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NEW MEASUREMENTS OF THE MASSES OF ATOMS WITH MASS NUMBERS FROM 46 TO 70
The number and accuracy of mass-spectrographic measurements are increasing. It was recently reported[^1] that precision measurements had been made of atomic masses near mass number 40. At present a work has been published[^2] extending precision mass-spectrographic measurements to the interval of mass numbers from 46 to 70. The paper under review describes measurements of a number of doublets by means of a mass spectrograph with double focusing. The masses of the atoms studied were compared with the masses of molecules, chiefly hydrocarbons. The mean values of the doublets obtained from numerous mass-spectrographic measurements are given in Table 1.
FROM CURRENT LITERATURE
Table I
Doublets for measuring the masses of atoms with mass numbers from 46 to 70
| Doublet | Number of series of measurements | Mean value of the doublet width in \(10^{-4}\) atomic mass units | Doublet | Number of series of measurements | Mean value of the doublet width in \(10^{-4}\) atomic mass units |
|---|---|---|---|---|---|
| \(\mathrm{CH_2S} — \mathrm{Ti}^{46}\) | 3 | \(354.0 \pm 0.4\) | \(\mathrm{C_4H_{10}} — \mathrm{Ni}^{58}\) | 4 | \(1433.8 \pm 0.9\) |
| \(\mathrm{CH_3S} — \mathrm{Ti}^{47}\) | 4 | \(438.3 \pm 0.9\) | \(\mathrm{C_5} — \mathrm{Ni}^{60}\) | 5 | \(702.0 \pm 2.9\) |
| \(\mathrm{C_4} — \mathrm{Ti}^{48}\) | 6 | \(522.0 \pm 0.6\) | \(\mathrm{C_5H} — \mathrm{Ni}^{61}\) | 4 | \(782.9 \pm 2.3\) |
| \(\mathrm{C_4H} — \mathrm{Ti}^{49}\) | 4 | \(599.3 \pm 0.5\) | \(\mathrm{C_5H_2} — \mathrm{Ni}^{62}\) | 4 | \(886.9 \pm 0.8\) |
| \(\mathrm{C_4H_2} — \mathrm{Ti}^{50}\) | 10* | \(*709.09 \pm 0.20\) | \(\mathrm{SO_2} — \mathrm{Ni}^{64}\) | 3 | \(346.9 \pm 0.7\) |
| \(\mathrm{C_4H_2} — \mathrm{V}^{50}\) | 5* | \(*683.6 \pm 1.2\) | |||
| \(\mathrm{C_4H_3} — \mathrm{V}^{51}\) | 6 | \(792.8 \pm 0.5\) | \(\mathrm{C_5H_3} — \mathrm{Cu}^{63}\) | 6 | \(943.9 \pm 0.5\) |
| \(\mathrm{C_5H_5} — \mathrm{Cu}^{65}\) | 7 | \(1115.9 \pm 0.5\) | |||
| \(\mathrm{C_4H_3} — \mathrm{Cr}^{50}\) | 9* | \(*696.07 \pm 0.37\) | |||
| \(\mathrm{C_4H_4} — \mathrm{Cr}^{52}\) | 4 | \(908.8 \pm 0.9\) | |||
| \(\mathrm{C_4H_5} — \mathrm{Cr}^{53}\) | 5 | \(983.8 \pm 0.8\) | \(\mathrm{SO_2} — \mathrm{Zn}^{64}\) | 4 | \(326.82 \pm 0.20\) |
| \(\mathrm{C_4H_6} — \mathrm{Cr}^{54}\) | 1 | \(1079 \pm 2\) | \(\mathrm{O_2} — \mathrm{Zn}^{64}/2\) | 4 | \(252.46 \pm 0.22\) |
| \(\mathrm{C_5H_6} — \mathrm{Zn}^{66}\) | 4 | \(1208.7 \pm 0.5\) | |||
| \(\mathrm{C_4H_7} — \mathrm{Mn}^{55}\) | 5 | \(1165.8 \pm 1.1\) | \(\mathrm{C_5H_7} — \mathrm{Zn}^{67}\) | 4 | \(1280.8 \pm 0.5\) |
| \(\mathrm{C_5H_8} — \mathrm{Zn}^{68}\) | 4 | \(1375.1 \pm 0.6\) | |||
| \(\mathrm{C_4H_6} — \mathrm{Fe}^{54}\) | 8 | \(1072.0 \pm 0.5\) | \(\mathrm{C_5H_{10}} — \mathrm{Zn}^{70}\) | 4 | \(1528.8 \pm 0.5\) |
| \(\mathrm{C_4H_8} — \mathrm{Fe}^{56}\) | 6 | \(1278.2 \pm 1.0\) | |||
| \(\mathrm{C_4H_9} — \mathrm{Fe}^{57}\) | 6 | \(1350.9 \pm 0.9\) | |||
| \(\mathrm{C_4H_{10}} — \mathrm{Fe}^{58}\) | 1 | \(1448 \pm 4\) |
Note. The figures marked with an asterisk* are taken with allowance for a more recent preliminary communication \(^{4}\), where new data for three doublets are given.
From the values of the doublets, the atomic masses of the isotopes listed in Table II were calculated (see p. 166). The calculation of the masses was made from the masses of the hydrogen and carbon atoms measured by the same authors in the preceding work \(^{1}\), namely:
\[ \mathrm{H}^{1} — 1.008146 \; (\pm 3), \]
\[ \mathrm{C}^{12} — 12.003842 \; (\pm 4). \]
It should be noted that recently the masses of hydrogen and carbon atoms have more often been taken from tables in which they were calculated from nuclear reactions; see \(^{3}\).
experimental data” obtained on the basis of ideas about the weak coupling of the meson and nucleon fields. The point is that the weak-coupling theory gives an isotropic cross section for the scattering of low-energy mesons, whereas the cross section obtained in the paper under review differs sharply from an isotropic one. This fact, like several other experimental data on meson scattering[^2], constitutes an urgent demand of experiment, compelling the search for new theoretical ideas on the question of the interaction of fields.
The scattering of positive \(\pi\)-mesons with energy \(53 \pm 10\) MeV was observed in the gas of a diffusion chamber filled with hydrogen and methyl-alcohol vapors at a pressure of 21 atmospheres; the \(\pi\)-mesons were produced on the Columbia University cyclotron. In all, 8400 photographs were obtained. \(\pi\)-mesons decaying into \(\mu\)-mesons in the chamber gas were recorded if the projection of the angle between the tracks of the \(\pi\)- and \(\mu\)-mesons was greater than \(4^\circ\). From the 967 decays found, it was calculated that in this way a meson path length of \(1820\ \mathrm{g/cm^2}\) of hydrogen had been studied. To compensate for \(\pi\)- and \(\mu\)-decays at small angles (less than \(4^\circ\)), many of which could have been missed, a correction was calculated. Further, the lifetime of the \(\pi\)-meson was taken to be \(2.6 \cdot 10^{-8}\) sec. The theoretical angular distribution of \(\pi\)- and \(\mu\)-decays cuts off sharply at an angle of \(17.5^\circ\) if the energy of the \(\pi\)-mesons is exactly 53 MeV. The measured distribution decreases slowly in the angular region \(> 30^\circ\); therefore the energy of the \(\pi\)-mesons should be regarded as determined with an accuracy of \(\pm 10\) MeV. This uncertainty is due partly to the energy distribution in the primary beam and partly to scattering in the walls of the diffusion chamber (\(5\ \mathrm{g/cm^2}\) of steel).
Observed
Isotropic
\(\cos^2 \theta_0\)
Scattering angle in the center-of-mass system
As a result, 21 scattering events were found, which leads to a total scattering cross section of \(\pi^+\)-mesons by protons of \(20 \pm 4 \cdot 10^{-27}\ \mathrm{cm^2}\). This agrees with the results[^2] of \(20 \pm 10 \cdot 10^{-27}\ \mathrm{cm^2}\) at 56 MeV and, probably, also with[^3], where at a mean energy of 58 MeV a cross section of \(27.8 \pm 2.5 \cdot 10^{-27}\ \mathrm{cm^2}\) was obtained. In this connection it is necessary to take into account the sharp increase of the cross section with increasing energy[^2]. All the events considered satisfy the requirements of the kinematics of elastic \(\pi^\pm - p\) scattering. The figure shows the differential cross section \(d\sigma/d\omega\) (\(10^{-27}\ \mathrm{cm^2/steradian}\)) as a function of the scattering angle in the center-of-mass system. Events with \(\theta_0 < 20^\circ\) are not included because of the shortness of the recoil-proton track and possible confusion with \(\pi\)- and \(\mu\)-decay. The figure also plots angular distributions according to the following laws: \(1 + 3\cos^2 \theta_0\), \(\cos^2 \theta_0\), and isotropic. It follows from the figure that the isotropic distribution predicted by the weak-coupling theory is incompatible with the experimental results.
V. S.
References
- E. C. Fowler, W. B. Fowler, R. P. Shutt, A. M. Thorndike, W. L. Whittemore, Phys. Rev. 86, 1053 (1952).
- A series of abstracts in UFN, vol. 48, nos. 1–3.
- Isaacs, Sachs and Steinberger, Phys. Rev. 85, 802 (1952).