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Neutron-proton radius differences and isovector deformations from π+ and π− inelastic scattering from 18O
Volume 82B, number 1
PHYSICS LETTERS
12 March 1979
NEUTRON-PROTON RADIUS DIFFERENCES AND ISOVECTOR DEFORMATIONS FROM ~+ AND a - INELASTIC SCATTERING FROM 180 ~ S. IVERSEN, H. NANN, A. OBST and Kamal K. SETH Northwestern University, Evanston, IL 60201, USA
N. T A N A K A , C.L. MORRIS and H.A. THIESSEN Los A larnos Scientific Laboratory, Los Alamos, NM 87545, USA
K. BOYER, W. COTTINGAME and C. Fred MOORE University of Texas, Austin, TX 78712, USA
R.L. BOUDR1E University of Colorado, Boulder, CO 80302, USA
D. DEHNHARD University o f Minnesota, Minneapolis, MN 55455, USA
Received 9 January 1979
o + and ~r- elastic and inelastic scattering from 180 have been measured at TOO = 164 MeV. Consistent with the results at 230 MeV, it is found that the ratio o0r-)/o0r +) for the 27 state is 1.86(16), while for the 3~ state it is 0.89(6). These results are interpreted as indicating differences in neutron and proton deformations characterizing the 27 transition and partial neutron blocking for the 3~ transition. Optical model analysis of elastic scattering leads to the conclusion that (/-2)1/2 _ (r~)! ]~ = 0.03(3) fm.
It has long been a fond hope in nuclear structure physics to separate the roles o f neutrons and protons in nuclear excitations [1]. Recent pion scattering experiments make it possible to realize this hope. In an earlier letter [2] we reported that the cross section for the excitation o f the 1.98 MeV 2~" state in 180 by inelastic scattering of 230 MeV negative pions was a factor 1.66(13) larger than that b y positive pions o f the same energy. Because o f the dominance o f the p i o n nucleon (3,3) resonance near this energy, enhancement of n - cross section over n + by a factor 1.25 is expected just because 18 0 contains 10 neutrons and only 8 protons. The much larger observed enhanceResearch supported by the U.S. Department of Energy, the Research Corporation and the Robert A. Welch Foundation.
ment interpreted as indicating a larger average deformation length (flR)n for neutrons than the deformation length (/3R)p for protons. These reactions were subsequently also studied at T,~ -- 163 MeV b y Jansen et al. [3] at SIN. However, these authors found the 7r- enhancement to be only 1.27(4), i.e., consistent with that due to n e u t r o n - p r o t o n number difference alone, and allowing for no differences in (/3R)n and (/3R)p. This complete disparity between our results and those o f Jansen et al. was considered serious. We have therefore repeated the entire experiment at TTr = 164 MeV and 230 MeV with several improvements in the experimental set-up and with a new target. The results from the new experiment at T~r = 164 MeV are presented in this letter in order to permit a direct comparison with the results o f Jansen et al. [3]. 51
Volume 82B, number 1
PHYSICS LETTERS
The general set-up of the EPICS spectrometer system at LAMPF has been described before [2]. For the present experiment, the small helium filled scattering chamber was replaced by a large vacuum scattering chamber, and the ionization chamber beam monitor at 0°was supplemented b y a three scintillator scattered beam monitor telescope at ~ 3 0 °. The old 180 water target was replaced b y 180 (94.9% enriched) ice targets of thickness 0.55 g/cm 2 and 0.31 g/cm 2, which were contained between 1 rail mylar windows. Data was taken from 17.5 ° to 80 ° in 2.5 ° steps. An energy resolution (FWHM) o f 425 keV was realized with the thin target. As before, the absolute cross sectipn normalization was determined b y measuring pion scattering from the hydrogen in the target, and using cross sections interpolated by means of Dodder's [4] phaseshift analysis o f 7r-+p total cross section and scattering data between 20 and 310 MeV. Errors in hydrogen cross sections and in the determination of normalization factors are estimated to be ~< -+5%. These are included in all numerical errors quoted in this letter. However, in fig. 1, where we show our measured differential cross sections, only statistical errors are indicated. Detailed comparison of our data with that of Jansen et al. [3] shows significant differences. For elastic scattering our first minima are more than three times as deep as theirs. Also in the region of the second maximum their cross sections are as much as 25 to 30% smaller than ours. For 2]" inelastic scattering the disagreement is worse and there are large shape differ+ 0) increase ences. In the data of Jansen et al. o Q r - , 21, monotonically at small angles [e.g. o(17.30)/0(29.5 °) 4.1]. In contrast, in our data o(0) is almost constant fo~ angles less than 30 ° [o(17.8°)/o(30.5 °) = 1.2], which is a much more reasonable behavior for an L = 2 transition. Our integrated cross section ratios, defined as p2 o(lr-)/o(rr +) = E sin 0 • o ( 0 , rr-)/~; sin 0 • o ( 0 , zr+)
are listed in table 1. The results from the present experiment are in excellent agreement with our earlier results. Our 2~ ratio is also in good agreement with p2(2~) = 1.58(15) found b y Lunke et al. [5] at TTr = 180 MeV in a new measurement done at SIN. Thus the only result which remains in sharp disagreement with all others is p2(2~) = 1.27(4) due to Jansen et al. [31.
52
12 March 1979
I0 I
I
I
I
I
I-
leO(~r,~)JSO ~,
T ("/T)= 164 MEV
• -__
/ I0
(,9 J~
7
E
I0 <\
ELASTIC
':k q //*
\'
if+
0.1 I
20
I
I
40
I
8C.M.
/÷, I
60
I
80
Fig. 1. Elastic and inelastic cross sections for ~r+ and 7r- scattering from 180 at T(w) = 164 MeV. The curves are from DWIA analysis described in the text.
1. Elastic scattering. The difference, A0min in the position of the first minimum in ~r+ and 7r- elastic
Volume 82B, number 1
PHYSICS LETTERS
Table 1 Ratios of integrated cross sections a), p2 ~ aOr-)/aOr+), Reference
Tzr Elastic (MeV)
Iversen et al. [2] b) 230 Present experiment 230 164 Lunke et al. I5] 180 Jansen et al. [3] 163
1.06(7) 1.01(7) 1.06(7) 1.04(2)
2~ 3~ (1.98 MeV) (5.10 MeV) 1.66(15) 1.58(13) 1.86(16) 1.58(15) 1.27(4)
0.92(10) 0.85(7) 0.89(6) 0.83(3)
a) The angular range over which all C.M. cross sections were integrated is from 0cm ~ 17.8 to 81° except when data was not available for some of the forward angles. b) These errors are somewhat larger than those quoted in ref. [2], since they include +-5%errors in hydrogen cross section normalizations also. These were not included in ref. [2]. scattering may be used to determine possible difference in neutron and proton radii, Arnp -= (r2)l/2 (r2p)1/2. From our data at T(rr) = 164 MeV, we find 0min (Tr-) = 43.9(2) ° and 0min(Tr+) = 46.2(2) °. Thus our A0min = 2.3(3) °, which is the same as that found by Jansen et al. [3]. Jansen et al. analyzed this difference in terms of a black nucleus model. However we believe that an optical model analysis of elastic scattering is much more meaningful. Unlike the black nucleus model, it can take proper account of differential Coulomb effects, as well as the differences in strong interaction amplitudes caused by unequal neutron proton numbers in the vicinity of the (3,3) resonance. We have therefore done a number of optical model calculations with free parameters, with Fermi-averaged parameters, with Kisslinger potential, with Laplacian potential, etc. We find that while the detailed predictions differ from calculation to calculation, the predictions for Arnp remain remarkably stable. We show in fig. 1 the results of calculations using a Kisslinger potential, free n - N amplitudes averaged over 8 protons and 10 neutrons, a modified Gaussian [P0 = 00 {(1 + a(r2/w2)} exp(-r2/w2)] point-proton density distribution from electron scattering [6] (c~ = 1.40, w = 1.793 fro), and Arnp = 0. The fits, especially at the second maxima, are far from perfect, but the locations of the minima are well reproduced, with A0min = 2.0(1) °. These results are borne out by a preliminary, but more sophisticated, momentum-space calculation with second order potential terms, "true absorption", Fermi-motion and binding energy corrections, etc., due
12 March 1979
to Liu [71. It provides improved fit to the data and also predicts A0min = 2.0 ° with Amp = 0. Thus, within the errors of the experiment and the uncertainties of the theory, only 0.3(3) ° of the shift is left to be explained in terms of Amp. This corresponds to Arnp= 0.03(3) fm, which is quite different from Arnp= 0.17 fm obtained by Lunke et al. [5] and Jansen et al. (as quoted in ref. [5]) from their black nucleus analyses.
2. Inelastic scattering. The inelastic scattering differential cross sections at T0r) = 164 MeV for the 2~ state at 1.98 MeV and the 3 i- state at 5.09 MeV are shown in fig. 1. It is clearly seen that for the 2~ state the differential cross sections a(0, 7r-), are considerably larger than a(0, ~r+), the ratio being ~1.9(2) at all angles except in a small region around the minima. It may also be noted that in constrast to Jansen et al. [3] we observe approximately the same 2 - 2 . 5 ° shift between the 7r+/n - minima in the 2~- angular distributions as we do in elastic scattering. This shift is also present in the 180 MeV data of Lunke et al. [5], and is reproduced by the DWIA calculations described below. Inelastic scattering is conventionally analyzed with distorted-wave codes using collective form-factors. This provides a convenient point of reference for comparisons between results for scattering of different particles and at different energies. We have done DWIA analysis of our 164 MeV data, with the potential parameters already described, using a modified version of the code DWPI [81 which permits input of different deformations fin and tip for neutrons and protons. For a starting value of tip, a value of fin was searched such that the integrated cross section ratios a(rr-)/oDW(rr- ) and aQr+)/oDw(n +) had the same value. This determines the ratio/3n//3 p. The absolute values of fin and tip are then determined by normalizing the DWIA curves to the data as shown in fig. 1. A certain degree of arbitrariness exists in how one fits the curves to the data. The fits in fig. 1 are optimised for the data for 0 ~> 30 °. However, since the quality of the fits would not change if the curves for Tr- and 7r+ were both normalized up to 10% higher or lower than shown, we include the contribution of these additional correlated errors in the fir values (obtained with our half density radius, R = 2.55 fro) quoted below. 53
Volume 82B, number 1
PHYSICS LETTERS
The method of DWIA analysis described above gives 03R)n = 1.19(8) fm 03R)p = 0.70(6) fro, and 03R)n / (~R)p = 1.68(13) for the 2~ transition. As discussed in ref. [2], this result reflects the important role played by the valence neutrons in this transition. Similar analysis of the 3 i- transition gives (/3R)n = 0.97(7) fm, 03R)p = 1.32(9) fm, and ((JR)n/(~R )p = 0.74(5). As discussed in ref. [2], the difference of this number from unity arises from the partial blocking of the s - d orbit for neutron excitations, because of the presence of the two valence neutrons. Since the valence neutrons play such an important role in the 2 + transition, collective model analysis of this transition is of questionable value. In recognition of this fact, in ref. [2] we also presented a schematic microscopic model analysis in terms of a deformed 160 core and a deformed distribution of two valence neutrons, and suggested that more realistic microscopic model calculations should be done. Several such improved analyses are forthcoming now [ 9 - 1 2 ] . These analyses start with better representations of 18 0 g.s. + and 21 wave functions in the framework of either the coexistence model [13,14] or the extended shell model [10,15]. 0~ -~ 2~ transition amplitudes are calculated from these wave functions and proton and neutron effective charges are determined to explain the experimental electromagnetic B(E2) for this transition. With these transition amplitudes and effective charges the ratio o(n-)/o(zr +) is calculated, either in terms o f the ratio of amplitudes [9,10] as we had done in ref. [2], or via a more proper DWlA calculation [11,12]. The predictions are found to be extremely sensitive to details of the wave functions and ratios in the range 1.5 to 2.6 are obtained [ 9 - 1 2 ] . In summary, we have shown that a comparative analysis of n + and zr- inelastic scattering at different energies yields consistent answers for separate neutron and proton deformations, or equivalently, isoscalar
54
12 March 1979
and isovector deformations. It has also been shown that the results are consistent with the current understanding of the structure of 180. It therefore appears that in pions we indeed have a powerful tool for exploring aspects of nuclear structure which were not so accessible before. The authors wish to express their thanks to Dr. L. Rosen, the Director of LAMPF, for permission to repeat this experiment and to the entire crew at EPICS for their support during the experiment. We also wish to thank Professors A. Arima, W. Bertozzi, G.E. Brown, P. Ellis, B. Mottelson, and B.H. Wildenthal, and Drs. B.A. Brown, R. Lawson, T.-S.H. Lee and K. Yazaki for numerous discussions and for communicating their results before publication.
References [1 ] A. Bohr and B. Mottelson, Nuclear structure (Benajmin, New York, 1975), vol. I1, p. 137, also vol. I, p. 344. [2] S. Iversen et al., Phys. Rev. Lett. 40 (1978) 17. [3] J. Jansen et al., Phys. Lett. 77B (1978) 359. [4] D.C. Dodder, private communication (1978). [5] C. Lunke et al., Phys. Lett. 78B (1978) 201. [6] W. Bertozzi et al., private communication (1977). [7] L. Liu, private communication (1978). [8] R.A. Eisenstein and G.A. Miller, Program DWPI, Comput Phys. Commun. 11 (1976) 95. Modified for separate ¢3n, j3p by C.L. Morris, private communications (1978). [9] G.E. Brown, private communication (1978). [10] B.A. Brown and B.H. Wildenthal, private communication (1978). [11] A. Arima, R. Seki, K. Yazaki, K. Kune and H. Ohtsubo, private communication (1978). [12] T.-S.H. Lee, D. Kurath and R.D. Lawson, private communication (1978). [13] T. Ericson and G.E. Brown, Nucl. Phys. A277 (1977) 1. [14] R.D. Lawson, F.J.D. Serduke and H.T. Fortune, Phys. Rev. C14 (1976) 1245. [15] A.P. Zucker, B. Buck and J.B. McGrory, Phys. Rev. Lett. 21 (1968) 39.
PHYSICS LETTERS
12 March 1979
NEUTRON-PROTON RADIUS DIFFERENCES AND ISOVECTOR DEFORMATIONS FROM ~+ AND a - INELASTIC SCATTERING FROM 180 ~ S. IVERSEN, H. NANN, A. OBST and Kamal K. SETH Northwestern University, Evanston, IL 60201, USA
N. T A N A K A , C.L. MORRIS and H.A. THIESSEN Los A larnos Scientific Laboratory, Los Alamos, NM 87545, USA
K. BOYER, W. COTTINGAME and C. Fred MOORE University of Texas, Austin, TX 78712, USA
R.L. BOUDR1E University of Colorado, Boulder, CO 80302, USA
D. DEHNHARD University o f Minnesota, Minneapolis, MN 55455, USA
Received 9 January 1979
o + and ~r- elastic and inelastic scattering from 180 have been measured at TOO = 164 MeV. Consistent with the results at 230 MeV, it is found that the ratio o0r-)/o0r +) for the 27 state is 1.86(16), while for the 3~ state it is 0.89(6). These results are interpreted as indicating differences in neutron and proton deformations characterizing the 27 transition and partial neutron blocking for the 3~ transition. Optical model analysis of elastic scattering leads to the conclusion that (/-2)1/2 _ (r~)! ]~ = 0.03(3) fm.
It has long been a fond hope in nuclear structure physics to separate the roles o f neutrons and protons in nuclear excitations [1]. Recent pion scattering experiments make it possible to realize this hope. In an earlier letter [2] we reported that the cross section for the excitation o f the 1.98 MeV 2~" state in 180 by inelastic scattering of 230 MeV negative pions was a factor 1.66(13) larger than that b y positive pions o f the same energy. Because o f the dominance o f the p i o n nucleon (3,3) resonance near this energy, enhancement of n - cross section over n + by a factor 1.25 is expected just because 18 0 contains 10 neutrons and only 8 protons. The much larger observed enhanceResearch supported by the U.S. Department of Energy, the Research Corporation and the Robert A. Welch Foundation.
ment interpreted as indicating a larger average deformation length (flR)n for neutrons than the deformation length (/3R)p for protons. These reactions were subsequently also studied at T,~ -- 163 MeV b y Jansen et al. [3] at SIN. However, these authors found the 7r- enhancement to be only 1.27(4), i.e., consistent with that due to n e u t r o n - p r o t o n number difference alone, and allowing for no differences in (/3R)n and (/3R)p. This complete disparity between our results and those o f Jansen et al. was considered serious. We have therefore repeated the entire experiment at TTr = 164 MeV and 230 MeV with several improvements in the experimental set-up and with a new target. The results from the new experiment at T~r = 164 MeV are presented in this letter in order to permit a direct comparison with the results o f Jansen et al. [3]. 51
Volume 82B, number 1
PHYSICS LETTERS
The general set-up of the EPICS spectrometer system at LAMPF has been described before [2]. For the present experiment, the small helium filled scattering chamber was replaced by a large vacuum scattering chamber, and the ionization chamber beam monitor at 0°was supplemented b y a three scintillator scattered beam monitor telescope at ~ 3 0 °. The old 180 water target was replaced b y 180 (94.9% enriched) ice targets of thickness 0.55 g/cm 2 and 0.31 g/cm 2, which were contained between 1 rail mylar windows. Data was taken from 17.5 ° to 80 ° in 2.5 ° steps. An energy resolution (FWHM) o f 425 keV was realized with the thin target. As before, the absolute cross sectipn normalization was determined b y measuring pion scattering from the hydrogen in the target, and using cross sections interpolated by means of Dodder's [4] phaseshift analysis o f 7r-+p total cross section and scattering data between 20 and 310 MeV. Errors in hydrogen cross sections and in the determination of normalization factors are estimated to be ~< -+5%. These are included in all numerical errors quoted in this letter. However, in fig. 1, where we show our measured differential cross sections, only statistical errors are indicated. Detailed comparison of our data with that of Jansen et al. [3] shows significant differences. For elastic scattering our first minima are more than three times as deep as theirs. Also in the region of the second maximum their cross sections are as much as 25 to 30% smaller than ours. For 2]" inelastic scattering the disagreement is worse and there are large shape differ+ 0) increase ences. In the data of Jansen et al. o Q r - , 21, monotonically at small angles [e.g. o(17.30)/0(29.5 °) 4.1]. In contrast, in our data o(0) is almost constant fo~ angles less than 30 ° [o(17.8°)/o(30.5 °) = 1.2], which is a much more reasonable behavior for an L = 2 transition. Our integrated cross section ratios, defined as p2 o(lr-)/o(rr +) = E sin 0 • o ( 0 , rr-)/~; sin 0 • o ( 0 , zr+)
are listed in table 1. The results from the present experiment are in excellent agreement with our earlier results. Our 2~ ratio is also in good agreement with p2(2~) = 1.58(15) found b y Lunke et al. [5] at TTr = 180 MeV in a new measurement done at SIN. Thus the only result which remains in sharp disagreement with all others is p2(2~) = 1.27(4) due to Jansen et al. [31.
52
12 March 1979
I0 I
I
I
I
I
I-
leO(~r,~)JSO ~,
T ("/T)= 164 MEV
• -__
/ I0
(,9 J~
7
E
I0 <\
ELASTIC
':k q //*
\'
if+
0.1 I
20
I
I
40
I
8C.M.
/÷, I
60
I
80
Fig. 1. Elastic and inelastic cross sections for ~r+ and 7r- scattering from 180 at T(w) = 164 MeV. The curves are from DWIA analysis described in the text.
1. Elastic scattering. The difference, A0min in the position of the first minimum in ~r+ and 7r- elastic
Volume 82B, number 1
PHYSICS LETTERS
Table 1 Ratios of integrated cross sections a), p2 ~ aOr-)/aOr+), Reference
Tzr Elastic (MeV)
Iversen et al. [2] b) 230 Present experiment 230 164 Lunke et al. I5] 180 Jansen et al. [3] 163
1.06(7) 1.01(7) 1.06(7) 1.04(2)
2~ 3~ (1.98 MeV) (5.10 MeV) 1.66(15) 1.58(13) 1.86(16) 1.58(15) 1.27(4)
0.92(10) 0.85(7) 0.89(6) 0.83(3)
a) The angular range over which all C.M. cross sections were integrated is from 0cm ~ 17.8 to 81° except when data was not available for some of the forward angles. b) These errors are somewhat larger than those quoted in ref. [2], since they include +-5%errors in hydrogen cross section normalizations also. These were not included in ref. [2]. scattering may be used to determine possible difference in neutron and proton radii, Arnp -= (r2)l/2 (r2p)1/2. From our data at T(rr) = 164 MeV, we find 0min (Tr-) = 43.9(2) ° and 0min(Tr+) = 46.2(2) °. Thus our A0min = 2.3(3) °, which is the same as that found by Jansen et al. [3]. Jansen et al. analyzed this difference in terms of a black nucleus model. However we believe that an optical model analysis of elastic scattering is much more meaningful. Unlike the black nucleus model, it can take proper account of differential Coulomb effects, as well as the differences in strong interaction amplitudes caused by unequal neutron proton numbers in the vicinity of the (3,3) resonance. We have therefore done a number of optical model calculations with free parameters, with Fermi-averaged parameters, with Kisslinger potential, with Laplacian potential, etc. We find that while the detailed predictions differ from calculation to calculation, the predictions for Arnp remain remarkably stable. We show in fig. 1 the results of calculations using a Kisslinger potential, free n - N amplitudes averaged over 8 protons and 10 neutrons, a modified Gaussian [P0 = 00 {(1 + a(r2/w2)} exp(-r2/w2)] point-proton density distribution from electron scattering [6] (c~ = 1.40, w = 1.793 fro), and Arnp = 0. The fits, especially at the second maxima, are far from perfect, but the locations of the minima are well reproduced, with A0min = 2.0(1) °. These results are borne out by a preliminary, but more sophisticated, momentum-space calculation with second order potential terms, "true absorption", Fermi-motion and binding energy corrections, etc., due
12 March 1979
to Liu [71. It provides improved fit to the data and also predicts A0min = 2.0 ° with Amp = 0. Thus, within the errors of the experiment and the uncertainties of the theory, only 0.3(3) ° of the shift is left to be explained in terms of Amp. This corresponds to Arnp= 0.03(3) fm, which is quite different from Arnp= 0.17 fm obtained by Lunke et al. [5] and Jansen et al. (as quoted in ref. [5]) from their black nucleus analyses.
2. Inelastic scattering. The inelastic scattering differential cross sections at T0r) = 164 MeV for the 2~ state at 1.98 MeV and the 3 i- state at 5.09 MeV are shown in fig. 1. It is clearly seen that for the 2~ state the differential cross sections a(0, 7r-), are considerably larger than a(0, ~r+), the ratio being ~1.9(2) at all angles except in a small region around the minima. It may also be noted that in constrast to Jansen et al. [3] we observe approximately the same 2 - 2 . 5 ° shift between the 7r+/n - minima in the 2~- angular distributions as we do in elastic scattering. This shift is also present in the 180 MeV data of Lunke et al. [5], and is reproduced by the DWIA calculations described below. Inelastic scattering is conventionally analyzed with distorted-wave codes using collective form-factors. This provides a convenient point of reference for comparisons between results for scattering of different particles and at different energies. We have done DWIA analysis of our 164 MeV data, with the potential parameters already described, using a modified version of the code DWPI [81 which permits input of different deformations fin and tip for neutrons and protons. For a starting value of tip, a value of fin was searched such that the integrated cross section ratios a(rr-)/oDW(rr- ) and aQr+)/oDw(n +) had the same value. This determines the ratio/3n//3 p. The absolute values of fin and tip are then determined by normalizing the DWIA curves to the data as shown in fig. 1. A certain degree of arbitrariness exists in how one fits the curves to the data. The fits in fig. 1 are optimised for the data for 0 ~> 30 °. However, since the quality of the fits would not change if the curves for Tr- and 7r+ were both normalized up to 10% higher or lower than shown, we include the contribution of these additional correlated errors in the fir values (obtained with our half density radius, R = 2.55 fro) quoted below. 53
Volume 82B, number 1
PHYSICS LETTERS
The method of DWIA analysis described above gives 03R)n = 1.19(8) fm 03R)p = 0.70(6) fro, and 03R)n / (~R)p = 1.68(13) for the 2~ transition. As discussed in ref. [2], this result reflects the important role played by the valence neutrons in this transition. Similar analysis of the 3 i- transition gives (/3R)n = 0.97(7) fm, 03R)p = 1.32(9) fm, and ((JR)n/(~R )p = 0.74(5). As discussed in ref. [2], the difference of this number from unity arises from the partial blocking of the s - d orbit for neutron excitations, because of the presence of the two valence neutrons. Since the valence neutrons play such an important role in the 2 + transition, collective model analysis of this transition is of questionable value. In recognition of this fact, in ref. [2] we also presented a schematic microscopic model analysis in terms of a deformed 160 core and a deformed distribution of two valence neutrons, and suggested that more realistic microscopic model calculations should be done. Several such improved analyses are forthcoming now [ 9 - 1 2 ] . These analyses start with better representations of 18 0 g.s. + and 21 wave functions in the framework of either the coexistence model [13,14] or the extended shell model [10,15]. 0~ -~ 2~ transition amplitudes are calculated from these wave functions and proton and neutron effective charges are determined to explain the experimental electromagnetic B(E2) for this transition. With these transition amplitudes and effective charges the ratio o(n-)/o(zr +) is calculated, either in terms o f the ratio of amplitudes [9,10] as we had done in ref. [2], or via a more proper DWlA calculation [11,12]. The predictions are found to be extremely sensitive to details of the wave functions and ratios in the range 1.5 to 2.6 are obtained [ 9 - 1 2 ] . In summary, we have shown that a comparative analysis of n + and zr- inelastic scattering at different energies yields consistent answers for separate neutron and proton deformations, or equivalently, isoscalar
54
12 March 1979
and isovector deformations. It has also been shown that the results are consistent with the current understanding of the structure of 180. It therefore appears that in pions we indeed have a powerful tool for exploring aspects of nuclear structure which were not so accessible before. The authors wish to express their thanks to Dr. L. Rosen, the Director of LAMPF, for permission to repeat this experiment and to the entire crew at EPICS for their support during the experiment. We also wish to thank Professors A. Arima, W. Bertozzi, G.E. Brown, P. Ellis, B. Mottelson, and B.H. Wildenthal, and Drs. B.A. Brown, R. Lawson, T.-S.H. Lee and K. Yazaki for numerous discussions and for communicating their results before publication.
References [1 ] A. Bohr and B. Mottelson, Nuclear structure (Benajmin, New York, 1975), vol. I1, p. 137, also vol. I, p. 344. [2] S. Iversen et al., Phys. Rev. Lett. 40 (1978) 17. [3] J. Jansen et al., Phys. Lett. 77B (1978) 359. [4] D.C. Dodder, private communication (1978). [5] C. Lunke et al., Phys. Lett. 78B (1978) 201. [6] W. Bertozzi et al., private communication (1977). [7] L. Liu, private communication (1978). [8] R.A. Eisenstein and G.A. Miller, Program DWPI, Comput Phys. Commun. 11 (1976) 95. Modified for separate ¢3n, j3p by C.L. Morris, private communications (1978). [9] G.E. Brown, private communication (1978). [10] B.A. Brown and B.H. Wildenthal, private communication (1978). [11] A. Arima, R. Seki, K. Yazaki, K. Kune and H. Ohtsubo, private communication (1978). [12] T.-S.H. Lee, D. Kurath and R.D. Lawson, private communication (1978). [13] T. Ericson and G.E. Brown, Nucl. Phys. A277 (1977) 1. [14] R.D. Lawson, F.J.D. Serduke and H.T. Fortune, Phys. Rev. C14 (1976) 1245. [15] A.P. Zucker, B. Buck and J.B. McGrory, Phys. Rev. Lett. 21 (1968) 39.