Muon capture revisited

The problem of inclusive muon capture in nuclei is studied by calculating the capture rate in asymmetric infinite nuclear matter and using the local density approximation to evaluate the capture rates in nuclei. It is shown that the method is rather reliable and allows one to improve on approximations used in the past. The need for a strong nuclear renormalization is shown, reducing the capture rates by about a factor two in medium and heavy nuclei. By using standard effective interactions in the spin-isospin channel one can account for this renormalization and one finds a remarkable overall agreement with the measured capture rates for a large list of nuclei through the periodic table.     

Nuclear polarization in muonic atoms of deformed nuclei

The treatment of nuclear polarization correction in muonic atoms belonging to deformed nuclei is analyzed. The geometrical factors involved are expanded into a series of multipoles and the exact expansion coefficients are calculated. It is shown that, using reasonable assumptions about the nuclear spectrum, the nuclear polarization correction may be expressed as a shift of all hyperfine components plus a renormalization of the even multipole hyperfine interaction constants. All nuclear excited states contribute to the shift, but the ground-state rotational band gives an over-whelming contribution to the multipole moment renormalization. The effect of the ground-state band is analyzed in detail. The radial coefficients are calculated and an approximate formula, applicable over a broad range of atomic numbers and deformations, is obtained. By comparing our results with exact calculations we conclude that this part of the nuclear polarization correction may be calculated with accuracy better than 10 %.     

The orbital g-factor and related sum rules

The renormalization of the orbital g-factor in nuclei is discussed on the basis of gauge invariance.The relation of the orbital g-factor to the integrated E1 photoabsorption cross section is reviewed,and its relation to the M1 sum rule for the scissors mode of deformed nuclei is examined.     

Pauli principle and renormalization of the pion nucleon interaction in nuclei

We show that the exclusion principle provides an alternative mechanism to the Lorentz-Lorenz effect for the renormalization of the pion-nucleon coupling constant in nuclei. This mechanism proves to be less sensitive to the range of the π - N forces. The implications for pion-nucleus scattering are discussed.     

On the calculation of matrix elements of one body operators in many nucleon systems

We demonstrate the connection between matrix elements of one body operators in odd nuclei and vertex functions. The procedure is free of assumptions on the pole distribution of the two point functions and it does not use perturbation theory. The renormalization of the external field, necessistated by configuration space limitations, is carried through for scalar, local fields, acting on the density and for radiation fields of the electric multipole type using the requirement of gauge invariance. It is shown that this renormalization is possible, even if the renormalized field is strongly energy dependent due to configuration mixing.     

Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter based on improved approximation schemes

We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter which are based on improved approximations schemes. The potential matrix elements have been adapted for isospin asymmetric nuclear matter in order to account for the proton-neutron mass splitting in a more consistent way. The proton properties are particularly sensitive to this adaption and its consequences, whereas the neutron properties remains almost unaffected in neutron-rich matter. Although at present full Brueckner calculations are still too complex to apply to finite nuclei, these relativistic Brueckner results can be used as a guidance to construct a density-dependent relativistic mean-field theory, which can be applied to finite nuclei. It is found that an accurate reproduction of the Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of these coupling functions.     

Shell-correction approach to state densities of nuclei

A consistent renormalization of ground state energy and state density as a function of deformation is presented. Renormalized state densities do not increase uniformly with deformation. Consequences for the fissionability of excited nuclei are pointed out.     

From low-momentum interactions to nuclear structure

We present an overview of low-momentum two-nucleon and many-body interactions and their use in calculations of nuclei and infinite matter. The softening of phenomenological and effective field theory (EFT) potentials by renormalization group (RG) transformations that decouple low and high momenta leads to greatly enhanced convergence in few- and many-body systems, while maintaining a decreasing hierarchy of many-body forces. This review surveys the RG-based technology and results, discusses the connections to chiral EFT, and clarifies various misconceptions.     

Nuclear masses and properties of nuclei in the vicinity of the remote magic nucleus <Superscript>100</Superscript>Sn

Results are presented that were obtained by calculating various properties of nuclei occurring in the vicinity of the doubly magic neutron-deficient nuclide ¹⁰⁰Sn, which are being intensively studied at present. The calculated features include the masses of 25 nuclei and the properties of excited states of the magic nuclide and of nuclei belonging to the magic core plus two quasiparticles type. The problems of effective quadrupole charges and of the renormalization of the weak axial constant in nuclei lying in the vicinity of ¹⁰⁰Sn are considered.     

Nuclear effects in neutrino induced coherent pion production at K2K and MiniBooNE

The coherent pion production induced by neutrinos in nuclei is studied using a delta hole model in the local density approximation taking into account the renormalization of Delta properties in a nuclear medium. The pion absorption effects are included in an eikonal approximation. These effects give a large reduction in the total cross section. The numerical results for the total cross section are found to be consistent with recent experimental results from the K2K and MiniBooNE Collaborations and other older experiments in the intermediate energy region.     

Probing the pion field in nuclei

It is suggested that muon absorption and doubly radiative pion absorption in nuclei can complement each other in probing the pion field in the nuclear medium. The relevant issues we consider are possible pion condensation and nuclear “renormalization” of weak and electromagnetic vertices, the adequate understanding of which is necessary to extract from nuclear experiments useful information on basic form factors in the weak Hamiltonian.     

μ－ CAPTURE IN NUCLEI

Using the many-body field theory the problems of μ^－ captures in nuclei are systematically studied.Without ajustable parameter,calculations are performed for the total nuclear capture rates of muon for nuclei ranging from light to heavy ones.It shows that the renormalization due to the spin-isospin-dependent strong interaction and the muon binding in the μ^－ atom are essential for a thorough understanding of this type of weak interaction processes.     

On the microscopic theory of electronic contributions to lattice dynamics of anharmonic crystals

A formalism is set up to study the electronic contribution to the phonon dynamics in an arbitrary crystal, conducting or insulating, without assuming small ionic oscillations. Therefore, in contrast to a harmonic Born-Oppenheimer approximation, such an approach allows for renormalization effects due to phonon-phonon interaction over the complete temperature range of the solid phase. The “weak coupling” approximation between nuclei and electrons is shown to be sufficient in order to obtain the dynamical matrix microscopically in terms of the complete inverse dielectric function of the electrons.     

Effective field theory for dilute fermions with pairing

Effective field theory (EFT) methods for a uniform system of fermions with short-range, natural interactions are extended to include pairing correlations, as part of a program to develop a systematic Kohn-Sham density functional theory (DFT) for medium and heavy nuclei. An effective action formalism for local composite operators leads to a free-energy functional that includes pairing by applying an inversion method order by order in the EFT expansion. A consistent renormalization scheme is demonstrated for the uniform system through next-to-leading order, which includes induced-interaction corrections to pairing.     

Description of the 2νββ decay within a fully renormalised RPA approach

The RPA treatment of a many body Hamiltonian describing the states of even-even nuclei involved in a 2νββ decay is revisited. One shows that renormalizing the dipole two quasiparticle operators by accounting for new correlations in the ground state requires a simillar renormalization for the dipole density operators which results in activating new boson degress of freedom. Possible consequences on Ikeda sum rule and Gamow-Teller transition amplitude are suggested. A numerical application for a two levels model is presented     

Consistency of effective,relativistic four-point interactions for nuclei

We derive consistency conditions for effective field theoretic models for nuclei with four-fermion couplings. The transformation properties of these consistency conditions under the renormalization group are discussed.Supported by Gesellschaft für Schwerionenforschung (GSI)     

Core polarization effects in the Hartree-Fock-random phase approximation schemes

Core polarization effects in odd nuclei are investigated in the framework of the Hartree-Fock and random phase approximation schemes. The results of the particle vibration coupling model are recovered by linearizing the equations of motion in the interaction Hamiltonian between the external and the core particles. The formalism is used to study the renormalization of diagonal and off-diagonal M1 matrix elements. It is found that M1 polarization effects exhibit a very strong dependence on the range of the force.     

Proton-neutron sdg boson model and spherical-deformed phase transition

The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing+quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.