There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Recurrence plots for the analysis of complex systems

The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications.

Self-consistent mean-field models for nuclear structure

The collective excitation phenomena in atomic nuclei are studied in two different formulations of the random-phase approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the unitary correlation operator method (UCOM) and (ii) relativistic RPA derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar giant monopole resonance in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the relativistic quasiparticle RPA (RQRPA) based on the relativistic Hartree-Bogolyubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance.

Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

Magnetic-dipole (M1) excitations of $^{18}$O and $^{42}$Ca nuclei are investigated within a relativistic nuclear energy density functional framework. In our last work \cite{2019OP}, these nuclei are found to have unique M1 excitation and its sum rule, because of their characteristic structure: the system consists of the shell-closure core plus two neutrons. For a more systematic investigation of the M1 mode, we have implemented a framework based on the relativistic nuclear energy density functional (RNEDF). For benchmark, we have performed the RNEDF calculations combined with the random-phase approximation (RPA). We evaluate the M1 excitation of $^{18}$O and $^{42}$Ca, whose sum-rule value (SRV) of the M1 transitions can be useful to test the computational implementation \cite{2019OP}. We also apply this RNEDF method to $^{208}$Pb, whose M1 property has been precisely measured \cite{1979Holt,1987Koehler,1988Laszewski,2016Birkhan}. Up to the level of the M1 sum rule, our result is in agreement with the experiments, except the discrepancy related with the quenching factors for $g$ coefficients.

Relativistic energy-density functional approach to magnetic-dipole excitation and its sum rule

The relativistic random phase approximation based on effective Lagrangian with density dependent meson-nucleon couplings has been extended to finite temperature and employed in studies of multipole excitations within the temperature range T = 1 − 2 MeV. The model calculations showed that isoscalar giant monopole and isovector giant dipole resonances are only slightly modified with temperature, but additional transition strength appears at low energies because of thermal unblocking of single-particle orbitals close to the Fermi level. The analysis of low-lying states shows that isoscalar monopole response in 132Sn results from single particle transitions, while the isovector dipole strength for 60Ni, located around 10 MeV, is composed of several single particle transitions, accumulating a small degree of collectivity.

Finite temperature effects on monopole and dipole excitations

The framework of relativistic self-consistent mean-field 
models is extended to include correlations related to the 
restoration of broken symmetries and to fluctuations of 
collective variables. The generator coordinate method is 
used to perform configuration mixing of angular-momentum and
particle-number projected relativistic wave functions, and 
the geometry is restricted to axially symmetric shapes. 
The relativistic (quasiparticle) random-phase approximation is
applied in the description of the evolution of low-lying 
dipole strength in neutron-rich and proton-rich nuclei.

Exotic nuclear structure: Relativistic mean-field and beyond

Magnetic quadrupole (M2) excitation represents a fundamental feature in atomic nucleus associated to nuclear magnetism induced by spin and orbital transition operator. Since it has only been investigated within the non-relativistic theoretical approaches, and available experimental data are rather limited, it is interesting to study the properties of M2 transitions using the framework of relativistic nuclear energy density functional. In this work the nuclear ground state is calculated with relativistic Hartree-Bogoliubov model, while the M2 excitations are described using the relativistic quasiparticle random phase approximation with the residual interaction extended with the isovector-pseudovector term. The M2 transition strength distributions are described and analyzed for closed shell nuclei $$^{16}$$ O, $$^{48}$$ Ca, $$^{208}$$ Pb, open-shell $$^{18} \mathrm O$$ , $$^{42}$$ Ca, $$^{56}$$ Fe, and semi-magic $$^{90}$$ Zr. The evolution of M2 transition properties has been investigated within the $$^{36-64} \mathrm Ca$$ isotope chain. The main M2 transitions have rather rich underlying structure and detailed analysis shows that collectivity increases with the mass number due to larger number of contributing particle-hole configurations. Pairing correlations in open shell nuclei have strong effect, causing the reduction of M2 strength and shifts of the centroid energies to higher values. The analysis of M2 transition strengths indicate that considerable amount of experimental strength may be missing, mainly due to limitations to rather restricted energy ranges. The calculated M2 strengths for Ca isotopes, together with the future experimental data will allow constraining the quenching of the g factors in nuclear medium. 

/pdf/magnetic-quadrupole-transitions-in-the-relativistic-energy-1h01ul3t.pdf

Nils Paar

Papers

Collective excitations in the unitary correlation operator method and relativistic QRPA studies of exotic nuclei

Relativistic energy-density functional approach to magnetic-dipole excitation and its sum rule

Finite temperature effects on monopole and dipole excitations

Exotic nuclear structure: Relativistic mean-field and beyond

Magnetic quadrupole transitions in the relativistic energy density functional theory