The binding energy of the triton has been calculated by the variational method. The forces between the particles are assumed to be charge independent and to be composed of central and tensor parts, the radial dependence of each being given by Yukawa wells. The binding energy calculation is employed to determine the range of the tensor component; the other constants are fixed by the low energy two-body data. The effective triplet range, the percentage D state in the triton, and the Coulomb energy of He 3 are then predicted. The first two of these are in satisfactory agreement with experiment; the third is in error by twentyfive percent. The final "best" potential contains only four constants, the ranges and depths of the central and tensor potentials. The triplet and singlet central forces are equal. Present. 18 If one chooses as variables the quantities 5=n+r2, t=ri-r2, and p, the integration scheme becomes ff(s, t, p)dr= f dsf dpf dtp(s*-t*)f(s, t, p), (Al) J J 0 J 0 J Q for which recursion formulas were developed. 18 However, this scheme proved overly difficult where the exponentials involved r\ and r 2 unsymmetrically. Instead of permuting the variables, we used the scheme of Coolidge and James, 16 which has the advantage of compartmenting the integrations. Making the substitutionsf=-ri+r 2 +p, and inserting a numerical factor chosen simply to give the same result as the Hylleraas method for the same integrand, one obtains f M,V, Mr = (1/8) f dif dr,f d$ J J 0 J 0 J 0

statistical considerations. With 2-kev x-rays the pulse height distribution shown in Fig. lb was obtained, on which we have plotted also the noise pulse height distribution. The interpretation of this curve in terms of detection efficiency must await further calculations and measurements, but rough considerations indicate a detection efficiency of greater than 50 and less than 80 percent. This high detection efficiency of Nal(Tl) crystals for low energy x-rays sees to differ markedly from the sharp drop in the detection efficiency of anthracene crystals for low energy electrons 2 (<15 kev). Part of the latter effect may perhaps be due to a low lightcollection efficiency in that experiment.The average pulse height, which we identified with the peak pulse height for all energies except for 2 kev, varied linearly (within the experimental error) with the x-ray energy from 2 to 411 kev. For the measurement at 411 kev we used the gamma-ray 3 from Au 198 . The linearity test was made in three different overlapping energy ranges, indicated by (a), (b), and (c) in Fig. 2. In each energy range different pulse height distributions were measured with a definite photo-multiplier tube voltage-about 700 volts for (a) and (b) and 800 volts for (c). One particular crystal was used CO M00 10 2 I O LU X Ld CO _J QL 10 10 100 ENERGY IN KV 1000 FIG. 2. Average pulse height (normalized to a gain of 1000) vs. incident x-ray energy for three different experimental arrangements, showing the proportionality of Nal(Tl) from 2 kev to 411 kev.during one day, so that the crystal surface would not deteriorate during one set of measurements. The pulse height distributions were not measured with the same amplifier gain, but in Fig. 2 the gain of all points is arbitrarily normalized to 1000.At incident x-ray energies above 33 kev, the binding energy of the iT-electrons in iodine, two peaks were seen in the pulse height distribution. Figure 3 shows the distribution obtained with 44-kev x-rays. The peak at the higher energy corresponds to the full energy of the incident x-ray: both the iodine photo-electron and the iodine K x-ray energy are absorbed in the crystal. The peak at the lower energy is caused by the occasional escape of the iodine K x-rays from the front face of the crystal. That this interpretation is correct is demonstrated by the fact that at different energies of the incident x-rays (above 33 kev) the energy difference between the two peaks remains constant and approximately equal to the iodine K x-ray energy.This "escape" peak is also observed in gas proportional counters, 4 where it is of the same order of magnitude as the main peak and where both the K a and K$ escape peaks can be resolved because of the much larger number of pulse-forming electrons available. In the present case the escape probability is at most \ for incident x-rays just above 33 kev and decreases rapidly for higher energies, in agreement with rough theoretical considerations. This escape of the iodine K x-rays will, of course, lower the over-all detection effic...

A necessary condition for positive definite energy density of the plane-wave components of a system described by a linear first-order wave equation is expressed as a condition on the wave-equation matrices alone. Hence the condition for positive-definite total energy of a system may be applied without the need for extracting the Hermitizing operator. The criterion is applied to a system discussed by Bhabha.

No abstract

It.would appear that one of Wyler's calculations of the fine-structure constant is based on an incorrect value of the coefficient of the Poisson kernel for Cartan's third (fourth) classical domain, and hence that the value of the fine-structure constant may not be derivable from Wyler's assumptions.An astonishingly accurate value of the fine-structure constant a was proposed by Wyler (1969, t 971) using certain geometrical arguments. There was considerable discussion (Physics Today, 1971 ;Robertson, 1971 ;Schwartz, 1971 ;Gilmore, 1972;Adler, 1973) o f his work; however, neither a strong justification nor a definite disproof of his arguments appeared.However, Wyler later issued a detailed analysis (1972) of~yler (1969), giving a much more specific basis for his value of c~. Further work, partially based on this analysis, was done by Vigier (1973), who was able to make a physical connection with quantum electrodynamics.On the basis of Wyter's detailed analysis of his work, it would appear that Wyler's value of the fine-structure constant does not follow from his premises.Wyler states (1972) that his value of a follows directly from the quantitywhere V(D n) and V(Q n) are the Euclidean volumes, respectively, of Cartan's (1935; cf. Hua, 1963; Piatetsky-Chapiro, 1966)