1,603 research outputs found

### Two-phonon $\gamma$-vibrational states in rotating triaxial odd-$A$ nuclei

Distribution of the two phonon $\gamma$ vibrational collectivity in the
rotating triaxial odd-$A$ nucleus, $^{103}$Nb, that is one of the three
nuclides for which experimental data were reported recently, is calculated in
the framework of the particle vibration coupling model based on the cranked
shell model plus random phase approximation. This framework was previously
utilized for analyses of the zero and one phonon bands in other mass region and
is applied to the two phonon band for the first time. In the present
calculation, three sequences of two phonon bands share collectivity almost
equally at finite rotation whereas the $K=\Omega+4$ state is the purest at zero
rotation.Comment: 15 pages, 3 figures, accepted for publication in Physical Review

### Two classes of generalized functions used in nonlocal field theory

We elucidate the relation between the two ways of formulating causality in
nonlocal quantum field theory: using analytic test functions belonging to the
space $S^0$ (which is the Fourier transform of the Schwartz space $\mathcal D$)
and using test functions in the Gelfand-Shilov spaces $S^0_\alpha$. We prove
that every functional defined on $S^0$ has the same carrier cones as its
restrictions to the smaller spaces $S^0_\alpha$. As an application of this
result, we derive a Paley-Wiener-Schwartz-type theorem for arbitrarily singular
generalized functions of tempered growth and obtain the corresponding extension
of Vladimirov's algebra of functions holomorphic on a tubular domain.Comment: AMS-LaTeX, 12 pages, no figure

### Extended Theory of Finite Fermi Systems: Application to the collective and non-collective E1 strength in $^{208}$Pb

The Extended Theory of Finite Fermi Systems is based on the conventional
Landau-Migdal theory and includes the coupling to the low-lying phonons in a
consistent way. The phonons give rise to a fragmentation of the single-particle
strength and to a compression of the single-particle spectrum. Both effects are
crucial for a quantitative understanding of nuclear structure properties. We
demonstrate the effects on the electric dipole states in $^{208}$Pb (which
possesses 50% more neutrons then protons) where we calculated the low-lying
non-collective spectrum as well as the high-lying collective resonances. Below
8 MeV, where one expects the so called isovector pygmy resonances, we also find
a strong admixture of isoscalar strength that comes from the coupling to the
high-lying isoscalar electric dipole resonance, which we obtain at about 22
MeV. The transition density of this resonance is very similar to the breathing
mode, which we also calculated. We shall show that the extended theory is the
correct approach for self-consistent calculations, where one starts with
effective Lagrangians and effective Hamiltonians, respectively, if one wishes
to describe simultaneously collective and non-collective properties of the
nuclear spectrum. In all cases for which experimental data exist the agreement
with the present theory results is good.Comment: 21 figures corrected typos in author fiel

### Relativistic quasiparticle time blocking approximation. II. Pygmy dipole resonance in neutron-rich nuclei

Theoretical studies of low-lying dipole strength in even-even spherical
nuclei within the relativistic quasiparticle time blocking approximation
(RQTBA) are presented. The RQTBA developed recently as an extension of the
self-consistent relativistic quasiparticle random phase approximation (RQRPA)
enables one to investigate effects of coupling of two-quasiparticle excitations
to collective vibrations within a fully consistent calculation scheme based on
covariant energy density functional theory. Dipole spectra of even-even
$^{130}$Sn -- $^{140}$Sn and $^{68}$Ni -- $^{78}$Ni isotopes calculated within
both RQRPA and RQTBA show two well separated collective structures: the
higher-lying giant dipole resonance (GDR) and the lower-lying pygmy dipole
resonance (PDR) which can be identified by a different behavior of the
transition densities of states in these regions.Comment: 28 pages, 13 figure

### Recent progress in the study of fission barriers in covariant density functional theory

Recent progress in the study of fission barriers of actinides and superheavy
nuclei within covariant density functional theory is overviewed.Comment: 10 pages, 5 figures. In press in International Journal of Modern
Physics

### Spectroscopic features of low-energy excitations in skin nuclei

Systematic studies of dipole and other multipole excitations in stable and
exotic nuclei are discussed theoretically. Exploring the relation of the
strengths of low-energy dipole and quadrupole pygmy resonances to the thickness
of the neutron (proton) skin a close connection between static and dynamic
properties of the nucleus is observed. The fine structure of low-energy dipole
strength in 138Ba nucleus is revealed from E1 and spin-flip M1 strengths
distributions.Comment: A Talk given at the Int. Symposium 'Forefronts of Researches in
Exotic Nuclear Structures - Niigata2010 -', 1-4 March, 2010, Tokamachi,
Niigata, Japan; to be published in a volume of Modern Physics Letters A
(MPLA)

### Expectation values of single-particle operators in the random phase approximation ground state

We developed a method for computing matrix elements of single-particle
operators in the correlated random phase approximation ground state. Working
with the explicit random phase approximation ground state wavefunction, we
derived practically useful and simple expression for a molecular property in
terms of random phase approximation amplitudes. The theory is illustrated by
the calculation of molecular dipole moments for a set of representative
molecules.Comment: Accepted to J.Chem.Phy

### PCT, spin and statistics, and analytic wave front set

A new, more general derivation of the spin-statistics and PCT theorems is
presented. It uses the notion of the analytic wave front set of
(ultra)distributions and, in contrast to the usual approach, covers nonlocal
quantum fields. The fields are defined as generalized functions with test
functions of compact support in momentum space. The vacuum expectation values
are thereby admitted to be arbitrarily singular in their space-time dependence.
The local commutativity condition is replaced by an asymptotic commutativity
condition, which develops generalizations of the microcausality axiom
previously proposed.Comment: LaTeX, 23 pages, no figures. This version is identical to the
original published paper, but with corrected typos and slight improvements in
the exposition. The proof of Theorem 5 stated in the paper has been published
in J. Math. Phys. 45 (2004) 1944-195

### Twisted convolution and Moyal star product of generalized functions

We consider nuclear function spaces on which the Weyl-Heisenberg group acts
continuously and study the basic properties of the twisted convolution product
of the functions with the dual space elements. The final theorem characterizes
the corresponding algebra of convolution multipliers and shows that it contains
all sufficiently rapidly decreasing functionals in the dual space.
Consequently, we obtain a general description of the Moyal multiplier algebra
of the Fourier-transformed space. The results extend the Weyl symbol calculus
beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure

### Axiomatic formulations of nonlocal and noncommutative field theories

We analyze functional analytic aspects of axiomatic formulations of nonlocal
and noncommutative quantum field theories. In particular, we completely clarify
the relation between the asymptotic commutativity condition, which ensures the
CPT symmetry and the standard spin-statistics relation for nonlocal fields, and
the regularity properties of the retarded Green's functions in momentum space
that are required for constructing a scattering theory and deriving reduction
formulas. This result is based on a relevant Paley-Wiener-Schwartz-type theorem
for analytic functionals. We also discuss the possibility of using analytic
test functions to extend the Wightman axioms to noncommutative field theory,
where the causal structure with the light cone is replaced by that with the
light wedge. We explain some essential peculiarities of deriving the CPT and
spin-statistics theorems in this enlarged framework.Comment: LaTeX, 13 pages, no figure

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