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Multiple excitation of the second 0+ state in 90Zr
Volume 42B, number 1
PHYSICS LETTERS
13 November 1972
M U L T I P L E E X C I T A T I O N O F T H E S E C O N D 0 + S T A T E I N 9OZr* W.G. LOVE University of Georgia. Athens, Georgia, USA Received 4 September 1972 Multiple excitation is found to be important for the inelastic excitation of the second 0+ state in 9°Zr when shell model wave functions supplemented by core polarization effects of the quadrupole type are used. Inelastic proton, deuteron, triton and s-particle scattering data are considered. ' The inelastic excitation of several low-lying monopole states is poorly understood [ 1 - 3 ] . A closely related problem is that of understanding core polarization effects of the monopole type [4]. Although such processes have largely eluded a reasonable and complete explanation, they are extremely important since they are quite sensitive to events occuring in the nuclear interior. Here we consider the inelastic excitation of the second 0 + state in 90Zr at 1.75 MeV. In an effort to understand the excitation of this state by protons with bombarding energies greater than 10 MeV, coupled channels calculations employing simple shell model wave functions were performed [5] several years ago at which time it was concluded that multiple excitation of the 0~ level via the 2 + state at 2.18 MeV is unimportant. This conclusion, however, was based on the use of a purely phenomenological nucleon-nucleon interaction which had been calibrated by fitting [6] calculated cross sections to experimental ones. Since neither core polarization [6] nor exchange [7, 8] effects were included explicitly, the effective nucleon-nucleon interaction found empirically was much larger than realistic interactions now believed [9] to be appropriate for scattering calculations. Even more important, the use of a single effective interaction for all the transitions is equivalent to assuming all multipolarities are enhanced equally by core polarization and exchange effects which is now known [4, 6, 8, 10] not to be the case. While electric quadrupole transitions in 90Zr are known to be enhanced [6], a recent study [4] of the decay of the 0~ level via internal conversion indicates that the monopole nuclear matrix element for * Research supported in part by the National Science Foundation (Grant Number GP-22559).
the 0~ ~ 0 I- transition is strongly quenched relative to the simple shell model prediction. In light of such recent developments, it is appropriate to reexamine the role of multiple excitation for the 0~ ~ 0~ transition. A comparison of the excitation of this level by various projectiles is of special interest in view of the newly proposed [ 11 ] two-step (pick-up~-~stripping) mechanism believed to be particularly important for the excitation of this level by tritons and deuterons. Apart from the above considerations, there is now available more experimental data for the inelastic excitation of this level by several projectiles. Except for proton scattering data at 12.7 MeV bombarding energy [2], the cross section for the 0~ level is more than an order of magnitude smaller than that for the 2~ state at 2.18 MeV. This result alone suggests that multiple excitation (and other processes which are usually weak) should be investigated. Of particular interest is the recent (p,p') data of Hinrichs et al. [10] at a proton bombarding energy (Ep) of 40 MeV, They find the peak cross section at 40 MeV to be smaller than that at Ep = 12.7 MeV by roughly a factor of 100. Such a strong energy dependence is convincing evidence that the transition is not a direct one over this energy range To investigate the role of multiple excitation for the excitation of the 0~ level, a modified version of the coupled channels program of Tamura [13] was used. A simple coupling scheme was considered in which the ground state, first excited 2 + state, and first excited 0 + state were included. A more complete calculation would include coupling to the strong 3 state at 2.75 MeV excitation, but little is known about the 0~ - 3 ] matrix element. In all of the calculations reported here, the shell model wave functions of the 13
Volume 42B, number 1
PHYSICS LETTERS
i0 °
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13 November 1972
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0+ --*0+ at proton bombarding energies of (a) 12.7 MeV and (b) 40 MeV. 0.[, O~ and 2~ states are (excluding core polarization) those described in ref. [13]. The excitation of the first 2+ level has been found [10] to be dominated by core polarization of the quadrupole type. Consequently a complex collective model form factor was used for the 0"[ - 2"[ and 0~ - 2"[ couplings. The matrix element for the 0 F ~ 2"[ transition was taken to be 4/3 times that for the 0 F ~ 2"[ transition. This is equivalent to assuming that the two lg9/2 protons in both the 0"[ and 0~ states are equally effective in polarizing the core. The multiple contribution to the 0~ cross section is very similar to what would be obtained using a two-quadrupole phonon model for the 0~ state. An essential difference is that the 2"[ ~ 0~ matrix element in the shell model picture is roughly twice the magnitude of that predicted in the two phonon model. Consequently, the multiple contributions to the 0~ cross section in the two models are quite different in magnitude. Nevertheless, one can introduce a deformation parameter (/32) which characterizes the strength of the transition from the ground state to the first excited 2+ state. Since multiple excitation is found to affect the 2 + cross section only slightly, 132 w a s taken to be 0.07 for all projectiles which roughly normalizes the calculated 2"[ cross section to experiment. Coulomb excitation and all spin-dependent twobody forces were neglected. Although the direct (one-step) amplitudes may be important for the excitation of this state are not calculated here since the phase relation betweeen the 14
direct (D) and multiple (M) contributions is critical and we do not feel this is well enough understood at present [10] to include both D and M amplitudes in a consistent way. Moreover, a detailed understanding of the quenching of the direct matrix element due to monopole core polarization [4] is unvailable which introduces another uncertainty into the calculation of the D amplitudes. First consider the excitation of the 0 F level by protons with Ep = 12.7 MeV and Ep = 40 MeV. The optical model (OM) parameters at Ep = 12.7 MeV are those of "set D" from ref. [1]. At Ep = 40 MeV the OM parameters are those from table 2 of ref. [14]. Fig. 1 shows the experimental data compared with the coupled channels calculations. At Ep = 12.7 MeV the multiple excitation cross section is seen to be about 60% as large as the experimental one. In addition, the shape of the multiple cross section is similar to that observed. Ignoring monopole core polarization, the direct cross section alone [8] accounts for only about 10% of the observed cross section and has a shape totally unlike the experimental data, particularly at large scatering angles. At Ep = 40 MeV the magnitude of the multiple excitation cross section is twice as large as experiment although the shape is in quite reasonable agreement with experiment. The direct cross section for this state has also been calculated [10~ at Ep = 40 MeV and is not only twice as large as experiment but has a shape less like experiment than the M contribution alone. Therefore, neither M or D alone (nor together [10] )
Volume 42B, number 1
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Fig. 2. A comparison between experimental and calculated (multiple excitation = M) cross sections for the excitation of the 0+ level in 9°Zr by (a) deuterons of 15 MeV, (b) tritons of 20 MeV and (c) a-particles of 65 MeV.
predict the correct energy dependence of this cross section although the energy dependence o f M alone is much closer to experiment. Next consider the excitation of the 0~ state by 15 MeV deuterons [15]. The OM parameters for the coupled channels calculations were taken from table 1 of ref. [16]. Fig. 2 shows a comparison between the calculated and measured cross sections. The multiple process accounts for roughly 40% of the cross section in this case, but the shape o f the M cross section is poor forward of about 45 ° . While multiple excitation is important for (d,d') there is room for an appreciable direct or other two-step contribution. The excitation of this 0~ level via inelastic triton scattering is of particular interest since there is ex-
pected to be strong competition from the two-step rearrangement process [l l ] mentioned earlier. In particular, the experimental angular distribution is known [3] to be essentially out of phase with the L = 0 cross section predicted by the direct mechanism alone. The two-step rearrangement [ 11] process predicts a large L = 1 component in the angular distribution which is expected to be in better agreement with experiment. The OM parameters for the (t,t') calculation are from ref. [3]. Fig. 2 shows that the M part of the predicted cross section has a shape very similar to that of the experimental data, and accounts for about 40% of the observed cross section. Therefore, the shape (and magnitude if M is underestimated) can be reproduced without invoking a two-step rearrangement process. 15
Volume 42B, number 1
PHYSICS LETTERS
However, if our estimate of the importance of multiple excition is reasonable there is still room for twostep processes of the rearrangement type. Finally we consider the excitation of the 05 level by inelastic a-particle scattering [1] at E a = 65 MeV. The excitation of this level by c~-particles is especially interesting since the two-step rearangement process [11] would require the propagation o f 5Li in the intermediate state. Since the spin of the c~-particle is zero it can only experience a net orbital angular momentum change of 0. Nevertheless, the experimental cross section tends to be out of phase with L = 0 predictions [1] particularly for 0cm t> 50 °. Coupled channels calculations were performed using the OM parameters of ref. [1] and are compared with the observed cross section in fig. 2. Although the shape of the calculated cross section is not significantly improved compared with the direct calculations (L = 0) of ref. [1], the magnitude o f the observed cross section is reproduced using f12 = 0.07. This is likely an upper limit to the multiple excitation mechanism since a more accurate value offl 2 at this energy is believed [1] to be f12 = 0.051. Use of this smaller value offl2 reduces the magnitude of the calculated cross section by a factor of ~ 3.5. This value offl 2 is, however, lower than that found at other c~-particle bombarding energies and has not been unambigously determined at this energy [ 1 ]. In conclusion it now appears that multiple excitation is important for the excitation of the 05 level in 90Zr by projectiles with A ~ 4. Multiple excitation is found to be relatively more important for protons than for composite particles in agreement with the recent results of Madsen et al. [171. These conclusions may also hold for the 05 states in 92Zr and 94Zr which are believed to possess a structure [18] similar to that of the 05 level in 9°Zr. Although the direct amplitudes were not included, coupled channels calculations may be useful (or necessary) in checking their phases.
16
13 November 1972
To better understand the role of the various participating reaction mechanisms for the excitation of this level, it is desirable to have more data for the compositie projectiles for a range of bombarding energies. The author gratefully acknowledges the authors of ref, [10] and [15] for use of their data prior to publication.
References [1] C.R. Bingham, M.L. Halbert and R.H. Bassel, Phys. Rev. 148 (1966) 1174. [2] J.K. Dickens, E. Eichler and G.R. Satchler, Phys. Rev. 168 (1968) 1355. [3] E.R. Flynn, A.G. Blair and D.D. Armstrong, Phys. Rev. 170 (1968) 1142. [4] L. Zamick, Phys. Lett. 39B (1972) 471; D. Burch et al., Phys. Lett. 40B (1972) 357. [5] W.G. Love, G.R. Satchler and T. Tamura, Phys. Lett. 22 (1966) 325. [6] W.G. Love and G.R. Satchler, Nucl. Phys. A101 (1967) 424. [7] K.A. Amos, V.A. Madsen and I.E. McCarthy, Nucl. Phys. A94 (1967) 103. [8] W.G. Love and G.R. Satchler, Nucl. Phys. A159 (1970) 1. [9] G.R. Satchler, Comm. Nucl. Particle Phys. 5 (1972) 39; R. Schaeffer, Nucl. Phys. A132 (1969) 186. [10] R.A. Hindchs, D. Larson and B.M. Preedom, Bull. Am. Phys. 8oc. 17 (1972) 446; R.A. Hinrichs et al., to be published. [11] R. Schaeffer and G.R. Bertsch, Phys. Lett. 38B (1972) 159. [12] T. Tamura, Revs. Mod. Phys. 37 (1965) 679. [13] M.B. Johnson, L.W. Owen and G.R. Satchler, Phys. Rev. 142 (1966) 748. [14] M.P. Fricke et al., Phys. Rev. 156 (1967) 1207. [15[ F. Todd Baker et al., Bull. Am. Phys. Soc. 17 (1972) 446. [16] C.M. Percy and F.G. Percy, Phys. Rev. 134 (1964) B353. [17] V.A. Madsen et al., Phys. Rev. Lett. 28 (1972) 629. [18] S. Cochavi, N. Cue and D.B. Fossan, Phys. Rev. C1 (1970) 1821.
PHYSICS LETTERS
13 November 1972
M U L T I P L E E X C I T A T I O N O F T H E S E C O N D 0 + S T A T E I N 9OZr* W.G. LOVE University of Georgia. Athens, Georgia, USA Received 4 September 1972 Multiple excitation is found to be important for the inelastic excitation of the second 0+ state in 9°Zr when shell model wave functions supplemented by core polarization effects of the quadrupole type are used. Inelastic proton, deuteron, triton and s-particle scattering data are considered. ' The inelastic excitation of several low-lying monopole states is poorly understood [ 1 - 3 ] . A closely related problem is that of understanding core polarization effects of the monopole type [4]. Although such processes have largely eluded a reasonable and complete explanation, they are extremely important since they are quite sensitive to events occuring in the nuclear interior. Here we consider the inelastic excitation of the second 0 + state in 90Zr at 1.75 MeV. In an effort to understand the excitation of this state by protons with bombarding energies greater than 10 MeV, coupled channels calculations employing simple shell model wave functions were performed [5] several years ago at which time it was concluded that multiple excitation of the 0~ level via the 2 + state at 2.18 MeV is unimportant. This conclusion, however, was based on the use of a purely phenomenological nucleon-nucleon interaction which had been calibrated by fitting [6] calculated cross sections to experimental ones. Since neither core polarization [6] nor exchange [7, 8] effects were included explicitly, the effective nucleon-nucleon interaction found empirically was much larger than realistic interactions now believed [9] to be appropriate for scattering calculations. Even more important, the use of a single effective interaction for all the transitions is equivalent to assuming all multipolarities are enhanced equally by core polarization and exchange effects which is now known [4, 6, 8, 10] not to be the case. While electric quadrupole transitions in 90Zr are known to be enhanced [6], a recent study [4] of the decay of the 0~ level via internal conversion indicates that the monopole nuclear matrix element for * Research supported in part by the National Science Foundation (Grant Number GP-22559).
the 0~ ~ 0 I- transition is strongly quenched relative to the simple shell model prediction. In light of such recent developments, it is appropriate to reexamine the role of multiple excitation for the 0~ ~ 0~ transition. A comparison of the excitation of this level by various projectiles is of special interest in view of the newly proposed [ 11 ] two-step (pick-up~-~stripping) mechanism believed to be particularly important for the excitation of this level by tritons and deuterons. Apart from the above considerations, there is now available more experimental data for the inelastic excitation of this level by several projectiles. Except for proton scattering data at 12.7 MeV bombarding energy [2], the cross section for the 0~ level is more than an order of magnitude smaller than that for the 2~ state at 2.18 MeV. This result alone suggests that multiple excitation (and other processes which are usually weak) should be investigated. Of particular interest is the recent (p,p') data of Hinrichs et al. [10] at a proton bombarding energy (Ep) of 40 MeV, They find the peak cross section at 40 MeV to be smaller than that at Ep = 12.7 MeV by roughly a factor of 100. Such a strong energy dependence is convincing evidence that the transition is not a direct one over this energy range To investigate the role of multiple excitation for the excitation of the 0~ level, a modified version of the coupled channels program of Tamura [13] was used. A simple coupling scheme was considered in which the ground state, first excited 2 + state, and first excited 0 + state were included. A more complete calculation would include coupling to the strong 3 state at 2.75 MeV excitation, but little is known about the 0~ - 3 ] matrix element. In all of the calculations reported here, the shell model wave functions of the 13
Volume 42B, number 1
PHYSICS LETTERS
i0 °
tt
"C
o)
,o-, , ',
t,t..t ',
t; I
,, ;
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13 November 1972
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Fig. 1. A comparison between experimental and calculated (multiple excitation = M ) cross sections f o r the reaction 9°Zr (p,p')
0+ --*0+ at proton bombarding energies of (a) 12.7 MeV and (b) 40 MeV. 0.[, O~ and 2~ states are (excluding core polarization) those described in ref. [13]. The excitation of the first 2+ level has been found [10] to be dominated by core polarization of the quadrupole type. Consequently a complex collective model form factor was used for the 0"[ - 2"[ and 0~ - 2"[ couplings. The matrix element for the 0 F ~ 2"[ transition was taken to be 4/3 times that for the 0 F ~ 2"[ transition. This is equivalent to assuming that the two lg9/2 protons in both the 0"[ and 0~ states are equally effective in polarizing the core. The multiple contribution to the 0~ cross section is very similar to what would be obtained using a two-quadrupole phonon model for the 0~ state. An essential difference is that the 2"[ ~ 0~ matrix element in the shell model picture is roughly twice the magnitude of that predicted in the two phonon model. Consequently, the multiple contributions to the 0~ cross section in the two models are quite different in magnitude. Nevertheless, one can introduce a deformation parameter (/32) which characterizes the strength of the transition from the ground state to the first excited 2+ state. Since multiple excitation is found to affect the 2 + cross section only slightly, 132 w a s taken to be 0.07 for all projectiles which roughly normalizes the calculated 2"[ cross section to experiment. Coulomb excitation and all spin-dependent twobody forces were neglected. Although the direct (one-step) amplitudes may be important for the excitation of this state are not calculated here since the phase relation betweeen the 14
direct (D) and multiple (M) contributions is critical and we do not feel this is well enough understood at present [10] to include both D and M amplitudes in a consistent way. Moreover, a detailed understanding of the quenching of the direct matrix element due to monopole core polarization [4] is unvailable which introduces another uncertainty into the calculation of the D amplitudes. First consider the excitation of the 0 F level by protons with Ep = 12.7 MeV and Ep = 40 MeV. The optical model (OM) parameters at Ep = 12.7 MeV are those of "set D" from ref. [1]. At Ep = 40 MeV the OM parameters are those from table 2 of ref. [14]. Fig. 1 shows the experimental data compared with the coupled channels calculations. At Ep = 12.7 MeV the multiple excitation cross section is seen to be about 60% as large as the experimental one. In addition, the shape of the multiple cross section is similar to that observed. Ignoring monopole core polarization, the direct cross section alone [8] accounts for only about 10% of the observed cross section and has a shape totally unlike the experimental data, particularly at large scatering angles. At Ep = 40 MeV the magnitude of the multiple excitation cross section is twice as large as experiment although the shape is in quite reasonable agreement with experiment. The direct cross section for this state has also been calculated [10~ at Ep = 40 MeV and is not only twice as large as experiment but has a shape less like experiment than the M contribution alone. Therefore, neither M or D alone (nor together [10] )
Volume 42B, number 1
I
•
PHYSICS LETTERS
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13 November 1972
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Fig. 2. A comparison between experimental and calculated (multiple excitation = M) cross sections for the excitation of the 0+ level in 9°Zr by (a) deuterons of 15 MeV, (b) tritons of 20 MeV and (c) a-particles of 65 MeV.
predict the correct energy dependence of this cross section although the energy dependence o f M alone is much closer to experiment. Next consider the excitation of the 0~ state by 15 MeV deuterons [15]. The OM parameters for the coupled channels calculations were taken from table 1 of ref. [16]. Fig. 2 shows a comparison between the calculated and measured cross sections. The multiple process accounts for roughly 40% of the cross section in this case, but the shape o f the M cross section is poor forward of about 45 ° . While multiple excitation is important for (d,d') there is room for an appreciable direct or other two-step contribution. The excitation of this 0~ level via inelastic triton scattering is of particular interest since there is ex-
pected to be strong competition from the two-step rearrangement process [l l ] mentioned earlier. In particular, the experimental angular distribution is known [3] to be essentially out of phase with the L = 0 cross section predicted by the direct mechanism alone. The two-step rearrangement [ 11] process predicts a large L = 1 component in the angular distribution which is expected to be in better agreement with experiment. The OM parameters for the (t,t') calculation are from ref. [3]. Fig. 2 shows that the M part of the predicted cross section has a shape very similar to that of the experimental data, and accounts for about 40% of the observed cross section. Therefore, the shape (and magnitude if M is underestimated) can be reproduced without invoking a two-step rearrangement process. 15
Volume 42B, number 1
PHYSICS LETTERS
However, if our estimate of the importance of multiple excition is reasonable there is still room for twostep processes of the rearrangement type. Finally we consider the excitation of the 05 level by inelastic a-particle scattering [1] at E a = 65 MeV. The excitation of this level by c~-particles is especially interesting since the two-step rearangement process [11] would require the propagation o f 5Li in the intermediate state. Since the spin of the c~-particle is zero it can only experience a net orbital angular momentum change of 0. Nevertheless, the experimental cross section tends to be out of phase with L = 0 predictions [1] particularly for 0cm t> 50 °. Coupled channels calculations were performed using the OM parameters of ref. [1] and are compared with the observed cross section in fig. 2. Although the shape of the calculated cross section is not significantly improved compared with the direct calculations (L = 0) of ref. [1], the magnitude o f the observed cross section is reproduced using f12 = 0.07. This is likely an upper limit to the multiple excitation mechanism since a more accurate value offl 2 at this energy is believed [1] to be f12 = 0.051. Use of this smaller value offl2 reduces the magnitude of the calculated cross section by a factor of ~ 3.5. This value offl 2 is, however, lower than that found at other c~-particle bombarding energies and has not been unambigously determined at this energy [ 1 ]. In conclusion it now appears that multiple excitation is important for the excitation of the 05 level in 90Zr by projectiles with A ~ 4. Multiple excitation is found to be relatively more important for protons than for composite particles in agreement with the recent results of Madsen et al. [171. These conclusions may also hold for the 05 states in 92Zr and 94Zr which are believed to possess a structure [18] similar to that of the 05 level in 9°Zr. Although the direct amplitudes were not included, coupled channels calculations may be useful (or necessary) in checking their phases.
16
13 November 1972
To better understand the role of the various participating reaction mechanisms for the excitation of this level, it is desirable to have more data for the compositie projectiles for a range of bombarding energies. The author gratefully acknowledges the authors of ref, [10] and [15] for use of their data prior to publication.
References [1] C.R. Bingham, M.L. Halbert and R.H. Bassel, Phys. Rev. 148 (1966) 1174. [2] J.K. Dickens, E. Eichler and G.R. Satchler, Phys. Rev. 168 (1968) 1355. [3] E.R. Flynn, A.G. Blair and D.D. Armstrong, Phys. Rev. 170 (1968) 1142. [4] L. Zamick, Phys. Lett. 39B (1972) 471; D. Burch et al., Phys. Lett. 40B (1972) 357. [5] W.G. Love, G.R. Satchler and T. Tamura, Phys. Lett. 22 (1966) 325. [6] W.G. Love and G.R. Satchler, Nucl. Phys. A101 (1967) 424. [7] K.A. Amos, V.A. Madsen and I.E. McCarthy, Nucl. Phys. A94 (1967) 103. [8] W.G. Love and G.R. Satchler, Nucl. Phys. A159 (1970) 1. [9] G.R. Satchler, Comm. Nucl. Particle Phys. 5 (1972) 39; R. Schaeffer, Nucl. Phys. A132 (1969) 186. [10] R.A. Hindchs, D. Larson and B.M. Preedom, Bull. Am. Phys. 8oc. 17 (1972) 446; R.A. Hinrichs et al., to be published. [11] R. Schaeffer and G.R. Bertsch, Phys. Lett. 38B (1972) 159. [12] T. Tamura, Revs. Mod. Phys. 37 (1965) 679. [13] M.B. Johnson, L.W. Owen and G.R. Satchler, Phys. Rev. 142 (1966) 748. [14] M.P. Fricke et al., Phys. Rev. 156 (1967) 1207. [15[ F. Todd Baker et al., Bull. Am. Phys. Soc. 17 (1972) 446. [16] C.M. Percy and F.G. Percy, Phys. Rev. 134 (1964) B353. [17] V.A. Madsen et al., Phys. Rev. Lett. 28 (1972) 629. [18] S. Cochavi, N. Cue and D.B. Fossan, Phys. Rev. C1 (1970) 1821.