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Elastic electron scattering at 30–80 MeV from 142,146,150Nd
Volume 48B, number 3
PHYSICS LETTERS
4 February 1974
E L A S T I C E L E C T R O N S C A T T E R I N G A T 3 0 - 8 0 MeV F R O M 142,146,150Nd R. MAAS and C.W DE JAGER lnstituut voor Kernphysisch Onderzoek, Amsterdam, The Netherlands
Received 4 December 1973 The elastic electron scattering cross sections for 142'146'15°Nd have been measured at momentum transfers between 0.2 and 0.8 fm -1 . The results do not support the anomalously small skin thickness values obtained in a previous low-energyelectron scattering experiment.
In the sequence of the even neodymium isotopes 142Nd-150Nd a rather sharp decrease in the excitation energy of the first 2÷ levels is observed. Calculations of the quadrupole deformation parameter/3 from B(E2) measurements [1] show a remarkable increase in/3 from 142Nd (/3 = 0.104) to 150Nd (/3 ,= 0.279). Apparently, the closed neutron shell (N = 82) of 142Nd gives rise to a rather tight struc'ture, while 150Nd, well away from the magic number of neutrons, exhibits a much looser, rotator-like, structure. For non-aligned nuclei one can only determine the average of the charge distribution over all directions. Hence, one expects an increasing deformation to manifest itself mainly in an increase in skin thickness. In several experiments the differences in the charge distribution parameters of neodymium isotopes have been studied. The muonic X-ray measurements of Macagno et al. [2], analysed in terms of the Fermi model, do not show a significant change in the skin thickness t (within the experimental accuracy of 3-4%) over the range 142Nd-150Nd. High-energy (up to 500 MeV) electron scattering experiments by Heisenberg et al. [3] indicate a large increase in t(13%) from 142Nd to 15°Nd. Results of low-energy (60 MeV) electron scattering experiments at Yale by Madsen et al. [5] are in total disagreement with the high-energy data. For 142Nd and 150Nd anomalously small skin thicknesses of 1.79 -+ 0.18 fm and 1.59 + 0.23 fm, respectively, are found, while the 146Nd data can only be fitted reasonably with a uniform charge distribution. In a recent reanalysis [4] of the Yale data the anomaly is partly removed: e.g. for 142Nd a, still unusually small, tvalue of 2.25 - 0.07 fm was obtained. The authors tentatively attributed this anomaly to dispersive effects. 212
To investigate this striking discrepancy it was decided to perform a series of measurement on 142,146,15°Nd at the 100 MeV electron scattering facility of Amsterdam [6]. As targets, isotopically enriched (> 95%) metallic foils of approximately 20 mg/cm 2 thickness were used. The relative thicknesses were determined by measuring the absorption of the 22 keV K s X-rays of 109Ag. Calibration of the absorption rate was obtained with an aqueous solution of Nd(NO 3)e' Since the targets are highly reactive with air, special handling arrangements were necessary. During the thickness measurements each target was conrained inside an argon-filled cassette, equipped with two mylar (30 ~tm) windows, whereas the targets were installed in the scattering area through an argon-filled glovebox, attached to the scattering chamber. Data were taken at energies and angles of resp. 40, 60 and 80 MeV and 90 ° to 130 ° in steps of 10°, plus one low-q point at 30 MeV and 90 °. Targets were placed in transmission. In most of the runs a resolution of 0.15% was obtained, which was sufficient to subtract the contribution of the 0.13 MeV level from the elastic peak in the 150Nd spectra. The scattered electrons were detected by a ladder counter array of 19 channels, 0.1% wide, placed in the focal plane of the magic-angle spectrometer [6]. For each measurement the elastic peak was shifted over the whole ladder in steps of AE/E = 0.03% down to a cut-off of 1.5%. The measuring sequence of the 40 and 60 MeV spectra was: 12C (as reference), 142Nd, 146Nd, 150Nd; at 30 and 80 MeV all three Nd-targets were interchanged at every separate spectrometer field setting. During the measurements the beam current was constantly monitored with a Faraday cup. Beam current loss downstream
4 February 1974
PHYSICS LETTERS
Volume 48B, number 3
Table 1 Charge distribution parameters obtained form the present and other experiments c (fm)
t (fro)
(r2) 1/2 (fm)
X2IN
Ref.
142Nd
5.839 ± 0.033 5.83 +-0.020 5.774 +-0.026 5.6838 5.75 ± 0.03
2.50 1.79 2.25 2.579 2.38
4.993 ± 0.035 4.77 -+0.04 4.863 ± 0.034 4.913
1.27 1.20
present work Madsenetal.[5] Cardman et al. [4] Heisenberg et al. [3] Macagno et al. [2]
146Nd
5.867 ± 0.032
2.44 ± 0.09
4.993 +- 0.037
1.21
present work
lS°Nd
5.865 -+0.035
2.51 ± 0.08
5.015 ± 0.037
0.67
present work
± 0.08 ±0.14 +-0.07 ± 0.013 ± 0.08
of the target due to multiple scattering was measured with a feedback system [6] between the cup and a toroid monitor situated upstream of the target. After applying corrections for dead-time losses, random coincidences, counter efficiencies and background, the sum spectra were fitted with an analytic function and the elastic peak was integrated down to the cut-off energy. The contribution from the oxygen contamination never exceeded 8%. Cross-section ratios were obtained, after applying additional corrections for beam current loss and radiative effects, to a statistical accuracy of 3%. The 12C cross sections were calculated with the Fischer-Rawitscher code [7], using the charge distribution parameters determined by Jansen et al. [10]. The data were analyzed in terms of the two-parameter Fermi model. The best-fit (c, t) values were determined with an iterative procedure. Since in the isotopic cross-section ratios most of the systematic errors are expected to cancel, we also fit-
ted the quantities o(146)/o(142), a(142)/0(150) and a(146)/0(150). In both these sets of fits the target thickness was treated as a free parameter. The results are summarized in tables 1 and 2. The errors quoted correspond to one standard deviation as determined from the covariance matrix. In table 1 the other available data on 142Nd are also listed. As an example fig. 1 shows the projection of the (c, t, d) covariance ellipsoid (d is target thickness) onto the (c, t) plane. The results are in good agreement with the muonic X-ray data of ref. [2]. There is still a discrepancy in the case of 146Nd and 150Nd with the, rather large, t-values obtained by Heisenberg et al. The tvalues determined from the present experiment do not show the anomalous behaviour found by Madsen et ai. It should be stressed again that the present experiment was performed over an energy range comparable to that of the Yale experiment. In our measurements no significant change in the skin thickness is observed
Table 2 Charge distribution parameter differences obtained from the present and other experiments. Ac (fm)
At (fm)
ACt2)v2 (fm)
X2/N
Ref.
-0.007 ± 0.034 0.018 ± 0.026 0.0297
0.04 ± 0.08 0.11 ± 0.05 0.199 ± 0.019
0.008 ± 0.039 0.0527 ± 0.0036 0.057
1.53 1.41
present work combined analysis *) [31
lS°Nd-142Nd
0.021 ± 0.039 0.078 ± 0.027 0.0347
0.05 ± 0.08 0.18 ± 0.06 0.283 ± 0.034
0.03 ± 0.04 0.115 + 0.005 0.135
1.74 2.19
present work combined analysis [3]
lS°Nd-146Nd
0.031 ± 0.036 0.046 ± 0.027 0.0644
0.06 5 0.09 0.10 ± 0.06 0.084 ± 0.034
0.04 +-0.04 0.067 -+0.004 0.078
1.42 1.35
present work combined analysis [3]
146Nd-142Nd
*) Combined analysis of the present results and
0"2yvaluesobtained from Kc~X-ray experiments of refs. [8, 9]. 213
Volume 48B, number 3
PHYSICS LETTERS i
i
4 February 1974
i
146Nd _15ONd
I
- 0.01
~ , -0.02 - 0.03
\
+
- 0.04 - 0.05 - 0,06 - 0.07
\ "~\q\~t - -
KO,X- rGys x
\ \\
-0114-0112-01.10-0:08-0106-0[04-0[02 ,at[,m]
O~C)O 502 .
Fig. 1. Projection of (c, t, d) covariance ellipsoids (d is target thickness) onto the (c, t) plane. The small ellipse results from a combined analysis of the present data and the 8 value from refs. [8, 9]. between the isotopes studied. In order to extract from the present experiment the most reliable differences in the charge distribution parameters, a combined analysis was performed o f the present data and the results of recent K a X-ray experiments [8, 9]. The results o f this combined analysis, also given in table 2, show a significant increase in skin thickness for 146Nd and 150Nd as compared with 142Nd. The skin thickness differences determined in this way are smaller than the results of Heisenberg et al., but considering the errors, this discrepancy is hardly significant. These authors showed that the increase in skin thickness from 142Nd to 150Nd can primarily be attributed to the larger (quadrupole) deformation of the heavier Nd isotopes. The authors wish to express their gratitude to Professor C. de Vries for his constant encouragement and interest in this work and to Professor G.H. Rawitscher for making available his computer code. This work is part of the research program o f the Institute for Nuclear Physics Research (I.K.O.), made
214
possible by financial support from the F o u n d a t i o n for Fundamental Research on Matter (F.O.M.) and the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).
References [1] P.H. Stelson and L. Grodzins, Nucl. Data 1A (1965) 1. [2] E.R. Macagno et al. Phys. Rev. C1 (1970) 1202. [3] J.H. Heisenberg, J.S. McCarthy, l.Sick and M.R. Yearian, Nucl. Phys. A164 (1971) 340. [4] L.S. Cardman et al. Nucl. Phys., to be published. [5] D.W. Madsen, L.S. Cardman, J.R. Legg and C.K. Bockel-. man, Nucl. Phys. A169 (1971) 97. [6] P.J.T. Bruinsma, J.G. Noomen and C. de Vries, Nucl. Instr. 74 (1969) 1, 5, 13, 20 and 27. [7] C.R. Fischer and G.H. Rawitscher, Phys. Rev. 135 (1964) B377. [8] S.K. Bhattacherjee and P.L. Lee, Phys. Rev. 188 (1969) 1919. [9] P.L. Lee and F. Boehm, Phys. Rev., to be published. [10] J.A. Jansen, R.T. Pegrdeman and C. de Vries, Nucl. Phys. A188 (1972) 337.
PHYSICS LETTERS
4 February 1974
E L A S T I C E L E C T R O N S C A T T E R I N G A T 3 0 - 8 0 MeV F R O M 142,146,150Nd R. MAAS and C.W DE JAGER lnstituut voor Kernphysisch Onderzoek, Amsterdam, The Netherlands
Received 4 December 1973 The elastic electron scattering cross sections for 142'146'15°Nd have been measured at momentum transfers between 0.2 and 0.8 fm -1 . The results do not support the anomalously small skin thickness values obtained in a previous low-energyelectron scattering experiment.
In the sequence of the even neodymium isotopes 142Nd-150Nd a rather sharp decrease in the excitation energy of the first 2÷ levels is observed. Calculations of the quadrupole deformation parameter/3 from B(E2) measurements [1] show a remarkable increase in/3 from 142Nd (/3 = 0.104) to 150Nd (/3 ,= 0.279). Apparently, the closed neutron shell (N = 82) of 142Nd gives rise to a rather tight struc'ture, while 150Nd, well away from the magic number of neutrons, exhibits a much looser, rotator-like, structure. For non-aligned nuclei one can only determine the average of the charge distribution over all directions. Hence, one expects an increasing deformation to manifest itself mainly in an increase in skin thickness. In several experiments the differences in the charge distribution parameters of neodymium isotopes have been studied. The muonic X-ray measurements of Macagno et al. [2], analysed in terms of the Fermi model, do not show a significant change in the skin thickness t (within the experimental accuracy of 3-4%) over the range 142Nd-150Nd. High-energy (up to 500 MeV) electron scattering experiments by Heisenberg et al. [3] indicate a large increase in t(13%) from 142Nd to 15°Nd. Results of low-energy (60 MeV) electron scattering experiments at Yale by Madsen et al. [5] are in total disagreement with the high-energy data. For 142Nd and 150Nd anomalously small skin thicknesses of 1.79 -+ 0.18 fm and 1.59 + 0.23 fm, respectively, are found, while the 146Nd data can only be fitted reasonably with a uniform charge distribution. In a recent reanalysis [4] of the Yale data the anomaly is partly removed: e.g. for 142Nd a, still unusually small, tvalue of 2.25 - 0.07 fm was obtained. The authors tentatively attributed this anomaly to dispersive effects. 212
To investigate this striking discrepancy it was decided to perform a series of measurement on 142,146,15°Nd at the 100 MeV electron scattering facility of Amsterdam [6]. As targets, isotopically enriched (> 95%) metallic foils of approximately 20 mg/cm 2 thickness were used. The relative thicknesses were determined by measuring the absorption of the 22 keV K s X-rays of 109Ag. Calibration of the absorption rate was obtained with an aqueous solution of Nd(NO 3)e' Since the targets are highly reactive with air, special handling arrangements were necessary. During the thickness measurements each target was conrained inside an argon-filled cassette, equipped with two mylar (30 ~tm) windows, whereas the targets were installed in the scattering area through an argon-filled glovebox, attached to the scattering chamber. Data were taken at energies and angles of resp. 40, 60 and 80 MeV and 90 ° to 130 ° in steps of 10°, plus one low-q point at 30 MeV and 90 °. Targets were placed in transmission. In most of the runs a resolution of 0.15% was obtained, which was sufficient to subtract the contribution of the 0.13 MeV level from the elastic peak in the 150Nd spectra. The scattered electrons were detected by a ladder counter array of 19 channels, 0.1% wide, placed in the focal plane of the magic-angle spectrometer [6]. For each measurement the elastic peak was shifted over the whole ladder in steps of AE/E = 0.03% down to a cut-off of 1.5%. The measuring sequence of the 40 and 60 MeV spectra was: 12C (as reference), 142Nd, 146Nd, 150Nd; at 30 and 80 MeV all three Nd-targets were interchanged at every separate spectrometer field setting. During the measurements the beam current was constantly monitored with a Faraday cup. Beam current loss downstream
4 February 1974
PHYSICS LETTERS
Volume 48B, number 3
Table 1 Charge distribution parameters obtained form the present and other experiments c (fm)
t (fro)
(r2) 1/2 (fm)
X2IN
Ref.
142Nd
5.839 ± 0.033 5.83 +-0.020 5.774 +-0.026 5.6838 5.75 ± 0.03
2.50 1.79 2.25 2.579 2.38
4.993 ± 0.035 4.77 -+0.04 4.863 ± 0.034 4.913
1.27 1.20
present work Madsenetal.[5] Cardman et al. [4] Heisenberg et al. [3] Macagno et al. [2]
146Nd
5.867 ± 0.032
2.44 ± 0.09
4.993 +- 0.037
1.21
present work
lS°Nd
5.865 -+0.035
2.51 ± 0.08
5.015 ± 0.037
0.67
present work
± 0.08 ±0.14 +-0.07 ± 0.013 ± 0.08
of the target due to multiple scattering was measured with a feedback system [6] between the cup and a toroid monitor situated upstream of the target. After applying corrections for dead-time losses, random coincidences, counter efficiencies and background, the sum spectra were fitted with an analytic function and the elastic peak was integrated down to the cut-off energy. The contribution from the oxygen contamination never exceeded 8%. Cross-section ratios were obtained, after applying additional corrections for beam current loss and radiative effects, to a statistical accuracy of 3%. The 12C cross sections were calculated with the Fischer-Rawitscher code [7], using the charge distribution parameters determined by Jansen et al. [10]. The data were analyzed in terms of the two-parameter Fermi model. The best-fit (c, t) values were determined with an iterative procedure. Since in the isotopic cross-section ratios most of the systematic errors are expected to cancel, we also fit-
ted the quantities o(146)/o(142), a(142)/0(150) and a(146)/0(150). In both these sets of fits the target thickness was treated as a free parameter. The results are summarized in tables 1 and 2. The errors quoted correspond to one standard deviation as determined from the covariance matrix. In table 1 the other available data on 142Nd are also listed. As an example fig. 1 shows the projection of the (c, t, d) covariance ellipsoid (d is target thickness) onto the (c, t) plane. The results are in good agreement with the muonic X-ray data of ref. [2]. There is still a discrepancy in the case of 146Nd and 150Nd with the, rather large, t-values obtained by Heisenberg et al. The tvalues determined from the present experiment do not show the anomalous behaviour found by Madsen et ai. It should be stressed again that the present experiment was performed over an energy range comparable to that of the Yale experiment. In our measurements no significant change in the skin thickness is observed
Table 2 Charge distribution parameter differences obtained from the present and other experiments. Ac (fm)
At (fm)
ACt2)v2 (fm)
X2/N
Ref.
-0.007 ± 0.034 0.018 ± 0.026 0.0297
0.04 ± 0.08 0.11 ± 0.05 0.199 ± 0.019
0.008 ± 0.039 0.0527 ± 0.0036 0.057
1.53 1.41
present work combined analysis *) [31
lS°Nd-142Nd
0.021 ± 0.039 0.078 ± 0.027 0.0347
0.05 ± 0.08 0.18 ± 0.06 0.283 ± 0.034
0.03 ± 0.04 0.115 + 0.005 0.135
1.74 2.19
present work combined analysis [3]
lS°Nd-146Nd
0.031 ± 0.036 0.046 ± 0.027 0.0644
0.06 5 0.09 0.10 ± 0.06 0.084 ± 0.034
0.04 +-0.04 0.067 -+0.004 0.078
1.42 1.35
present work combined analysis [3]
146Nd-142Nd
*) Combined analysis of the present results and
0"2yvaluesobtained from Kc~X-ray experiments of refs. [8, 9]. 213
Volume 48B, number 3
PHYSICS LETTERS i
i
4 February 1974
i
146Nd _15ONd
I
- 0.01
~ , -0.02 - 0.03
\
+
- 0.04 - 0.05 - 0,06 - 0.07
\ "~\q\~t - -
KO,X- rGys x
\ \\
-0114-0112-01.10-0:08-0106-0[04-0[02 ,at[,m]
O~C)O 502 .
Fig. 1. Projection of (c, t, d) covariance ellipsoids (d is target thickness) onto the (c, t) plane. The small ellipse results from a combined analysis of the present data and the 8
214
possible by financial support from the F o u n d a t i o n for Fundamental Research on Matter (F.O.M.) and the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).
References [1] P.H. Stelson and L. Grodzins, Nucl. Data 1A (1965) 1. [2] E.R. Macagno et al. Phys. Rev. C1 (1970) 1202. [3] J.H. Heisenberg, J.S. McCarthy, l.Sick and M.R. Yearian, Nucl. Phys. A164 (1971) 340. [4] L.S. Cardman et al. Nucl. Phys., to be published. [5] D.W. Madsen, L.S. Cardman, J.R. Legg and C.K. Bockel-. man, Nucl. Phys. A169 (1971) 97. [6] P.J.T. Bruinsma, J.G. Noomen and C. de Vries, Nucl. Instr. 74 (1969) 1, 5, 13, 20 and 27. [7] C.R. Fischer and G.H. Rawitscher, Phys. Rev. 135 (1964) B377. [8] S.K. Bhattacherjee and P.L. Lee, Phys. Rev. 188 (1969) 1919. [9] P.L. Lee and F. Boehm, Phys. Rev., to be published. [10] J.A. Jansen, R.T. Pegrdeman and C. de Vries, Nucl. Phys. A188 (1972) 337.