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On the validity of microscopic calculations for inelastic proton scattering
Volume 162B, number 4,5,6
PHYSICS LETTERS
14 November 1985
ON T H E VALIDITY OF M I C R O S C O P I C CALCULATIONS FOR INELASTIC P R O T O N SCATTERING D.K. McDANIELS, J. LISANTTI, J. TINSLEY, I. BERGQVIST 1, L.W. SWENSON 2 University of Oregon, Eugene, OR 97403, USA
F.E. BERTRAND, E.E. GROSS and D.J. H O R E N Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Received 17 May 1985
Recent measurements of transition rates for low-lying collective states and giant resonances in 2°spb using inelastic scattering of 200 and 334 MeV protons are in accord with accepted values. This is in sharp disagreement with earlier medium-energy proton inelastic scattering studies in which the validity of the collective model formalism was questioned. Combining these results with measurements at other energies, we conclude that the extraction of deformation lengths with the collective distorted wave Born approximation formalism is satisfactory to at least 800 MeV. The present results bring into question the microscopic calculations of inelastic scattering using RPA wave functions.
Measurements with low energy probes show that for nuclei with mass number greater than about 100, the isoscalar giant quadrupole resonance (GQR) depletes most of the theoretical sum rule within measurement uncertainties [1 ]. However, it has been found in several medium-energy inelastic proton scattering measurements of giant resonances that the use of the collective model DWBA calculation led to an estimation of the GQR energy weighted sum rule depletion considerably lower than expected. Furthermore, transition rates for known low-lying states as deduced from the same experiments were often low. This was first observed in a survey experiment in which 156 MeV protons [2] were inelastically scattered by targets from 27AI to 209Bi. The authors reported EWSR strengths for the heavier targets were less than one-half of the value obtained with lower energy probes. Another experiment [3] using 200 MeV protons reported that the GQR was excited in 90Zr and 120Sn with only about one-half of the expected EWSR strength. That experiment was performed with 1 Lund Institute of Technology, Lund, S-223 62, Sweden. 2 Oregon State University, Corvallis, O R 97330, USA.
0370-2693/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
~1.1 MeV energy resolution for the scattered protons, so that the magnitude of the underlying continuum background was difficult to determine. More recently proton scattering experiments at 201 [4] and 104 [5] MeV reported a similar anomalous behavior of the GQR cross section for heavy targets. Kailas et al. [5] summarized the situation with a figure in their paper showing that the measured EWSR strength for the GQR in 208pb ostensibly went from 100% at low incident proton energies to about 30% at 200 MeV. They conjectured that this anomalous behavior was due to the more penetrating nature of the medium-energy protons. The experimental situation for the reduced transition probability for low-lying collective states is equally confusing. In the study with 156 MeV protons, where the problem with the EWSR for the GQR first surfaced, the reduced transition probability measured for the 2 + state at 4.086 MeV in 208pb was found to be within 20% of the adopted values. On the other hand, the studies with 104 MeV and 201 MeV protons [4,5] reported B(E3). values for the excitation of the collective 3 - state at 2.614 MeV in 208pb which were low by almost a factor of two compared to adopted values. 277
Volume 162B, number 4,5,6
PHYSICS LETTERS
It was proposed by Madsen et al. [6] that the most likely resolution of the problem was that deformation lengths extracted from a collective DWBA analysis of medium-energy proton inelastic scattering could no longer be compared directly with a theoretical sum rule derived assuming a transition operator of the form r L YLM(12r). Another suggestion [7] for the solution of the problem used a "wine-bottle" potential in an effort to account for the reduced EWSR strengths. Osterfeld et al. [8] have provided a detailed study of the microscopic aspects of medium-energy proton inelastic scattering. They started by considering the transition matrix element
Tie =fort(r) OLM(O,r) dr.
(1)
If the interaction potential is expanded in a multipole series, then the hadronic transition operator OLM(r) can be expressed as,
OLM(O, r) =f xf-*(kf, rl) VLM(t)I, r) × YLM(~rl) x+(ki, rl) dr 1 .
(2)
For the case of plane waves and a delta-function interaction, the transition operator becomes r L Y~l(I2r) if the momentum transfer is not too large [9]. The behavior of the hadronic transition operator was studied theoretically at several different incident proton energies and scattering angles. A detailed comparison of numerical results for the hadronic transition operator and OLM ~ r L was made. Numerical calculations supported the conclusion that the actual transition operator weighted the interior wave function considerably more than does the electromagnetic form factor r L YLM(S2r).
As a test of the hadronic transition operator in the collective DWBA approach, Osterfeld et al. [8] analyzed "data" with a standard DWBA program for several incident proton energies up to 156 MeV. The "data" for this comparison consisted of calculated inelastic cross sections for the excitation of the 2.614 MeV 3 - state in 208pb calculated at various proton energies using RPA transition densities. Results [8] from this approach showed a dependence of B(E3) for the 2.61 MeV state on the incident proton energy. The E3 reduced transition probability extracted with the collective DWBA program was found to decrease with in278
14 November 1985
creasing energy. At 156 MeVB(E3) was ~60% of the adopted value ,t of 6.11 X 105 e 2 fm 6. The conclusion was drawn that this study showed the impropriety of using the collective DWBA formalism to extract deformation parameters for reactions involving deeply penetrating probes such as medium-energy protons. Application of the collective DWBA formalism to extract deformation lengths and EWSR strengths for low-lying states in 208pb from recent measurements at 200 [11] and 334 MeV [12] is in sharp disagreement with the results quoted above. In our 334 MeV experiment [12], angular distributions were obtained with an overall energy resolution of " 7 0 keV, for the excitation of the 3 - (2.614 MeV), 2 + (4.086 MeV) and 4 + (4.323 MeV) states in 208pb. These results are presented in fig. 1. The solid curves in fig. 1 are from collective model DWBA calculations. The optical model parameters [12] were deduced from an average geometry potential obtained by analysis of 200, 300 and 400 MeV elastic scattering cross sections and analyzing powers. The reduced transition probability obtained from these data for the 3 - state is (6.8 -+0.7) X 105 e 2 fm 6 which agrees with the adopted values [10] of 6.11 X 105 e 2 fm 6 within experimental uncertainty. For the 4.086 MeV, 2 + state the deduced B(E2) is 3400 -+ 600 e 2 fm 4 as compared with the adopted value [10] of 3180 --+160 e 2 fm 4. Finally, B(E4) for the 4 ÷ state at 4.323 MeV is (11.4 -+ 1.9) × 106 e 2 fm 8, which should be compared with an adopted value [10] of(13 + 1.5) × 106 e2fm 8. Measurements [13] at 800 MeV support our findings, giving B (E2) = 4200 e 2 fm4 and B(E4) = 14.8 X 106 e 2 fm 8 for the 2 + and 4 + states respectively. These results all indicate that the extraction of deformation lengths with the collective DWBA formalism is valid for 334 MeV protons. Our measurement at TRIUMF [11] of B(E3) for the 3 - state in 208pb at TRIUMF using 200 MeV protons also supports the validity of using DWBA formalism. Our result of(5.5 + 0.4) × 105 e 2 fm 6 is again in agreement with the adopted value [10]. In fig. 2 we plot the ratio of the adopted value of B(E3) for the 3 - , 2.614 MeV state to values deduced from proton inelastic scattering experiments up to 800 MeV. The data used in this figure are summarized in ,I See ref. [10] for 2°spb. The authors of ref. [9] assumed B(E3) = 6.68 X l0 s e 2 fm6, but this does not seriously affect the conclusions.
Volume 162B, n u m b e r 4,5,6
lOZ
I
PHYSICS LETTERS
I
I
}
1
I
-"
208pb (~, p') 5
- Ex=2.613 MeV
-.
E~=334 MeV (/3R)SO=(~'R)R -_ _ _ {~R)so= 0.75(BR)R -
Jr=3-
B~ =o.es 2
,
5_
//i
5t-
I-
-
L
I
:
,,/
\ !
!
J'=2"
:
BR=O.4,
-_
i,/
:_
I|
-
U
E x= 4.086 MeV
1oo -
-
/"
,f
~1 Fig. 1. Measured and calculated differential cross sections for the excitation o f the three strongly collective low-lying states in 2 ° s p b by inelastic scattering o f 334 MeV polarized protons. The solid curve is from a DWBA calculation using the real potential deformation length equal to the spin-orbit potential
deformation length (#RRR =/3soRso). The dashed curve corresponds to the same DWBAcalculation with #RRR = 0.75 ~soRso-
I
~ 1 o 1 _-
14 November 1985
~
-
" ~\
/
~\
I
-
\\
-
table 1. With the exception of the points at 104 and 201 MeV, all of the measured values for B(E3) are in accord with the adopted value. The low result at 201 MeV may have been due to difficulties with absolute normalization inasmuch as both their elastic scattering and their 3 - cross sections were low [ 11 ]. As noted above, similar agreement for 208pb with adopted values is found for measurements of B(E2) and B(E4) to the 4.086 and 4.323 MeV states. Earlier proton studies [16] on 58Ni to collective states at 1.45 and 4.47 MeV found that the deformation lengths extracted at 1047 MeV were identical to those required at 178 MeV. The inescapable conclusion is that reduced transition rates extracted via the collective DWBA for low spin, strongly collective states excited by medium energy protons agree with values from electromagnetic interaction and are the same, independent of incident energy, up to at least 800 MeV. Our 200 MeV [11] and 334 MeV [12] measure-
101 - - E x = 4.323 MeV
5-j',r
BR-0"478
2
V
4"
/!'~ |
i
X
l/
Z
-\
] 1.8 1.7-
,oO
~_
B(E3) RATIO 2.614 MeV 3- STATE
-
~ t.6 m LS-
L4-~ 5
1 0.9
2 10-I
.
0
5 0
/I
t
I
I
I
I
2.5
5.0
7.5
t0.0
12.5
15.0
ec.m. (deg)
17.0
0
~
200 4 0 0 600 800 PROTON ENERGY (MeV)
I000
Fig. 2. Ratio o f reduced transition probabilities measured from
inelastic proton scattering to the 2.614 MeV, 3 - state in 2°spb to the adopted value from low-energy measurements plotted as a function of incident proton laboratory energy. 279
Volume 162B, number 4,5,6
PHYSICS LETTERS
Table 1 Reduced transition probabilities for the 2.614, 3 - state in 2espb. Incident proton energy (MeV)
B (E3) (e 2 fm6 X105)
B (E3)accepted B (E3)experimental
Referenee
adopted 104 135 156 200 201 334 800 800
6.11 4.4 5.8 4.8 5.5 3.2 6.8 5.6 6.7
1.00 1.40 1.05 1.06 1.11 1.89 0.91 1.09 0.92
[10] [5] [14] [2] [11] [4] [12] [15] [13]
± 0.13 ± 0.2 ± 0.8 ± 0.9 ± 0.4 ± 0.2 a) ± 0.7 ± 1.0 ± 0.4 b)
± 0.07 ± 0.15 ± 0.17 ± 0.08 ± 0.14 ± 0.10 ± 0.19 ± 0.06
a) The variance of the three different results obtained using the different sets of optical parameters was computed. The uncertainty stated above is equal to this variance. b) An uncertainty in fir of 3% was assumed, corresponding to the authors statement about searches on optical parameters. ments yield a value for the EWSR depletion o f the giant quadrupole resonance in 208pb o f 6 5 - 7 0 % . This value was deduced using the same collective model DWBA calculation as used for analysis o f the low.lying states. These results for the EWSR are in excellent agreement with results obtained with'other hadronic probes and with inelastic proton scattering o f 65 MeV protons. We have presented evidence that supports the validity o f the collective formalism for medium-energy inelastic proton scattering. Values o f B(EL) (hence, deformation lengths) for low-lying states extracted with the collective DWBA model are constant up to inciden( proton energies o f 800 MeV. If, as suggested here, the collective DWBA approach can be relied upon to extract transition probabilities and isoscalar energy weighted sum rule depletions, then there could be a problem with microscopic RPA calculations o f inelastic proton scattering to collective states. At least the validity o f the calculations o f ref. [8] is now in question. The above data and analysis should only be construed as a first step in a program to explore the situation comparing the use of the collective model and microscopic approaches to describe inelastic scattering o f medium-energy protons. The entire problem needs much further study with particular stress on obtaining a better data base including full angular distributions 280
14 November 1985
for a variety o f targets and energies and for a wide range o f multipolarities, along with good elastic scattering data. It is a pleasure to acknowledge useful suggestions by Professor Vic Madsen on a preliminary draft o f this paper. This work was supported by Oak Ridge National Laboratory, operated by Martin Marietta Energy Systems, Inc. under contract DE-AC05-840R31400 with the US Department o f Energy. The University o f Oregon and Oregon State University participants were supported in part by grants from the National Science Foundation.
[1] F.E. Bertrand, Nucl. Phys. A354 (1981) 129c. [2] N. Marry, M. Morlet, A. Willis, V. Comparat and R. Frascaria, Nucl. Phys. A238 (1975) 93. [3] F.E. Bertrand, E.E. Gross, D.J. Horen, J.R. Wu, J. TinsIcy, D.K. McDaniels, L.W. Swenson and R. Liljestrand, Phys. Lett. 103B (1981) 326. [4] C. Djalaii, N. Marty, M. Morlet and A. Willis, Nucl. Phys. A380 (1982) 42. [5] S. Kailas, P.P. Singh, D.L. Friesel, C.C. Foster, P. Schwandt and J. Wiggins, Phys. Rev. C29 (1984) 2075. [6] V.A. Madsen, F. Osterfeld and J. Wambach, in: Giant multipole resonances, Prec. Giant multipole resonance topical Conf. (Oak Ridge, TN, October 1979), Vol. 1, ed. F.E. Bertrand (Harwood Academic, New York, 1980) p. 93. [7] G.R. Satchler, Nucl. Phys. A394 (1983) 349. [8] F. Osterfeld, J. Wambach and H. Lenske, Nucl. Phys. A318 (1979) 45. [9] G.R. Satehler, Direct nuclear reactions (Oxford U.P., London, 1983) Ch. 14. [10] M.J. Martin, Nucl. Data Sheets, to be published. [11] D.K. McDaulels, J.R. Tinsley, J. Lisantti, D.M. Drake, I. Bergqvist, L.W. Swenson, F.E. Bertrand, E.E. Gross, D.J. Horen, T.P. Sjoreen, R. Liljestrand and H. Wilson, submitted for publication. [12] F. Bertrand, E.E. Gross, D.J. Horen, J. Tinsley, D.K. McDaniels, J. Lisantti, L.W. Swenson, K. Jones, T.A. Carey, J.B. MeClelland and S.J. Seestrom-Morris, submitted for publication. [13] M. Gazzaly, N.M. Hintz, G.S. Kyle, R.K. Owen, G.W. Hoffman, M. Barlett and G. Blanpied, Phys. Rev. C25 (1982) 408. [14] G.S. Adams, A.D. Bather, G.T. Emery, W.P. Jones, D.W. Miller, W.G. Love and F. Petrovieh, Phys. Lett. 91B (1980) 23. [15] T.A. Carey, W.D. Cornelius, N.J. DiGiacomo, J.M. Moss, G.S. Adams, J.B. McClelland, G. Pauletta, C. Whitten, M. Gazzaly, N. Hintz and C. Glashauser, Phys. Lett. 45 (1980) 239. [16] A. Ingemarsson, T. Johanssan and G. Tibell, Nucl. Phys. A322 (1979) 285.
PHYSICS LETTERS
14 November 1985
ON T H E VALIDITY OF M I C R O S C O P I C CALCULATIONS FOR INELASTIC P R O T O N SCATTERING D.K. McDANIELS, J. LISANTTI, J. TINSLEY, I. BERGQVIST 1, L.W. SWENSON 2 University of Oregon, Eugene, OR 97403, USA
F.E. BERTRAND, E.E. GROSS and D.J. H O R E N Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Received 17 May 1985
Recent measurements of transition rates for low-lying collective states and giant resonances in 2°spb using inelastic scattering of 200 and 334 MeV protons are in accord with accepted values. This is in sharp disagreement with earlier medium-energy proton inelastic scattering studies in which the validity of the collective model formalism was questioned. Combining these results with measurements at other energies, we conclude that the extraction of deformation lengths with the collective distorted wave Born approximation formalism is satisfactory to at least 800 MeV. The present results bring into question the microscopic calculations of inelastic scattering using RPA wave functions.
Measurements with low energy probes show that for nuclei with mass number greater than about 100, the isoscalar giant quadrupole resonance (GQR) depletes most of the theoretical sum rule within measurement uncertainties [1 ]. However, it has been found in several medium-energy inelastic proton scattering measurements of giant resonances that the use of the collective model DWBA calculation led to an estimation of the GQR energy weighted sum rule depletion considerably lower than expected. Furthermore, transition rates for known low-lying states as deduced from the same experiments were often low. This was first observed in a survey experiment in which 156 MeV protons [2] were inelastically scattered by targets from 27AI to 209Bi. The authors reported EWSR strengths for the heavier targets were less than one-half of the value obtained with lower energy probes. Another experiment [3] using 200 MeV protons reported that the GQR was excited in 90Zr and 120Sn with only about one-half of the expected EWSR strength. That experiment was performed with 1 Lund Institute of Technology, Lund, S-223 62, Sweden. 2 Oregon State University, Corvallis, O R 97330, USA.
0370-2693/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
~1.1 MeV energy resolution for the scattered protons, so that the magnitude of the underlying continuum background was difficult to determine. More recently proton scattering experiments at 201 [4] and 104 [5] MeV reported a similar anomalous behavior of the GQR cross section for heavy targets. Kailas et al. [5] summarized the situation with a figure in their paper showing that the measured EWSR strength for the GQR in 208pb ostensibly went from 100% at low incident proton energies to about 30% at 200 MeV. They conjectured that this anomalous behavior was due to the more penetrating nature of the medium-energy protons. The experimental situation for the reduced transition probability for low-lying collective states is equally confusing. In the study with 156 MeV protons, where the problem with the EWSR for the GQR first surfaced, the reduced transition probability measured for the 2 + state at 4.086 MeV in 208pb was found to be within 20% of the adopted values. On the other hand, the studies with 104 MeV and 201 MeV protons [4,5] reported B(E3). values for the excitation of the collective 3 - state at 2.614 MeV in 208pb which were low by almost a factor of two compared to adopted values. 277
Volume 162B, number 4,5,6
PHYSICS LETTERS
It was proposed by Madsen et al. [6] that the most likely resolution of the problem was that deformation lengths extracted from a collective DWBA analysis of medium-energy proton inelastic scattering could no longer be compared directly with a theoretical sum rule derived assuming a transition operator of the form r L YLM(12r). Another suggestion [7] for the solution of the problem used a "wine-bottle" potential in an effort to account for the reduced EWSR strengths. Osterfeld et al. [8] have provided a detailed study of the microscopic aspects of medium-energy proton inelastic scattering. They started by considering the transition matrix element
Tie =fort(r) OLM(O,r) dr.
(1)
If the interaction potential is expanded in a multipole series, then the hadronic transition operator OLM(r) can be expressed as,
OLM(O, r) =f xf-*(kf, rl) VLM(t)I, r) × YLM(~rl) x+(ki, rl) dr 1 .
(2)
For the case of plane waves and a delta-function interaction, the transition operator becomes r L Y~l(I2r) if the momentum transfer is not too large [9]. The behavior of the hadronic transition operator was studied theoretically at several different incident proton energies and scattering angles. A detailed comparison of numerical results for the hadronic transition operator and OLM ~ r L was made. Numerical calculations supported the conclusion that the actual transition operator weighted the interior wave function considerably more than does the electromagnetic form factor r L YLM(S2r).
As a test of the hadronic transition operator in the collective DWBA approach, Osterfeld et al. [8] analyzed "data" with a standard DWBA program for several incident proton energies up to 156 MeV. The "data" for this comparison consisted of calculated inelastic cross sections for the excitation of the 2.614 MeV 3 - state in 208pb calculated at various proton energies using RPA transition densities. Results [8] from this approach showed a dependence of B(E3) for the 2.61 MeV state on the incident proton energy. The E3 reduced transition probability extracted with the collective DWBA program was found to decrease with in278
14 November 1985
creasing energy. At 156 MeVB(E3) was ~60% of the adopted value ,t of 6.11 X 105 e 2 fm 6. The conclusion was drawn that this study showed the impropriety of using the collective DWBA formalism to extract deformation parameters for reactions involving deeply penetrating probes such as medium-energy protons. Application of the collective DWBA formalism to extract deformation lengths and EWSR strengths for low-lying states in 208pb from recent measurements at 200 [11] and 334 MeV [12] is in sharp disagreement with the results quoted above. In our 334 MeV experiment [12], angular distributions were obtained with an overall energy resolution of " 7 0 keV, for the excitation of the 3 - (2.614 MeV), 2 + (4.086 MeV) and 4 + (4.323 MeV) states in 208pb. These results are presented in fig. 1. The solid curves in fig. 1 are from collective model DWBA calculations. The optical model parameters [12] were deduced from an average geometry potential obtained by analysis of 200, 300 and 400 MeV elastic scattering cross sections and analyzing powers. The reduced transition probability obtained from these data for the 3 - state is (6.8 -+0.7) X 105 e 2 fm 6 which agrees with the adopted values [10] of 6.11 X 105 e 2 fm 6 within experimental uncertainty. For the 4.086 MeV, 2 + state the deduced B(E2) is 3400 -+ 600 e 2 fm 4 as compared with the adopted value [10] of 3180 --+160 e 2 fm 4. Finally, B(E4) for the 4 ÷ state at 4.323 MeV is (11.4 -+ 1.9) × 106 e 2 fm 8, which should be compared with an adopted value [10] of(13 + 1.5) × 106 e2fm 8. Measurements [13] at 800 MeV support our findings, giving B (E2) = 4200 e 2 fm4 and B(E4) = 14.8 X 106 e 2 fm 8 for the 2 + and 4 + states respectively. These results all indicate that the extraction of deformation lengths with the collective DWBA formalism is valid for 334 MeV protons. Our measurement at TRIUMF [11] of B(E3) for the 3 - state in 208pb at TRIUMF using 200 MeV protons also supports the validity of using DWBA formalism. Our result of(5.5 + 0.4) × 105 e 2 fm 6 is again in agreement with the adopted value [10]. In fig. 2 we plot the ratio of the adopted value of B(E3) for the 3 - , 2.614 MeV state to values deduced from proton inelastic scattering experiments up to 800 MeV. The data used in this figure are summarized in ,I See ref. [10] for 2°spb. The authors of ref. [9] assumed B(E3) = 6.68 X l0 s e 2 fm6, but this does not seriously affect the conclusions.
Volume 162B, n u m b e r 4,5,6
lOZ
I
PHYSICS LETTERS
I
I
}
1
I
-"
208pb (~, p') 5
- Ex=2.613 MeV
-.
E~=334 MeV (/3R)SO=(~'R)R -_ _ _ {~R)so= 0.75(BR)R -
Jr=3-
B~ =o.es 2
,
5_
//i
5t-
I-
-
L
I
:
,,/
\ !
!
J'=2"
:
BR=O.4,
-_
i,/
:_
I|
-
U
E x= 4.086 MeV
1oo -
-
/"
,f
~1 Fig. 1. Measured and calculated differential cross sections for the excitation o f the three strongly collective low-lying states in 2 ° s p b by inelastic scattering o f 334 MeV polarized protons. The solid curve is from a DWBA calculation using the real potential deformation length equal to the spin-orbit potential
deformation length (#RRR =/3soRso). The dashed curve corresponds to the same DWBAcalculation with #RRR = 0.75 ~soRso-
I
~ 1 o 1 _-
14 November 1985
~
-
" ~\
/
~\
I
-
\\
-
table 1. With the exception of the points at 104 and 201 MeV, all of the measured values for B(E3) are in accord with the adopted value. The low result at 201 MeV may have been due to difficulties with absolute normalization inasmuch as both their elastic scattering and their 3 - cross sections were low [ 11 ]. As noted above, similar agreement for 208pb with adopted values is found for measurements of B(E2) and B(E4) to the 4.086 and 4.323 MeV states. Earlier proton studies [16] on 58Ni to collective states at 1.45 and 4.47 MeV found that the deformation lengths extracted at 1047 MeV were identical to those required at 178 MeV. The inescapable conclusion is that reduced transition rates extracted via the collective DWBA for low spin, strongly collective states excited by medium energy protons agree with values from electromagnetic interaction and are the same, independent of incident energy, up to at least 800 MeV. Our 200 MeV [11] and 334 MeV [12] measure-
101 - - E x = 4.323 MeV
5-j',r
BR-0"478
2
V
4"
/!'~ |
i
X
l/
Z
-\
] 1.8 1.7-
,oO
~_
B(E3) RATIO 2.614 MeV 3- STATE
-
~ t.6 m LS-
L4-~ 5
1 0.9
2 10-I
.
0
5 0
/I
t
I
I
I
I
2.5
5.0
7.5
t0.0
12.5
15.0
ec.m. (deg)
17.0
0
~
200 4 0 0 600 800 PROTON ENERGY (MeV)
I000
Fig. 2. Ratio o f reduced transition probabilities measured from
inelastic proton scattering to the 2.614 MeV, 3 - state in 2°spb to the adopted value from low-energy measurements plotted as a function of incident proton laboratory energy. 279
Volume 162B, number 4,5,6
PHYSICS LETTERS
Table 1 Reduced transition probabilities for the 2.614, 3 - state in 2espb. Incident proton energy (MeV)
B (E3) (e 2 fm6 X105)
B (E3)accepted B (E3)experimental
Referenee
adopted 104 135 156 200 201 334 800 800
6.11 4.4 5.8 4.8 5.5 3.2 6.8 5.6 6.7
1.00 1.40 1.05 1.06 1.11 1.89 0.91 1.09 0.92
[10] [5] [14] [2] [11] [4] [12] [15] [13]
± 0.13 ± 0.2 ± 0.8 ± 0.9 ± 0.4 ± 0.2 a) ± 0.7 ± 1.0 ± 0.4 b)
± 0.07 ± 0.15 ± 0.17 ± 0.08 ± 0.14 ± 0.10 ± 0.19 ± 0.06
a) The variance of the three different results obtained using the different sets of optical parameters was computed. The uncertainty stated above is equal to this variance. b) An uncertainty in fir of 3% was assumed, corresponding to the authors statement about searches on optical parameters. ments yield a value for the EWSR depletion o f the giant quadrupole resonance in 208pb o f 6 5 - 7 0 % . This value was deduced using the same collective model DWBA calculation as used for analysis o f the low.lying states. These results for the EWSR are in excellent agreement with results obtained with'other hadronic probes and with inelastic proton scattering o f 65 MeV protons. We have presented evidence that supports the validity o f the collective formalism for medium-energy inelastic proton scattering. Values o f B(EL) (hence, deformation lengths) for low-lying states extracted with the collective DWBA model are constant up to inciden( proton energies o f 800 MeV. If, as suggested here, the collective DWBA approach can be relied upon to extract transition probabilities and isoscalar energy weighted sum rule depletions, then there could be a problem with microscopic RPA calculations o f inelastic proton scattering to collective states. At least the validity o f the calculations o f ref. [8] is now in question. The above data and analysis should only be construed as a first step in a program to explore the situation comparing the use of the collective model and microscopic approaches to describe inelastic scattering o f medium-energy protons. The entire problem needs much further study with particular stress on obtaining a better data base including full angular distributions 280
14 November 1985
for a variety o f targets and energies and for a wide range o f multipolarities, along with good elastic scattering data. It is a pleasure to acknowledge useful suggestions by Professor Vic Madsen on a preliminary draft o f this paper. This work was supported by Oak Ridge National Laboratory, operated by Martin Marietta Energy Systems, Inc. under contract DE-AC05-840R31400 with the US Department o f Energy. The University o f Oregon and Oregon State University participants were supported in part by grants from the National Science Foundation.
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