- Email: [email protected]
The shears mechanism in the lead isotopes
19 November 1998
Physics Letters B 440 Ž1998. 251–256
The shears mechanism in the lead isotopes a,1 R.M. Clark a , R. Krucken , 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 Lawrence LiÕermore National Laboratory, LiÕermore, CA 94550, USA Institut fur ¨ Strahlen- und Kernphysik, UniÕersitat ¨ Bonn, D-53115 Bonn, Germany d Department of Physics, UniÕersity of York, Heslington, York YO1 5DD, UK e Gesellschaft fur ¨ Schwerionenforschung mbH, D-64291 Darmstadt, Germany b
c
Received 20 July 1998 Editor: J.P. Schiffer
Abstract Lifetimes of states in at least one of the M1 bands in each nucleus from 193y197 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 BŽM1. 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: 23.20.Lv; 21.10.Tg; 27.80.q w
Sequences of magnetic dipole ŽM1. 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 i 13r2 and h 9r2 orbitals which couple to give an angular mo-
1
Present address: W.A. Wright Nuclear Structure Laboratory, Physics Department, Yale University, P.O. Box 208124, New Haven, CT 06520.
mentum which can be represented by a vector, jp . combined with i 13r2 neutron holes Žwhich couple to j n .. The proton particles and the neutron holes couple to maximize the wavefunction overlap at the bandhead, such that jp and j n are essentially perpendicular to each other. This coupling has been recently confirmed in an experiment that measured the g-factor of the bandhead of an M1 band in 193 Pb w3x. The total angular momentum vector, J, then lies between jp and j n . Calculations using the Tilted-
0370-2693r98r$ - see front matter q 1998 Published by Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 9 8 . 0 1 1 7 9 - 4
252
R.M. Clark et al.r Physics Letters B 440 (1998) 251–256
Axis-Cranking ŽTAC. model w4x 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’ w2x. However, both TAC w2,4x and standard cranking w1x 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 BŽM1.’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 jp and j n align. The BŽM1., which is proportional to m2H , should then decrease sharply in a similar way. In standard cranking model approaches, such as the Donau and Frauendorf for¨ malism w5x, which assumes a fixed K value and that the alignment is perpendicular to the symmetry axis Ži.e., no shears mechanism., such a rapid decrease in the BŽM1. values is not possible. Recent DopplerShift Attenuation Method ŽDSAM. lifetime measurements provide clear evidence that the M1 bands in 198,199 Pb can only be explained in terms of the shears mechanism w6x. The states in these shears bands generally follow a rotational-like behavior with the energies following the pattern of D EŽI. s EŽI. –EŽI b . ; AŽI–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 2 < F 0.1.. Why then do such weakly deformed structures have such striking rotational-like properties? A new form of nuclear rotation known as ‘magnetic rotation’ w7x 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 Žfrom 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 vectors w8x arising from a particle–vibration coupling
w9x. 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 197 Pb. Lifetimes of states in at least one previously observed band in 193 Pb w10,11x, 194 Pb w12,13x, 195 Pb w14x, 196 Pb w15– 18x, and 197 Pb w19–22x have been measured and BŽM1. values deduced. Combined with the previous DSAM lifetime measurements in 198,199 Pb w6x, and the results of a recent Recoil Distance Doppler Shift ŽRDDS. experiment which measured lifetimes of low-lying states in one of the bands in 198 Pb w23x, 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 193y197 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 channels, with the exception of the 172 YbŽ26 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 , 1 mgrcm2 Yb Ženrichment ) 95%. on 12 mgrcm2 Pb backings which slowed down and stopped the recoils. Gamma rays were detected with the Gammasphere array w24x, 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 100.88, 7 at 110.28, 5 at 121.78, 10 at 129.98, 5 at 142.68, 5 at 148.38, and 5 at 162.78. 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 Eg –Eg correlation matrices. Level lifetimes were extracted by the analysis of observed Doppler-broadened lineshapes using the codes of Wells and Johnson w25x. The complete stopping was modeled using the prescription discussed in detail by Gascon et al. w26x. The tabulations of Northcliffe and Schilling w27x with shell corrections were used for
R.M. Clark et al.r Physics Letters B 440 (1998) 251–256
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 0.002 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 Žsee Table 1.. The side-feeding lifetimes were always found to be faster than the in-band lifetimes Žgenerally, 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. w6x. 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 197 Pb. We obtained lifetimes of states in one band of 193 Pb, 194 Pb, 195 Pb, and 196 Pb, and in two bands of 197 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 BŽM1. 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
253
Table 1 Measured lifetimes of states in the bands, t Žps., and reduced transition strengths, BŽM1. Ž m2N .. I SF is the percentage of sidefeeding into each state. The errors on the BŽM1. values were estimated from the standard Žlinear. 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 i 13r2 quasineutrons, E, F the natural parity quasineutrons, and the proton configuration is denoted by its aligned spin. Eg ŽkeV.
Ii
I SF Ž%.
t Žps.
BŽM1. Ž m2N .
193
Pb ŽABE11.
291 365 389 416
45r2 47r2 49r2 51r2
23Ž7. 38Ž10. 51Ž10. 43Ž15.
q0.04 0.33y0 .04 q0.04 0.23y0 .03 q0.04 0.21y0 .05 q0.03 0.25y0 .03
q0.64 5.27y0.64 q0.56 4.32y0.75 q0.95 4.01y0.76 q0.34 2.83y0.34
194 Pb ŽAB11.
260 336 376 417
20 21 22 23
24Ž7. 34Ž8. 51Ž10. 54Ž10.
q0.04 0.23y0 .06 q0.02 0.21y0 .02 q0.05 0.18y0 .04 q0.04 0.18y0 .04
q2.55 9.79y1.70 q0.56 5.86y0.56 q1.14 5.13y1.43 q0.87 3.90y0.87
195 Pb ŽABC11.
276 329 366
47r2 49r2 51r2
24Ž8. 36Ž10. 51Ž10.
q0.05 0.28y0 .08 q0.03 0.21y0 .03 q0.03 0.22y0 .02
q2.00 7.01y1.25 q0.88 6.14y0.88 q0.41 4.48y0.61
196
Pb ŽABCE11.
286 339 398 449 490
25 26 27 28 29
31Ž10. 30Ž10. 32Ž12. 40Ž15. 43Ž17.
q0.03 0.19y0 .04 q0.03 0.17y0 .04 q0.03 0.15y0 .03 q0.03 0.13y0 .02 q0.04 0.18y0 .04
q2.01 9.57y1.51 q1.66 7.05y1.24 q1.06 5.28y1.06 q0.70 4.52y1.04 q0.58 2.59y0.58
197
PbŽa. ŽABC11.
285 327 339 353
47r2 49r2 51r2 53r2
25Ž6. 24Ž6. 32Ž6. 48Ž8.
q0.02 0.40y0 .02 .03 0.29q0 y0 .02 q0.02 0.17y0 .01 q0.02 0.17y0 .01
q0.23 4.59y0.23 4.53q0.31 y0.47 q0.41 7.05y0.83 q0.37 6.35y0.75
197 PbŽb. ŽABE11.
337 404 446 467
47r2 49r2 51r2 53r2
26Ž7. 35Ž8. 34Ž10. 46Ž12.
q0.03 0.17y0 .03 q0.03 0.13y0 .02 q0.02 0.16y0 .02 q0.05 0.28y0 .06
q1.27 7.18y1.27 q0.90 5.88y1.36 q0.47 3.72y0.47 q0.41 1.90y0.34
transitions were assumed to be of pure M1 character. Note, the M1 branching ratios ŽBg s I M 1rwI M 1 q I E 2 x. 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 Bg G 0.9 over the range of the observed transitions. Fig. 2. presents plots of the BŽM1. values as functions of transition energy for all of the bands in the Pb isotopes for which lifetimes have been measured Žexcept 197 PbŽa. which will be discussed later..
254
R.M. Clark et al.r Physics Letters B 440 (1998) 251–256
Fig. 1. Experimental data and fitted lineshapes for the 404, 446, and 467 keV transitions of 197 PbŽb.. 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.
Fig. 2. Plots of BŽM1. versus transition energy, Eg , for bands in 193y199 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 i 13r2 quasineutrons, E, F the natural parity quasineutrons, and the proton configuration is denoted by its aligned spin.
R.M. Clark et al.r Physics Letters B 440 (1998) 251–256
Included are the previous DSAM results on 198,199 Pb w6x and the new RDDS results for a band in 198 Pb w23x. For comparison, absolute BŽM1. 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. w28x. These calculations were performed for 198,199 Pb with the deformation kept constant, close to the equilibrium value for " v s 0.3 MeV. Neutron-pairing effects are included while proton pairing is ignored due to the proximity of the large Z s 82 spherical shell gap. We investigated the influence of changing the mass number for the calculated BŽM1.’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 BŽM1. 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 BŽM1.’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 ŽQ.Q. coupling constant. can yield a sharper decrease in the calculated BŽM1. values w29x. 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. w9x, 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 BŽM1.’s for 197 PbŽa.. These are plotted as a function of transition energy in Fig. 3a.. Instead of a smooth decrease, the BŽM1.’s show a sharp jump. The possible explana-
255
Fig. 3. a. Plot of BŽM1. versus transition energy for 197 PbŽa.. b. Plot of angular momentum, I, versus transition energy, Eg , for 197 PbŽa.. 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, Eg , as shown in Fig. 3b.. The data points overlap an up-bend, which corresponds to an alignment process involving a pair of natural parity quasineutrons w22x. In terms of the shears mechanism, an additional contribution lengthens the vector j n ; thus, by increasing the angle between each other, jp and j n can reorient to a lower energy configuration with the same total spin, J. Above the alignment, the shears mechanism continues as before. Unfortunately, the BŽM1.’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 13r2 quasineutrons w22x. It would be very interesting to deduce BŽM1.’s over the range of this alignment process, as such results would provide a stringent test of calculations.
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R.M. Clark et al.r Physics Letters B 440 (1998) 251–256
To summarize, we have determined the lifetimes of states in M1-bands of 193y197 Pb through the fitting of Doppler-broadened lineshapes. The deduced BŽM1.’s generally show a decrease with increasing angular momentum. Together with the previous results of lifetime measurements for states in the M1bands 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 ŽLBNL. and W–7405–ENG–48 ŽLLNL.. Funding from the U.K. came from the EPSRC. The work of the Bonn group was supported by BMBF Germany and NATO.
References w1x R.M. Clark et al., Nucl. Phys. A 562 Ž1993. 121, and references therein.
w2x G. Baldsiefen et al., Nucl. Phys. A 574 Ž1994. 521, and references therein. w3x S. Chmel et al., Phys. Rev. Lett. 79 Ž1997. 2002. w4x S. Frauendorf, Nucl. Phys. A 557 Ž1993. 259c. w5x 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. 143. w6x R.M. Clark et al., Phys. Rev. Lett. 78 Ž1997. 1868. w7x 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. w8x A.O. Macchiavelli et al., Phys. Rev. C 57 Ž1998. R1073. w9x A.O. Macchiavelli et al., accepted Phys. Rev. C. w10x G. Baldsiefen et al., Phys. Rev. C 54 Ž1996. 1106. w11x L. Ducroux et al., Z. Phys. A 356 Ž1996. 241. w12x D. Mehta et al., Z. Phys. A 346 Ž1996. 169. w13x M.-G. Porquet et al., J. Phys. G 20 Ž1994. 765. w14x M. Kaci et al., Z. Phys. A 354 Ž1996. 267. w15x P.J. Dagnall et al., J. Phys. G 19 Ž1993. 465. w16x J.R. Hughes et al., Phys. Rev. C 47 Ž1993. R1337. w17x E.F. Moore et al., Phys. Rev. C 51 Ž1995. 115. w18x G. Baldsiefen et al., Z. Phys. A 355 Ž1996. 337. w19x R.M. Clark et al., Z. Phys. A 342 Ž1992. 371. w20x A. Kuhnert et al., Phys. Rev. C 46 Ž1992. 133. w21x J.R. Hughes et al., Phys. Rev. C 48 Ž1993. R2135. w22x G. Baldsiefen et al., Nucl. Phys. A 587 Ž1995. 562. w23x R. Krucken et al., to be published. ¨ w24x I.Y. Lee, Nucl. Phys. A 520 Ž1990. 641c. w25x J.C. Wells, N. Johnson Žprivate communication.. Modified from the original code by J.C. Bacelar. w26x J. Gascon et al., Nucl. Phys. A 513 Ž1990. 344. w27x L.C. Northcliffe, R.F. Schilling, Nucl. Data Tables 7 Ž1970. 233. w28x M. Neffgen et al., Nucl. Phys. A 595 Ž1995. 499. w29x S. Frauendorf, S. Chmel, private communication.
Physics Letters B 440 Ž1998. 251–256
The shears mechanism in the lead isotopes a,1 R.M. Clark a , R. Krucken , 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 Lawrence LiÕermore National Laboratory, LiÕermore, CA 94550, USA Institut fur ¨ Strahlen- und Kernphysik, UniÕersitat ¨ Bonn, D-53115 Bonn, Germany d Department of Physics, UniÕersity of York, Heslington, York YO1 5DD, UK e Gesellschaft fur ¨ Schwerionenforschung mbH, D-64291 Darmstadt, Germany b
c
Received 20 July 1998 Editor: J.P. Schiffer
Abstract Lifetimes of states in at least one of the M1 bands in each nucleus from 193y197 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 BŽM1. 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: 23.20.Lv; 21.10.Tg; 27.80.q w
Sequences of magnetic dipole ŽM1. 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 i 13r2 and h 9r2 orbitals which couple to give an angular mo-
1
Present address: W.A. Wright Nuclear Structure Laboratory, Physics Department, Yale University, P.O. Box 208124, New Haven, CT 06520.
mentum which can be represented by a vector, jp . combined with i 13r2 neutron holes Žwhich couple to j n .. The proton particles and the neutron holes couple to maximize the wavefunction overlap at the bandhead, such that jp and j n are essentially perpendicular to each other. This coupling has been recently confirmed in an experiment that measured the g-factor of the bandhead of an M1 band in 193 Pb w3x. The total angular momentum vector, J, then lies between jp and j n . Calculations using the Tilted-
0370-2693r98r$ - see front matter q 1998 Published by Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 Ž 9 8 . 0 1 1 7 9 - 4
252
R.M. Clark et al.r Physics Letters B 440 (1998) 251–256
Axis-Cranking ŽTAC. model w4x 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’ w2x. However, both TAC w2,4x and standard cranking w1x 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 BŽM1.’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 jp and j n align. The BŽM1., which is proportional to m2H , should then decrease sharply in a similar way. In standard cranking model approaches, such as the Donau and Frauendorf for¨ malism w5x, which assumes a fixed K value and that the alignment is perpendicular to the symmetry axis Ži.e., no shears mechanism., such a rapid decrease in the BŽM1. values is not possible. Recent DopplerShift Attenuation Method ŽDSAM. lifetime measurements provide clear evidence that the M1 bands in 198,199 Pb can only be explained in terms of the shears mechanism w6x. The states in these shears bands generally follow a rotational-like behavior with the energies following the pattern of D EŽI. s EŽI. –EŽI b . ; AŽI–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 2 < F 0.1.. Why then do such weakly deformed structures have such striking rotational-like properties? A new form of nuclear rotation known as ‘magnetic rotation’ w7x 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 Žfrom 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 vectors w8x arising from a particle–vibration coupling
w9x. 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 197 Pb. Lifetimes of states in at least one previously observed band in 193 Pb w10,11x, 194 Pb w12,13x, 195 Pb w14x, 196 Pb w15– 18x, and 197 Pb w19–22x have been measured and BŽM1. values deduced. Combined with the previous DSAM lifetime measurements in 198,199 Pb w6x, and the results of a recent Recoil Distance Doppler Shift ŽRDDS. experiment which measured lifetimes of low-lying states in one of the bands in 198 Pb w23x, 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 193y197 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 channels, with the exception of the 172 YbŽ26 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 , 1 mgrcm2 Yb Ženrichment ) 95%. on 12 mgrcm2 Pb backings which slowed down and stopped the recoils. Gamma rays were detected with the Gammasphere array w24x, 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 100.88, 7 at 110.28, 5 at 121.78, 10 at 129.98, 5 at 142.68, 5 at 148.38, and 5 at 162.78. 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 Eg –Eg correlation matrices. Level lifetimes were extracted by the analysis of observed Doppler-broadened lineshapes using the codes of Wells and Johnson w25x. The complete stopping was modeled using the prescription discussed in detail by Gascon et al. w26x. The tabulations of Northcliffe and Schilling w27x with shell corrections were used for
R.M. Clark et al.r Physics Letters B 440 (1998) 251–256
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 0.002 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 Žsee Table 1.. The side-feeding lifetimes were always found to be faster than the in-band lifetimes Žgenerally, 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. w6x. 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 197 Pb. We obtained lifetimes of states in one band of 193 Pb, 194 Pb, 195 Pb, and 196 Pb, and in two bands of 197 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 BŽM1. 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
253
Table 1 Measured lifetimes of states in the bands, t Žps., and reduced transition strengths, BŽM1. Ž m2N .. I SF is the percentage of sidefeeding into each state. The errors on the BŽM1. values were estimated from the standard Žlinear. 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 i 13r2 quasineutrons, E, F the natural parity quasineutrons, and the proton configuration is denoted by its aligned spin. Eg ŽkeV.
Ii
I SF Ž%.
t Žps.
BŽM1. Ž m2N .
193
Pb ŽABE11.
291 365 389 416
45r2 47r2 49r2 51r2
23Ž7. 38Ž10. 51Ž10. 43Ž15.
q0.04 0.33y0 .04 q0.04 0.23y0 .03 q0.04 0.21y0 .05 q0.03 0.25y0 .03
q0.64 5.27y0.64 q0.56 4.32y0.75 q0.95 4.01y0.76 q0.34 2.83y0.34
194 Pb ŽAB11.
260 336 376 417
20 21 22 23
24Ž7. 34Ž8. 51Ž10. 54Ž10.
q0.04 0.23y0 .06 q0.02 0.21y0 .02 q0.05 0.18y0 .04 q0.04 0.18y0 .04
q2.55 9.79y1.70 q0.56 5.86y0.56 q1.14 5.13y1.43 q0.87 3.90y0.87
195 Pb ŽABC11.
276 329 366
47r2 49r2 51r2
24Ž8. 36Ž10. 51Ž10.
q0.05 0.28y0 .08 q0.03 0.21y0 .03 q0.03 0.22y0 .02
q2.00 7.01y1.25 q0.88 6.14y0.88 q0.41 4.48y0.61
196
Pb ŽABCE11.
286 339 398 449 490
25 26 27 28 29
31Ž10. 30Ž10. 32Ž12. 40Ž15. 43Ž17.
q0.03 0.19y0 .04 q0.03 0.17y0 .04 q0.03 0.15y0 .03 q0.03 0.13y0 .02 q0.04 0.18y0 .04
q2.01 9.57y1.51 q1.66 7.05y1.24 q1.06 5.28y1.06 q0.70 4.52y1.04 q0.58 2.59y0.58
197
PbŽa. ŽABC11.
285 327 339 353
47r2 49r2 51r2 53r2
25Ž6. 24Ž6. 32Ž6. 48Ž8.
q0.02 0.40y0 .02 .03 0.29q0 y0 .02 q0.02 0.17y0 .01 q0.02 0.17y0 .01
q0.23 4.59y0.23 4.53q0.31 y0.47 q0.41 7.05y0.83 q0.37 6.35y0.75
197 PbŽb. ŽABE11.
337 404 446 467
47r2 49r2 51r2 53r2
26Ž7. 35Ž8. 34Ž10. 46Ž12.
q0.03 0.17y0 .03 q0.03 0.13y0 .02 q0.02 0.16y0 .02 q0.05 0.28y0 .06
q1.27 7.18y1.27 q0.90 5.88y1.36 q0.47 3.72y0.47 q0.41 1.90y0.34
transitions were assumed to be of pure M1 character. Note, the M1 branching ratios ŽBg s I M 1rwI M 1 q I E 2 x. 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 Bg G 0.9 over the range of the observed transitions. Fig. 2. presents plots of the BŽM1. values as functions of transition energy for all of the bands in the Pb isotopes for which lifetimes have been measured Žexcept 197 PbŽa. which will be discussed later..
254
R.M. Clark et al.r Physics Letters B 440 (1998) 251–256
Fig. 1. Experimental data and fitted lineshapes for the 404, 446, and 467 keV transitions of 197 PbŽb.. 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.
Fig. 2. Plots of BŽM1. versus transition energy, Eg , for bands in 193y199 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 i 13r2 quasineutrons, E, F the natural parity quasineutrons, and the proton configuration is denoted by its aligned spin.
R.M. Clark et al.r Physics Letters B 440 (1998) 251–256
Included are the previous DSAM results on 198,199 Pb w6x and the new RDDS results for a band in 198 Pb w23x. For comparison, absolute BŽM1. 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. w28x. These calculations were performed for 198,199 Pb with the deformation kept constant, close to the equilibrium value for " v s 0.3 MeV. Neutron-pairing effects are included while proton pairing is ignored due to the proximity of the large Z s 82 spherical shell gap. We investigated the influence of changing the mass number for the calculated BŽM1.’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 BŽM1. 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 BŽM1.’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 ŽQ.Q. coupling constant. can yield a sharper decrease in the calculated BŽM1. values w29x. 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. w9x, 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 BŽM1.’s for 197 PbŽa.. These are plotted as a function of transition energy in Fig. 3a.. Instead of a smooth decrease, the BŽM1.’s show a sharp jump. The possible explana-
255
Fig. 3. a. Plot of BŽM1. versus transition energy for 197 PbŽa.. b. Plot of angular momentum, I, versus transition energy, Eg , for 197 PbŽa.. 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, Eg , as shown in Fig. 3b.. The data points overlap an up-bend, which corresponds to an alignment process involving a pair of natural parity quasineutrons w22x. In terms of the shears mechanism, an additional contribution lengthens the vector j n ; thus, by increasing the angle between each other, jp and j n can reorient to a lower energy configuration with the same total spin, J. Above the alignment, the shears mechanism continues as before. Unfortunately, the BŽM1.’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 13r2 quasineutrons w22x. It would be very interesting to deduce BŽM1.’s over the range of this alignment process, as such results would provide a stringent test of calculations.
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To summarize, we have determined the lifetimes of states in M1-bands of 193y197 Pb through the fitting of Doppler-broadened lineshapes. The deduced BŽM1.’s generally show a decrease with increasing angular momentum. Together with the previous results of lifetime measurements for states in the M1bands 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 ŽLBNL. and W–7405–ENG–48 ŽLLNL.. Funding from the U.K. came from the EPSRC. The work of the Bonn group was supported by BMBF Germany and NATO.
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