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CHART OF NUCLEI ON TRILINEAR COORDINATES D. E. HULL1and W. H. SULLIVAN2 Clinton Laboratories, Oak Ridge, Tennessee
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CRARTS DEPICTING the systematics of atomic nuclei have in the past been constructed as.functions of the mass number A (or the number of neutrons, N = A - Z) and the atomic numher Z in rectangular coordinate systems. In several such charts, there have been used as ordinates and abscissa, respectively: A - Z versus Z (Rasetti)ia Z versus'~ - Z (Seahorg);' Z versus A (Seaborg and Kohman);= and A - 22 versus Z (Evans and Living~ton).~ AU of these charts, except the last, suffer the disadvantage that the stable isotopes lie on a line with a slope of approximately 45", and it is necessary to break the sequence a t several points in order to fit all the nuclei into a rectangular frame of reasonable size. I n the system employing A - 2 2 (the neutron excess, or isotopic number) and Z as coordinates, the stable nuclei are brought into a nearly horizontal line, but neighboring isobaric nuclei are thrown into awkward "knight's move" positions with respect to one another, and this result is most unsatisfactory for showing genetic relationships among radioactive nuclei. The several disadvantages and difficulties of the graphical methods hitherto employed may be resolved by using trilinear coordinates. In such a,system one may plot simultaneously A versus Z, N versus Z, and A versus N, as shown in Figure 1. Inspection of the diagram reveals that this system has the following pr~perties:~ (1) All isotopes of a given element (atomic numher, Z, constant) lie along a line inclined a t 30' above the horizontal. (2) All isobars8 (mass number, A, constant) lie in a vertical line. 1 On leave from Carbide and Carbon Chemicals Corporation, Oak Ridge, Tennessee. On leave to the Atomic Energy Commission. "ABETTI, F., "Elements of Nuclear Physics," Prentice-Hall, Iic., New Yark, 1936, p. 1 5 P 6 . SEABORG. G. T., privately circulated. %SEBORG, G. T., AND T. P. KOHMAN, "Plutonium Project Handbook," CL-697,Chapt,er 111. 'EVANS.R. D., AND M. S. LIVINGSTON, Rev. Modem Phys., 7, 229 (1935). 7 This system may be regarded as a modification of one used by W. BOHRAND J. A. WHEELER, P h p Rev., 56,445 (1930). in which the isotopes are plotted on slanting lines against the mass number. Their svstem gives vertical alignment of isobars, but not the horizontal nlignment of isodiapheres. STEWART, J. Q., Phil. Mag., (6) 36, 326 (1918).
(3) All isotoness (number of neutrons, N, constant) lie along a line inclined a t 30' below the horizontal. (4) All isodiapheres1° (isotopic number, N - Z, constant) lie on a horizontal line. Since the isotopic number of all the light elements ranges only from -1 to 2 and since i t increases relatively tittle compared to the mass number even for the heavy elements, one finds that a plot of all stable nuclei will extend in a horizontal direction, with only a moderate upward drift in the region of the heavier nuclei, as shown in Figure 2. This characteristic makes the triangular coordinate system more convenient than most of t h e in common use, since all nuclei can be represented in a single continuous plot on paper of conventional rectangular shape. Although such a complete plot is a strip of considerable length (ratio of height to length approximately 1:7), it can be folded accordion-like to give a very satisfactory and
'GUGOENAEIMER, J.. J . phy8. Radium, (7) 5 , 253 (1934). l o S ~ ~J., Oeslmr. ~ ~Chem. ~ Zlg., s 41, ~ 315~(1938). ~ ,
SEPTEMBER, 1947
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2. Plot of st.bl*I.otop.n
usable chart, since any section may be examined with ease by opening the appropriate folds. By making only two breaks in the continuity (one a t mass number 118, the other a t 189) and starting again a t the initial base line, the height may be still further compressed (to a ratio of about 1:16); such a chart has bwn made to fit a pocket notebook and has been found quite useful. In Figure 3 is shown the light end of this chart.
various radioisotopes may be symbolized with ease, since the most common nuclear reactions are represented in a simple pattern with the product nuclei grouped in immediate juxtaposition around the target nucleus. Several of the more common reactions are shown diagrammatically in Figure 5. The symbols indicate the bombarding and emergent light particles of any given nuclear reaction.
F i r 3. Plot of Upht N"&i
Stable nuclei are represented by hexagons, radioactive I t is believed that one using this chart can quickly nuclei by circles. Radioactive disintegrations follow familiarize himself with the pattern of nuclear reactions a very simple pattern on the chart. Beta disintegra- and that the arrangement, therefore, will be useful for
tions follow a vertical line, the displacement being one unit downward for each negatron emitted and one unit upward for each positron emitted or orbital electron captured. Alpha disintegrations proceed horizontally to the left four mass units. See Fig. 4. The nuclear reactipns involved in producing the
instructional purposes. As an example, note that if a line. is drawn through isodiapheres with isotopic number zero (including He4 and Ole), the "mirror" nuclei will be found reflected perpendicularly across this line. The remarkable sequences of decreasing half-lives in the series Be7-Sc4' is brought out clearly. This work was done in part (by the senior author) a t the School of Chemistry of the University of Minnesota. J. W. Atchley prepared the plot of the nuclei.
