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On the influence of correlation of the atomic electrons on the elastic electron scattering by helium atoms
ABSTRACTS
OF
PAPERS
TO
A4PPEAR
IN
FUTURE
471
ISSUES
in the experimental ratio of bound to free muon decay rates for heavy elements, thus removing the previous theoretical-esperiment,al discrepancy for these elements. The observed peak in the bound mu011 decay rate near iron is not predicted, but a consideration of possible additional contributions to the experimental decay rate suggests that the large background of low-energy gamma rays associated wit,h the accompanying muon capt.xxe tttight be connected with this peak. Synrmr,!ry Theory oj the Aharonov-Bohm Effect: Quantum Mechanics in a Nultiply Connected He~iolL. LINDSAY d. TASSIE ANI) MT-RRAY PESHKIN. The conventional Sehrbdinger treatment of the Aharonov-Bohnt effect of inaccessible magnetic fields postulates the use of single-valued wave funct,ions, even in a multiply connected region. The principles of symmetry theory are shown to justify this postulate in a cylindrically symmetric system, and to lead directly to the Aharonov-Bohm effect. The necessity for the canonical angular momentum Tao be an integer or half-integer is the crux of the argument. On the Connection Detween Spiro a& Statistics. It is proven that the axioms of field theory nlcnt, of (ant.i-)commutation relat,ions to a field it. is shown that, if one wants to require that a with it,self at space-like distances, one is forced forms according to a single-valued irreducible commutation relations if $ t,ransforms according
GIANFAVSTO
DELL'ASTONIO.
are not compatible with a dilferent assignand it,s hermitean conjugate. As a corollary field $(x) either commutes or anticommutes to choose commutation relations if + transrepresentation of the Lorentz group; antito a double-valued represent,at,ion.
Scattering. J. J. DE SWART AND C. L)T.LLEMOND The hyperon nucleon scattering is calculated for A-laboratory energies up to 315 Mev. The potentials used were those linear combinations of the nucleon-nucleon potentials as prescribed by global symmetry. We have taken the mass difference hetween the :I- and V-hyperon exactly into account in the kinematics. However, t,he mass differences het,ween the 2.hyperons and between the nucleons are neglected. Angular dist,rihutions and total cross sections are given for all possible hyperomnucleon scattering reactions. Where possihle :I coml~arison with experiment is made. H!/pe,cln-5nc,/eorL
On thr Influence Heli
Wl
iik)mS.
oj (‘orrelation w.
SOLOS
of the ;itomic AND
K.
Electrons
on the Etasfir
Electron
Scattering
by
PECVL.
The different ial cross section for the elost,ic scattering of eleci.rons hy helium atoms has been ralculat~etl using the 2., 3., and B-term Hylleraas wave functions, and the analytical approuimat.ions to the self-consistent, field wave functions. The latter have been found to give rcliahle results which in the case of short expansions can be even better than those obtainlpd using the much more laborious Hylleraas wave functions with the same number of parameters. On the 7’her,,rod?~-lnn,,lic Ph.asc Diayrums or Heli,um Three. LO~:IS ( ~LDS'I‘EIX. The object of the present paper is an analysis of the thermodynamic consequences resulting from the observed anomaly at the temperature T, of the melting pressure line P(Y) of He3 through the formation of a minimum at this temperature. One is led to prove first the anomalous character of the volume line V,(T) of the liquid, in equilibrium with the solid, on t,he basis of data available on t.he high temperature side of T, and at T, . This volume anomaly consists in a maximum of Vi(T) at 7’, The similar anomaly of the solid volume line V,?(T) at 7’, will also be shown to result from the t,emperat.ure double-valuedness of the isobaric and isochoric states of the liquid and solid along the phase equilibrium lines. The $addlc point type character of the states (P(T,), V~jl’~)) and (PC’f,), V&(2”,)), combined
OF
PAPERS
TO
A4PPEAR
IN
FUTURE
471
ISSUES
in the experimental ratio of bound to free muon decay rates for heavy elements, thus removing the previous theoretical-esperiment,al discrepancy for these elements. The observed peak in the bound mu011 decay rate near iron is not predicted, but a consideration of possible additional contributions to the experimental decay rate suggests that the large background of low-energy gamma rays associated wit,h the accompanying muon capt.xxe tttight be connected with this peak. Synrmr,!ry Theory oj the Aharonov-Bohm Effect: Quantum Mechanics in a Nultiply Connected He~iolL. LINDSAY d. TASSIE ANI) MT-RRAY PESHKIN. The conventional Sehrbdinger treatment of the Aharonov-Bohnt effect of inaccessible magnetic fields postulates the use of single-valued wave funct,ions, even in a multiply connected region. The principles of symmetry theory are shown to justify this postulate in a cylindrically symmetric system, and to lead directly to the Aharonov-Bohm effect. The necessity for the canonical angular momentum Tao be an integer or half-integer is the crux of the argument. On the Connection Detween Spiro a& Statistics. It is proven that the axioms of field theory nlcnt, of (ant.i-)commutation relat,ions to a field it. is shown that, if one wants to require that a with it,self at space-like distances, one is forced forms according to a single-valued irreducible commutation relations if $ t,ransforms according
GIANFAVSTO
DELL'ASTONIO.
are not compatible with a dilferent assignand it,s hermitean conjugate. As a corollary field $(x) either commutes or anticommutes to choose commutation relations if + transrepresentation of the Lorentz group; antito a double-valued represent,at,ion.
Scattering. J. J. DE SWART AND C. L)T.LLEMOND The hyperon nucleon scattering is calculated for A-laboratory energies up to 315 Mev. The potentials used were those linear combinations of the nucleon-nucleon potentials as prescribed by global symmetry. We have taken the mass difference hetween the :I- and V-hyperon exactly into account in the kinematics. However, t,he mass differences het,ween the 2.hyperons and between the nucleons are neglected. Angular dist,rihutions and total cross sections are given for all possible hyperomnucleon scattering reactions. Where possihle :I coml~arison with experiment is made. H!/pe,cln-5nc,/eorL
On thr Influence Heli
Wl
iik)mS.
oj (‘orrelation w.
SOLOS
of the ;itomic AND
K.
Electrons
on the Etasfir
Electron
Scattering
by
PECVL.
The different ial cross section for the elost,ic scattering of eleci.rons hy helium atoms has been ralculat~etl using the 2., 3., and B-term Hylleraas wave functions, and the analytical approuimat.ions to the self-consistent, field wave functions. The latter have been found to give rcliahle results which in the case of short expansions can be even better than those obtainlpd using the much more laborious Hylleraas wave functions with the same number of parameters. On the 7’her,,rod?~-lnn,,lic Ph.asc Diayrums or Heli,um Three. LO~:IS ( ~LDS'I‘EIX. The object of the present paper is an analysis of the thermodynamic consequences resulting from the observed anomaly at the temperature T, of the melting pressure line P(Y) of He3 through the formation of a minimum at this temperature. One is led to prove first the anomalous character of the volume line V,(T) of the liquid, in equilibrium with the solid, on t,he basis of data available on t.he high temperature side of T, and at T, . This volume anomaly consists in a maximum of Vi(T) at 7’, The similar anomaly of the solid volume line V,?(T) at 7’, will also be shown to result from the t,emperat.ure double-valuedness of the isobaric and isochoric states of the liquid and solid along the phase equilibrium lines. The $addlc point type character of the states (P(T,), V~jl’~)) and (PC’f,), V&(2”,)), combined