Isospin character of the first quadrupole transition in the A~100 region

Transcription

1 Isospin character of the first quadrupole transition in the A~100 region Cleber Lima Rodrigues 1, Márcia Regina Dias Rodrigues 1, Thereza Borello-Lewin 1, Lighia B. Horodynski-Matsushigue 1, José Luciano Miranda Duarte 1 and Gilberto Mitsuo Ukita. 1 Instituto de Física, Universidade de São Paulo (IFUSP), São Paulo, Brazil Faculdade de Psicologia, Universidade de Santo Amaro, São Paulo, Brazil Abstract Angular distributions for the inelastic scattering of 13 MeV deuterons were obtained for states of 99, Ru at low excitation energies at the São Paulo Pelletron Accelerator Enge Magnetic Spectrograph facility. The excellent resolution of ~ 8 kev achieved was important for the good definition of the minimum of the Coulomb-uclear Interference (CI) in the angular distribution. This, in turn, permitted the characterization of the parentage of the states in the odd nuclei with respect to the first quadrupole excitations of the cores through a macroscopic analysis. The analysis employs the Distorted Wave Born Approximation formalism, taking the Deformed Optical Model as transition potential, under well established global optical parameters. Values of the mass deformation length and the ratio between charge and L mass deformation lengths C were extracted by fitting the predictions to the experimental angular distributions. The values of C are larger than 1. in 99 Ru and 1.3 in Ru, indicating a decrease as a neutron pair is added, of the contribution of the neutrons relative to that of the protons, in the first quadrupole excitation in the odd isotopes, when compared to that previously measured in the even ones. I - Introduction Through the selection of a hadronic projectile at a convenient bombarding energy, with respect to the Coulomb barrier of the mass region under study, it is possible to gather simultaneously information on the response of the nuclear system under both, the nuclear and electromagnetic interactions. The São Paulo uclear Spectroscopy with Light Ions Group has developed a method for a systematic analysis of the Coulomb-uclear Interference (CI) (1) in the inelastic scattering of projectiles which interact isoscalarly with the nuclei under study. This method is suitable for obtaining reliable information, especially for a comparative evaluation, of the relative contributions of protons and neutrons to the first quadrupole excitation, an excellent structure indicator. The A ~ 100 mass region, where the important role played by the neutrons is recognized, constitutes an interesting field of investigation, since the usual assumption of dominance of simple collective effects is certainly not warranted. In this region, alpha particles and, in particular, deuterons were taken as convenient isoscalar projectiles, considering the bombarding energies suitable for the operation of the S. Paulo Pelletron accelerator. The inelastic scattering is described through the Distorted Wave Born Approximation (DWBA) formalism and the nuclear transition potential is treated as given by the deformed optical model potential (DOMP). To maintain free parameters under control, it is of utmost importance to choose global optical potential parameters. Through this macroscopic CI analysis, the square of

2 the mass deformation length, ( ) L, is extracted as a scale factor from the fit of the predicted cross sections to the experimental data and, analyzing the characteristic changes in the angular C distribution shape, the value of the ratio between charge ( ) and mass ( ) L deformation lengths, C L, is also obtained. These quantities can be put into correspondence with the value of the reduced isoscalar transition probability B(ISL) and with the ratio B(EL)/B(ISL), respectively. Focusing on the chain of even Ru isotopes, the CI was formerly investigated through excitation function data with the aim of assessing the collectivity of the first quadrupole excitation in the 100,10,104 Ru nuclei (). The values of C C / = indicate a decrease of the effective contribution of the neutrons, when compared to the protons, when one and two pairs of neutrons are added to 100 Ru, this latter isotope being characterized by a C of approximately one. On the other hand, agreement with the results of Coulomb excitation studies was obtained for the C values. The interest in investigating the evolution of the collectivity also in the odd Ru isotopes was reinforced by the experimental diagnosis of a possible shape coexistence at low energies (3) and by problems in the theoretical description of these nuclei (4-6). One of the intrinsic difficulties of inelastic scattering studies in odd-even nuclei is the dilution of the collective degrees of freedom of the nuclear system among many states. Therefore, the total transition probability associated with the low energy excitations, with given multipolarity L of interest, which is normally concentrated in one or a few states in the even-even nuclei, is fractioned into L+1, or more, states in the neighboring odd-even nuclei. In the analysis, the collectivity of these states is taken as associated with the excitation of the corresponding core states, the clear predominance of the correct value of the angular momentum transfer, L, being the criterion to be employed. The present contribution refers to CI measurements with deuterons on 99, Ru, the only odd stable isotopes in the Ru chain. II - Experimental Procedure Deuterons of 13 MeV from the Pelletron accelerator in S. Paulo were focused, after passing defining slits, on targets of 99, Ru and inelastic scattering angular distributions were measured with the Enge Spectrograph facility using emulsion plates (Fuji G6B - 50µm thick), covering 5cm along the focal surface. The targets produced by the electron bombardment method were both isotopically enriched to 97.5%, with thicknesses of ~10µg/cm. After processing, the emulsion plates were scanned, in strips of 00µm, and position spectra associated with respectively fourteen and sixteen scattering angles were obtained for 99 Ru and Ru. An excellent energy resolution of ~8 kev was achieved and a good characterization of the interference minimum in the angular distributions corresponding to the first quadrupole excitation of the cores was obtained. Fig. 1 displays two examples of complete spectra of inelastic deuteron scattering on 99 Ru, at θ lab = 9, and on Ru, at θ lab = 7. Indicated are the peaks corresponding to the 5/ +, 7/ + and 9/ + states, associated with the first quadrupole excitation of the cores, identified according to the DS compilation (7, 8). The here obtained excitation energies are in excellent L

3 (7, 8) agreement with the adopted excitation energy values. Some contaminant peaks are also indicated. The predicted 1/ + and 3/ + states, expected to be weakly populated, were not observed. counts / 0. x 10 mm C 7/ + 5/ + 9/ + 8 Si ( + ) 99 = 9º 3 S ( + ) counts / 0. x 10 mm C 7/ + 5/ + 9/ + 1 9/ + = 7º 8 Si ( + ) 3 S ( + ) distance along the focal plane L(cm) Figure 1 Spectra of inelastic scattered deuterons for 99 Ru and Ru, at θ lab =9º and θ lab =7º, respectively. The peaks corresponding to the 5/ +, 7/ + and 9/ + states, associated with the first quadrupole excitation of the cores [7,8], are indicated. Also indicated are some contaminant peaks. Shown in Fig. are portions of interest of the inelastic spectra, at laboratory scattering angles of 1 and 45, for 99 Ru, and 1 and 57, for Ru, illustrating that the good energy resolution is essential to enhance the peaks with respect to the background. Relative normalization of the spectra was obtained by considering the total number of incident deuterons determined by a current integrator, which measured the charge collected in a Faraday cup, with electron suppression, while the direction of the beam was continuously monitored. Elastic scattering spectra were measured under similar conditions, on the same targets for each isotope, at laboratory scattering angles in the range of 30 θ lab 70. The absolute normalization of the cross sections was thus obtained by referring these data to optical model predictions for the elastic scattering. The scale uncertainty is estimated as 5% for both isotopes.

4 10 3 9/ + 5/ + 7/ / + + 9/ 1 + 9/ 5/ + counts / 0. x 10 mm = 13 MeV = 1º counts / 0. x 10 mm 10 = 13 MeV = 1º counts / 0. x 10 mm a 9/ + 7/ + 99 = 13 MeV = 45º 5/ + 16 O counts / 0. x 10 mm S 7/ + 8 Si = 13 MeV = 57º 9/ 1 + 9/ L(cm) L(cm) Figure Portion of interest of inelastic spectra at θ lab =1º and θ lab =45º, for 99 Ru, and θ lab =1º and θ lab =57º, for Ru (see Figure 1). III Analysis For convenience, two parameters are chosen to characterize the collectivity of the first quadrupole excitation starting from a O + G.S.. When the excitation occurs starting from the G.S. of an odd-even nucleus, the predominance of a single value of L, in particular L =, is indicative of the fact that the parentage with the quadrupole excitation of the core is not disrupted by the coupling to the extra particle. In this case, the CI analysis of the experimental angular distribution, ' also results in the extraction of two parameters: ( ) C ' C ' C ( J + 1) 1/ ( ) f = and, ( J i + 1)( L + 1) = = where J i and J f are the spins of initial and final states, respectively. It is to be noted ' 'C that the definitions of and take care of the expected splitting in a weak-coupling situation ' ' C C and that for an even-even nucleus = and =. The reduced isoscalar transition probability B(IS) is related to ' through the 3ZRm ' expression: ( IS ) = ( ) B, 4π

5 where the scaling through Z, as proposed by Bernstein et al (9) is considered in the definition. This definition implies that the summed B(IS) values of the expected multiplet equals that of the core state. Furthermore, from the value of C it is possible to calculate the ratio: ( E) ( IS) B rc = e C B rm where r c and r m are, respectively, the characteristic reduced radii of the charge and the mass distributions of the nucleus. If a simple weak coupling situation should prevail this ratio should be equal to that verified for the neighboring even-even nucleus. The states 5/ + (575.89(11) KeV), 7/ + (617.6(13) KeV) and 9/ + (719.85(1) KeV) of 99 Ru (7) and 5/ + (616.30(10) KeV), 7/ + + ( (7) KeV), 9/ 1 (70.0(5) KeV) and 9/ + (98.77(5) KeV) of Ru (8) were identified as possible members of the multiplet which results from the weak coupling of the first quadrupole core excitation to the d 5/ particle. The perfect agreement of the excitation energies measured in the present experiment, with those attributed by the DS compilation (7, 8) was considered in the identification. Fig. 3 presents the corresponding experimental angular distributions and the DWBA-DOMP predictions adjusted to the data through χ minimization, by the iterative Gauss-Marquardt method. The global deuteron optical potential parameters of Perey & Perey (10) were employed for both, generating the distorted waves in the DWBA, and giving the DOMP transition potential. Also indicated in the figure are the correlated parameters C and obtained from the extracted '. The uncertainties presented in the Fig. 3 are only the random ones, however, the absolute scale of the cross sections does not affect the value of C. Two other curves, for each experimental angular distribution, corresponding to values of C around the value of best fit illustrate visually the sensibility of the method. In order to evaluate the adequacy of the method employed to extract the two correlated parameters C and, and their respective random uncertainties, a direct statistical test was performed through a simulation of 5,000 new data sets. Each new data set was generated, starting from the measured data set, by randomly choosing, from Gaussian distribution with the given standard deviation, new values around each experimental point. So, the best fit to each new data set was determined, resulting in the extraction of the respective C and. Comparing the best fit of each new data set with the original data, a χ value was also determined. Two different views of the thus obtained χ surface of 5,000 Monte Carlo simulated results for the 99 Ru 5/ + state are seen in Fig. 4, in correspondence with the associated parameters and C. The χ contour lines obtained for the 68.3% and 95.3% confidence levels, employing the same procedure for all detected states are almost perfect ellipses for both isotopes in very good agreement with the outcomes of the Gauss-Marquardt approximation.

6 99 5/ + E exc = (11) kev 5/ + E exc = (10) kev C = χ = 3.9 C = 1.47(9) - = 0.53(3) fm - χ =.4 C = χ = 9.9 C = χ = 17.7 C = 1.48(11) - = 0.45(3) fm - χ = 8.7 C = χ = 15.8 dσ/dω (fm /sr) dσ/dω (fm /sr) / + E exc = (13) kev 7/ + E exc = (7) kev C = χ = 6. C = 1.5(4) - = 0.91() fm - χ = 17.0 C = χ = 45.1 C = 1.36(3) - = 1.01() fm - χ = 36.0 C = χ = 5.7 C = χ = 44.9 dσ/dω (fm /sr) dσ/dω (fm /sr) Figure 3 Experimental angular distributions and best fit (minimum χ ) DWBA-DOMP predictions. Also presented for each angular distribution are the parameters C and extracted from the fit and two curves corresponding to values of C around the best fit value.

7 99 9/ + E exc = (1) kev 9/ + E exc = 70.0(5) kev C = χ = 3.3 C = 1.6(4) - = 1.01(3) fm - χ = 14.1 C = χ =.7 C = χ = 3.4 C = 1.43(6) - = 0.73() fm - χ = 14.0 C = χ =.1 dσ/dω (fm /sr) dσ/dω (fm /sr) / + E exc = 98.77(5) kev C = χ =.5 C = 1.61(9) - = 0.37() fm - χ = 1.1 C = χ = 19.5 dσ/dω (fm /sr) Figure 3 (continuation) Experimental angular distributions and best fit (minimum χ ) DWBA- DOMP predictions. Also presented for each angular distribution are the parameters C and extracted from the fit and two curves corresponding to values of C around the best fit value.

8 99 Ru(d,d ) 99 Ru 5/ + E d = 13.0 MeV χ C χ Figure 4 Views of the χ surface of 5,000 Monte Carlo simulated results for the 5/ + state of 99 Ru, in correspondence with the respective parameters and C. C

9 IV Comments and results The Ru chain, as already mentioned, is an interesting testing ground for an experimental assessment of the B(E)/B(IS) ratio. In the CI method a direct extraction of this ratio is achieved, favoring more accurate results, since a cancellation of the scale uncertainties occurs. The values of B(IS) and B(E)/B(IS) obtained in the present work for the low lying states associated with the first quadrupole excitation in 99 Ru and in Ru are shown in Table I. Also shown, are the corresponding values in the neighboring nuclei 100 Ru and 10 Ru, calculated from the measurements of Gomes et al () and the respective excitation energies adopted by the DS compilation (11, 1). ucleus J π E X (kev) B(IS) (b ) B(E)/B(IS) (e ) 5/ + a (11) a ().4 (3) 99 Ru 7/ + a (13) a (5) 1.74 (11) 9/ + a (1) a (9) 1.67 (1) 100 Ru (5) b 0.39 () c 1.0 (7) c 7/ + d (7) d (5).04 (10) 5/ + d (10) d (16).4 (4) Ru 9/ + 1 d 70.0 (5) d (5). () 9/ + d (5) d (15).9 (3) 10 Ru (4) e 0.40 () c 1.44 (8) c Table 1: Values of B(IS) and B(E)/B(IS) for states identified by the respective spin and parity J π and excitation energy E X, adopted by the DS. a) ref. 7; b) ref. 11; c) ref. ; d) ref. 8; e) ref. 1; r c = 1. fm and r m = 1.16 fm were used Although the predominance of L= in the excitation of the referred states in the odd nuclei was revealed by the measurements, indicating that the parentage to the first quadrupole excitation is not disrupted, the ratios B(E)/B(IS) for 99 Ru and Ru are far from ~1e. This value is predicted by the homogeneous collective model, considering a weak coupling of the extra particle to the core. As can be appreciated in Table I, the values obtained for both odd nuclei are + larger than the corresponding ones for the 1 excitation of the neighboring even nuclei, extracted from the results of Gomes et al. (). The intensity of the B(IS) associated with the states which where identified as members of the multiplet in each odd nucleus is hindered, specially for the 5/ + state, in comparison with the predictions are obtained starting from the isoscalar transition probability of the even neighbor (), considering the respective statistical weights. It is to be noted, however, that the appointed hindrance does not support quantitatively the findings of the one particle - rotor model calculations (4), that had to resort to a deformation length reduced by about a factor of two with respect to the even neighbor.

10 Acknowledgments This work was partially supported by Fundação do Amparo à Pesquisa do Estado de São Paulo (FAPESP) References [1] J.L.M. Duarte, G.M. Ukita, T. Borello-Lewin, L.B. Horodynski-Matsushigue and L.C. Gomes, Phys. Rev. C56, 1855 (1997). [] L. C. Gomes et al., Phys. Rev. C54, 96 (1996). [3] T. Borello-Lewin, J. L. M. Duarte, L. B. Horodynski-Matsushigue and M. D. L. Barbosa, Phys. Rev. C57, 967 (1998). [4] C.S. Whisnant, K.D. Carnes, R.H. Castain, F. A. Rickey, G.S. Samudra, e P.C. Simms, Phys. Rev. C34, 443 (1986). [5] J. M. Arias, C. E. Alonso, and M. Lozano, ucl. Phys. A466, 95 (1987). [6] A. Maino, A. Ventura, A. M. Bizzeti-Sona, and P. Blasi, Z.,Phys. A340, 41 (1991). [7] L. K. Peker, uclear Data Sheets Update for A = 99, uclear Data Sheets 73, 1 (1994). [8] J. Blachot, uclear Data Sheets for A =, uclear Data Sheets 83, 1 (1998). [9] A. M. Bernstein, Adv. ucl. Phys. 3, 35 (1969). [10] C. M. Perey and F. G. Perey, At. Data and ucl. Data Tables 17, 1 (1976). [11] B. Singh, uclear Data Sheets for A = 100, uclear Data Sheets, 81, 1 (1997). [1] D. de Frenne and E. Jacobs, uclear Data Sheets for A = 10, uclear Data Sheets 83, 535 (1998).