- Email: [email protected]
On the effect of nucleon number parity on the magnitude of radiative capture cross sections
364
Letters to the editors
Thus a figure of 1.307 x lo3 for channel 1 and 1.329 x lo3 for channel 2 were taken for the calibration. To check that there was no alteration in the functioning of the Geiger tubes, periodic tests were made with a &OCosource placed in a fixed geometry. Using the above efficiencies the output of the americium/beryllium source, after corrections were applied for self-absorption in the source, fast neutron capture in oxygen and sulphur, neutron escape from the sphere and the various counting corrections, was found to be 7.54 x lo6 n/set. This compares with the figure of 7.57 x IO8 n/set as measured at the National Physical Laboratory by their new technique (AXTONer al., 1963). The advantages of the method used in the calibration described are: (i) Its great simplicity. (ii) There are no pipetting errors, the whole of the activity counted in the 4~ counter being also counted by the dip counters. By placing the active solution into the small vessels there are no errors in mixing and sampling from the large sphere. (iii) The thickness of the foil is known accurately as well as its purity. The disadvantage of the method is the self-absorption correction for the foil. This 5 per cent correction is larger than for the first two techniques. To overcome this it is proposed to set up 4$-y coincidence equipment to determine the manganese foil activity. The comparison between the measurement at Berkeley and at the National Physical Laboratory seems to justify the method used and it should prove useful to laboratories whose source preparation facilities are limited. Acknowledgmenf-This paper is published by permission of the Director of the Berkeley Nuclear Laboratories, Central Electricity Generating Board, Berkeley, Glos. Berkeley Nuclear Laboratories CEGB, Berkeley, Glos.
I. M. G. THOMPSON R. W. CLARKE A. LAVENDER REFERENCES
ALDER F. and HUBER P. (1949) Helv. phys. acta 22, 368. AXTONE. J. and CROSS P. (1961) Reactor Sci. Technol. (J. Nucl. Energy Parts A/B) 15,22. AXTONE. J., CROS P. and ROBERTSON J. C. (1963) Reactor Sci. Technol. (J. Nucl. Energy Parts A/B) 17,440. GEIGERK. W. and WHYTEG. N. (1959) Cunad. J. Phys. 37,256. JUREN J. DE and CHIN J. (1955) J. Res. nut. Bur. Stand. 55, 311. MEISTERH. (1958) Z. Naturf. 13a, 722. O’NEAL R. D. and SCHARFF-GOLDHABER G. (1946) Phys. Rev. 69, 368. S~~LARDL. and CHALMERST. A. (1934) Nature, Lond. 134,462.
Journalof Nuclear EnergyParts A/B,
1965.Vol.
19. pp. 364 to 367. PergamonPress Ltd. Printedin NorthernIreland
On the effect of nucleon number parity on the magnitude of radiative capture cross sections (Received 1 December 1964) IN
a paper by BELANOVA and KAZACHKOVSKII (1963) the effect of number parity of nucleons in a nucleus upon the magnitude of radiative capture cross sections a, below 1 MeV was investigated. By means of such an analysis, the authors arrive at the conclusion that for a given energy the values of ‘J, for even-odd nuclei greatly exceed the values of o, for evenxven as well as for oddxven neighbouring nuclei. The result that the values of uc (e-o) are considerably in excess of oc (o-e) contradicts the supposition of HURWITZ and BET-HE(1951) about the existence of a characteristic level from which the excitation energy of a nucleus has to be evaluated in order to estimate nuclear level densities. A conclusion of this kind seems to be of great importance from a theoretical point of view as well as for practical purposes. For example, the evaluation of capture cross sections of fission product nuclei, which are needed for fast reactor core-life estimates, is greatly simplified if one can assume the validity of the HURWITZ-BETHE prescription. Therefore it seems worthwhile to repeat the evaluations of BELANOVA and KAZACHKOVSKII using more recent data. In doing this we have considered only capture cross sections for -25 keV neutrons
365
Letters to the editors
because, in our opinion, inelastic scattering processes which can occur at higher energies make it quite difficult to determine capture cross sections accurately. Following BELANOVA and KAZACHKOVSKII, the capture cross sections for even-odd nuclei not experimentally available were found by subtracting the known capture cross sections for even-even isotopes from the total absorption cross sections for the natural mixture of isotopes. When a cross section for even-even isotope was not known, we have assumed an averaged value on the basis of the other known cross sections. In many cases cross sections at higher energies (-30 keV) were extrapolated at -25 keV; this was done using as a guide the slope of the cross section for the element or isotope given in the BNL-325 Suppl. No. 1, or tracing on a semilogarithmic paper a straight line between the values at 30 and 65 keV given by MACKLIN et al. (1963b). The experimental and adopted values are given in Table 1. Our estimated capture cross sections for even-odd nuclei are given in Table 2 (column 3), together with those estimated by BELANOVA and KAZACHKOVSKH (column 2). TABLE
Element or isotope
I .-ADOPTED Energy (keV) 30 ! 7 -25 -25 -25 -30 -25
102%100,110Pd ‘08Pd*(13.6h) I’Sn llsSn S,Ba
162 16REr liOEr ,*W lS”,182W l*&W*(74d) 186W 7RPt 180-194Pt l=Pt *( 19h) lg@Pt z&g
-25 35 -‘- 15 -25 -25 305 7 -25 -25 30.4 $ 16 30.4 3: 16 30 : 7 -25 -25 -30 -30 30 i_ 7 -25 3;:‘7 -25 -25 -25 -25 -25 -25
CAPTURE CROSS SECTIONSFOR -25
keV NEUTRONS
References
ui, adopted at -25 keV
~-31 :: 6 5.6 % 2 24 & 4.8 59 1 10 250 ~.- 40 37 i12 415 * 98 148 $ 39 454 :i: 41 290 .r 35 390 * 82 243 A 51 61 -c 5.5 -8.6 -’ 1.7 1173 ir 192 1622 :t_279 1175 _f 106 710 :i: 71 775 Iti 70 330 1 130 900 --!:90 298 + 30 340 pi- 50
MACKLIN ef al.
(1963b)
BOOTH et al. (1958) KONONOV et a/. (1959) MACKLIN ef a/. (1963~) KAPCHIGASHEVand POPOV (1963) MACKLIN ef al. (1963a) VERVIER(1959) VERVIER(1959) MACKLIN et nl. (1963b) LYON and MACKLIN (1959) MACKLIN et al. (1962) MACKLIN et a/. (1962) MACKLIN et al. (1963b) KONONOV et MACKLIN ef MACKLIN ef MACKLIN ef
al. al. al. al.
(1959) (1963~) (1963~) (1963b)
MACKLIN (1958) MACKLIN et al. (1963b) BOOTH et al. (1958) GIBBONS et al. (1961) MACKLIN (1958) KAPCHIGASHEVand POPOV
34 29.6 5.6 24 29.6 65 250
T 7 A. 6.8 5 2 + 4.8 _t- 6.8 :I 11 ~I 40
203 47 415 148 522 290 290 429 267 67 8.4 8.6 1478 2044 1328 710 710 922 330 330 900 298 298 340
i 51 + 15 % 39 + 47 :! 35 f 35 + 90 i 56 i 6 & 1.7 :z 1.7 + 242 + 352 h 120 :j: 71 + 71 -:: 83 1: 130 _k 130 * 90 + 30 + 30 1 50
310 350 270 373 225 210 240 325 57 57
mv~ 125 ~1~180 * 70 + 34 i 70 It: 60 + 80 -‘~50 i_ 13 :c- 13
to 98
( 1963) -25 -25 -25 30 .‘- 7 -25 -25 -25 24 $ 2 -25 -25
350 IT 180 270 + 70 330 i 30
BOOTH el al. (1958) BOOTH et al. (I 958) MACKLIN et al. (1963b)
210 rF 60 240 -r_ 80 325 -r 50
BOOTH et al. (1958) BOOTH et al. (1958) COOK and SCHMITT (1959)
57 t 13
MACKLIN (1958)
366
Letters to the editors
TABLE Z.-CAPTURE
CROSS SECTIONS FOR EVEN-ODD
BELANOVA and KAZACHKOVSKII (1963)
Isotope
160 700 500 1530 260 2750 2150 1630 2920 1060 1120 630
-
It * * f
60 180 50 380
& & + i = * + &
300 640 570 310 590 430 240 30
o. (e-o) This work 137 65 310 & 1314 343 335 1750 2742 < 1681 2921 G 514 & 673 948
TABLE 3.--CAPTURE CROSS SECTIONS FOR ODD-EVEN Isotope 'IGa '5A~ BIBr sjRb*(18.6d) “:Rb “j,“,Rb aQY g3Nb*(6.6m) 1”7A “&54-) 121Sb*(2.8d) lz3Sb*(6W) 121,123Sb 1271 =3cs lasLa lalPr 158Tb lslTa I&l*sRe
’97A~
uc (mb) 140 650 550 181 29 2140 28 120 1330 823 810 230 2562 885 900 50 155 2100 900 950 960
NUCLEI AT ~25 keV
& 30 & 160 * 55 zt 35 + 6 I 30 i 7 i 24 & 250 * 60 5 250 & 100 11:57 + 90 * 300 * 7 $ 15 * 200 & 100 Sr 106 + 190
-‘+ + ir i i_ i % = + & -+ t
CLAVT~N et al. (1961)
330 11 328 327 74 41 295 556 356 492 1111 231 196
NUCLEI AT ~25keV References
L~o~and MACKLIN(~~~~) BOOTH et al. (1958) MACKLIN (1958) MACKLIN(~~~~) KONONOV et al. (1959) BOOTH et al. (1958) KONONOV et al. (1959) KONONOV et al. (1959) SCHMITT~~~COOK(~~~O) BOOTH et al. (1958) BOOTH et al. (1958) SCHMITT~~~COOK(~~~O) BOOTH et al. (1958) MACKLIN (1958) LYON and MACKLIN(~~~~) GIBBONS et al. (1961) GIBBONS et al. (1961) MACKLIN et al. (1963b) KONONOV et al. (1959)
144 37 280 960 243 92 392 1560 881 1000 1155 780 683
Letters to the editors
Magic
N
Magic Z
Magic N
I
367
I
+
I
50
60
I
70
I
80
2
FIG. 1 .-Dependence
of C&on Z for -25 keV neutrons: O-a, (e-o); O-a, (o-e). The dashed line is intended only as a guide for the eye.
It is interesting to note that in many cases our values agree reasonably well with the values adopted by CLAYTON et al. (1961) on the basis of an empirical relationship between cross sections and isotopic abundance (column 4). In Fig. 1, the values obtained in our analysis for uC (e-o) are plotted as a function of proton number Z together with experimental values of oC for odd-even nuclei at ~25 keV. With the exception of 170Er all the data seem to lie on a smooth curve which shows the characteristic behaviour due to shell and deformation effects. It does not seem that there is any definite indication that oe (e-o)values are systematically higher than neighbouring oe (o-e) values, and therefore no contradiction is found with the supposition of HURWITZ and BETHE. Centro di Calcolo de1 CNEN Bologna, Italy
V. BENZI M. V. BORTOLANI REFERENCES
14, 185; J. Nucl. Ener,v?t BELANOVAT. S. and KAZACHKOVSKII0. D. (1963) Atomnaya Enerpju (Parts A/B Reactor Sci. Technol.) 18, 225 (1964). BOOTHR., BALL W. P. and MCGREGOR M. H. (1958) Phys. Rev. 112,226. CLAYTON D. D., FOWLER W. A., HULL T. E. and ZIMMERMANB. A. (1961) Ann. Phys. 12, 331. COOK C. W. and SCHMITTH. W. (1959) Bull. amer. Phys. Sot. Ser. II. 4, 359. GIBBONS J. H., MACKLIN R. L., MILLER P. D. and NEILERJ. H. (1961) Phys. Rev. 122, 182. HURWITZ H. and BETHEH. A. (1951) Phys. Rev. 81,898. KAPCHIGASHEVS. P. and POPOV U. P. (1963) Atomnaya Energi)la 15,120. KONONOVV. N., STAVISSKIIYu. YA. and TOLSTTKOV V. A. (1959) Reactor SC;. (J. Nucl. Energy Part A)
l&46. LYON W. S. and MACKLIN R. L. (1959) Phys. Rev. 114, 1619. MACKLIN R. L. (1958) Proceedings of the Second International Conference on the Peace@1 Uses of Atomic Energy, Geneva, P/671, Vol. 15, p. 68. United Nations, N.Y. MACKLIN R. L., INADA T. and GIBBONSJ, H. (1962) Nature, Land. 194, 1272. MACKLIN R. L. and GIBBONSJ. H. (1963a) Report WASH 1042. MACKLIN R. L., GIBBONSJ. H. and INADA T. (1963b) Phys. Rev. 129, 2695. MACKLIN R. L., INADA T. and GIBBONSJ. H. (1963~) Bull. amer. Phys. Sot. 8,81. SCHMITTH. W. and Coon C. W. (1960) Nucl. Phys. 20,202. VERVIERJ. (1959) Nucl. Phys. 9, 569.
Letters to the editors
Thus a figure of 1.307 x lo3 for channel 1 and 1.329 x lo3 for channel 2 were taken for the calibration. To check that there was no alteration in the functioning of the Geiger tubes, periodic tests were made with a &OCosource placed in a fixed geometry. Using the above efficiencies the output of the americium/beryllium source, after corrections were applied for self-absorption in the source, fast neutron capture in oxygen and sulphur, neutron escape from the sphere and the various counting corrections, was found to be 7.54 x lo6 n/set. This compares with the figure of 7.57 x IO8 n/set as measured at the National Physical Laboratory by their new technique (AXTONer al., 1963). The advantages of the method used in the calibration described are: (i) Its great simplicity. (ii) There are no pipetting errors, the whole of the activity counted in the 4~ counter being also counted by the dip counters. By placing the active solution into the small vessels there are no errors in mixing and sampling from the large sphere. (iii) The thickness of the foil is known accurately as well as its purity. The disadvantage of the method is the self-absorption correction for the foil. This 5 per cent correction is larger than for the first two techniques. To overcome this it is proposed to set up 4$-y coincidence equipment to determine the manganese foil activity. The comparison between the measurement at Berkeley and at the National Physical Laboratory seems to justify the method used and it should prove useful to laboratories whose source preparation facilities are limited. Acknowledgmenf-This paper is published by permission of the Director of the Berkeley Nuclear Laboratories, Central Electricity Generating Board, Berkeley, Glos. Berkeley Nuclear Laboratories CEGB, Berkeley, Glos.
I. M. G. THOMPSON R. W. CLARKE A. LAVENDER REFERENCES
ALDER F. and HUBER P. (1949) Helv. phys. acta 22, 368. AXTONE. J. and CROSS P. (1961) Reactor Sci. Technol. (J. Nucl. Energy Parts A/B) 15,22. AXTONE. J., CROS P. and ROBERTSON J. C. (1963) Reactor Sci. Technol. (J. Nucl. Energy Parts A/B) 17,440. GEIGERK. W. and WHYTEG. N. (1959) Cunad. J. Phys. 37,256. JUREN J. DE and CHIN J. (1955) J. Res. nut. Bur. Stand. 55, 311. MEISTERH. (1958) Z. Naturf. 13a, 722. O’NEAL R. D. and SCHARFF-GOLDHABER G. (1946) Phys. Rev. 69, 368. S~~LARDL. and CHALMERST. A. (1934) Nature, Lond. 134,462.
Journalof Nuclear EnergyParts A/B,
1965.Vol.
19. pp. 364 to 367. PergamonPress Ltd. Printedin NorthernIreland
On the effect of nucleon number parity on the magnitude of radiative capture cross sections (Received 1 December 1964) IN
a paper by BELANOVA and KAZACHKOVSKII (1963) the effect of number parity of nucleons in a nucleus upon the magnitude of radiative capture cross sections a, below 1 MeV was investigated. By means of such an analysis, the authors arrive at the conclusion that for a given energy the values of ‘J, for even-odd nuclei greatly exceed the values of o, for evenxven as well as for oddxven neighbouring nuclei. The result that the values of uc (e-o) are considerably in excess of oc (o-e) contradicts the supposition of HURWITZ and BET-HE(1951) about the existence of a characteristic level from which the excitation energy of a nucleus has to be evaluated in order to estimate nuclear level densities. A conclusion of this kind seems to be of great importance from a theoretical point of view as well as for practical purposes. For example, the evaluation of capture cross sections of fission product nuclei, which are needed for fast reactor core-life estimates, is greatly simplified if one can assume the validity of the HURWITZ-BETHE prescription. Therefore it seems worthwhile to repeat the evaluations of BELANOVA and KAZACHKOVSKII using more recent data. In doing this we have considered only capture cross sections for -25 keV neutrons
365
Letters to the editors
because, in our opinion, inelastic scattering processes which can occur at higher energies make it quite difficult to determine capture cross sections accurately. Following BELANOVA and KAZACHKOVSKII, the capture cross sections for even-odd nuclei not experimentally available were found by subtracting the known capture cross sections for even-even isotopes from the total absorption cross sections for the natural mixture of isotopes. When a cross section for even-even isotope was not known, we have assumed an averaged value on the basis of the other known cross sections. In many cases cross sections at higher energies (-30 keV) were extrapolated at -25 keV; this was done using as a guide the slope of the cross section for the element or isotope given in the BNL-325 Suppl. No. 1, or tracing on a semilogarithmic paper a straight line between the values at 30 and 65 keV given by MACKLIN et al. (1963b). The experimental and adopted values are given in Table 1. Our estimated capture cross sections for even-odd nuclei are given in Table 2 (column 3), together with those estimated by BELANOVA and KAZACHKOVSKH (column 2). TABLE
Element or isotope
I .-ADOPTED Energy (keV) 30 ! 7 -25 -25 -25 -30 -25
102%100,110Pd ‘08Pd*(13.6h) I’Sn llsSn S,Ba
162 16REr liOEr ,*W lS”,182W l*&W*(74d) 186W 7RPt 180-194Pt l=Pt *( 19h) lg@Pt z&g
-25 35 -‘- 15 -25 -25 305 7 -25 -25 30.4 $ 16 30.4 3: 16 30 : 7 -25 -25 -30 -30 30 i_ 7 -25 3;:‘7 -25 -25 -25 -25 -25 -25
CAPTURE CROSS SECTIONSFOR -25
keV NEUTRONS
References
ui, adopted at -25 keV
~-31 :: 6 5.6 % 2 24 & 4.8 59 1 10 250 ~.- 40 37 i12 415 * 98 148 $ 39 454 :i: 41 290 .r 35 390 * 82 243 A 51 61 -c 5.5 -8.6 -’ 1.7 1173 ir 192 1622 :t_279 1175 _f 106 710 :i: 71 775 Iti 70 330 1 130 900 --!:90 298 + 30 340 pi- 50
MACKLIN ef al.
(1963b)
BOOTH et al. (1958) KONONOV et a/. (1959) MACKLIN ef a/. (1963~) KAPCHIGASHEVand POPOV (1963) MACKLIN ef al. (1963a) VERVIER(1959) VERVIER(1959) MACKLIN et nl. (1963b) LYON and MACKLIN (1959) MACKLIN et al. (1962) MACKLIN et a/. (1962) MACKLIN et al. (1963b) KONONOV et MACKLIN ef MACKLIN ef MACKLIN ef
al. al. al. al.
(1959) (1963~) (1963~) (1963b)
MACKLIN (1958) MACKLIN et al. (1963b) BOOTH et al. (1958) GIBBONS et al. (1961) MACKLIN (1958) KAPCHIGASHEVand POPOV
34 29.6 5.6 24 29.6 65 250
T 7 A. 6.8 5 2 + 4.8 _t- 6.8 :I 11 ~I 40
203 47 415 148 522 290 290 429 267 67 8.4 8.6 1478 2044 1328 710 710 922 330 330 900 298 298 340
i 51 + 15 % 39 + 47 :! 35 f 35 + 90 i 56 i 6 & 1.7 :z 1.7 + 242 + 352 h 120 :j: 71 + 71 -:: 83 1: 130 _k 130 * 90 + 30 + 30 1 50
310 350 270 373 225 210 240 325 57 57
mv~ 125 ~1~180 * 70 + 34 i 70 It: 60 + 80 -‘~50 i_ 13 :c- 13
to 98
( 1963) -25 -25 -25 30 .‘- 7 -25 -25 -25 24 $ 2 -25 -25
350 IT 180 270 + 70 330 i 30
BOOTH el al. (1958) BOOTH et al. (I 958) MACKLIN et al. (1963b)
210 rF 60 240 -r_ 80 325 -r 50
BOOTH et al. (1958) BOOTH et al. (1958) COOK and SCHMITT (1959)
57 t 13
MACKLIN (1958)
366
Letters to the editors
TABLE Z.-CAPTURE
CROSS SECTIONS FOR EVEN-ODD
BELANOVA and KAZACHKOVSKII (1963)
Isotope
160 700 500 1530 260 2750 2150 1630 2920 1060 1120 630
-
It * * f
60 180 50 380
& & + i = * + &
300 640 570 310 590 430 240 30
o. (e-o) This work 137 65 310 & 1314 343 335 1750 2742 < 1681 2921 G 514 & 673 948
TABLE 3.--CAPTURE CROSS SECTIONS FOR ODD-EVEN Isotope 'IGa '5A~ BIBr sjRb*(18.6d) “:Rb “j,“,Rb aQY g3Nb*(6.6m) 1”7A “&54-) 121Sb*(2.8d) lz3Sb*(6W) 121,123Sb 1271 =3cs lasLa lalPr 158Tb lslTa I&l*sRe
’97A~
uc (mb) 140 650 550 181 29 2140 28 120 1330 823 810 230 2562 885 900 50 155 2100 900 950 960
NUCLEI AT ~25 keV
& 30 & 160 * 55 zt 35 + 6 I 30 i 7 i 24 & 250 * 60 5 250 & 100 11:57 + 90 * 300 * 7 $ 15 * 200 & 100 Sr 106 + 190
-‘+ + ir i i_ i % = + & -+ t
CLAVT~N et al. (1961)
330 11 328 327 74 41 295 556 356 492 1111 231 196
NUCLEI AT ~25keV References
L~o~and MACKLIN(~~~~) BOOTH et al. (1958) MACKLIN (1958) MACKLIN(~~~~) KONONOV et al. (1959) BOOTH et al. (1958) KONONOV et al. (1959) KONONOV et al. (1959) SCHMITT~~~COOK(~~~O) BOOTH et al. (1958) BOOTH et al. (1958) SCHMITT~~~COOK(~~~O) BOOTH et al. (1958) MACKLIN (1958) LYON and MACKLIN(~~~~) GIBBONS et al. (1961) GIBBONS et al. (1961) MACKLIN et al. (1963b) KONONOV et al. (1959)
144 37 280 960 243 92 392 1560 881 1000 1155 780 683
Letters to the editors
Magic
N
Magic Z
Magic N
I
367
I
+
I
50
60
I
70
I
80
2
FIG. 1 .-Dependence
of C&on Z for -25 keV neutrons: O-a, (e-o); O-a, (o-e). The dashed line is intended only as a guide for the eye.
It is interesting to note that in many cases our values agree reasonably well with the values adopted by CLAYTON et al. (1961) on the basis of an empirical relationship between cross sections and isotopic abundance (column 4). In Fig. 1, the values obtained in our analysis for uC (e-o) are plotted as a function of proton number Z together with experimental values of oC for odd-even nuclei at ~25 keV. With the exception of 170Er all the data seem to lie on a smooth curve which shows the characteristic behaviour due to shell and deformation effects. It does not seem that there is any definite indication that oe (e-o)values are systematically higher than neighbouring oe (o-e) values, and therefore no contradiction is found with the supposition of HURWITZ and BETHE. Centro di Calcolo de1 CNEN Bologna, Italy
V. BENZI M. V. BORTOLANI REFERENCES
14, 185; J. Nucl. Ener,v?t BELANOVAT. S. and KAZACHKOVSKII0. D. (1963) Atomnaya Enerpju (Parts A/B Reactor Sci. Technol.) 18, 225 (1964). BOOTHR., BALL W. P. and MCGREGOR M. H. (1958) Phys. Rev. 112,226. CLAYTON D. D., FOWLER W. A., HULL T. E. and ZIMMERMANB. A. (1961) Ann. Phys. 12, 331. COOK C. W. and SCHMITTH. W. (1959) Bull. amer. Phys. Sot. Ser. II. 4, 359. GIBBONS J. H., MACKLIN R. L., MILLER P. D. and NEILERJ. H. (1961) Phys. Rev. 122, 182. HURWITZ H. and BETHEH. A. (1951) Phys. Rev. 81,898. KAPCHIGASHEVS. P. and POPOV U. P. (1963) Atomnaya Energi)la 15,120. KONONOVV. N., STAVISSKIIYu. YA. and TOLSTTKOV V. A. (1959) Reactor SC;. (J. Nucl. Energy Part A)
l&46. LYON W. S. and MACKLIN R. L. (1959) Phys. Rev. 114, 1619. MACKLIN R. L. (1958) Proceedings of the Second International Conference on the Peace@1 Uses of Atomic Energy, Geneva, P/671, Vol. 15, p. 68. United Nations, N.Y. MACKLIN R. L., INADA T. and GIBBONSJ, H. (1962) Nature, Land. 194, 1272. MACKLIN R. L. and GIBBONSJ. H. (1963a) Report WASH 1042. MACKLIN R. L., GIBBONSJ. H. and INADA T. (1963b) Phys. Rev. 129, 2695. MACKLIN R. L., INADA T. and GIBBONSJ. H. (1963~) Bull. amer. Phys. Sot. 8,81. SCHMITTH. W. and Coon C. W. (1960) Nucl. Phys. 20,202. VERVIERJ. (1959) Nucl. Phys. 9, 569.