scholarly journals The anomalous scattering of protons in light elements

1936 ◽  
Vol 157 (891) ◽  
pp. 302-310 ◽  
Keyword(s):  
Single Scattering ◽  
Anomalous Scattering ◽  
Light Elements ◽  
Inverse Square Law ◽  
Atomic Nuclei ◽  
Coulomb Law ◽  
Scattering Material ◽  
Thick Layers

By a study of the scattering of protons by atomic nuclei we can gain information about the interactions of these particles. For sufficiently low velocities of the impinging protons, corresponding to 30 electron kilovolts, it has been shown by Gerthsen that they are scattered by celluloid according to the Rutherford law, and by hydrogen according to the Mott law of scattering of similar particles. At a distance of approach represented by this energy, the inverse square law of force still holds between the particles. Schneider has investigated the scattering of protons of energies up to 300 e.-kv. in aluminium, carbon, and boron. He found a pronounced maximum in the scattering by boron, compared with that by aluminium, at 200 e.-kv. It is not possible to say whether this anomaly is due to a breakdown in the Coulomb law of force between the boron nucleus and a proton, as he used thick layers of scattering material, a fact which renders the interpretation of his results difficult. The present work was undertaken with a view to checking these results, using sufficiently thin targets to ensure single scattering. Schneider’s observations have not been confirmed, although other anomalies have presented themselves.

scholarly journals Remarks on the anomalous scattering of α-particles from the quantum mechanical point of view

1930 ◽  
Vol 127 (806) ◽  
pp. 671-677 ◽  
Keyword(s):  
Cross Section ◽  
Point Of View ◽  
Light Nuclei ◽  
Fourth Power ◽  
Quantum Mechanical ◽  
Anomalous Scattering ◽  
Particle Scattering ◽  
Scattering Angle ◽  
Coulomb Law ◽  
Α Particles

1. It has been established experimentally by Bieler and Rutherford and Chadwick that α-particle scattering by light nuclei does not obey the Rutherford formula if the velocity of the incident particles be sufficiently large (of the order 2 × 10 9 cm. per second). Bieler showed that the scattering becomes less than the classical value for moderate angles (up to 70° scattering angle), while Rutherford and Chadwick found that it increases again for 135° scattering angle. It is at once obvious that these results indicate a departure from the Coulomb law of force, and various laws have been invoked to explain the devia­tions. Thus Bieler showed how the inverse fourth power law was capable of explaining his results, and he found the radius of the neutral surface of the nucleus to be 3⋅44 × 10 -13 cm. Hardmeier used an inverse fifth power polarisation law and was able to explain the increase again at high velocities. However it is desirable to consider the validity of these calculations from the standpoint of the new mechanics. 2. Dimensional Considerations .—Consider scattering by a centre of force exerting a potential F r -n . This scattering will depend not only on the mass m , and velocity v of the incident particles, and on F, but also on Planck’s constant h . The possible dependence on h is not taken into account in any of the above attempts to explain anomalous scattering. Put the scattering cross section proportional to h s v t m u F w .

scholarly journals The structure of atomic nuclei

1936 ◽  
Vol 153 (880) ◽  
pp. 493-504
Keyword(s):  
Nuclear Reactions ◽  
Atomic Weight ◽  
The Other ◽  
Light Elements ◽  
Atomic Nuclei ◽  
Reaction Energies ◽  
Reaction Equations ◽  
Independent Reaction

In a previous paper it was shown that the energies of nuclear reactions are multiples of q = 0·000415 in atomic weight units and that the atomic weights of the light elements may be supposed equal to N (1 + b ) sq , where N and s are integer and b is a small quantity the same for all elements. In the reaction equations the terms N (1 + b ) cancel out so that the reaction energies are given by nq = Σ sq . Thus the equation 4 Be 9 + 1 H 1 = 4 Be 8 + 1 H 2 + nq gives 9 (1 + b ) + 33 q + 1 + b + 19 q = 8 (1 + b ) + 17 q + 2 (1 + b ) + 34 q + nq , so that 33 q + 19 q = 17 q + 34 q + nq which gives 52 = 51 + n , or n = 1. The number of independent reaction equations is two less than the number of elements involved so that two of the values of the energy integer s can be elected. In the previous paper the values of s for 2 He 4 1 H 1 were taken to be 8 and 19 respectively and the values of s for the other elements were calculated by means of the reaction equations.

scholarly journals Deviation from the Coulomb law for the proton

1939 ◽  
Vol 171 (945) ◽  
pp. 269-280 ◽  
Keyword(s):  
Wave Equation ◽  
Fine Structure ◽  
Hydrogen Atom ◽  
Anomalous Scattering ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Heavy Particles ◽  
Theoretical Predictions ◽  
Structure Formula ◽  
Coulomb Law

In a recent paper R. C. Williams (1938) has found that the fine structure of the H α line in the spectrum of the hydrogen atom is not quite in agreement with the theoretical predictions (Sommerfeld’s fine structure formula). In discussing these experiments, Pasternack (1938) has pointed out that these deviations can be described by a simple shift of the 2 2 S level of hydrogen by an amount of 0.03 cm. -1 in the direction of higher energies. At the present state of our knowledge it seems conceivable that such a departure from the theory may be ascribed to a deviation from the Coulomb law of force at small distances rather than to a breakdown of the relativistic wave equation for the electron. A departure from the Coulomb law of force has often been discussed in connexion with the anomalous scattering of heavy particles. We know now, however, that this anomalous scattering is due to the internuclear forces and has no direct connexion with a possible departure from the Coulomb law. In view of the above experiments a new examination of the validity of the Coulomb law seems to be desirable.

The Effect of Anisotropic Scattering on Radiant Transport

1965 ◽  
Vol 87 (3) ◽  
pp. 381-387 ◽  
Author(s):  
L. B. Evans ◽  
C. M. Chu ◽  
S. W. Churchill
Keyword(s):  
Angular Distribution ◽  
Integrodifferential Equation ◽  
Legendre Polynomials ◽  
Rayleigh Scattering ◽  
Single Scattering ◽  
Anisotropic Scattering ◽  
Reflection And Transmission ◽  
Scattering Material ◽  
Phase Functions ◽  
Infinite Media

Numerical values are presented for the reflection and transmission of radiation falling obliquely on finite slabs of absorbing and anisotropically scattering material. The angular distribution for single scattering was represented by a finite series of Legendre polynomials. The method of Chandrasekhar was used to reduce the representation of radiant transport from an integrodifferential equation to a set of integral equations. This set of equations was solved reiteratively on a digital computer. Previous solutions have been limited to isotropic and Rayleigh scattering or infinite media. The results for different phase functions for single scattering can be interpreted reasonably well in terms of only the forward-scattered fraction.

scholarly journals The scattering of fast ᵦ-particles by nitrogen nuclei

1936 ◽  
Vol 153 (879) ◽  
pp. 353-358 ◽  
Keyword(s):  
Atomic Number ◽  
Ionization Chamber ◽  
Rest Mass ◽  
Single Scattering ◽  
Fair Agreement ◽  
Aluminium Foil ◽  
Annular Ring ◽  
Atomic Nuclei ◽  
Relativistic Formula ◽  
Ring Method

Of the man conflicting experiments* which have been performed on the single scattering of fast β-particles by atomic nuclei, it is generally accepted that the most reliable are those of Chadwick and Mercier, and of Neher. The former experimenter used the annular ring method and an ionization chamber to examine the scattering of the non-homogeneous β-rays from RaE by an aluminium foil, between angles of 20° and 40°. the results were in fair agreement with Darwin's classical relativistic formula: q = π nt (Z e 2 / m 0 c 2 ) 2 . (1- β 2 )/β 4 . β 2 cosec 2 ψ, (1) where q = fraction scattered through an angIe greater than θ, Z, t and n — atomic number, number of atoms per cc, and thickness of scatterer respectively, e and m 0 = charge and rest mass of electron, β = v/c = ratio of velocity of β-particle to that of light, and ψ is defined by the relation β cot ψ = tan [π-1/2(π + θ) cos ψ].

scholarly journals Optical properties of a heated aerosol in an urban atmosphere: a case study

2010 ◽  
Vol 3 (2) ◽  
pp. 1583-1614
Author(s):  
J. Backman ◽  
A. Virkkula ◽  
T. Petäjä ◽  
M. Aurela ◽  
A. Frey ◽  
...  
Keyword(s):  
Optical Properties ◽  
Light Scattering ◽  
Light Absorption ◽  
Volume Fraction ◽  
Measurement Techniques ◽  
Single Scattering ◽  
Urban Atmosphere ◽  
Urban Aerosol ◽  
Different Temperatures ◽  
Scattering Material

Abstract. Light absorption measurements most commonly rely on filter-based measurement techniques. These methods are disturbed by light scattering constituents in the aerosol phase deposited on the filters. The light scattering material changes the optical path of light in the filter matrix increasing the light absorption of the filter. Measurement equipment interpret this wrongly as light absorption by the aerosol. Most light scattering constituents in a sub-micron aerosol are volatile by their nature and they can be volatilized by heating the sample air. This volatilisation significantly alters the optical properties of the urban aerosol and was studied during a short field campaign with two groups of equipment measuring in parallel for six days in April 2009 at the SMEAR III station in Helsinki. When heated, the light scattering constituents were evaporated thus reducing the single-scattering albedo (ω0) of the aerosol by as much as 0.4. With less light scattering constituents in the aerosol phase the mass absorption cross section (MAC) of soot was calculated to be 13.5±0.5 m2 g−1 at λ=545 nm. An oven was set to scan different temperatures which revealed the volatility of the urban aerosol at different temperatures as well as the single-scattering albedo's dependence on the non-volatile volume fraction remaining (NVFR). At 50 °C 79±13% of the volume remained while only 46±8% remained at 150 °C and just 23±6% at 280 °C. At 50 °C ω0 was 0.65±0.06, at 150 °C ω0=0.54±0.06 and at 280 °C ω0=0.33±0.06. We found that absorption coefficients measured at different temperatures showed a temperature dependency possibly indicating initially different mixing states of the non-volatile constituents.

scholarly journals The interaction energy of two α-particles at close distances, determined from the anomalous scattering in helium

1931 ◽  
Vol 134 (823) ◽  
pp. 103-125 ◽  
Keyword(s):  
Potential Energy ◽  
Potential Field ◽  
Repulsive Force ◽  
Experimental Results ◽  
Heavy Elements ◽  
Anomalous Scattering ◽  
Inverse Square Law ◽  
Rutherford Scattering ◽  
Two Parameters ◽  
Α Particles

1. In order to explain the fact that the scattering of high velocity α-particles by the lighter elements does not obey the Rutherford scattering law, it is necessary to assume that the inverse square law does not hold for the force between an α-particle and a nucleus when the distance between them becomes exceedingly small. There is evidence to show that the inverse square law does hold down to distances of about 10 -12 cm., but that, as the distance is further reduced, the repulsive force changes to an attractive one, and it has been assumed by Gamow and others that the potential energy of an α-particle in the field of a nucleus varies with the distance, as is shown in fig. 1 by the curve t q p o .The divergence from Coulomb’s law, which is represented by the curve t q v u , does not become marked until a distance a is reached, but, for distances less than a , the force changes sign. Sexl has used a simplified form of such a potential field to calculate the decay periods of radioactive substances, and, in the present paper, an account is given of a method by which the anomalous scattering of α-particles by helium can be explained by assuming a potential field of the above type. In order to obtain a form for which the calculation is not unreasonably difficult, the field was simplified to the curve t q v w x of fig. 1. This field is defined by the two parameters a and d , and it is shown how the values of these parameters may be determined from the experimental results; the actual values obtained for the mutual potential energy of two α-particles are shown to scale in fig. 8. It is of interest to note that Sexl assumed the depth d of the “hole” to be zero in the case of the heavy elements, whereas it appears in this discussion that the depth is quite large in the case of helium (fig. 8), and that it is essential for the explanation of the experimental results to have the parameter d at our disposal.

scholarly journals The scattering of α-particles by light elements

1931 ◽  
Vol 134 (823) ◽  
pp. 154-170 ◽  
Keyword(s):  
Complex Structure ◽  
Coulomb Field ◽  
Anomalous Scattering ◽  
Light Elements ◽  
Centre Of Gravity ◽  
Oblate Spheroidal ◽  
A Value ◽  
Spheroidal Shape ◽  
Α Particles ◽  
Number Of Particles

It is well known that the scattering of fast a-particles by light elements shows very remarkable deviations from the classical law of scattering deduced from the assumption that the nuclei behave as point charges, surrounded by a Coulomb field of force. The first anomalous effects of this kind were obtained in 1919 by Rutherford in an investigation of the collisions of α-particles with hydrogen nuclei. Chadwick and Bieler found in later experiments that the number of H-particles observed at small angles, which, seen from the centre of gravity of the colliding system, correspond to α-particles scattered through large angles, was for the fastest α-particles about 100 times larger than the number calculated on the assumption of Coulomb forces between the colliding particles. They suggested that this effect was due to an oblate spheroidal shape of the α-particle. This assumption also agreed with subsequent experiments by Rutherford and Chadwick on the scattering of α-particles in helium. They found that for high velocities of the incident α-particles the number of particles scattered through 45° was about twenty times larger than expected. For smaller initial velocities and smaller angles this ratio became much less, for certain velocities only one-third. The scattering of a-particles by the nuclei of other light elements has been observed only in two cases, those of magnesium and aluminium. The first investigations of this kind were those of Bieler. He found that the ratio of the observed scattering to that given by inverse square forces is close to unity for small angles, but diminishes as the angle increases, gradually for slow α-particles, more rapidly for the faster ones. Rutherford and Chadwick extended these results and found that for large angles and fast α-particles the ratio of observed to calculated scattering after diminishing to a value of about one-third, began to increase again. In later (unpublished) experiments Chadwick found that the ratio increased in the case of fast α-particles scattered through very large angles to a value considerably higher than unity, An explanation for the anomalous scattering shown by magnesium and aluminium has been advanced by Debye and Hardmeier on general lines. If, as we suppose, the aluminium nucleus is a complex structure of positive and negative charges, this structure may be distorted or polarised in the field of the approaching α-particle. The polarisation gives rise to an attracting force on the α-particle, which varies inversely as the fifth power of the distance. Debye and Hardmeier showed that this hypothesis would account very fairly for the experimental results.

scholarly journals Artificial disintegration by radium C' α-particles-aluminium and magnesium

1934 ◽  
Vol 146 (857) ◽  
pp. 396-419 ◽  
Keyword(s):  
Experimental Evidence ◽  
Nuclear Energy ◽  
Absorption Curve ◽  
Discrete Groups ◽  
Light Elements ◽  
Atomic Nuclei ◽  
Scintillation Method ◽  
Electrical Methods ◽  
Α Particles

A study of the protons emitted from certain elements when bombarded by α-particles has yielded valuable information on the structure of the atomic nuclei of light elements. The development of electrical counters for α-particles and protons has provided a method by which the emitted protons can be analysed in a more detailed manner than was possible by the scintillation method. These electrical methods have been applied to the examination of the protons emitted from many elements when bombarded by α-particles. For several elements the absorption curve of these protons reveals the presence of a number of discrete groups of protons each ending at a definite range. It is a found that an α-particle of given energy may give rise to one or more groups of protons, each group corresponding to a transmutation process in which a definite amount of nuclear energy is either absorbed or released. It also appears that α-particles of all energies are not equally effective in producing protons, since the energies of the α-particles which produce protons fall into definite discrete groups. The experimental evidence so far obtained has been co-ordinated by adopting the picture of the nucleus shown in fig. 1.

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