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Density distribution differences of protons in 16,18O from ratios of π+ elastic scattering cross sections
Volume 156B, number 3,4
PHYSICS LETTERS
20 June 1985
D E N S I T Y D I S T R I B U T I O N D I F F E R E N C E S O F P R O T O N S I N t6'lSO F R O M R A T I O S O F '~ + E L A S T I C S C A T F E R I N G C R O S S S E C T I O N S ~ B.M. B A R N E T T , W. G Y L E S 1, R.R. J O H N S O N , R. T A C I K 1, K.L. E R D M A N , H.W. R O S E R 2 Department of Physws, Universtty of Brmsh Columbta, Vancouver, B C, Canada, V6T 2A6
D.R. G I L L , E.W. B L A C K M O R E TRIUMF, Vancouver, B. C, Canada, V6T 2A3
S. M A R T I N Kernforschungsanlage, D- 5170 Juhch 1, West Germany
C.A. W I E D N E R Max Planck lnsntut fur Kernphystk, D-6900 Hetdelberg 1, West Germany
R.J. SOBIE 3, T.E. D R A K E Department of Physws, Unwerstty of Toronto, Toronto, Ontarto, Canada, M5S 1A 7
and J. A L S T E R Physics Department, Unwerszty of Tel Avw, Tel Avw, Israel
Received 26 November 1984
Differential ~r+ elastic scattering cross sections and ratios have been measured on 16"180 at 48 3 and 62.8 MeV Optical potential analyses were used to extract proton density distribution differences between nuclei The results compare well with preoslon electromagnetic measurements The optical potential parameter dependence is chscussed.
The use o f pions to probe nuclear structure has been hindered by an incomplete understanding o f the n - n u c l e u s interaction. An exception is the study o f ratios o f low energy pion elastic cross sections [1,2] This work was supported In part by the Natural Sciences and Engmeenng Research Council of Canada. 1 Present address Kernforschungszentrum Karlsruhe, Institut fur Experlmentelle Kernphysd¢ der Umversltat Karlsruhe, D-7500 Karlsruhe, West Germany. 2 Present address: InstltUt for Phystk, The Umverstty of Basel, CH-4056 Basel, Switzerland. 3 Present address: CERN EP Dmsion, CH-1211 Geneva 23, Switzerland. 172
o f neighbouring nuclei, where the isospin selectivity o f the zr- has been used to study the RMS radius differences o f the nuclear neutron distributions o f 16,18 O and 12,13C [1 ] . The technique's reliability was studied using the zt+ to measure RMS radius differences between proton distributions in the isotones l l B and 12C [3]. Here we extend this work to establish proton density distribution differences from ~r+ elastic scattering cross section ratios on 16,180 in comparison with precision electromagnetic measurements o f the charge density difference [ 4 - 6 ] . Early studies o f nuclear size, including those o f refs. [1,3], used simple analytic forms to describe the 0370-2693/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 156B, n u m b e r 3,4
PHYSICS LETTERS
20 June 1985
lsh, and PO(r) is a starting density. We use the FB and
radial density of the nucleus [7]. The modified gaussian (MG):
also a Fourier-Laguerre (FL) expansion:
p(r) o~ [1 + b(r/a) 2 ] exp[-(r/a) 2 ]
p(r) = PO(r) + ~ ctnL ln/2(2(r/a) 2) exp [-(r/a)2] , (lb)
and the parabolic Fermi: where a is a potential strength parameter, and L is the Laguerre polynomial. The FL expansion is complete and orthonormal with each term a linear combination of harmonic oscillator densities. Expansion of the nuclear matter density in terms of ( l b ) is expected to converge rapidly. We choose Po(r) as MG, with b = (N - 2)/3 for N nucleons, in both cases. The experiments were performed with the TRIUMF QQD spectrometer [10] on the M11 [11] and M13 [12] channels. The experimental techniques are presented elsewhere [13,14]. The targets were gelled water (1.5% agar) supported in aluminium frames. The target windows were 50 #m tensioned kapton covered with 12.5/am aluminium. The 180 target material was 95.0% H 2 180 [15], whereas the 160 target material
p(r)
p(r) = PO(r) + ~ o~ sin(nur/R c)/r ,
(la)
where R c is a cutoff radius beyond which the a n van14 .,,
8
62 8 MeV 12
A \ %
4
// /
\
/
db
\
//
x Xx
I
08
2
06 b 48 3 MeV
(b)
"0
8 b "~
w v
4
14
b 2
12
"0
I
(a) =
0 4O
I
I
60
80
I
I00
ANGLE (deg c m )
I
120
140
08
(c) .
.
.
.
20
.
I , , ,
40
I
,
,
,
I
,
.
,
L . , .
60 80 I00 ANGLE (deg c m)
i
.
120
.
.
140
Fig. 1 (a) 7r+, 1 6 0 elastic differential scattering cross sections. Broken curves use set E optical parameters. Solid curves are fitted (see text, sets EIM50 and EIM65). (b), (c) ~r+ cross section ratios. Calculations use t h e optical parameters and best fit densities of figs. 3b a n d 2b, respectively.
173
Volume 156B, number 3,4
PHYSICS LETTERS
was natural water. An identical empty target (MT) frame was constructed for background measurements. The mass densities of the 1 8 0 , 1 6 0 , and MT targets were 361,317 and 17 mg/cm 2, respectively. As the system resolution was 1.6 MeV FWHM, peak fitting was used to separate the 2 + (1.98 MeV) inelastic scattering from the elastic scattering in the case of the 180. To avoid systematic effects in the cross section ratios, the 160 spectra were also fitted. The peak shapes were constrained by 12C scattering spectra. Fig. la shows the Ir+, 160 elastic scattering angular distributions at 48.3 and 62.8 MeV. The normalisation is absolute (not derived from other measured cross sections) with an uncertainty of 10% [13,14]. The 48.3 MeV data set agrees with those of refs. [16,17]. The cross section calculations were performed with the MSU optical potential [18], where parameter sets E50 and E65 are global set E [18] scaled with energy. Parameter sets EIM50 and EIM65 were then derived from the 160 cross section data by varying the imaginary parts of optical parameters b0, B 0 and C O to achieve best fits. The density of the 180 proton matter distribution was assumed Fourier (1) where P0 had ~.2)1/2 = 2.67 fm [4]. The neutron distribution of 180 was assumed MG with radius obtained from the measured 1 8 0 - 1 6 0 neutron radius difference ~(r2) 1/2 = 0.21 fm [1]. The 160 proton and neutron distributions were assumed MG with (r2) 1/2 = 2.59 fm [4]. The ratios, figs. lb and lc, were fitted by varying the Fourier coefficients, a n (1 < n < nmax), and R c (or a) for the heavier nucleus so that the Fourier sum volume integral was zero and all densities were positive. Density error envelopes include effects of a n error matrix off-diagonal terms and a completeness error [8] due to Fourier sum truncation at nma x terms. The completeness error was determined by fitting (1) to a realistic density (the 180 electron scattering proton matter density distribution [4,5] ). The difference between that fit and density was used for the completeness error. Figs. 2b and 3b present derived proton density difference distributions: 8pp(r) = 18pp(r) - 16pp(r). Table 1 shows the RMS radii. The rr+ results agree with those of electron scattering [4,5] and muonic atoms [6]. There is little sensitivity to energy or assumed 180 neutron density. The proton charge form factor [19] has been unfolded from the electron scattering charge distributions [4,5]. 174
20 June 1985 5.0
(a) 25
0 aE -2 5
-5.0
-7.5 iii~
-I00
0
=v-H/
.
I
2
3
i
i
50
.
.
. 4
5
6
i
(b) 2.5
0 x
o
'-
-2.5 O.
l ,.~
-5.0 ¢I.
-75
Ioo
.- so.,,.,=°
o
I
2
3
RADIUS
4
5
6
(fm)
Fig. 2. Proton matter density differences 6(lapp(r) - 16pp(r)) derived from 48.3 MeV 7r+ ratios. (a) Variation in derived 5p(r) with +10% variations (except as indicated) in optical parameters from set EIM50 values: Broken curve (+5%), Im bo; Dotted curve, ImBo; (i), Re bo; (iii), Im co; (iv), Im Co; (ii), those remaining. (b) Best fit FL density with set EIM50 optical parameters. Error envelope includes completeness error. Electron scattering matter densities are shown for comparison.
The gradient potential characterising I t - nuclear scattering obscures correlations between optical parameters and 8pp(r): changes in 5pp(r) are mimicked by optical parameter variations. Figs. 2 and 3 show effects of + 10% changes in various optical parameters upon the derived 8pp(r). At 48.3 MeV (fig. 2a), the changes are from set EIM50 parameters, where imaginary terms Im b0, Im B0, and Im C O produce the most dramatic changes in 8pp(r). Im b 0 is so influential (a
Volume 156B, number 3,4
PHYSICS LETTERS
50
Table 1 Proton matter distribution differences: 180-160
25
Energy Optical parameter set
Density nmax a)
6
62.8
FB FL FL c) FL FL FB
0.091(26) 0.079(12) 0.100(37) O.O97(28) 0.084(11) 0.087(15)
0
I
,y
E
-2.5
IiIvl
-75
-I00
O
62 8 MeV
2
3
'
'
5O
'
4
5
6
'(b)]
E65 EIM65 E65 E65 EIM50 EIM50
4 3 3 3 3 3
precision electron scattering d)
0.077(5)
muorac atom studies e)
O.079(5)
a) Typical values: R c m 6.0 fm (FB);a m 1.5 fm (FL). b) Errors shown in parenthesis are statistical. c) In this case only, the laO neutron matter rms radius was set equal to its proton matter rms radius. d) Refs. [4,5]. e) Ref. [6].
25 O
X
-~
48.3
ii
-50
O o c)
20 June 1985
-25 -50
I00
I
0
2
I
3
I
4
I
5
6
RADIUS (fm) Fig. 3. Same as fig. 2 at 62.8 MeV. (a) Variation in derived t~p(r) with +10% variations in optical parameters from set E65 values; (i), Im Bo; (ii), Im co; (iv), TLL; (iii), those remaining. (b) Best fit FB density with set E65 optical parameters. Error envelope includes completeness error. Electron scattering matter densities are shown for comparison.
+5% change is shown for this variable at 48.3 MeV) that the set E parameters prohibit a reasonable fit to 8pp(r) for the 48.3 MeV data set. The 62.8 MeV 8pp(r) (fig. 3a) is sensitive to the L o r e n t z - L o r e n z parameter, TLL, in addition to the aforementioned imaginary terms. These variations are from set E65 parameters. The Ir+ data error envelopes encompass those resulting from a +10% optical parameter set uncertainty, provided that otherwise poorly determined imaginary
terms in the potential are derived from cross section fitting. The pion probes the nucleus at radii greater than 1.5 fm, limited by m o m e n t u m transfer, and sampies density differences with a radial resolution characterised by ~( ~ 1.5 fm. The radial sensitivity of the probe [20,21 ] is determined by details of the interaction's dependence on the nuclear densities and their derivatives. We present these results as testimony to the ability of the rt+ to probe tSpp(r) reliably. We observe some optical parameter sensitivity. This is minimal when cross section fitting is used to determine the reference nucleus optical parameters. Starting with the electron scattering densities one might have proceeded to study isotopic dependence in the optical potential [2,22]. Without reliable neutron density measurement~ such studies are of limited scope. This strengthens the original motivation of this work: the provision of corroboration for the l r - neutron density measurements [1,3].
References [1] [2] [3] [4] [5] [6] [7] [8]
R.R. Johnson et al., Phys. Rev. Lett. 43 (1979) 844. S.A. Dytman et al., Phys. Rex,.C18 (1978) 2316. B.M. Barnett et al., Phys. Lett. 97B (1980) 45. H. Miska et al., Phys. Lett. 83B (1979) 165. B. Notum et al., Phys. Rev. C25 (1982) 1778. G. Backenstoss et al., Phys. Lett. 95B (1980) 212. R.C. Barrett, Nucleonika 26 (1981) 1033. J.L. Friar and J.W. Negele, Adv. Nucl. Phys. 8 (1975) 219. 175
Volume 156B, number 3,4
PHYSICS LETTERS
[9] E. Friedman and C.J. Batty, Phys. Rev. C19 (1978) 34. [10] R.J. Sobie et al., Nucl. Instrum. Methods 219 (1984) 501. [11] G.M. Stinson, TRIUMF Design Note TRI-DNA-80-5 (Vancouver, 1980) unpublished. [12] C.J. Oram et al., Nucl. Instrum. Methods 179 (1981) 95. [13] W. Gyles et al., TRIUMF preprint TRI-PP-84-29, Nucl. Phys. A, to be published. [14] B.M. Barnett, Ph.D. thesis, The University of British Columbia (1985), unpublished; and to be published. [15] I.H. Crocker and J. Mislan, Atomic Energy of Canada Ltd., private communication.
176
20 June 1985
[16] B.M. Preedom et al., Phys. Rev. C23 (1981) 1134. [17] S.A. Dymaan et al., Phys. Rev. C19 (1979) 971. [18] J.P. Cart, H. McManus and K. Stncker-Bauer, Phys. Rev. C25 (1982) 952. [19] H. Chandxa and G. Sauer, Phys. Rev. C13 (1976) 245. [20] E. Friedman, H.J. Gils and H. Rebel, Phys. Rev. C25 (1982) 1551. [21] E. Friedman, Phys. Rev. C28 (1983) 1264. [22] M. Blecher, Phys. Rev. C28 (1983) 2033.
PHYSICS LETTERS
20 June 1985
D E N S I T Y D I S T R I B U T I O N D I F F E R E N C E S O F P R O T O N S I N t6'lSO F R O M R A T I O S O F '~ + E L A S T I C S C A T F E R I N G C R O S S S E C T I O N S ~ B.M. B A R N E T T , W. G Y L E S 1, R.R. J O H N S O N , R. T A C I K 1, K.L. E R D M A N , H.W. R O S E R 2 Department of Physws, Universtty of Brmsh Columbta, Vancouver, B C, Canada, V6T 2A6
D.R. G I L L , E.W. B L A C K M O R E TRIUMF, Vancouver, B. C, Canada, V6T 2A3
S. M A R T I N Kernforschungsanlage, D- 5170 Juhch 1, West Germany
C.A. W I E D N E R Max Planck lnsntut fur Kernphystk, D-6900 Hetdelberg 1, West Germany
R.J. SOBIE 3, T.E. D R A K E Department of Physws, Unwerstty of Toronto, Toronto, Ontarto, Canada, M5S 1A 7
and J. A L S T E R Physics Department, Unwerszty of Tel Avw, Tel Avw, Israel
Received 26 November 1984
Differential ~r+ elastic scattering cross sections and ratios have been measured on 16"180 at 48 3 and 62.8 MeV Optical potential analyses were used to extract proton density distribution differences between nuclei The results compare well with preoslon electromagnetic measurements The optical potential parameter dependence is chscussed.
The use o f pions to probe nuclear structure has been hindered by an incomplete understanding o f the n - n u c l e u s interaction. An exception is the study o f ratios o f low energy pion elastic cross sections [1,2] This work was supported In part by the Natural Sciences and Engmeenng Research Council of Canada. 1 Present address Kernforschungszentrum Karlsruhe, Institut fur Experlmentelle Kernphysd¢ der Umversltat Karlsruhe, D-7500 Karlsruhe, West Germany. 2 Present address: InstltUt for Phystk, The Umverstty of Basel, CH-4056 Basel, Switzerland. 3 Present address: CERN EP Dmsion, CH-1211 Geneva 23, Switzerland. 172
o f neighbouring nuclei, where the isospin selectivity o f the zr- has been used to study the RMS radius differences o f the nuclear neutron distributions o f 16,18 O and 12,13C [1 ] . The technique's reliability was studied using the zt+ to measure RMS radius differences between proton distributions in the isotones l l B and 12C [3]. Here we extend this work to establish proton density distribution differences from ~r+ elastic scattering cross section ratios on 16,180 in comparison with precision electromagnetic measurements o f the charge density difference [ 4 - 6 ] . Early studies o f nuclear size, including those o f refs. [1,3], used simple analytic forms to describe the 0370-2693/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
Volume 156B, n u m b e r 3,4
PHYSICS LETTERS
20 June 1985
lsh, and PO(r) is a starting density. We use the FB and
radial density of the nucleus [7]. The modified gaussian (MG):
also a Fourier-Laguerre (FL) expansion:
p(r) o~ [1 + b(r/a) 2 ] exp[-(r/a) 2 ]
p(r) = PO(r) + ~ ctnL ln/2(2(r/a) 2) exp [-(r/a)2] , (lb)
and the parabolic Fermi: where a is a potential strength parameter, and L is the Laguerre polynomial. The FL expansion is complete and orthonormal with each term a linear combination of harmonic oscillator densities. Expansion of the nuclear matter density in terms of ( l b ) is expected to converge rapidly. We choose Po(r) as MG, with b = (N - 2)/3 for N nucleons, in both cases. The experiments were performed with the TRIUMF QQD spectrometer [10] on the M11 [11] and M13 [12] channels. The experimental techniques are presented elsewhere [13,14]. The targets were gelled water (1.5% agar) supported in aluminium frames. The target windows were 50 #m tensioned kapton covered with 12.5/am aluminium. The 180 target material was 95.0% H 2 180 [15], whereas the 160 target material
p(r)
p(r) = PO(r) + ~ o~ sin(nur/R c)/r ,
(la)
where R c is a cutoff radius beyond which the a n van14 .,,
8
62 8 MeV 12
A \ %
4
// /
\
/
db
\
//
x Xx
I
08
2
06 b 48 3 MeV
(b)
"0
8 b "~
w v
4
14
b 2
12
"0
I
(a) =
0 4O
I
I
60
80
I
I00
ANGLE (deg c m )
I
120
140
08
(c) .
.
.
.
20
.
I , , ,
40
I
,
,
,
I
,
.
,
L . , .
60 80 I00 ANGLE (deg c m)
i
.
120
.
.
140
Fig. 1 (a) 7r+, 1 6 0 elastic differential scattering cross sections. Broken curves use set E optical parameters. Solid curves are fitted (see text, sets EIM50 and EIM65). (b), (c) ~r+ cross section ratios. Calculations use t h e optical parameters and best fit densities of figs. 3b a n d 2b, respectively.
173
Volume 156B, number 3,4
PHYSICS LETTERS
was natural water. An identical empty target (MT) frame was constructed for background measurements. The mass densities of the 1 8 0 , 1 6 0 , and MT targets were 361,317 and 17 mg/cm 2, respectively. As the system resolution was 1.6 MeV FWHM, peak fitting was used to separate the 2 + (1.98 MeV) inelastic scattering from the elastic scattering in the case of the 180. To avoid systematic effects in the cross section ratios, the 160 spectra were also fitted. The peak shapes were constrained by 12C scattering spectra. Fig. la shows the Ir+, 160 elastic scattering angular distributions at 48.3 and 62.8 MeV. The normalisation is absolute (not derived from other measured cross sections) with an uncertainty of 10% [13,14]. The 48.3 MeV data set agrees with those of refs. [16,17]. The cross section calculations were performed with the MSU optical potential [18], where parameter sets E50 and E65 are global set E [18] scaled with energy. Parameter sets EIM50 and EIM65 were then derived from the 160 cross section data by varying the imaginary parts of optical parameters b0, B 0 and C O to achieve best fits. The density of the 180 proton matter distribution was assumed Fourier (1) where P0 had ~.2)1/2 = 2.67 fm [4]. The neutron distribution of 180 was assumed MG with radius obtained from the measured 1 8 0 - 1 6 0 neutron radius difference ~(r2) 1/2 = 0.21 fm [1]. The 160 proton and neutron distributions were assumed MG with (r2) 1/2 = 2.59 fm [4]. The ratios, figs. lb and lc, were fitted by varying the Fourier coefficients, a n (1 < n < nmax), and R c (or a) for the heavier nucleus so that the Fourier sum volume integral was zero and all densities were positive. Density error envelopes include effects of a n error matrix off-diagonal terms and a completeness error [8] due to Fourier sum truncation at nma x terms. The completeness error was determined by fitting (1) to a realistic density (the 180 electron scattering proton matter density distribution [4,5] ). The difference between that fit and density was used for the completeness error. Figs. 2b and 3b present derived proton density difference distributions: 8pp(r) = 18pp(r) - 16pp(r). Table 1 shows the RMS radii. The rr+ results agree with those of electron scattering [4,5] and muonic atoms [6]. There is little sensitivity to energy or assumed 180 neutron density. The proton charge form factor [19] has been unfolded from the electron scattering charge distributions [4,5]. 174
20 June 1985 5.0
(a) 25
0 aE -2 5
-5.0
-7.5 iii~
-I00
0
=v-H/
.
I
2
3
i
i
50
.
.
. 4
5
6
i
(b) 2.5
0 x
o
'-
-2.5 O.
l ,.~
-5.0 ¢I.
-75
Ioo
.- so.,,.,=°
o
I
2
3
RADIUS
4
5
6
(fm)
Fig. 2. Proton matter density differences 6(lapp(r) - 16pp(r)) derived from 48.3 MeV 7r+ ratios. (a) Variation in derived 5p(r) with +10% variations (except as indicated) in optical parameters from set EIM50 values: Broken curve (+5%), Im bo; Dotted curve, ImBo; (i), Re bo; (iii), Im co; (iv), Im Co; (ii), those remaining. (b) Best fit FL density with set EIM50 optical parameters. Error envelope includes completeness error. Electron scattering matter densities are shown for comparison.
The gradient potential characterising I t - nuclear scattering obscures correlations between optical parameters and 8pp(r): changes in 5pp(r) are mimicked by optical parameter variations. Figs. 2 and 3 show effects of + 10% changes in various optical parameters upon the derived 8pp(r). At 48.3 MeV (fig. 2a), the changes are from set EIM50 parameters, where imaginary terms Im b0, Im B0, and Im C O produce the most dramatic changes in 8pp(r). Im b 0 is so influential (a
Volume 156B, number 3,4
PHYSICS LETTERS
50
Table 1 Proton matter distribution differences: 180-160
25
Energy Optical parameter set
Density nmax a)
6
62.8
FB FL FL c) FL FL FB
0.091(26) 0.079(12) 0.100(37) O.O97(28) 0.084(11) 0.087(15)
0
I
,y
E
-2.5
IiIvl
-75
-I00
O
62 8 MeV
2
3
'
'
5O
'
4
5
6
'(b)]
E65 EIM65 E65 E65 EIM50 EIM50
4 3 3 3 3 3
precision electron scattering d)
0.077(5)
muorac atom studies e)
O.079(5)
a) Typical values: R c m 6.0 fm (FB);a m 1.5 fm (FL). b) Errors shown in parenthesis are statistical. c) In this case only, the laO neutron matter rms radius was set equal to its proton matter rms radius. d) Refs. [4,5]. e) Ref. [6].
25 O
X
-~
48.3
ii
-50
O o c)
20 June 1985
-25 -50
I00
I
0
2
I
3
I
4
I
5
6
RADIUS (fm) Fig. 3. Same as fig. 2 at 62.8 MeV. (a) Variation in derived t~p(r) with +10% variations in optical parameters from set E65 values; (i), Im Bo; (ii), Im co; (iv), TLL; (iii), those remaining. (b) Best fit FB density with set E65 optical parameters. Error envelope includes completeness error. Electron scattering matter densities are shown for comparison.
+5% change is shown for this variable at 48.3 MeV) that the set E parameters prohibit a reasonable fit to 8pp(r) for the 48.3 MeV data set. The 62.8 MeV 8pp(r) (fig. 3a) is sensitive to the L o r e n t z - L o r e n z parameter, TLL, in addition to the aforementioned imaginary terms. These variations are from set E65 parameters. The Ir+ data error envelopes encompass those resulting from a +10% optical parameter set uncertainty, provided that otherwise poorly determined imaginary
terms in the potential are derived from cross section fitting. The pion probes the nucleus at radii greater than 1.5 fm, limited by m o m e n t u m transfer, and sampies density differences with a radial resolution characterised by ~( ~ 1.5 fm. The radial sensitivity of the probe [20,21 ] is determined by details of the interaction's dependence on the nuclear densities and their derivatives. We present these results as testimony to the ability of the rt+ to probe tSpp(r) reliably. We observe some optical parameter sensitivity. This is minimal when cross section fitting is used to determine the reference nucleus optical parameters. Starting with the electron scattering densities one might have proceeded to study isotopic dependence in the optical potential [2,22]. Without reliable neutron density measurement~ such studies are of limited scope. This strengthens the original motivation of this work: the provision of corroboration for the l r - neutron density measurements [1,3].
References [1] [2] [3] [4] [5] [6] [7] [8]
R.R. Johnson et al., Phys. Rev. Lett. 43 (1979) 844. S.A. Dytman et al., Phys. Rex,.C18 (1978) 2316. B.M. Barnett et al., Phys. Lett. 97B (1980) 45. H. Miska et al., Phys. Lett. 83B (1979) 165. B. Notum et al., Phys. Rev. C25 (1982) 1778. G. Backenstoss et al., Phys. Lett. 95B (1980) 212. R.C. Barrett, Nucleonika 26 (1981) 1033. J.L. Friar and J.W. Negele, Adv. Nucl. Phys. 8 (1975) 219. 175
Volume 156B, number 3,4
PHYSICS LETTERS
[9] E. Friedman and C.J. Batty, Phys. Rev. C19 (1978) 34. [10] R.J. Sobie et al., Nucl. Instrum. Methods 219 (1984) 501. [11] G.M. Stinson, TRIUMF Design Note TRI-DNA-80-5 (Vancouver, 1980) unpublished. [12] C.J. Oram et al., Nucl. Instrum. Methods 179 (1981) 95. [13] W. Gyles et al., TRIUMF preprint TRI-PP-84-29, Nucl. Phys. A, to be published. [14] B.M. Barnett, Ph.D. thesis, The University of British Columbia (1985), unpublished; and to be published. [15] I.H. Crocker and J. Mislan, Atomic Energy of Canada Ltd., private communication.
176
20 June 1985
[16] B.M. Preedom et al., Phys. Rev. C23 (1981) 1134. [17] S.A. Dymaan et al., Phys. Rev. C19 (1979) 971. [18] J.P. Cart, H. McManus and K. Stncker-Bauer, Phys. Rev. C25 (1982) 952. [19] H. Chandxa and G. Sauer, Phys. Rev. C13 (1976) 245. [20] E. Friedman, H.J. Gils and H. Rebel, Phys. Rev. C25 (1982) 1551. [21] E. Friedman, Phys. Rev. C28 (1983) 1264. [22] M. Blecher, Phys. Rev. C28 (1983) 2033.