- Email: [email protected]
Pionic x-rays and the neutron radius of 44Ca
Volume
8lB, number
2
PHYSICS
LETTERS
12 February
1979
PIONIC X-RAYS AND THE NEUTRON RADIUS OF 44Ca C.J. BATTY, S.F. BIAGI, E. FRIEDMAN ’ and S.D. HOATH Rutherford
Laboratory,
Chilton, Didcot, Oxon, UK
J.D. DAVIES, G.J. PYLE and G.T.A. SQUIER Physics Department,
University of Birmingham, Birmingham,
UK
D.M. ASBURY Physics Department,
University of Surrey, Guildford,
UK
and
M. LEON University of California, Los Alamos Scientific Laboratory Los Alamos, NM 87545, USA
Received
10 October
1978
Differences between strong interaction level shifts and widths for 2p states in pionic atoms of 44j40Ca have been measured Analysis in terms of an effective pion-nucleus potential leads to a difference in neutron rms radii of r,(44) - r,(40) = 0.05 i 0.05 fm.
The density distribution of neutrons in nuclei has recently been the subject of many investigations [l] . The analysis of strong interaction shifts and widths of pionic atoms could in principle provide useful information on neutron density distributions since the p-wave rr- interaction occurs predominantly with neutrons. In the present letter we report experimental results for the differences between shifts and widths of the 2p level in pionic atoms of 44Ca and 4oCa, where the accuracy is almost an order of magnitude better than that of the previous measurement [2] of the same quantities. These results are analysed using an effective r- -nucleus potential whose parameters have been determined recently [3] from other data for 2p states of pionic atoms. The experiment was performed using the stopped meson beam [4] from the 7 GeV proton synchrotron t Permanent address: Hebrew University,
The Racah Institute Jerusalem, Israel.
of Physics,
The
Nimrod. A low background was achieved using an electrostatically separated beam of 200 MeV/c pions. Stopping pions were identified with a counter telescope system [4], X-rays were detected using a coaxial 70 cm3 Ge(Li) detector with 1.68 keV resolution at 1.33 MeV. The 44Ca target consisted of 282 g of 44CaC03 enriched to 98.6%. For natural Ca (consisting of 97% of 40Ca) a similar target of CaCO, was used. It was essential to have the same chemical form for both isotopes so that similar procedures for analysing the peaks and background could be employed. Data and calibration spectra were taken simultaneously and routed into different 8192 channel regions of an ADC computer system. The strong interaction shifts and widths were determined from a least-squares analysis of both X-ray peaks and calibration peaks, as described earlier [5] . A contribution from the muonic n = 4 + 2 X-ray line which has a very similar energy was included in the analysis but had only a small effect on the final result. The spectrum obtained with 165
Volume
8 1 B, number
2
PHYSICS
LETTERS
12 February
1979
COUNTS i 2000
r
r 1600
0 2‘ioo PION:C
2430 CA
2460
2490
2820
2550
2580 CHANNEL
44
NO
Fig. 1. Measured X-ray spectrum for the 3d + 2p transition in the 44 CaCOa target. Also shown are the fits to the data and the individual contributions from the pionic 3d + 2p peak and the small underlying muonic 4d + 2p3,a, 1,2 peaks.
the 44Ca carbonate target and the fit to the data are shown in fig. 1. Table 1 shows the measured energies for the 3d + 2p transitions for the natural Ca and for the d4Ca target. The results for Ca are in good agreement with the previous measurement [3] using a metal target which is also given in table 1. Taking only the CaC03 and 44CaC03 targets and correcting the results for the small amount of 44Ca present in natural calcium, we obtain for the difference between the shifts for the two isotopes &E= ~(44) - ~(40) = -0.331 + 0.027 keV and for the widths 6r= r‘(44) - r(40)= - 0.040
+ 0.075 keV. These results are in good agreement with and considerably more precise than the results SE = -0.36 + 0.17 keV and 6r = -0.22 f 0.20 keV obtained by Kunselman and Grin [2]. Analysis of the strong interaction effects in pionic atoms in terms of an effective pion-nucleus potential related to the nucleon density distribution can be used to investigate the difference A between the rms radii of the neutron and proton distributions [6]. In their analysis Anderson et al. assumed A was independent of mass for a range of pionic atom data and obtained A = -0.01 f 0.16 fm [6]. However, Kunselman and
Table 1 Results for 3d + 2p transitions. Target
CaCOs (nat) 44CaCOs Ca metal [3] a)
Measured energy
Electromagnetic energy
tkeV)
(keV)
209.609 209.359 209.612
+ 0.025 f 0.013 + 0.014
a) There is a small error in the values for Ca given in ref.
166
207.683 207.753 207.683
[ 31.
Shift
Width
(keV)
(keV)
1.926 1.606 1.929
1.692 f 0.063 1.652 * 0.038 1.613 f 0.023
Volume
81B, number
2
PHYSICS
Grin [2] , using their 44Ca results found A(44) = 0.35 + 0.15 fm for one set of optical potential parameters while Tauscher and Wycech found A(44) = 0.49 f 0.30 fm [7] using another set. Our recent determination of the optical potential parameters [3] permits these findings to be checked using the more precise result for 44 Ca given above. The potential used in the present work follows that of Krell and Ericson [g] and is given by I?)
= [4(r) -V@.)
*VIDP ,
(1)
where the local part, q(r), and the non-local part o(r), are related to the nuclear density distributions as follows: 4(r) = -4nNl +b,(p,
+ /J/m) VJo (P, + P,) -@I
(2)
+(1 +~/2m)~o4pP~~,)~
44 = “0 W/i 1 - ia0 (41 , ao(r) = p4n ((1 + plm)-’
LETTERS
12 February
with the results for Is, 3f and 4d levels will be published elsewhere [lo] . Fig. 2 shows 8~ and 6 F calculated as functions of r (44) - r (40), the difference in neutron rms radii of 4’4 Ca and 60 Ca, for four sets of potential and density distributions. For curve A parabolic Fermi charge density distributions from electron scattering measurements [l I] were used for the protons (rp(40) = 3.482 fm and rP(44) = 3.510 fm), and A(40) = r,(40) - rP(40) = 0.0 assumed. Curve B had A(40) = -0.04 fm as predicted by Hartree-Fock calculations [ 121 . Curve C had this change in neutron radius compensated by reducing Ke C,/Im Co from 1.9 to 1.6 so as to fit the 4oCa results, while curve D used single particle point nucleon distributions for pP and pn calculated from a SaxonWoods potential adjusted, after folding in the finite proton size, to reproduce the charge distributions used in curve B. The four models clearly give very similar
(3)
IcO(Pn + PP)
+ cl (P, - pP)l + (1 + ~/2m)-1~04pP~,]
1979
6= uCa-LoCa
.
(4)
b is the pion reduced mass and m is the mass of the nucleon. p,(r) and p,(r) are the density distributions of neutrons and protons, respectively. We have written 4pPp, instead of the customary (p, + P,)~ since the absorption of pions occurs preferentially on neutronproton pairs [9] and the present form should be more suitable for nuclei with an excess of neutrons. Eq. (3) describes the Lorentz-Lorenz (short-range anticorrelation) effect [8]. The parameters of the local and non-local parts of the potential have been determined using fits to a wide range of 2p data [3]. The procedure (b) of that work used b, and B, from the analysis of 1s state data, fixed co and ct at the free pion-nucleon values and adjusted Co to reproduce the 4o Ca result assuming equal neutron and proton distributions. The value of b, = a.13 + 0.02m;’ was then obtained by fitting the 2p level data for Fe, Cu and Zn, for which the x2 minima gave A = 0.05 to 0.15 fm. Smaller values of b, = 4.08m;’ [8] were found to require A - 0.3 fm for nuclei as light as P and Ar, as well as for Fe, Cu and Zn and were hence rejected [3]. A detailed description of the analysis of the 2p level data including a discusSiOn of various forms fOJ the potential and comparisons
1
koV 0.6
0.5
0.4
0.3
0.2
0.1
00
-0
1
Fig. 2. Calculated and measured differences of shifts (6~ = ~(44) - ~(40)) and widths (6 I? = l-(44) - r(40)) for 2p pionic levels in 44’40Ca . The various curves are discussed in the text.
167
Volume 81B, number 2
PHYSICS
predictions for 6~ and 6r versus the change in neutron radius r,(44) - r,(40). Comparing our results with these calculations using fig. 2, it is seen that both 6e and 6r are consistent with each other and with a small neutron radius change between 44Ca and 4oCa. This result is independent of whether the charge or the point nucleon distributions are assumed. Furthermore, replacing the value of rP(44) - rP(40) = 0.028 fm [ 1 l] used above with the value 0.053 fm given very recently by muonic isotope shift experiments [ 131 reduces r,(44) - r,(40) by only 0.01 fm. The dependence of the derived neutron radius for 44Ca on the effective pion-nucleus potential is one of the crucial points of the present analysis. When isotopic differences are studied it is found that only the b, and c1 coefficients of the potential have a marked effect on the predictions and that the largest effect on the predicted r,(44) - r,(40) values comes from the uncertainties in b, . Fig. 2 shows two limiting curves forcase Bwithb, =-0.1%?~;~ andbl =-O.llm,‘, corresponding to the analysis of ref. [3] . Taking these into account and using the results from curve D it is concluded that r,(44) - r,(40) = 0.05 ?0.05 fm. This is obtained essentially from an optical model analysis of 2p state data above and below Ca, including nuclei with an excess of neutrons, together with the precise measurements of the strong interaction isotope effect in pionic calcium. The present result gives A(44) = -0.02 _+0.05 fm if the value rp(44) - rp(40) = 0.03 fm is used or A(44) = -0.05 + 0.05 fm if the the very recent [13] value rp(44) - rp (40) = 0.05 fm is used. These results disagree strongly with the analyses of Tauscher and Wycech [7] and of Kunselman and Grin [2] which were based on the older pion data and different optical potential parameters. Tauscher and Wycech also used the average of two different experiments for 4oCa where in only one of them was 44Ca also measured. As a result they effectively used a value of 6~ roughly twice the directly measured value. The derived difference in neutron radius r,(44) - r,,(40) = 0.05 + 0.05 fm is in good agreement with that of Jackobson et al. [14] who obtained 0.09 + 0.05 fm from measurements of pion total cross sections in the 3-3 resonance region. The result is also in excel-
168
LETTERS
12 February
1979
lent agreement with the work of Shlomo and Schaeffer [ 151 who have carefully reevaluated recent analyses of 1 GeV proton scattering and obtain r,(44) _ r,(40) = 0.09 + 0.03 fm. Experiments on the elastic scattering of a-particles at I 66 MeV [ 161 and at 1.37 GeV [17] givevaluesofr,(44)-r,(40)=0.18*0.20 and 0.14 + 0.07 fm, respectively, which again show good agreement with the present experiment. To summarize we have measured the difference between the strong interaction level shifts and widths for 2p states in pionic atoms of 44$40Ca. Analysis of the results using an effective pion-nucleus potential gives a value for the difference in neutron rms radii in excellent agreement with values determined by other methods. We wish to thank Messrs. C.A. Baker, A.1 Kilvington, J. Moir and A.G.D. Payne for their assistance in setting up the experiment and taking the data. References
111 S. Shlomo and E. Friedman,
Phys. Rev. Lett. 39 (1977) 1180 and references therein. [21 R. Kunselman and G.A. Grin, Phys. Rev. Lett. 24 (1970) 838. [31 C.J. Batty et al., Phys. Rev. Lett. 40 (1978) 931. [41 C.J. Batty et al., Nucl. Phys. A282 (1977) 487. [51 B.L. Rc Serts, R.A.J. Riddle and G.T.A. Squier, Nucl. Instr. Meth. 130 (1975) 559; 144 (1977) 369; C.J. Batty, S.D. Hoath and B.L. Roberts, Nucl. Instr. Meth. 137 (1976) 179. [61 D.K. Anderson, D.A. Jenkins and R.J. Powers, Phys. Rev. Lett. 24 (1970) 71. [71 L. Tauscher and S. Wycech, Phys. Lett. 62B (1976) 413. ISI M. Krell and T.E.O. Ericson, Nucl. Phys. Bll (1969) 521. L91J. Hiifner, Phys. Rep. 21C (1975) 1. 1101 C.J. Batty et al., to be published. [Ill C.W. de Jager, H. de Vries and C. de Vries, At. Data Nucl. Data Tables 14 (1974) 479. [I21 J.W. Negele, Phys. Rev. Cl (1970) 1260; J.W Negele and D. Vautherin, Phys. Rev. C5 (1972) 1472; X. Campi and D.W. Sprung, Nucl. Phys. Al94 (1972) 401. H.D. Wohlfahrt et al., Phys. Lett. 73B (1978) 131. M.J. Jakobson et al., Phys. Rev. Lett. 38 (1977) 1201. S. Shlomo and R. Schaeffer, to be published. 1. Brissaud et al., Nucl. Phys. A191 (1972) 145. G.D. Alkhazov et al., Nucl. Phys. A280 (1977) 365.
8lB, number
2
PHYSICS
LETTERS
12 February
1979
PIONIC X-RAYS AND THE NEUTRON RADIUS OF 44Ca C.J. BATTY, S.F. BIAGI, E. FRIEDMAN ’ and S.D. HOATH Rutherford
Laboratory,
Chilton, Didcot, Oxon, UK
J.D. DAVIES, G.J. PYLE and G.T.A. SQUIER Physics Department,
University of Birmingham, Birmingham,
UK
D.M. ASBURY Physics Department,
University of Surrey, Guildford,
UK
and
M. LEON University of California, Los Alamos Scientific Laboratory Los Alamos, NM 87545, USA
Received
10 October
1978
Differences between strong interaction level shifts and widths for 2p states in pionic atoms of 44j40Ca have been measured Analysis in terms of an effective pion-nucleus potential leads to a difference in neutron rms radii of r,(44) - r,(40) = 0.05 i 0.05 fm.
The density distribution of neutrons in nuclei has recently been the subject of many investigations [l] . The analysis of strong interaction shifts and widths of pionic atoms could in principle provide useful information on neutron density distributions since the p-wave rr- interaction occurs predominantly with neutrons. In the present letter we report experimental results for the differences between shifts and widths of the 2p level in pionic atoms of 44Ca and 4oCa, where the accuracy is almost an order of magnitude better than that of the previous measurement [2] of the same quantities. These results are analysed using an effective r- -nucleus potential whose parameters have been determined recently [3] from other data for 2p states of pionic atoms. The experiment was performed using the stopped meson beam [4] from the 7 GeV proton synchrotron t Permanent address: Hebrew University,
The Racah Institute Jerusalem, Israel.
of Physics,
The
Nimrod. A low background was achieved using an electrostatically separated beam of 200 MeV/c pions. Stopping pions were identified with a counter telescope system [4], X-rays were detected using a coaxial 70 cm3 Ge(Li) detector with 1.68 keV resolution at 1.33 MeV. The 44Ca target consisted of 282 g of 44CaC03 enriched to 98.6%. For natural Ca (consisting of 97% of 40Ca) a similar target of CaCO, was used. It was essential to have the same chemical form for both isotopes so that similar procedures for analysing the peaks and background could be employed. Data and calibration spectra were taken simultaneously and routed into different 8192 channel regions of an ADC computer system. The strong interaction shifts and widths were determined from a least-squares analysis of both X-ray peaks and calibration peaks, as described earlier [5] . A contribution from the muonic n = 4 + 2 X-ray line which has a very similar energy was included in the analysis but had only a small effect on the final result. The spectrum obtained with 165
Volume
8 1 B, number
2
PHYSICS
LETTERS
12 February
1979
COUNTS i 2000
r
r 1600
0 2‘ioo PION:C
2430 CA
2460
2490
2820
2550
2580 CHANNEL
44
NO
Fig. 1. Measured X-ray spectrum for the 3d + 2p transition in the 44 CaCOa target. Also shown are the fits to the data and the individual contributions from the pionic 3d + 2p peak and the small underlying muonic 4d + 2p3,a, 1,2 peaks.
the 44Ca carbonate target and the fit to the data are shown in fig. 1. Table 1 shows the measured energies for the 3d + 2p transitions for the natural Ca and for the d4Ca target. The results for Ca are in good agreement with the previous measurement [3] using a metal target which is also given in table 1. Taking only the CaC03 and 44CaC03 targets and correcting the results for the small amount of 44Ca present in natural calcium, we obtain for the difference between the shifts for the two isotopes &E= ~(44) - ~(40) = -0.331 + 0.027 keV and for the widths 6r= r‘(44) - r(40)= - 0.040
+ 0.075 keV. These results are in good agreement with and considerably more precise than the results SE = -0.36 + 0.17 keV and 6r = -0.22 f 0.20 keV obtained by Kunselman and Grin [2]. Analysis of the strong interaction effects in pionic atoms in terms of an effective pion-nucleus potential related to the nucleon density distribution can be used to investigate the difference A between the rms radii of the neutron and proton distributions [6]. In their analysis Anderson et al. assumed A was independent of mass for a range of pionic atom data and obtained A = -0.01 f 0.16 fm [6]. However, Kunselman and
Table 1 Results for 3d + 2p transitions. Target
CaCOs (nat) 44CaCOs Ca metal [3] a)
Measured energy
Electromagnetic energy
tkeV)
(keV)
209.609 209.359 209.612
+ 0.025 f 0.013 + 0.014
a) There is a small error in the values for Ca given in ref.
166
207.683 207.753 207.683
[ 31.
Shift
Width
(keV)
(keV)
1.926 1.606 1.929
1.692 f 0.063 1.652 * 0.038 1.613 f 0.023
Volume
81B, number
2
PHYSICS
Grin [2] , using their 44Ca results found A(44) = 0.35 + 0.15 fm for one set of optical potential parameters while Tauscher and Wycech found A(44) = 0.49 f 0.30 fm [7] using another set. Our recent determination of the optical potential parameters [3] permits these findings to be checked using the more precise result for 44 Ca given above. The potential used in the present work follows that of Krell and Ericson [g] and is given by I?)
= [4(r) -V@.)
*VIDP ,
(1)
where the local part, q(r), and the non-local part o(r), are related to the nuclear density distributions as follows: 4(r) = -4nNl +b,(p,
+ /J/m) VJo (P, + P,) -@I
(2)
+(1 +~/2m)~o4pP~~,)~
44 = “0 W/i 1 - ia0 (41 , ao(r) = p4n ((1 + plm)-’
LETTERS
12 February
with the results for Is, 3f and 4d levels will be published elsewhere [lo] . Fig. 2 shows 8~ and 6 F calculated as functions of r (44) - r (40), the difference in neutron rms radii of 4’4 Ca and 60 Ca, for four sets of potential and density distributions. For curve A parabolic Fermi charge density distributions from electron scattering measurements [l I] were used for the protons (rp(40) = 3.482 fm and rP(44) = 3.510 fm), and A(40) = r,(40) - rP(40) = 0.0 assumed. Curve B had A(40) = -0.04 fm as predicted by Hartree-Fock calculations [ 121 . Curve C had this change in neutron radius compensated by reducing Ke C,/Im Co from 1.9 to 1.6 so as to fit the 4oCa results, while curve D used single particle point nucleon distributions for pP and pn calculated from a SaxonWoods potential adjusted, after folding in the finite proton size, to reproduce the charge distributions used in curve B. The four models clearly give very similar
(3)
IcO(Pn + PP)
+ cl (P, - pP)l + (1 + ~/2m)-1~04pP~,]
1979
6= uCa-LoCa
.
(4)
b is the pion reduced mass and m is the mass of the nucleon. p,(r) and p,(r) are the density distributions of neutrons and protons, respectively. We have written 4pPp, instead of the customary (p, + P,)~ since the absorption of pions occurs preferentially on neutronproton pairs [9] and the present form should be more suitable for nuclei with an excess of neutrons. Eq. (3) describes the Lorentz-Lorenz (short-range anticorrelation) effect [8]. The parameters of the local and non-local parts of the potential have been determined using fits to a wide range of 2p data [3]. The procedure (b) of that work used b, and B, from the analysis of 1s state data, fixed co and ct at the free pion-nucleon values and adjusted Co to reproduce the 4o Ca result assuming equal neutron and proton distributions. The value of b, = a.13 + 0.02m;’ was then obtained by fitting the 2p level data for Fe, Cu and Zn, for which the x2 minima gave A = 0.05 to 0.15 fm. Smaller values of b, = 4.08m;’ [8] were found to require A - 0.3 fm for nuclei as light as P and Ar, as well as for Fe, Cu and Zn and were hence rejected [3]. A detailed description of the analysis of the 2p level data including a discusSiOn of various forms fOJ the potential and comparisons
1
koV 0.6
0.5
0.4
0.3
0.2
0.1
00
-0
1
Fig. 2. Calculated and measured differences of shifts (6~ = ~(44) - ~(40)) and widths (6 I? = l-(44) - r(40)) for 2p pionic levels in 44’40Ca . The various curves are discussed in the text.
167
Volume 81B, number 2
PHYSICS
predictions for 6~ and 6r versus the change in neutron radius r,(44) - r,(40). Comparing our results with these calculations using fig. 2, it is seen that both 6e and 6r are consistent with each other and with a small neutron radius change between 44Ca and 4oCa. This result is independent of whether the charge or the point nucleon distributions are assumed. Furthermore, replacing the value of rP(44) - rP(40) = 0.028 fm [ 1 l] used above with the value 0.053 fm given very recently by muonic isotope shift experiments [ 131 reduces r,(44) - r,(40) by only 0.01 fm. The dependence of the derived neutron radius for 44Ca on the effective pion-nucleus potential is one of the crucial points of the present analysis. When isotopic differences are studied it is found that only the b, and c1 coefficients of the potential have a marked effect on the predictions and that the largest effect on the predicted r,(44) - r,(40) values comes from the uncertainties in b, . Fig. 2 shows two limiting curves forcase Bwithb, =-0.1%?~;~ andbl =-O.llm,‘, corresponding to the analysis of ref. [3] . Taking these into account and using the results from curve D it is concluded that r,(44) - r,(40) = 0.05 ?0.05 fm. This is obtained essentially from an optical model analysis of 2p state data above and below Ca, including nuclei with an excess of neutrons, together with the precise measurements of the strong interaction isotope effect in pionic calcium. The present result gives A(44) = -0.02 _+0.05 fm if the value rp(44) - rp(40) = 0.03 fm is used or A(44) = -0.05 + 0.05 fm if the the very recent [13] value rp(44) - rp (40) = 0.05 fm is used. These results disagree strongly with the analyses of Tauscher and Wycech [7] and of Kunselman and Grin [2] which were based on the older pion data and different optical potential parameters. Tauscher and Wycech also used the average of two different experiments for 4oCa where in only one of them was 44Ca also measured. As a result they effectively used a value of 6~ roughly twice the directly measured value. The derived difference in neutron radius r,(44) - r,,(40) = 0.05 + 0.05 fm is in good agreement with that of Jackobson et al. [14] who obtained 0.09 + 0.05 fm from measurements of pion total cross sections in the 3-3 resonance region. The result is also in excel-
168
LETTERS
12 February
1979
lent agreement with the work of Shlomo and Schaeffer [ 151 who have carefully reevaluated recent analyses of 1 GeV proton scattering and obtain r,(44) _ r,(40) = 0.09 + 0.03 fm. Experiments on the elastic scattering of a-particles at I 66 MeV [ 161 and at 1.37 GeV [17] givevaluesofr,(44)-r,(40)=0.18*0.20 and 0.14 + 0.07 fm, respectively, which again show good agreement with the present experiment. To summarize we have measured the difference between the strong interaction level shifts and widths for 2p states in pionic atoms of 44$40Ca. Analysis of the results using an effective pion-nucleus potential gives a value for the difference in neutron rms radii in excellent agreement with values determined by other methods. We wish to thank Messrs. C.A. Baker, A.1 Kilvington, J. Moir and A.G.D. Payne for their assistance in setting up the experiment and taking the data. References
111 S. Shlomo and E. Friedman,
Phys. Rev. Lett. 39 (1977) 1180 and references therein. [21 R. Kunselman and G.A. Grin, Phys. Rev. Lett. 24 (1970) 838. [31 C.J. Batty et al., Phys. Rev. Lett. 40 (1978) 931. [41 C.J. Batty et al., Nucl. Phys. A282 (1977) 487. [51 B.L. Rc Serts, R.A.J. Riddle and G.T.A. Squier, Nucl. Instr. Meth. 130 (1975) 559; 144 (1977) 369; C.J. Batty, S.D. Hoath and B.L. Roberts, Nucl. Instr. Meth. 137 (1976) 179. [61 D.K. Anderson, D.A. Jenkins and R.J. Powers, Phys. Rev. Lett. 24 (1970) 71. [71 L. Tauscher and S. Wycech, Phys. Lett. 62B (1976) 413. ISI M. Krell and T.E.O. Ericson, Nucl. Phys. Bll (1969) 521. L91J. Hiifner, Phys. Rep. 21C (1975) 1. 1101 C.J. Batty et al., to be published. [Ill C.W. de Jager, H. de Vries and C. de Vries, At. Data Nucl. Data Tables 14 (1974) 479. [I21 J.W. Negele, Phys. Rev. Cl (1970) 1260; J.W Negele and D. Vautherin, Phys. Rev. C5 (1972) 1472; X. Campi and D.W. Sprung, Nucl. Phys. Al94 (1972) 401. H.D. Wohlfahrt et al., Phys. Lett. 73B (1978) 131. M.J. Jakobson et al., Phys. Rev. Lett. 38 (1977) 1201. S. Shlomo and R. Schaeffer, to be published. 1. Brissaud et al., Nucl. Phys. A191 (1972) 145. G.D. Alkhazov et al., Nucl. Phys. A280 (1977) 365.