Migdal Theory Research Articles

Inelastic electron scattering form factors of low-lying states in 208Pb

Inelastic electron scattering form factors for some low-lying excited states of 208Pb are calculated within the Migdal theory of interacting quasiparticles. The fairly good agreement with experiment is discussed.

Scaling Laws and the Specific Heat of Bose Liquid

The scaling laws of Widom1> and Kadanof£2> are obtained for the spin system in a weak external field. These laws cannot be applied to the Bose liquid directly since the Bose liquid corresponds to the system in a strong external field.3l Migdal has recently discussed the phase transition in a Bose liquid and has shown that the scaling laws hold for the Green's function and ':ertex parts. According to him the Green's function is expressed in the form G(p, tt, T)-~·rg(pf~) and the heat capacity cP has a singularity of the form ~sv-z, where ~=tt-ttc(T) is the distance from the phase-transition curve, and r, v and g(.x) are universal quantities. If v~2/3, then the singularity becomes logarithmic. In this note we wish to apply the scaling law to the discussion of the specific heat of Bose liquid. It will be shown that Migdal's theory does not lead to logarithmically singular specific heat cP. We consider the phase transition from the side of the normal phase. Let np be the thermal average of occupation nu!D.ber ap+ap. np is the Fourier transform of the one-particle density matrix C(r) =<<V (0) X<{l(r)). We assume that the scaling property holds for our problem, i.e., np is expressed in the form np'-'r0 rg(r0p) where r is a universal constant and r0 (-~-) is the correlation radius. In order that np be finite on the transition line, we must have g(.x)-1/.xr for .x~l. Suppose that

Einfluß einer Quasiteilchen-Spinbahnwechselwirkung auf die magnetischen Momente leichter Atomkerne

Using Migdal's theory of interacting quasiparticles, the influence of a two-body spin-orbit interaction in addition to the spin-spin interaction on magnetic moments of nuclei was investigated in the mass regionA=11 toA=65. The coupling constants of the spin-orbit interaction were determined from spin-orbit splittings of single particle energies, and those of the spin-spin interaction were adjusted by fitting magnetic moments. The constants of the spin-spin interaction were found to be dependent on the mass value. The inclusion of the spin-orbit interaction led to a better agreement of theoretical and experimental magnetic moments of light nuclei. The spin-orbit contribution was averaged 7% over all nuclei, but reached 20–30% for some of them.

Final State Interactions in the Reaction T(3He,4He)np

A triple correlation cross section was measured for the reaction T(3He,4He)np in a complete experiment at a 3He bombarding energy of 1.5 MeV. The Watson–Migdal and Phillips, Griffy, and Biedenharn (PGB) final state interaction theories are compared in the analysis of the experimental data. The Watson–Migdal theory gives a good description of both the 5He ground state and singlet n–p cross section enhancements. One form of the PGB theory gives a prediction of the singlet n–p enhancement which is indistinguishable from the Watson–Migdal prediction in this experiment. The measured cross section was found to be dominated by direct statistical breakup and sequential decay through a virtual singlet n–p state and the ground state of 5He. A singlet n–p scattering length of [Formula: see text] was determined from the analysis of the three-body data. The reaction T(T,4He)2n is similar to the reaction T(3He,4He)np. Consequently using a complete experimental technique to estimate the anns from T(T,4He)2n would lead to similar error estimates, i.e. [Formula: see text].

Der Einflu\ einer Spin-Spinwechselwirkung auf das magnetische Moment schwerer Atomkerne

The corrections to the magnetic moments of heavy nuclei on account of a spindependent two-body-interaction of the form (σ1σ2)V(r1–r2) are determined in the Fermi model calculating the second order contribution for the selfenergy part. It is shown using conservation laws that this contribution is connected to the local Vertex Tω [σ] of Migdal's theory of finite Fermi systems.

A note on the sum rule for the parameters in Migdal's theory of nuclei

The Pauli principle sum rule is violated if the interaction of quasiparticles in Landau's theory of normal Fermi liquids is calculated by functional differentiation of the binding energy obtained by Brueckner's method. The reason is the unsymmetrical treatment of particles and holes in Brueckner's theory. The fact that the phenomenologically determined values of Migdal's parameters also violate the sum rule is discussed.

Critique of a Bootstrap Theory of Phase Transitions

It is shown that the bootstraplike equation of Migdal's recent theory of phase transitions has a spurious solution if truncated improperly and must be handled with caution if physically sensible solutions are to be obtained.

Monopole states in 40Ca

The τ = 1 and τ = 0 one-particle-one-hole monopole states in 40Ca are calculated within the hydrodynamical model and with realistic forces and within the framework of the Migdal theory.

A calculation of some parameters in Migdal's theory of nuclei

Some of the parameters in Migdal's theory of nuclei have been calculated. We used principally Landau's phenomenological approach to obtain the quasi-particle interaction. The energy was calculated by Brueckner's theory. We have used effective interactions which in infinite nuclear matter give the same potential energies in ( 1 S 0+ 1 D 2 and ( 3 S 1+ 3 D 1) states as the Hamada-Johnston potential. Other contributions to the binding energy were neglected. The nuclear compressibility K was calculated both from the energy-versus-density curve and from the calculated parameters of Migdal's theory. The results were not in conflict with each other. The values of K obtained were 100–150 MeV, which agrees reasonably well with other calculations in infinite nuclear matter, but they are only about 1 3 of the values bsed by Migdal and collaborators. We obtained 0.7 for the effective mass and 22–25 MeV for the symmetry energy. The latter result agrees reasonably well with empirical values. An attempt to use the Green function approach in the calculations of the parameters was not successful because of poor convergence, if any.

Neutron and proton distribution in nuclei

We calculate the energy gap for deformed nuclei using the gap equation which appears in the Migdal theory of finite Fermi systems with pair correlations. To obtain good agreement with experiment for nuclei with neutron excess, it is necessary to choose differently the forms of the density dependent residual interaction for the protons and neutrons because of the difference between their density distributions. The distributions we get are in good agreement with experiment as well as with other theoretical predictions. We also show which approximations are required to reduce the general gap equation to the special Migdal equation.

Isotope effect and the density-dependent nucleon-nucleon interaction

The isotope shift is calculated for 208Pb and for the Ca region in perturbation theory using a density-dependent nucleon-nucleon interaction. Rearrangement terms are estimated and some connection is made with the Migdal theory of finite nuclei. The density deppendence is of great importance in obtaining isotope shifts of the right sign and magnitude.

Shell model approach to intermediate resonances

Migdal's theory of nuclear structure is extended to treat the low energy intermediate scattering resonances. It is shown that the position and width of resonances can be calculated using the same effective force as for the calculation of response functions and nuclear moments.

Total Muon-Capture Rate and the Consistency of Migdal's Theory

Migdal's theory of nuclear structure is recast in the shell-model language, enabling us to show that the excellent agreement with experiment of the theory applied to the total muon-capture rate is obtained by an appreciable symmetry breaking of the Wigner's SU(4) supermultiplet structure contrary to other models where the symmetry seems to be well preserved. Thus, the $\ensuremath{\mu}$-capture result is inconsistent with the dipole photoabsorption and inelastic electron scattering processes reflecting the possible breakdown of the quasiparticle hypothesis.

Migdal's Theory of Nuclear Structure and Partial Muon Capture Rates inO16

Migdal's Theory of Nuclear Structure and Partial Muon Capture Rates in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>16</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

Migdal'S Theory of Nuclear Structure and Partial Muon Capture Rates inO16

The partial muon-capture rates in ${\mathrm{O}}^{16}$ leading to low-lying states in ${\mathrm{N}}^{16}$ are calculated in Migdal's theory of nuclear structure, with results that agree well with the available experiments for suitable values of ${C}_{P}=\frac{{m}_{\ensuremath{\mu}}{F}_{P}}{{F}_{A}}$. It is thus argued that the neglect of $G$-parity irregular terms was not the cause of previous apparent disagreement. The capture rates are in turn employed to examine the effect of the velocity-dependent terms in Migdal's effective amplitude.

The μ-atom isotopic shift

Using Migdal's theory of finite Fermi systems, the isotope shift is calculated for calcium and oxygen isotopes. An approximate connection with the electronic isotope shift is made.