proton-proton and proton-neutron interactions for the morse potential
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246 LETTERS TO T H E EDITOR
where h is in meters of water, the variation of air shower counting rate should vary as he~°-bh. The latter function is represented by the dotted curve in Fig. 1 and it is in fair agreement with the experimental points representing the air shower intensity.
These flights have been made with financial support from the Carnegie Institution of Washington.
THOMAS H. JOHNSON
J. GRIFFITHS BARRY The Bartol Research Foundation of the Franklin Institute,
Swarthmore, Pennsylvania, January 10, 1940.
i T . H. Johnson and J. G. Barry, Phys. Rev. 56, 219 (1939); T. H. Johnson, Rev. Mod. Phys. 11, 208 (1939).
2 T . H. Johnson, Phys. Rev. 56, 228 (1939). 3 J. R. Oppenheimer, private communication. 4 L. W. Nordheim, Phys. Rev. 51, 1110 (1937).
Ferromagnetic Anisotropy in Body-Centered Cubic Iron-Nickel Alloys
It may be worth pointing out that the results for the first ferromagnetic anisotropy constant in body-centered cubic iron-nickel alloys up to 16 atomic percent nickel, recently reported by L. P. Tarasov1 are in agreement as to direction of change and its order of magnitude with predictions2
based upon a somewhat crude theory for magnetic interaction.
L. W. M C K E E H A N Sloane Physics Laboratory,
Yale University, New Haven, Connecticut,
January 4, 1940.
!L. P. Tarasov, Phys. Rev. 56, 1245-1246 (1939). *L. W. McKeehan, Phys. Rev. 52, 18-30 (1937), Table IV.
Proton-Proton and Proton-Neutron Interactions for the Morse Potential
The potential
- D [ e x p ( - 4 r / a ) - 2 exp ( - 2 r / a ) ]
has been introduced into molecular problems by Morse and has been applied to nuclear problems by Morse, Schiff and Fisk.1 It was found by them to represent satisfactorily the data on the scattering of neutrons by protons, the binding energy of the deuteron and the photoelectric effect of the
deuteron. It was thought of interest to adjust the constants D and a so as to fit the newer data. For proton-proton scattering the adjustment of the constants was made so as to fit the values of the phase shift obtained2 from the newer experiments3 on the scattering of protons by protons. The values D —119.36 mc2, a — e2/2mc2 give a satisfactory agreement with the experimentally determined phase shifts. The phase shifts were computed using numerical integration of the wave equation up to a distance of 3e2/mc2 where the wave function was joined to the Coulomb function. The computed phase shifts are given in Table I.
TABLE I. Computed phase shifts.
E IN KEV
670 776 867
Ko
24.27° 27.17° 29.33°
E IN KEV
860 1200 1390
Ko
29.17° 36.00° 38.83°
E IN KEV
1830 2105 2392
Ko
43.73° 46.12° 47.85°
At the lower energies there is some systematic difference between the experimental and theoretical values. This, however, exists for other potentials also2 in varying degrees. The Morse potential was used above as an addition to the Coulomb potential.
With the same range of force the proton-neutron potential in the 1 5 state has been determined so as to fit Simons' value4 (14.8 X10~24 cm2) for the scattering cross section of slow neutrons. The ratio of the proton-neutron potential obtained, using the above value of D, is 1.006 confirming a close equality of the proton-proton and proton-neutron forces.5
HUBERT M. THAXTON
A. M. MONROE Department of Physics,
Agricultural and Technical College of North Carolina, Greensboro, North Carolina,
January 12, 1940.
i P. M. Morse, J. B. Fisk and L. I. Schiff, Phys. Rev. 50, 748 (1936); 51, 706 (1937).
*G. Breit, H. M. Thaxton and L. Eisenbud, Phys. Rev. 55, 1018 (1939).
3 R. G. Herb, D. W. Kerst, D. B. Parkinson and G. J. Plain, Phys. Rev. 55, 998 (1939); N. P. Heydenburg, L. R. Hafstad and M. A. Tuve, Phys. Rev. 56, 1078 (1939).
*L. Simons, Phys. Rev. 55, 792 (1939). 5 G. Breit, E. U. Condon and R. D. Present, Phys. Rev. 50, 825
(1936); G. Breit and J. R. Stehn, Phys. Rev. 52, 396 (1937); G. Breit, L. E. Hoisington, S. S. Share and H. M. Thaxton, Phys. Rev. 55, 1103 (L) (1939); L. E. Hoisington, S. S, Share and G. Breit, Phys. Rev. 56, 884 (1939).