The Phenornenological Theory of Exchange Currents in Nuclei

As was first pointed out by Siegert, the existence of exchange forces in nuclei implies the existence of accompanying exchange currents. Sachs has calculated an expression for these, by making the Hamiltonian containing exchange potentials gauge-invariant, and has applied it to the calculations of exchange magnetic moments in H3 and He3. The Hamiltonian obtained by Sachs is not the most general admissible one. More generally, the exchange current density is found to depend on a vector function whose irrotational part is completely determined by gauge-invariance but whose solenoidal part is arbitrary except for the requirements (following from conditions of translational invariance and symmetry in all nucleons on the Hamiltonian) that it be translationally invariant and antisymmetric under the exchange of the spin and space coordinates of each pair of nucleons. Making use of these conditions on the Hamiltonian, the explicit form of the dependence of the solenoidal part of the exchange current upon the spin and isotopic spin coordinates of the nucleons has been derived. In the resultant exchange moments, the irrotational part leads to the expression obtained by Sachs, while the solenoidal term contribution contains the spin operators of the nucleons in particular combinations, together with arbitrary functions of the nucleon separation. Villars' exchange moment expression, as obtained from meson theory, is included as a special case and hence the exchange contributions to the moments of H3 and He3 are explicable on a phenomenological basis, contrary to the results obtained in Sachs' special case. The generality and significance of the results are discussed in relation to the various meson theories.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86129/1/PhysRev.79.795-RKO.pd

Physical Consequences of Anomalies in Nonlocal Potential Problems

An s-wave two-body separable potential may give rise to several phenomena which are absent for nonsingular local potentials. We examine the physical implications of a well known example of such phenomena, the continuum bound state, as well as of two lesser known anomalies, the so-called positive energy spurious state and negative energy bound states with improper long-range behavior. By examining these anomalies in light of Levinson\u27s theorem, Wigner\u27s phase shift inequality, and the effect of a perturbation on the anomalous states by their insertion in a three-body scattering situation, we find in agreement with previous studies that the continuum bound state acts as a resonance of negligible width. However, we find it difficult to see how the presence of a spurious state can be detected experimentally

I. The Isotopic Foldy-Wouthuysen Representation and Chiral Symmetry

The paper introduces the isotopic Foldy-Wouthuysen representation. This representation was used to derive equations for massive interacting fermion fields. When the interaction Hamiltonian commutes with the matrix, these equations possess chiral invariance irrespective of whether fermions have mass or are massless. The isotopic Foldy-Wouthuysen representation preserves the vector and axial currents irrespective of the fermion mass value. In the Dirac representation, the axial current is preserved only for massless fermions. In the isotopic Foldy-Wouthuysen representation, the ground state of fermions (vacuum) turns out to be degenerate, and therefore there is the possibility of spontaneously breaking parity (P - symmetry). This study considers the example of constructing a chirally symmetric quantum electrodynamics framework in the isotopic Foldy-Wouthuysen representation. A number of physical processes are calculated in the lowest orders of the perturbation theory. Final results of the calculations agree with the results of the standard quantum electrodynamics.Comment: 37 pages, 9 figure

Signatures of the chiral two-pion exchange electromagnetic currents in the 2H and 3He photodisintegration reactions

The recently derived long-range two-pion exchange (TPE) contributions to the nuclear current operator which appear at next-to-leading order (NLO) of the chiral expansion are used to describe electromagnetic processes. We study their role in the photodisintegration of 2H and 3He and compare our predictions with experimental data. The bound and scattering states are calculated using five different parametrizations of the chiral next-to-next-to-leading order (N2LO) nucleon-nucleon (NN) potential which allows us to estimate the theoretical uncertainty at a given order in the chiral expansion. For some observables the results are very close to the predictions based on the AV18 NN potential and the current operator (partly) consistent with this force. In the most cases, the addition of long-range TPE currents improved the description of the experimental data.Comment: 11 pages, 6 figures (35 eps files

Approximate degeneracies of zone boundary phonons in alkali halide crystals

We point out the existence of a pervasive pattern of near degeneracies of phonon frequencies in isobaric alkali halide crystals (NaBr, KCl, RbBr, CsI) which strongly suggests that their dynamical matrices are almost invariant under transformations which exchange positive and negative ions. We extend this hypothesis to a relation between phonon properties of "mirror" alkali halides in which the ions of one crystal are replaced by the oppositely charged isobaric ions of the other, such as RbCl and KBr. Experimental evidence supporting this can also be adduced. Similar near degeneracies universally occurring in NaCl structure alkali halides and alkaline earth oxides are also noted and a possible dynamical basis for understanding these suggested.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24456/1/0000730.pd

Variational Monte Carlo Calculations of 3^3H and 4^4He with a relativistic Hamiltonian - II

In relativistic Hamiltonians the two-nucleon interaction is expressed as a sum of $\tilde{v}_{ij}$, the interaction in the ${\bf P}_{ij}=0$ rest frame, and the ``boost interaction'' $\delta v({\bf P}_{ij})$ which depends upon the total momentum ${\bf P}_{ij}$ and vanishes in the rest frame. The $\delta v$ can be regarded as a sum of four terms: $\delta v_{RE}$, $\delta v_{LC}$, $\delta v_{TP}$ and $\delta v_{QM}$; the first three originate from the relativistic energy-momentum relation, Lorentz contraction and Thomas precession, while the last is purely quantum. The contributions of $\delta v_{RE}$ and $\delta v_{LC}$ have been previously calculated with the variational Monte Carlo method for $^3$H and $^4$He. In this brief note we report the results of similar calculations for the contributions of $\delta v_{TP}$ and $\delta v_{QM}$. These are found to be rather small.Comment: 7 pages, P-94-09-07

Connection Between Wave Functions in the Dirac and Foldy-Wouthuysen Representations

The connection between wave functions in the Dirac and Foldy-Wouthuysen representations is found. When the Foldy-Wouthuysen transformation is exact, upper spinors in two representations differ only by constant factors, and lower spinors in the Foldy-Wouthuysen representation are equal to zero.Comment: 7 page

The Second-Quantized Theory of Spin-1/2 Particles in the Nonrelativistic Limit

The second-quantized Dirac Hamiltonian for free electrons is transformed by a canonical transformation to a representation in which the positive and negative energy wave operators are separately represented by two-component operators. The transformation employed is the second-quantized analog of the one derived by Foldy and Wouthuysen in their discussion of the one-particle Dirac theory and its nonrelativistic limit. This transformation is then applied to the wave operators and the Hamiltonian in the second-quantized, charge-conjugate formalism for Dirac particles. The wave operators for positrons and electrons become linearly-independent two-component operators, and the Hamiltonian separates into an electron and a positron part, each of which contains only the corresponding two-component wave operators. It is also shown that by means of an appropriate, readily determinable sequence of canonical transformations, Hamiltonians for fields of spin-_ particles interacting via intermediary fields can also be reduced to nonrelativistic form. This is accomplished by transforming the Hamiltonian to a representation in which it is exhibited effectively as a series expansion in powers of the Compton wavelength of the spin-_ particle. Illustration of the method is provided by detailed examination of the case of nucleons interacting via the pseudoscalar meson field.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86127/1/PhysRev.86.340-RKO.pd

Multicomponent dense electron gas as a model of Si MOSFET

We solve two-dimensional model of $N$-component dense electron gas in the limit of large $N$ and in a range of the Coulomb interaction parameter: $N^{-3/2}\ll r_s\ll 1$. The quasiparticle interaction on the Fermi circle vanishes as 1/N. The ground state energy and the effective mass are found as series in powers of $r_s^{2/3}$. In the quantum Hall state on the lowest Landau level at integer filling: $1\ll\nu<N$, the charge activation energy gap and the exchange constant are found.Comment: 10 pages, 4 figure