proton-proton and proton-neutron interactions for the morse potential

1
246 LETTERS TO THE 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. iT. 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. Tarasov 1 are in agreement as to direction of change and its order of magnitude with predictions 2 based upon a somewhat crude theory for magnetic in- teraction. L. W. MCKEEHAN 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[exp (-4r/a)-2 exp (-2r/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 obtained 2 from the newer experiments 3 on the scattering of protons by protons. The values D —119.36 mc 2 , a — e 2 /2mc 2 give a satisfactory agree- ment with the experimentally determined phase shifts. The phase shifts were computed using numerical integration of the wave equation up to a distance of 3e 2 /mc 2 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 also 2 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 po- tential in the 1 5 state has been determined so as to fit Simons' value 4 (14.8 X10~ 24 cm 2 ) 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).

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Page 1: Proton-Proton and Proton-Neutron Interactions for the Morse Potential

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).