclear Data Sheets, 83, 1 (1998).
• [6] P. D. Kunz, computer code DWUCK4, University of Colorado, 1974.
• [7] C. M. Perey and F. G. Perey, At. Data and Nucl. Data Tables 17, 1 (1976).
• [8] V. R. Vanin, P. Gouffon, Tópicos Avançados em Tratamento Estatístico de Dados em Física Experimental, LAL-IFUSP (1996).

Publication Dates

• Publication in this collection
  26 Oct 2004
• Date of issue
  Sept 2004

History

• Received
  09 Sept 2003