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Teaching Documents by Benjamin J Bloch

Einstein's famous equation E = mc 2 is the mathematical equivalence between energy and mass. This... more Einstein's famous equation E = mc 2 is the mathematical equivalence between energy and mass. This terse format yields no additional information. There is, however, a different form that yields additional information. Writing the equation as E = cmc still obeys the mathematics but adds a picture of energy E equivalent to mass m now enclosed by light c.

A new method defines a universal octave address UA for all subatomic particles and cosmic bodies,... more A new method defines a universal octave address UA for all subatomic particles and cosmic bodies, from neutrinos to supermassive black holes, for display on a single graph. Based on music octaves and mod 360, this permits the study of symmetry and resonance patterns of all frequencies, masses, and energies in toto. The UA is defined by octave n and projected degree DP, [n;DP]. A newly discovered LHC particle of mass 750 GeV/c2 has the UA [87; 81.4]. Visible radiation frequencies occupy red [48;218] to violet [49;149] with no frequencies between approximately 150 DP and 210 DP; Planet revolution frequencies occupy Neptune [-32;99] to the Moon [-21;259], Planet rotation frequencies range from Venus [-24;243] to Neptune [-5;64]. Mass UA occupy: muon neutrino [65;55] to top quark [85;4], Pluto [240;73] to Sun [267;69]; while supermassive black holes are at n ≥ 284. The Periodic Table Atomic Weight UA are from [77;209] to [85;284] and beyond, a range of approximately nine octaves. From the smallest mass of approximately 10-40 kg to the approximate mass of the universe, 1097 kg their UA is from [33;237] to [488;274], a range of over 456 octaves. New discoveries are well suited to UA designations.

Papers by Benjamin J Bloch

PhDT, 1973

Compton profiles are calculated for LLL-shell electrons within the Born approximation by use of n... more Compton profiles are calculated for LLL-shell electrons within the Born approximation by use of nonrelativistic "exact" hydrogenic bound- and continuum-state wave functions. The wave functions are expressed in parabolic coordinates and the resulting matrix elements are evaluated following the method of F. Bloch (1934). Impulse-approximation profiles are calculated, and comparisons with the "exact" profiles show that, as expected, the two profiles lie very close to one another for weak binding and high incident photon energies. However, even when these conditions are not fulfilled, the two curves have a tendency to cross one another in the neighborhood of the profile center. This tendency has been observed in previous studies of KKK-shell profiles. However, unlike KKK-shell profiles, the 2S2S2S Compton profiles exhibit a secondary maximum. The secondary maxima occur at approximately the same region in qqq, where the impulse-approximation profiles exhibit a plateau. The location of this plateau is shown to be related to a node in the bound-state wave function and is around q=fracZ2q=\frac{Z}{2}q=fracZ2 for the 2S2S2S profiles. The impulse approximation, being a monotonic decreasing function in ∣q∣|q|∣q∣, cannot exhibit the secondary-maximum structure appearing in the "exact" hydrogenic profiles. The intensity of the secondary maximum in the 2S2S2S profiles is reduced by over an order of magnitude from the central peak. The 2P(0)2{P}^{(0)}2P(0) Compton profiles also exhibit structure, however, unlike the relatively small secondary maximum in the 2S2S2S, the two maxima in the 2P(0)2{P}^{(0)}2P(0) profiles are of the same order of magnitude. Integrated profiles (incoherent-scattering factors) are calculated and the impulse-approximation results agree with the "exact" results over a wide range of binding energies owing to profile crossover near the center. Waller-Hartree incoherent-scattering factors give a closer agreement with the "exact" results than observed for KKK-shell electrons; however, for low-momentum transfer the Waller-Hartree results can differ from "exact" results by more than 50%. In such regions, impulse-scattering factors represent a considerable improvement over the Waller-Hartree factors.

Physical review, Oct 1, 1975

A new method for determining atomic shielding factors to use in hydrogenlike wave functions which... more A new method for determining atomic shielding factors to use in hydrogenlike wave functions which gives "exact" Compton profiles in close agreement with experiment was recently developed by the present authors. These shielding factors Z*(0) are determined by imposing the requirement for each atomic orbital that the "impulse" hydrogenic Compton-profile value at its center, q = 0, match the Hartree-Fock Compton-profile value. We now compare the use of Z*(0) hydrogenic values in the calculation of the moments &r), &r'&, and & r') with values of these moments obtained using Slater, Clementi, Burns, and binding-energymatched Z s used in hydrogenic wave functions for K-, Land nd M-shell orbitals for rare-gas atoms up through xenon. Relative accuracy is determined by comparison to Hartree-Fock results for these moments. It is found that for ls, 2p, and 3d states, our Z*(0) values give the most consistently accurate results. A table of recommended Z values is given for all atoms and states considered.

Physical review, Aug 1, 1975

The techniques we developed previously for calculating L-shell Compton profiles within the Born a... more The techniques we developed previously for calculating L-shell Compton profiles within the Born approximation are applied to the calculation of improved core Compton profiles for real atoms. The method is referred to as the exact hydrogenic (EH) method. We introduce a new method for determining effective nuclear charges Z* to use in hydrogeniclike wave functions and our EH method. These nuclear charges Z*(0) are determined by imposing the requirement for each atomic orbital that the impulse hydrogenic (IH) Compton profile at its center q = 0.0 match the impulse Hartree-F«k (IHF) Compton-profile value at q = 0.0.-It is then demonstrated that the two L-shell impuse profiles are found to lie very close to one another as we go away from the profile center, the agreement improving as we go to atoms of higher atomic number. The wave functions for the 2s and 2p orbitals are studied'and it is observed that hydrogenic wave functions with our values of Z*(0) fit the Hartree-Fock wave functions much more accurately than if a Z* associated with the binding energy is used. We demonstrate in the case of Mo Ka. radiation scattering from neon and aluminum that our EH method using Z*(0) gives results in better agreement with experiment than any impulse calculation. In the neon case, the EH correction to the IHF result is-2.4% at the profile center. Dependence of the Compton profile on incident photon energy is demonstrated theoretically and observed to be in agreement with experiment.

Physical Review Letters, Jul 30, 1973

PHYSICAL REVIEW LETTERS)0 JUr.v 1975 tively exciting pump beam at X = 285.2 nm will also cause io... more PHYSICAL REVIEW LETTERS)0 JUr.v 1975 tively exciting pump beam at X = 285.2 nm will also cause ionization from the 3s3p'P, ' state, and recombination can leave the atom in one of the excited triplet states. We have recorded emission lines terminating in the 3s3p 'P level from 3sns 'S, 3snd'D, and 3p''P levels. When the argon buffer gas pressure was increased to 600 Torr from the 300-Torr pressure normally used, these emission lines generally disappeared and often appeared in absorption. This indicates that intersystem crossing is then occurring during the lifetime of the background pulse. Calculations' carried out using a 'D, continuum state also gave resonance structure in the absorption from the 3s3p 'P, ' level at wavelengths less than 200 nm which could be identified as 3pnp 'D for n~4. Since the present computer code cannot treat satisfactorily the cases of low-energy ejected electrons, the region near to threshold was not investigated. The only conclusion that could be reached about the 3p"D, resonance was that its position is at a wavelength greater than 320 nm. Experiments are in progress to locate this resonance and to measure the 3s3p P, ' 3P' 'S, photoionization cross section photoelectrically with a second tunable dye-laser probe. We wish to thank the Science Research Council for financial support.

Physical review, 1974

Compton profiles are calculated for L-shell electrons within the Born approximation by use of non... more Compton profiles are calculated for L-shell electrons within the Born approximation by use of nonrelativistic "exact" hydrogenic boundand continuum-state wave functions. The wave functions are expressed in parabohc coordinates and the resulting matrix elements are evaluated following the method of F. Bloch (1934). Impulse-approximation profiles are calculated, and comparisons with the "exact" profiles show that, as expected, the two profiles lie very close to one another for weak binding and high incident photon energies. However, even when these conditions are not fulfilled, the two curves have a tendency to cross one another in the neighborhood of the profile center. This tendency has been observed in previous studies of K-shell profiles. However, unlike K-shell profiles, the 2S Compton profiles exhibit a secondary maximum. The secondary maxima occur at approximately the same region in q, where the impulse-approximation profiles exhibit a plateau. The location of this plateau is shown to be related to a node in the bound-state wave function and is around q = Z/2 for the 2S profiles. The impulse approximation, being a monotonic decreasing function in gj, cannot exhibit the secondary-maximum structure appearing in the "exact" hydrogenic profiles. The intensity of the secondary maximum in the 2S profiles is reduced by over an order of magnitude from the central peak. The 2P Compton profiles also exhibit structure, however, unlike the relatively small secondary maximum in the 2S, the two maxima in the 2P profiles are of the same order of magnitude. Integrated profiles {incoherent-scattering factors) are calculated and the impulse-approximation results agree with the "exact" results over a wide range of binding energies owing to profile crossover near the center. Wailer-Hartree incoherent-scattering factors give a closer agreement with the "exact" results than observed for K-shell electrons; however, for low-momentum transfer the %aller-Hartree results can differ from "exact" results by more than 50%%uo. In such regions, impulse-scattering factors represent a considerable improvement over the %aller-Hartree factors.

Physical Review Letters, 1973

... 5P. G. Burke and DL Moores, J. Phys. B: Proc. Phys. Soc., London 1, 575 (1968). 6A. Hibbert, ... more ... 5P. G. Burke and DL Moores, J. Phys. B: Proc. Phys. Soc., London 1, 575 (1968). 6A. Hibbert, private communication. 7D. J. Bradley, AJF Durrant, GM Gale, M. Moore, and PD Smith, J. Quantum Electron. 4, 707 (1968). 8D. J. Bradley, Appl. Opt. 5, 1957 (1969). 9T. ...

Phys Rev a, 1975

The techniques we developed previously for calculating L-shell Compton profiles within the Born a... more The techniques we developed previously for calculating L-shell Compton profiles within the Born approximation are applied to the calculation of improved core Compton profiles for real atoms. The method is referred to as the exact hydrogenic (EH) method. We introduce a new method for determining effective nuclear charges Z* to use in hydrogeniclike wave functions and our EH method. These nuclear charges Z*(0) are determined by imposing the requirement for each atomic orbital that the impulse hydrogenic (IH) Compton profile at its center q=0.0 match the impulse Hartree-Fock (IHF) Compton-profile value at q=0.0. It is then demonstrated that the two L-shell impuse profiles are found to lie very close to one another as we go away from the profile center, the agreement improving as we go to atoms of higher atomic number. The wave functions for the 2s and 2p orbitals are studied and it is observed that hydrogenic wave functions with our values of Z*(0) fit the Hartree-Fock wave functions much more accurately than if a Z* associated with the binding energy is used. We demonstrate in the case of Mo Kα radiation scattering from neon and aluminum that our EH method using Z*(0) gives results in better agreement with experiment than any impulse calculation. In the neon case, the EH correction to the IHF result is ~2.4% at the profile center. Dependence of the Compton profile on incident photon energy is demonstrated theoretically and observed to be in agreement with experiment.

Phys Rev a, 1974

Compton profiles are calculated for L-shell electrons within the Born approximation by use of non... more Compton profiles are calculated for L-shell electrons within the Born approximation by use of nonrelativistic "exact" hydrogenic bound- and continuum-state wave functions. The wave functions are expressed in parabolic coordinates and the resulting matrix elements are evaluated following the method of F. Bloch (1934). Impulse-approximation profiles are calculated, and comparisons with the "exact" profiles show that, as expected, the two profiles lie very close to one another for weak binding and high incident photon energies. However, even when these conditions are not fulfilled, the two curves have a tendency to cross one another in the neighborhood of the profile center. This tendency has been observed in previous studies of K-shell profiles. However, unlike K-shell profiles, the 2S Compton profiles exhibit a secondary maximum. The secondary maxima occur at approximately the same region in q, where the impulse-approximation profiles exhibit a plateau. The location of this plateau is shown to be related to a node in the bound-state wave function and is around q=Z2 for the 2S profiles. The impulse approximation, being a monotonic decreasing function in |q|, cannot exhibit the secondary-maximum structure appearing in the "exact" hydrogenic profiles. The intensity of the secondary maximum in the 2S profiles is reduced by over an order of magnitude from the central peak. The 2P(0) Compton profiles also exhibit structure, however, unlike the relatively small secondary maximum in the 2S, the two maxima in the 2P(0) profiles are of the same order of magnitude. Integrated profiles (incoherent-scattering factors) are calculated and the impulse-approximation results agree with the "exact" results over a wide range of binding energies owing to profile crossover near the center. Waller-Hartree incoherent-scattering factors give a closer agreement with the "exact" results than observed for K-shell electrons; however, for low-momentum transfer the Waller-Hartree results can differ from "exact" results by more than 50%. In such regions, impulse-scattering factors represent a considerable improvement over the Waller-Hartree factors.

Physical Review A, 1975

... The latter results indicate that for small mome'~ 12 Page 2. LA WHENCE B. ME NDEL SOHN AN... more ... The latter results indicate that for small mome'~ 12 Page 2. LA WHENCE B. ME NDEL SOHN AND BEN JAMIN J. BLQCH transfers ... lations. For the Ag Ke neon scattering case no improvement is obtained using our EH method. II. ...

Physical Review A, 1974

Compton profiles are calculated for L-shell electrons within the Born ; approximation by use of n... more Compton profiles are calculated for L-shell electrons within the Born ; approximation by use of nonrelativistic exact&amp;amp;amp;amp;#39;&amp;amp;amp;amp;#39; hydrogenic bound- and continuum-; state wave functions. The wave functions are expressed in parabolic coordinates ; and the resulting matrix elements are evaluated following the method of F. Bloch ; (1934). Impulse-approximation profiles are calculated, and comparisons with the ; exact&amp;amp;amp;amp;#39;&amp;amp;amp;amp;#39; profiles show

Drafts by Benjamin J Bloch

PhDT, 1973

Physical review, Oct 1, 1975

Physical review, Aug 1, 1975

Physical Review Letters, Jul 30, 1973

Physical review, 1974

Physical Review Letters, 1973

Phys Rev a, 1975

The techniques we developed previously for calculating L-shell Compton profiles within the Born a... more The techniques we developed previously for calculating L-shell Compton profiles within the Born approximation are applied to the calculation of improved core Compton profiles for real atoms. The method is referred to as the exact hydrogenic (EH) method. We introduce a new method for determining effective nuclear charges Z* to use in hydrogeniclike wave functions and our EH method. These nuclear charges Z*(0) are determined by imposing the requirement for each atomic orbital that the impulse hydrogenic (IH) Compton profile at its center q=0.0 match the impulse Hartree-Fock (IHF) Compton-profile value at q=0.0. It is then demonstrated that the two L-shell impuse profiles are found to lie very close to one another as we go away from the profile center, the agreement improving as we go to atoms of higher atomic number. The wave functions for the 2s and 2p orbitals are studied and it is observed that hydrogenic wave functions with our values of Z*(0) fit the Hartree-Fock wave functions much more accurately than if a Z* associated with the binding energy is used. We demonstrate in the case of Mo Kα radiation scattering from neon and aluminum that our EH method using Z*(0) gives results in better agreement with experiment than any impulse calculation. In the neon case, the EH correction to the IHF result is ~2.4% at the profile center. Dependence of the Compton profile on incident photon energy is demonstrated theoretically and observed to be in agreement with experiment.

Phys Rev a, 1974

Compton profiles are calculated for L-shell electrons within the Born approximation by use of non... more Compton profiles are calculated for L-shell electrons within the Born approximation by use of nonrelativistic "exact" hydrogenic bound- and continuum-state wave functions. The wave functions are expressed in parabolic coordinates and the resulting matrix elements are evaluated following the method of F. Bloch (1934). Impulse-approximation profiles are calculated, and comparisons with the "exact" profiles show that, as expected, the two profiles lie very close to one another for weak binding and high incident photon energies. However, even when these conditions are not fulfilled, the two curves have a tendency to cross one another in the neighborhood of the profile center. This tendency has been observed in previous studies of K-shell profiles. However, unlike K-shell profiles, the 2S Compton profiles exhibit a secondary maximum. The secondary maxima occur at approximately the same region in q, where the impulse-approximation profiles exhibit a plateau. The location of this plateau is shown to be related to a node in the bound-state wave function and is around q=Z2 for the 2S profiles. The impulse approximation, being a monotonic decreasing function in |q|, cannot exhibit the secondary-maximum structure appearing in the "exact" hydrogenic profiles. The intensity of the secondary maximum in the 2S profiles is reduced by over an order of magnitude from the central peak. The 2P(0) Compton profiles also exhibit structure, however, unlike the relatively small secondary maximum in the 2S, the two maxima in the 2P(0) profiles are of the same order of magnitude. Integrated profiles (incoherent-scattering factors) are calculated and the impulse-approximation results agree with the "exact" results over a wide range of binding energies owing to profile crossover near the center. Waller-Hartree incoherent-scattering factors give a closer agreement with the "exact" results than observed for K-shell electrons; however, for low-momentum transfer the Waller-Hartree results can differ from "exact" results by more than 50%. In such regions, impulse-scattering factors represent a considerable improvement over the Waller-Hartree factors.

Physical Review A, 1975

Physical Review A, 1974