- Email: [email protected]
nucleon- 238U ions with light target atoms of CR-39 polycarbonate
428
Nuclear
INTERACTION OF 960 MeV/NUCLEONOF CR-39 POLYCARBONATE
=%
Instruments
and Methods
in Physics Research B27 (1987) 428-431 North-Holland, Amsterdam
IONS WITH LIGHT TARGET ATOMS
Khalid JAMIL, Fauzia Rauf KHAN, and Hameed Ahmed KHAN SSNTD-Laboratory, Nuclear Engineering Division, Pakistan Institute of Nuclear Science & Technology (PINSTECH) P. 0. Nilore, Islamabad, Pakistan
Reinhard BRANDT Kernchemie, FB 14, Philipps- Universitat Marburg. FRG
Gerhard KRAFT GSI, Darmstadt, FRG Received
21 January
1986 and in revised form 27 February
1987
CR-39 plastic track detectors have been employed both as the target and as the detector to study MeV/nucleon-238U ions with light target atoms (hydrogen, carbon, and oxygen), the constituents of CR-39. of the mean free path (mfp) for the relativistic uranium ions has been obtained and compared with the value The range of the uranium ions has been found to be 6.5 cm in the composite medium of CR-39 track multiplicity due to fission of the uranium projectiles in CR-39 track detecting medium has been found to be binary fission is the most common mode of interaction.
the interaction of 960 The experimental value computed theoretically. detectors. The average 2.1, which indicates that
1. Introduction
2. Experimental details
The first ever evidence for the existence of energetic heavy ions was produced in 1948 in cosmic rays [l]. The discovery paved the way for heavy ion interaction studies. During the past decade or so, the field of heavy ion physics attained great importance in nuclear physics [2,3]. At present, there exist a large number of accelerators, capable of accelerating heavy ions up to quite high energies. The highest energy available for heavy elements can be obtained from the BEVALAC at the Lawrence Berkeley Laboratory, University of California, Berkeley. Here, we could obtain 960 MeV/ nucleon-238U ions for irradiation of Solid State Nuclear Track Detectors (SSNTD). After irradiation one can etch the tracks and study their properties. The diameters of the tracks can provide significant information about the nuclear particles producing them. Since very little is known about the physics of relativistic heavy ions, a knowledge of different cross-sections and the mode of interaction is very useful in nuclear physics, medical physics and other branches of science. Here, we report the results obtained during the study of the interaction of 960 MeV/nucleon-238U ions with the light target atoms of CR-39, a transparent thermoset plastic, having a composition of C,,H,sO,.
In our experiments, CR-39 nuclear track detectors served both as the target and the detector. A stack consisting of 73 detectors of CR-39, each having an area of 5 x 5 cm and a thickness of 0.13 gcmm2 was used. The stack was exposed to 238U ions having an energy of 960 MeV/nucleon, obtained from the BEVALAC to the surface as shown in fig. 1. The exposed detectors from the stack were etched in 6N NaOH at (70 + l)O C in steps of 30 min. On development, tracks due to projectiles and the reaction products were observed. An optimum etching time of 5 h was selected. Under these etching conditions, protons and heavier reaction products, having energies of about 10 MeV/nucleon could
0168-583X/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
STACK
OF
CR-3S
TRACK
DETECTORS
I
960 WV/ NUCLEON
f
2=‘U-10NS
Fig. 1. Stack of CR-39 track detectors exposed perpendicularly to 960 MeV/nucleon 238U-ions.
K. Jamil et al. / Inieraction of 230 GeV 238U with CR-39polycarbonate
be revealed. The diameter of the etch pits due to 238Uprojectiles, passing through the CR-39 detectors, were found to be about 14 pm. The etch pits, having diameters less than 14 pm were considered to be due to the reaction products. Track diameters were measured as a function of the distance traversed in the stack.
3. Results and discussion Fig. 2 shows the density of etch pits due to the projectiles (having the largest size) as a function of the distance traversed (downstream) in the CR-39 stack. The fluence along the stack seems to be an exponentially decreasing function upto about 6 cm. Afterwards, there exists a sharp fall, which is followed by another exponentially decreasing pattern in the fluence of 238Uions with further distance traversed in the stack. The diameters do not vary significantly from one exponential decay to the next. The range of 238U-ions in CR-39 is taken to be 6.5 cm. The change in the exponentially function could be due to the quasi-elastic interactions of 238U-ions, which produce ions close to the original nucleus. The reaction products close to uranium are difficult to discriminate. The data follows the expression: p(x)
= pa eex/‘,
429
such as CR-39 is available in literature at this stage, we used theoretical models to check the experimental value obtained by us. 3.1. Geometrical
overlap
model
It has been reported that above an energy of a few hundred MeV/nucleon, the total nucleus-nucleus cross-section attains a constant value and it varies more or less with the geometrical size of the colliding particles [4-111. The nuclear cross-section has been found to have the form: u
T
=
7rr,‘( A’p/’ + A:j3
- 6r)*,
where A, = mass number of the projectile; A, = mass number of the target; = extrapolated single nucleon radius, close to r0 charge density radius; S, = a constant, accounting for the nuclear surface transparency. Eq. (2) is known as the Bradt-Peters expression [lo]. The total cross-section and the mean free path are reciprocally related by the expession;
(I)
where p(x) = fluence of the incident 238U-projectiles as a function of distance (x); = incident fluence of 238U-ions; PO = distance traversed in the stack; = charge changing mean free path (mfp). Z From the above expression the experimental value of charge changing mean free path comes out to be (4.35 + 0.30) cm. Since no experimental value of the mean free path (mfp) of 960 MeV/nucleon-238U in materials
960
M.V/NUCLEON
236
U
C&Q
where N = number of target nuclei per unit volume (cmw3). The value of A’ for a composite, inhomogenous medium like CR-39 can be obtained by using the relation:
1
A’=
CwN where, 0, is the cross-section tional abundance, n ;_ Thus,
Af=f
( n CCIY +nldHH
for the nuclei with frac-
(5)
+no 00 1’
with N = 1.06 x 1023, and for CR-39 0.324, nH = 0.486, No = 0.189.
putting
nc =
0, = rrro“( A’p/’ + A’c/’ - 6r)*, 0 H = 7rro A’p/’ + A’H/’ - 6r)*, ‘( u.
‘( A’p/’ + Ab/ -
= vro
Sr)‘,
in the above equation and taking r, = 1.35 x lo-l3 cm, and Sr = 0.83 from the work of Westfall et al. [ll] we find the mfp for 238U projectiles to be DISTANCE
Fig. 2. Variation
IN THE STACK (cm)
in the fluence of *‘*U-ions with the distance traversed in the CR-39 stack.
h’= 3.45 cm. One can see that the model-calculated of 238U is less than the experimentally
(6) value of the mfp determined value.
430
K. Jamil et al. / Interaction
of 230 GeV 2381J with CR-39 polycarbonate
The experimental value of the mfp is about 20% higher than the value obtained by using the geometric-overlap model (GOLM). The difference in calculated and experimental values may be due to the reason that only those interactions of 238U with CR-39 are observable, which involve charge changes. Also GOLM does not deal with charge changing cross-section only. It takes into account the total cross-section, which is the sum of charge changing and the non-charge changing cross-sections, i.e. e,=eZ+eN.
=nz-b,
(8)
where A = scaled mean free path and b = constant. For CR-39, A = 52.25 and b = 0.58. Thus the mfp for 238U from this expression is found to be 3.79 cm. This value of mean-free-path (mfp) is close to our experimentally determined value. Fig. 3 shows the variation of the fluence due to diameters of the reaction products (5.6 < D Q 14.6 pm) with the distance traversed in the stack. The fluence in the stack increases up to the range of the 238U projectiles and then decreases. Fig. 4 shows the change in the ratio of the fluence of the reaction products to that of the projectile as a function of the penetration distance (x), in the stack. Using the ratio, R(x) and knowing that PS( x) = ePxjh,
MeV / NUCLEON -BEST
of
U IONS + CR-39
FIT (THEORETICAL
p EXPERIMENTAL
(7)
According to the experimental evidence, uN (non-charge changing cross-section is lo-20% of the total cross-section [12,13]. Here we have obtained the value of the mfp, which is only due to charge changing interactions. Tincknell et al. [14] have carried out extensive experimentation using medium heavy ion projectiles along with CR-39 track detecting medium. Their results have been used to determine the following empirical relationship for mean free path (mfp): X(Z)
238
960
CURVE)
PcllNTS
y%: DISTANCE
IN THE
STACK km)
Fig. 4. Variation in the ratio of the fluence of reaction products to the fluence of 238U-projectiles as a function of the (downstream) distance in the stack.
P,(x) = l-
Ps(x>,
(10)
where, p,(x) is the surviving probability of the projectile and Pd(x) is the probability that projectile will be fragmented. We can find the average number of fragments in the fragmentation process by using the relation: v=
R(x)P,(x)/P,(x).
(11)
Fig. 5 shows the plot of 7 as a function of the distance x in the stack. The best fit line gives value of multiplicity as 2.01 + 0.31. This implies that binary fission is the most dominant mode of interaction for 238U-ions, passing through the 960 MeV/nucleon medium of CR-39 (containing, hydrogen, carbon, and oxygen as its constituents)
(9)
960 960
MeV / NUCLEON
238 U IONS
MeV / NUCLEON‘“U + CR-3.9
-
+ CR-39
BEST
FIT
p
EXPERIMENTAL
v
- (2.01
z
DISTANCE
TRAVERSED
DISTANCE
IN THE STACK (cm)
Fig. 3. Change in the fluence of the reaction products function of the distance traversed in the stack.
as a
POlNTS
* 0.31)
4
IN THE
D
STACK
km)
Fig. 5. Plot of the average number of the projectile-fragments with the distance (downstream) traversed in the stack of CR-39.
K. Jamil et al. / Interaction of 230 GeV 238U with CR-39 polycarbonate
4. Conclusions
(1) CR-39 track detector
is capable of detecting 238Uions at relativistic energies. (2) The fluence of relativistic 238U and other heavy ions, while passing through CR-39 (a medium containing hydrogen, carbon, and oxygen as its constituents) decreases exponentially. values of the mean free path and (3) The experimental the range of 960 MeV/nucleon 238U in CR-39 have been found to be 4.35 + 0.31 cm, and 6.5 cm, respectively. The average multiplicity of uranium projectiles at (4) the relativistic energies has been found to be 2.01 k 0.31, indicating that binary fission is the most dorninant mode of interaction in inhomogenous media containing nearly 50% hydrogen. The results are helpful for heavy ion dosimetry in medical physics, since the composition of the human tissue is fairly similar to that of CR-39 plastic track detector, This work has been performed under a bilateral collaboration between the Pakistan Atomic Energy Commission (PAEC) and KfK (Karlsruhe, FRG), which has been instrumental in promoting the Pakistan-German team efforts for carrying out work in heavy ion physics. We are grateful to the PAEC and Karlsrnhe (KfK) authorities for the financial grant. One of us (H.A.K.) is grateful to the Alexander von Humboldt Stiftung for giving him the opportunity to work at the Philipps UniversitPt (Marburg) and at GSI (Darmstadt). Last but not least, we are grateful to our friends at Bevalac for kindly exposing the samples, and PINS-
431
TECH, Philipps Universitat, and GSI, for their advice and fruitful discussions during the analysis of the samples.
References
VI P. Freier, E.J. Lofgren,
E.P. Ney, F. Oppenheimer, H.L. Bradt and B. Peters, Phys. Rev. 74 (1984) 213. PI A. Bromley (ed.), Treatise on Heavy-Ion Science (Plenum, New York and London, 1984). et al. (eds.), Proc. of the 2nd Int. Conf. [31 H.A. Gustafsson on Nucleus-Nucleus Collisions, Visby, Sweden, June 10-14, 1985 (North-Holland. Amsterdam, Oxford, New York, 1986). and H.H. Heckman, Ann. Rev. Nucl. and 141 A.S. Goldhaber Part. Sci. 28 (1978) 161. D.E. Greiner, P.J. Lindstrom, and H. 151 H.H. Heckmann, Shwe, Phys. Rev. Cl7 (1978) 1735. and R. Kullberg, Phys. Scripta 13 (1976) [61 B. Jakobsson 327. B. Lindkvist and I Otter[71 R. Kullberg, K. Kristiansson, lund, Nucl. Phys. A280 (1977) 491. PI S. Barshay, C.B. Dover and J.P. Vary, Phys. Rev. Cl1 (1975) 360. 191 P.J. Karol, Phys. Rev. Cl1 (1975) 1203. WI H.L. Bradt and B. Peters, Phys. Rev. 77 (1950) 54. H.J. CrawP11 G.D. Westfall, L.W. Wilson, P.J. Lindstorm, ford, D.E. Greiner, and H.H. Heckman, Phys. Rev. Cl9 (1979) 1309. R.W. Stoenner and P.E. Haustein, Phys. [W J.B. Cumming, Rev. Cl4 (1967) 1554. [I31 J.R. Grover and A.A. Caretto, Ann. Rev. Nucl. Sci. 14 (1967) 51. Phys. Rev. 1141 M.L. Tincknell, P.B. Price and S. Perlmutter, Lett. 51 (1983) 1948.
Nuclear
INTERACTION OF 960 MeV/NUCLEONOF CR-39 POLYCARBONATE
=%
Instruments
and Methods
in Physics Research B27 (1987) 428-431 North-Holland, Amsterdam
IONS WITH LIGHT TARGET ATOMS
Khalid JAMIL, Fauzia Rauf KHAN, and Hameed Ahmed KHAN SSNTD-Laboratory, Nuclear Engineering Division, Pakistan Institute of Nuclear Science & Technology (PINSTECH) P. 0. Nilore, Islamabad, Pakistan
Reinhard BRANDT Kernchemie, FB 14, Philipps- Universitat Marburg. FRG
Gerhard KRAFT GSI, Darmstadt, FRG Received
21 January
1986 and in revised form 27 February
1987
CR-39 plastic track detectors have been employed both as the target and as the detector to study MeV/nucleon-238U ions with light target atoms (hydrogen, carbon, and oxygen), the constituents of CR-39. of the mean free path (mfp) for the relativistic uranium ions has been obtained and compared with the value The range of the uranium ions has been found to be 6.5 cm in the composite medium of CR-39 track multiplicity due to fission of the uranium projectiles in CR-39 track detecting medium has been found to be binary fission is the most common mode of interaction.
the interaction of 960 The experimental value computed theoretically. detectors. The average 2.1, which indicates that
1. Introduction
2. Experimental details
The first ever evidence for the existence of energetic heavy ions was produced in 1948 in cosmic rays [l]. The discovery paved the way for heavy ion interaction studies. During the past decade or so, the field of heavy ion physics attained great importance in nuclear physics [2,3]. At present, there exist a large number of accelerators, capable of accelerating heavy ions up to quite high energies. The highest energy available for heavy elements can be obtained from the BEVALAC at the Lawrence Berkeley Laboratory, University of California, Berkeley. Here, we could obtain 960 MeV/ nucleon-238U ions for irradiation of Solid State Nuclear Track Detectors (SSNTD). After irradiation one can etch the tracks and study their properties. The diameters of the tracks can provide significant information about the nuclear particles producing them. Since very little is known about the physics of relativistic heavy ions, a knowledge of different cross-sections and the mode of interaction is very useful in nuclear physics, medical physics and other branches of science. Here, we report the results obtained during the study of the interaction of 960 MeV/nucleon-238U ions with the light target atoms of CR-39, a transparent thermoset plastic, having a composition of C,,H,sO,.
In our experiments, CR-39 nuclear track detectors served both as the target and the detector. A stack consisting of 73 detectors of CR-39, each having an area of 5 x 5 cm and a thickness of 0.13 gcmm2 was used. The stack was exposed to 238U ions having an energy of 960 MeV/nucleon, obtained from the BEVALAC to the surface as shown in fig. 1. The exposed detectors from the stack were etched in 6N NaOH at (70 + l)O C in steps of 30 min. On development, tracks due to projectiles and the reaction products were observed. An optimum etching time of 5 h was selected. Under these etching conditions, protons and heavier reaction products, having energies of about 10 MeV/nucleon could
0168-583X/87/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
B.V.
STACK
OF
CR-3S
TRACK
DETECTORS
I
960 WV/ NUCLEON
f
2=‘U-10NS
Fig. 1. Stack of CR-39 track detectors exposed perpendicularly to 960 MeV/nucleon 238U-ions.
K. Jamil et al. / Inieraction of 230 GeV 238U with CR-39polycarbonate
be revealed. The diameter of the etch pits due to 238Uprojectiles, passing through the CR-39 detectors, were found to be about 14 pm. The etch pits, having diameters less than 14 pm were considered to be due to the reaction products. Track diameters were measured as a function of the distance traversed in the stack.
3. Results and discussion Fig. 2 shows the density of etch pits due to the projectiles (having the largest size) as a function of the distance traversed (downstream) in the CR-39 stack. The fluence along the stack seems to be an exponentially decreasing function upto about 6 cm. Afterwards, there exists a sharp fall, which is followed by another exponentially decreasing pattern in the fluence of 238Uions with further distance traversed in the stack. The diameters do not vary significantly from one exponential decay to the next. The range of 238U-ions in CR-39 is taken to be 6.5 cm. The change in the exponentially function could be due to the quasi-elastic interactions of 238U-ions, which produce ions close to the original nucleus. The reaction products close to uranium are difficult to discriminate. The data follows the expression: p(x)
= pa eex/‘,
429
such as CR-39 is available in literature at this stage, we used theoretical models to check the experimental value obtained by us. 3.1. Geometrical
overlap
model
It has been reported that above an energy of a few hundred MeV/nucleon, the total nucleus-nucleus cross-section attains a constant value and it varies more or less with the geometrical size of the colliding particles [4-111. The nuclear cross-section has been found to have the form: u
T
=
7rr,‘( A’p/’ + A:j3
- 6r)*,
where A, = mass number of the projectile; A, = mass number of the target; = extrapolated single nucleon radius, close to r0 charge density radius; S, = a constant, accounting for the nuclear surface transparency. Eq. (2) is known as the Bradt-Peters expression [lo]. The total cross-section and the mean free path are reciprocally related by the expession;
(I)
where p(x) = fluence of the incident 238U-projectiles as a function of distance (x); = incident fluence of 238U-ions; PO = distance traversed in the stack; = charge changing mean free path (mfp). Z From the above expression the experimental value of charge changing mean free path comes out to be (4.35 + 0.30) cm. Since no experimental value of the mean free path (mfp) of 960 MeV/nucleon-238U in materials
960
M.V/NUCLEON
236
U
C&Q
where N = number of target nuclei per unit volume (cmw3). The value of A’ for a composite, inhomogenous medium like CR-39 can be obtained by using the relation:
1
A’=
CwN where, 0, is the cross-section tional abundance, n ;_ Thus,
Af=f
( n CCIY +nldHH
for the nuclei with frac-
(5)
+no 00 1’
with N = 1.06 x 1023, and for CR-39 0.324, nH = 0.486, No = 0.189.
putting
nc =
0, = rrro“( A’p/’ + A’c/’ - 6r)*, 0 H = 7rro A’p/’ + A’H/’ - 6r)*, ‘( u.
‘( A’p/’ + Ab/ -
= vro
Sr)‘,
in the above equation and taking r, = 1.35 x lo-l3 cm, and Sr = 0.83 from the work of Westfall et al. [ll] we find the mfp for 238U projectiles to be DISTANCE
Fig. 2. Variation
IN THE STACK (cm)
in the fluence of *‘*U-ions with the distance traversed in the CR-39 stack.
h’= 3.45 cm. One can see that the model-calculated of 238U is less than the experimentally
(6) value of the mfp determined value.
430
K. Jamil et al. / Interaction
of 230 GeV 2381J with CR-39 polycarbonate
The experimental value of the mfp is about 20% higher than the value obtained by using the geometric-overlap model (GOLM). The difference in calculated and experimental values may be due to the reason that only those interactions of 238U with CR-39 are observable, which involve charge changes. Also GOLM does not deal with charge changing cross-section only. It takes into account the total cross-section, which is the sum of charge changing and the non-charge changing cross-sections, i.e. e,=eZ+eN.
=nz-b,
(8)
where A = scaled mean free path and b = constant. For CR-39, A = 52.25 and b = 0.58. Thus the mfp for 238U from this expression is found to be 3.79 cm. This value of mean-free-path (mfp) is close to our experimentally determined value. Fig. 3 shows the variation of the fluence due to diameters of the reaction products (5.6 < D Q 14.6 pm) with the distance traversed in the stack. The fluence in the stack increases up to the range of the 238U projectiles and then decreases. Fig. 4 shows the change in the ratio of the fluence of the reaction products to that of the projectile as a function of the penetration distance (x), in the stack. Using the ratio, R(x) and knowing that PS( x) = ePxjh,
MeV / NUCLEON -BEST
of
U IONS + CR-39
FIT (THEORETICAL
p EXPERIMENTAL
(7)
According to the experimental evidence, uN (non-charge changing cross-section is lo-20% of the total cross-section [12,13]. Here we have obtained the value of the mfp, which is only due to charge changing interactions. Tincknell et al. [14] have carried out extensive experimentation using medium heavy ion projectiles along with CR-39 track detecting medium. Their results have been used to determine the following empirical relationship for mean free path (mfp): X(Z)
238
960
CURVE)
PcllNTS
y%: DISTANCE
IN THE
STACK km)
Fig. 4. Variation in the ratio of the fluence of reaction products to the fluence of 238U-projectiles as a function of the (downstream) distance in the stack.
P,(x) = l-
Ps(x>,
(10)
where, p,(x) is the surviving probability of the projectile and Pd(x) is the probability that projectile will be fragmented. We can find the average number of fragments in the fragmentation process by using the relation: v=
R(x)P,(x)/P,(x).
(11)
Fig. 5 shows the plot of 7 as a function of the distance x in the stack. The best fit line gives value of multiplicity as 2.01 + 0.31. This implies that binary fission is the most dominant mode of interaction for 238U-ions, passing through the 960 MeV/nucleon medium of CR-39 (containing, hydrogen, carbon, and oxygen as its constituents)
(9)
960 960
MeV / NUCLEON
238 U IONS
MeV / NUCLEON‘“U + CR-3.9
-
+ CR-39
BEST
FIT
p
EXPERIMENTAL
v
- (2.01
z
DISTANCE
TRAVERSED
DISTANCE
IN THE STACK (cm)
Fig. 3. Change in the fluence of the reaction products function of the distance traversed in the stack.
as a
POlNTS
* 0.31)
4
IN THE
D
STACK
km)
Fig. 5. Plot of the average number of the projectile-fragments with the distance (downstream) traversed in the stack of CR-39.
K. Jamil et al. / Interaction of 230 GeV 238U with CR-39 polycarbonate
4. Conclusions
(1) CR-39 track detector
is capable of detecting 238Uions at relativistic energies. (2) The fluence of relativistic 238U and other heavy ions, while passing through CR-39 (a medium containing hydrogen, carbon, and oxygen as its constituents) decreases exponentially. values of the mean free path and (3) The experimental the range of 960 MeV/nucleon 238U in CR-39 have been found to be 4.35 + 0.31 cm, and 6.5 cm, respectively. The average multiplicity of uranium projectiles at (4) the relativistic energies has been found to be 2.01 k 0.31, indicating that binary fission is the most dorninant mode of interaction in inhomogenous media containing nearly 50% hydrogen. The results are helpful for heavy ion dosimetry in medical physics, since the composition of the human tissue is fairly similar to that of CR-39 plastic track detector, This work has been performed under a bilateral collaboration between the Pakistan Atomic Energy Commission (PAEC) and KfK (Karlsruhe, FRG), which has been instrumental in promoting the Pakistan-German team efforts for carrying out work in heavy ion physics. We are grateful to the PAEC and Karlsrnhe (KfK) authorities for the financial grant. One of us (H.A.K.) is grateful to the Alexander von Humboldt Stiftung for giving him the opportunity to work at the Philipps UniversitPt (Marburg) and at GSI (Darmstadt). Last but not least, we are grateful to our friends at Bevalac for kindly exposing the samples, and PINS-
431
TECH, Philipps Universitat, and GSI, for their advice and fruitful discussions during the analysis of the samples.
References
VI P. Freier, E.J. Lofgren,
E.P. Ney, F. Oppenheimer, H.L. Bradt and B. Peters, Phys. Rev. 74 (1984) 213. PI A. Bromley (ed.), Treatise on Heavy-Ion Science (Plenum, New York and London, 1984). et al. (eds.), Proc. of the 2nd Int. Conf. [31 H.A. Gustafsson on Nucleus-Nucleus Collisions, Visby, Sweden, June 10-14, 1985 (North-Holland. Amsterdam, Oxford, New York, 1986). and H.H. Heckman, Ann. Rev. Nucl. and 141 A.S. Goldhaber Part. Sci. 28 (1978) 161. D.E. Greiner, P.J. Lindstrom, and H. 151 H.H. Heckmann, Shwe, Phys. Rev. Cl7 (1978) 1735. and R. Kullberg, Phys. Scripta 13 (1976) [61 B. Jakobsson 327. B. Lindkvist and I Otter[71 R. Kullberg, K. Kristiansson, lund, Nucl. Phys. A280 (1977) 491. PI S. Barshay, C.B. Dover and J.P. Vary, Phys. Rev. Cl1 (1975) 360. 191 P.J. Karol, Phys. Rev. Cl1 (1975) 1203. WI H.L. Bradt and B. Peters, Phys. Rev. 77 (1950) 54. H.J. CrawP11 G.D. Westfall, L.W. Wilson, P.J. Lindstorm, ford, D.E. Greiner, and H.H. Heckman, Phys. Rev. Cl9 (1979) 1309. R.W. Stoenner and P.E. Haustein, Phys. [W J.B. Cumming, Rev. Cl4 (1967) 1554. [I31 J.R. Grover and A.A. Caretto, Ann. Rev. Nucl. Sci. 14 (1967) 51. Phys. Rev. 1141 M.L. Tincknell, P.B. Price and S. Perlmutter, Lett. 51 (1983) 1948.