The shears mechanism in the lead isotopes

Transcription

1 19 November 1998 Physics Letters B The shears mechanism in the lead isotopes R.M. Clark a, R. Krucken a,1, S.J. Asztalos a, J.A. Becker b, B. Busse a, S. Chmel c, M.A. Deleplanque a, R.M. Diamond a, P. Fallon a, D. Jenkins d, K. Hauschild b, I.M. Hibbert d, H. Hubel c, I.Y. Lee a, A.O. Macchiavelli a, R.W. MacLeod a, G. Schmid a, F.S. Stephens a, U.J. van Severen c, K. Vetter a, R. Wadsworth d, S. Wan e a Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA b Lawrence LiÕermore National Laboratory, LiÕermore, CA 94550, USA c Institut fur Strahlen- und Kernphysik, UniÕersitat Bonn, D Bonn, Germany d Department of Physics, UniÕersity of York, Heslington, York YO1 5DD, UK e Gesellschaft fur Schwerionenforschung mbh, D Darmstadt, Germany Received 20 July 1998 Editor: J.P. Schiffer Abstract Lifetimes of states in at least one of the M1 bands in each nucleus from 193y Pb have been determined through Doppler-Shift Attenuation Method experiments performed with the Gammasphere array. The nuclei were populated under similar conditions allowing accurate relative measurements of the state lifetimes. The deduced BŽ M1. values display the characteristic decrease with increasing angular momentum which is a clear signature of the shears mechanism. Combined with the recent results for 198,199 Pb an impressive body of evidence now exists which supports the interpretation of these structures as examples of a new mode of nuclear behavior: magnetic rotation. q 1998 Published by Elsevier Science B.V. All rights reserved. PACS: Lv; Tg; qw Sequences of magnetic dipole Ž M1. g-ray transitions have been observed in the neutron-deficient Pb w1,2x nuclei. The structures are thought to be built on high-j proton excitations Žinvolving the i13r2 and h orbitals which couple to give an angular mo- 9r2 1 Present address: W.A. Wright Nuclear Structure Laboratory, Physics Department, Yale University, P.O. Box , New Haven, CT mentum which can be represented by a vector, j p. combined with i neutron holes Ž 13r2 which couple to j. n. The proton particles and the neutron holes cou- ple to maximize the wavefunction overlap at the bandhead, such that jp and jn are essentially perpen- dicular to each other. This coupling has been recently confirmed in an experiment that measured the 193 g-factor of the bandhead of an M1 band in Pb wx 3. The total angular momentum vector, J, then lies between j and j. Calculations using the Tiltedp n r98r$ - see front matter q 1998 Published by Elsevier Science B.V. All rights reserved. PII: S

2 252 ( ) R.M. Clark et al.rphysics Letters B Axis-Cranking Ž TAC. model wx 4 predict that higher angular momentum states are generated by aligning the two spin vectors along the direction of J in a way that resembles the closing of the blades of a pair of shears; hence, the name shears bands wx 2. However, both TAC w2,4x and standard cranking wx 1 calculations were able to reproduce the general behavior of the experimental routhians, angular momenta, and moments of inertia of these bands. A definitive way to differentiate between the calculations is offered by the behavior of the BŽ M1. s. The coupling of proton particles and neutron holes as described above results in a large magnetic dipole moment Ž m.. If the shears mechanism is generating the in-band states then the perpendicular component Ž m. H of the magnetic dipole moment decreases in a characteristic manner as j and j align. The BŽ M1. p n, which is proportional to m 2 H, should then decrease sharply in a similar way. In standard cranking model approaches, such as the Donau and Frauendorf formalism wx 5, which assumes a fixed K value and that the alignment is perpendicular to the symmetry axis Ž i.e., no shears mechanism., such a rapid decrease in the BŽ M1. values is not possible. Recent Doppler- Shift Attenuation Method Ž DSAM. lifetime measurements provide clear evidence that the M1 bands in 198,199 Pb can only be explained in terms of the shears mechanism wx 6. The states in these shears bands generally follow a rotational-like behavior with the energies following the pattern of DE IsE I EI b ;A I I b 2, where I is the spin of the state and I b is the spin of the bandhead. However, the measured mixing ratios and lifetimes indicate that they are based on weakly deformed oblate shapes Ž< e < F Why then do such weakly deformed structures have such striking rotational-like properties? A new form of nuclear rotation known as magnetic rotation wx 7 has been suggested as a possible explanation. Unlike the familiar notion of nuclear rotation, arising when an intrinsic deformation breaks the spherical symmetry, it is the anisotropic arrangement of nucleon currents Ž from which the blades of the shears also arise. internal to the nucleus that is responsible for the symmetry breaking. Another, possibly related, explanation has been suggested in terms of a residual interaction between the proton and neutron spin vecwx tors 8 arising from a particle vibration coupling wx 9. It is of great interest to further investigate the origin of these structures. We have performed a series of experiments to investigate the systematic behavior of the M1 bands across the Pb isotopes from 193 Pb to Pb. Lifetimes of states in at least one previously observed band in Pb w10,11 x, Pb w12,13 x, Pb w14 x, Pb w15 18 x, and Pb w19 22x have been measured and BŽ M1. values deduced. Combined with the previous 198,199 DSAM lifetime measurements in Pb wx 6, and the results of a recent Recoil Distance Doppler Shift Ž RDDS. experiment which measured lifetimes of 198 low-lying states in one of the bands in Pb w23 x, the results presented in this Letter represent an impressive body of work in support of the shears mechanism and the concept of magnetic rotation. High-spin states in 193y Pb were populated using beams of 26 Mg at energies of 139, 137, and 135 MeV incident on targets of 172 Yb, 174 Yb and 176 Yb, respectively. At the chosen bombarding energies the population of the fusion-evaporation residues was evenly divided between the 5n and 6n reaction chan- 172 Ž 26. nels, with the exception of the Yb Mg reaction which strongly favored the population of 193 Pb via the 5n channel. The beams were accelerated by the 88-Inch Cyclotron of the Lawrence Berkeley National Laboratory. The targets comprised, mgrcm Yb enrichment ) 95% on 12 mgrcm Pb backings which slowed down and stopped the recoils. Gamma rays were detected with the Gamma- sphere array w24 x, which for this experiment consisted of 97 large-volume Ž, 75% efficiency. Compton-suppressed Ge detectors situated at the following angles relative to the direction of the beam: 5 at 17.38, 5 at 31.78, 5 at 37.48, 10 at 50.18, 5 at 58.38, 8 at 69.88, 3 at 79.28, 3 at 80.78, 7 at 90.08, 4 at 99.38, 5 at , 7 at , 5 at , 10 at , 5 at , 5 at , and 5 at A total of,9=10 8 events with a coincidence fold of four or higher were collected for each reaction. The data were sorted into gated, angle-dependent spectra and E g Eg correlation matrices. Level life- times were extracted by the analysis of observed Doppler-broadened lineshapes using the codes of Wells and Johnson w25 x. The complete stopping was modeled using the prescription discussed in detail by Gascon et al. w26 x. The tabulations of Northcliffe and Schilling w27x with shell corrections were used for

3 ( ) R.M. Clark et al.rphysics Letters B the electronic stopping powers. The detailed slowing-down history of the recoils in the target and backing material was simulated using a Monte Carlo technique Ž5000 histories with a time step of ps. and then sorted according to detector geometry. Calculated lineshapes for each transition were obtained assuming: 1. feeding into the top of the band through a cascade of five transitions with the same moment of inertia as the in-band states. The topmost lineshape was fitted and the extracted depopulation time was used as an input parameter to extract lifetimes of states lower in the cascade. 2. Side-feeding into each state assuming initially a rotational cascade of five transitions. The intensity of the sidefeeding was constrained to reproduce that observed experimentally Ž see Table 1.. The side-feeding lifetimes were always found to be faster than the in-band lifetimes Ž generally, up to 2 times faster.; the sensitivity of the fits due to side-feeding variations diminished for the states lower in the cascades these observations are in agreement with the behavior of the side-feeding as reported in Ref. wx 6. Simultaneous fits to forward, backward, and transverse spectra were performed. Final results were obtained from a global fit of the cascade with independently variable lifetimes for each state and the associated side-feeding. As a representative example of the quality of the data, Fig. 1. presents the experimental spectra, along with calculated fits, for a range of lineshapes for an M1 band in Pb. We obtained lifetimes of states in one band of 193 Pb, 194 Pb, 195 Pb, and 196 Pb, and in two bands of Pb. Other M1-bands are known in some of the nuclei, but we were unable to extract reliable results for them either because of poor statistics or because of large contaminations of the resulting spectra. The results are presented in Table 1. The quoted errors reflect the behavior of the x 2 value in the vicinity of the best fit as the free parameters are varied, including the effect of side-feeding. The errors do not include the systematic errors introduced through the treatment of the stopping powers, and these may be as large as "20%. Comparisons of the relative behavior of the BŽ M1. values for the different bands should not be subject to this systematic error since the experimental conditions used to populate the bands, and the energy range of the transitions for which lifetimes were extracted, are very similar. The Table 1 Measured lifetimes of states in the bands, t Ž ps., and reduced transition strengths, BŽ M1. Žm 2. N. ISF is the percentage of sidefeeding into each state. The errors on the BŽ M1. values were estimated from the standard Ž linear. transformation of the errors on the values of t. Note, systematic errors introduced through the treatment of the stopping powers are not included. The suggested configurations of each of the bands is also given. A, B, C, D denote i13r2 quasineutrons, E, F the natural parity quasineutrons, and the proton configuration is denoted by its aligned spin. E I I t BM1 g i SF Ž 2 kev % ps m N. 193 q0.04 q0.64 Pb r y y0.64 q0.04 q0.56 ABE r y y0.75 q0.04 q r y y0.76 q0.03 q r y y q0.04 q2.55 Pb y y1.70 q0.02 q0.56 AB y y0.56 q0.05 q y y1.43 q0.04 q y y q0.05 q2.00 Pb r y y1.25 q0.03 q0.88 ABC r y y0.88 q0.03 q r y y q0.03 q2.01 Pb y y1.51 q0.03 q1.66 ABCE y y1.24 q0.03 q y y1.06 q0.03 q y y1.04 q0.04 q y y0.58 q0.02 q0.23 Pb a r y y0.23 q0.03 q0.31 ABC r y y0.47 q0.02 q r y y0.83 q0.02 q r y0.01 y0.75 q0.03 q1.27 Pb b r y y1.27 q0.03 q0.90 ABE r y y1.36 q0.02 q r y y0.47 q0.05 q r y y0.34 transitions were assumed to be of pure M1 character. Note, the M1 branching ratios ŽB s I rw g M 1 I M 1q I x. E2 were assumed to be 1.0, since the crossover E2 transitions have not been observed in many cases. However, it is reasonable to expect that BgG 0.9 over the range of the observed transitions. Fig. 2. presents plots of the BŽ M1. values as functions of transition energy for all of the bands in the Pb isotopes for which lifetimes have been mea- sured Žexcept Pb a which will be discussed later..

4 254 ( ) R.M. Clark et al.rphysics Letters B Fig. 1. Experimental data and fitted lineshapes for the 404, 446, and 467 kev transitions of Pb b. The spectra were formed from a combination of all clean gates on transitions lower in the cascade. The rows are labeled by the angles at which the detectors were situated. 193y199 Fig. 2. Plots of BŽ M1. versus transition energy, E g, for bands in Pb for which lifetimes of states have been determined. The solid lines represent the results of TAC calculations for the suggested configurations of the bands. A, B, C, D denote i13r2 quasineutrons, E, F the natural parity quasineutrons, and the proton configuration is denoted by its aligned spin.

5 ( ) R.M. Clark et al.rphysics Letters B Included are the previous DSAM results on 198,199 Pb 198 wx 6 and the new RDDS results for a band in Pb w23 x. For comparison, absolute BŽ M1. values calculated using the TAC model are also shown for possible configurations in the odd and even mass Pb isotopes following the nomenclature in Ref. w28 x. These calculations were performed for 198,199 Pb with the deformation kept constant, close to the equilibrium value for "vs0.3 MeV. Neutron-pairing effects are included while proton pairing is ignored due to the proximity of the large Zs82 spherical shell gap. We investigated the influence of changing the mass number for the calculated BŽ M1. s and found that the differences were quite small Žof the same magnitude as the experimental errors. over the full range of frequency for similar configurations in the different nuclei. This indicates that the effect of changes in the core is small. It is clear that the experimental values are in excellent agreement with the TAC calculations. The BŽ M1. values show the sharp decrease with increasing angular momentum that is the clear signature of the shears mechanism. We should emphasize the fact that this behavior can not be reproduced in a standard cranking model. Fig. 2. might suggest that there is a general trend in which the slope of the decrease of the experimental BŽ M1. s is somewhat greater than that of the predictions. It has also been found that reasonable alterations in the parameters of the TAC calculations Žsuch as varying the strength of the quadrupole quadrupole Ž Q.Q. coupling constant. can yield a sharper decrease in the calculated BŽ M1. values w29 x. A general comment is that the TAC model requires a deformed mean-field while the shears bands in the Pb nuclei are based on very weakly deformed shapes. One of the primary motivations of this work is to provide accurate data against which the current models can be tested. Alternative approaches such as the particle phonon coupling picture as suggested in Ref. wx 9, which allows the shears mechanism in spherical nuclei, may reproduce the results more closely. There is a need for more detailed calculations from the different theoretical approaches. We now examine the behavior of the BŽ M1. s for Pb a. These are plotted as a function of transition energy in Fig. 3a.. Instead of a smooth decrease, the BŽ M1. s show a sharp jump. The possible explana- Fig. 3. a. Plot of BŽ M1. versus transition energy for Pb a. b. Plot of angular momentum, I, versus transition energy, E g, for Pb a. At the lowest frequencies the configuration of the band is thought to be A11. Above the large backbend the configuration is ABC11, while above the upbend it is ABCEF11. tion of this behavior becomes clear when one examines a plot of angular momentum, I, as a function of transition energy, E, as shown in Fig. 3b. g. The data points overlap an up-bend, which corresponds to an alignment process involving a pair of natural parity quasineutrons w22 x. In terms of the shears mechanism, an additional contribution lengthens the vector j n ; thus, by increasing the angle between each other, jp and jn can reorient to a lower energy configura- tion with the same total spin, J. Above the alignment, the shears mechanism continues as before. Unfortunately, the BŽ M1. s that we have deduced do not extend around the frequency of the alignment making it difficult for a quantitative comparison. Moreover, the spin increase from the aligning pair of quasineutrons is small and the alignment process is completed over 2 3 states. However, it is clear from Fig. 3b. that lower in this band there is a very large alignment process over many states giving a backbend in the I Eg plot. This is thought to be from the alignment of a pair of i quasineutrons w22 x 13r2. It would be very interesting to deduce BŽ M1. s over the range of this alignment process, as such results would provide a stringent test of calculations.

6 256 ( ) R.M. Clark et al.rphysics Letters B To summarize, we have determined the lifetimes of states in M1-bands of 193y Pb through the fitting of Doppler-broadened lineshapes. The deduced BŽ M1. s generally show a decrease with increasing angular momentum. Together with the previous results of lifetime measurements for states in the M1- bands in 198,199 Pb, the data represent an impressive body of work in support of the shears mechanism and the underlying concept of magnetic rotation. Acknowledgements We would like to express our gratitude to Dr. John Wells for providing the lineshape analysis package, and to the crew and staff of the 88-Inch Cyclotron for excellent operation. Thanks to Joanne Heagney of Micromatter Co. for manufacture of the high-quality targets. This work has been supported in part by the US DoE under Contract Nos. DE AC03 76SF00098 Ž LBNL. and W 7405 ENG 48 Ž LLNL.. Funding from the U.K. came from the EPSRC. The work of the Bonn group was supported by BMBF Germany and NATO. References wx 1 R.M. Clark et al., Nucl. Phys. A 562 Ž , and references therein. wx 2 G. Baldsiefen et al., Nucl. Phys. A 574 Ž , and references therein. wx 3 S. Chmel et al., Phys. Rev. Lett. 79 Ž wx 4 S. Frauendorf, Nucl. Phys. A 557 Ž c. wx 5 F. Donau, S. Frauendorf, in: Proceedings of the International Conference on High Angular Momentum Properties of Nuclei, Oak Ridge, 1982, Nucl. Sci. Res. Conf. Series, Vol. 4 Harwood, New York, 1983, p wx 6 R.M. Clark et al., Phys. Rev. Lett. 78 Ž wx 7 S. Frauendorf, in: Proceedings of the Conference on Physics from Large Gamma-Ray Detector Arrays, Berkeley, 1994, Report No. LBL-35687, Vol. 2, p. 52. wx 8 A.O. Macchiavelli et al., Phys. Rev. C 57 Ž R1073. wx 9 A.O. Macchiavelli et al., accepted Phys. Rev. C. w10x G. Baldsiefen et al., Phys. Rev. C 54 Ž w11x L. Ducroux et al., Z. Phys. A 356 Ž w12x D. Mehta et al., Z. Phys. A 346 Ž w13x M.-G. Porquet et al., J. Phys. G 20 Ž w14x M. Kaci et al., Z. Phys. A 354 Ž w15x P.J. Dagnall et al., J. Phys. G 19 Ž w16x J.R. Hughes et al., Phys. Rev. C 47 Ž R1337. w17x E.F. Moore et al., Phys. Rev. C 51 Ž w18x G. Baldsiefen et al., Z. Phys. A 355 Ž w19x R.M. Clark et al., Z. Phys. A 342 Ž w20x A. Kuhnert et al., Phys. Rev. C 46 Ž w21x J.R. Hughes et al., Phys. Rev. C 48 Ž R2135. w22x G. Baldsiefen et al., Nucl. Phys. A 587 Ž w23x R. Krucken et al., to be published. w24x I.Y. Lee, Nucl. Phys. A 520 Ž c. w25x J.C. Wells, N. Johnson Ž private communication.. Modified from the original code by J.C. Bacelar. w26x J. Gascon et al., Nucl. Phys. A 513 Ž w27x L.C. Northcliffe, R.F. Schilling, Nucl. Data Tables 7 Ž w28x M. Neffgen et al., Nucl. Phys. A 595 Ž w29x S. Frauendorf, S. Chmel, private communication.