arXiv subjects
Publications and source records attributed to Kiyoshi Kato.
Detailed description of the calculation of the 2-loop self-energy for a scalar particle is presented. By employing a simple sector decomposition method, the ultraviolet divergent part is efficiently separated from the finite part. The resulting expression can be used for both analytic and numerical computation to renormalize the divergence and to provide finite results for physics.
Four 3-loop two-point functions are studied analytically and numerically using a simplified sector decomposition method. The coefficients of the ultraviolet divergent part are determined analytically, and those of the finite part are computed numerically. The energy dependence of the integrals is shown explicitly, and a discussion of its behavior is presented.
The use of the dimensional regularization in the on-mass-shell renormalization scheme sometimes fails to locally cancel the ultraviolet divergence for a class of diagrams in the two-loop order. The mechanism is discussed based on an example with explicit computation.
We propose a new basis state, which satisfies the Pauli principle in the nuclear cluster model. The basis state is defined as the generalized coherent state of the harmonic oscillator wave function using a pair of the creation operators and is orthogonal to the Pauli-forbidden states having smaller quanta. In the coherent basis state, the range parameter is changeable and controls the radial dilation. This property is utilized for the precise description of the relative motion between nuclear clusters. We show the reliability of this framework for the $2α$ system of $^8$Be in the semi-microscopic orthogonality condition model. We obtain the resonances and non-resonant continuum states of $2α$ with complex scaling. The resonance solutions and the phase shifts of the $α$-$α$ scattering agree with those using the conventional projection operator method to remove the Pauli-forbidden states. We further discuss the extension of the present framework to the multi-$α$ cluster systems using the SU(3) wave functions.
We investigate the soft dipole resonance in the proton-rich nucleus $^8_6$C$_2$, which is a collective dipole oscillation of four valence protons against the $α$ core,and discuss the isospin symmetry with the mirror nucleus $^8_2$He$_6$. We use the $α+N+N+N+N$ five-body cluster model and many-body resonances are obtained using the complex-scaling method. The $1^-$ resonance of $^8_6$C$_2$ is confirmed at the excitation energy of 13 MeV with a large decay width of 24 MeV, and its structure is similar to the soft dipole resonance in $^8_2$He$_6$, such as the configuration mixing and the spatial properties. These results indicate a good isospin symmetry in the soft dipole resonances of two nuclei with a common collective excitation of multiproton and multineutron, while the ground states of two nuclei show different properties due to the Coulomb repulsion of valence protons in $^8_6$C$_2$, leading to the symmetry breaking. In conclusion, the appearance of the isospin symmetry differs depending on the states of $^8_6$C$_2$ and $^8_2$He$_6$.
We propose a possible scheme to interpret the complex expectation values associated with resonances having the complex eigenenergies. Using the Green's function for resonances, the expectation value is basically described by the Breit-Wigner distribution as a function of the real excitation energy. In the expression of the complex expectation values for resonances, the real part brings the integral value of the distribution, while the imaginary part produces the deviation from the Breit-Wigner distribution,which explains a shift of the peak in the strength from the resonance energy. We apply the present scheme to the several nuclear resonances of $^{12}$C including the Hoyle state, and neutron/proton-rich nuclei of $^6$He, $^6$Be, $^8$He, and $^8$C. In these nuclei, many-body resonances are obtained as the complex-energy eigenstates under the correct boundary condition using the complex scaling method, and their nuclear radii are uniquely evaluated. We discuss the peculiar energy dependence of the strength function of the square radius for the resonances in these nuclei.
In neutron-rich $^8$He, we study the soft dipole resonance, which is regarded as a dipole oscillation of four valence neutrons against the $^4$He core, and its effect on the low-energy electric dipole strength with a $^4$He+$n$+$n$+$n$+$n$ five-body cluster model. This work is an extended study of an earlier letter [T. Myo and K. Katō, Phys. Rev. C106, L021302 (2022)]. The five-body unbound $1^-$ states of $^8$He are obtained with the complex energy eigenvalues by using the complex scaling method and the dipole strength is calculated in terms of the complex-scaled Green's function. Two kinds of the dominant excitation modes are confirmed in the dipole strength below 20 MeV of the excitation energy. The strengths below 10 MeV are exhausted by the $^7$He+$n$ channel, which sequentially decays to $^6$He+$n$+$n$. Above 10 MeV, the strengths arise from the soft dipole mode of four neutrons ($4n$) oscillating against the $^4$He core. We further explore the possibility of the soft dipole resonance for this state by carefully searching for the resonance pole and finally predict the corresponding resonance with the excitation energy of 14 MeV and the decay width of 21 MeV. The soft dipole resonance exhausts about half of the dipole strength in the relative motion between the $^4$He core and $4n$.
We investigate the multineutron excitations of neutron-rich $^8$He in the electric dipole strength using a $^4$He+$n$+$n$+$n$+$n$ five-body model. Many-body unbound states of $^8$He are obtained in the complex scaling method. We found that the different excitation modes coexist in the dipole strength below the excitation energy of 20 MeV. The strength below 10 MeV comes from the $^7$He+$n$ channel, indicating the sequential breakup of $^8$He via the $^7$He resonance to $^6$He+$n$+$n$. Above 10 MeV, the strength is obtained from many-body continuum states with strong configuration mixings, suggesting a new collective motion of four neutrons with the dipole oscillation against $^4$He.
The complex scaling method (CSM) is one of the most powerful methods of describing the resonances with complex energy eigenstates, based on non-Hermitian quantum mechanics. We present the basic application of CSM to the properties of the unbound phenomena of light nuclei. In particular, we focus on many-body resonant and non-resonant continuum states observed in unstable nuclei. We also investigate the continuum level density (CLD) in the scattering problem in terms of the Green's function with CSM. We discuss the explicit effects of resonant and non-resonant contributions in CLD and transition strength functions.
The 1-loop effects of the MSSM at the ILC are investigated through numerical analysis. We studied the higgs production processes $e^-e^+\rightarrow Zh$ and $e^-e^+\rightarrow ν\barνh$ at the ILC. It is found that the magnitude of the MSSM contribution through the 1-loop effects is sizable enough to be detected. In the study, three sets of the MSSM parameters are proposed, which are consistent with the observed higgs mass, the muon $g$-$2$, the dark matter abundance and the decay branching ratios of $B$ mesons. In the $e^-e^+\rightarrow Zh$ process, the 1-loop effects of the MSSM are visible and the distinction of the parameter sets is partially possible. For the study of $e^-e^+\rightarrow ν\barνh$, we used the equivalent $\it W$-boson approximation in the evaluation of the 1-loop cross section. While the 1-loop effect of the MSSM is visible, the distinction of the parameter sets might not be possible in this process under the value of realistic luminosity at the ILC.
Within the framework of the Minimal Supersymmetric Standard Model, we investigate the 1-loop effects of supersymmetric particles on the third-generation fermion-pair production at the ILC. Three sets of the SUSY parameters are proposed which are consistent with the observed Higgs mass, the muon g-2, the Dark Matter abundance and the decay branching ratio of B meson. We discuss on the possibility of discovering the signals consistent with SUSY as well as of experimentally distinguishing the proposed sets of SUSY parameters.
We study the character of the first excited 1/2^{+} state of {9}^Be, which is observed as a low-lying sharp peak in the cross section of 9^Be(γ,n)2α just above the {8}^Be+n threshold. Using the α+α+n three-body model, we describe the ground and excited unbound states of {9}^Be above the α+α+n threshold. Applying the complex scaling method to the three-body model, we find no 1/2^{+} resonant solutions, while the low-lying peak in the photodisintegration cross section is reproduced in the present calculation. It is found that the low-lying peak is dominantly explained by the 8^Be+n component. Furthermore, using the analytical continuation of the coupling constant of the three-body interaction for the α+α+n system, we discuss the virtual-state character of the 1/2^{+} state.
The complex scaling method (CSM) is a useful similarity transformation of the Schrödinger equation, in which bound-state spectra are not changed but continuum spectra are separated into resonant and non-resonant continuum ones. Because the asymptotic wave functions of the separated resonant states are regularized by the CSM, many-body resonances can be obtained by solving an eigenvalue problem with the $L^2$ basis functions. Applying this method to a system consisting of a core and valence nucleons, we investigate many-body resonant states in weakly bound nuclei very far from the stability lines. Non-resonant continuum states are also obtained with the discretized eigenvalues on the rotated branch cuts. Using these complex eigenvalues and eigenstates in CSM, we construct the extended completeness relations and Green's functions to calculate strength functions and breakup cross sections. Various kinds of theoretical calculations and comparisons with experimental data are presented.
We study the mirror symmetry breaking of $^6$He-$^6$Be and $^8$He-$^8$C using the $^4$He + $X$N ($X$=2, 4) cluster model. The many-body resonances are treated for the correct boundary condition using the complex scaling method. We find that the ground state radius of $^8$C is larger than that of $^8$He due to the Coulomb repulsion in $^8$C. On the other hand, the $0^+_2$ resonances of the two nuclei exhibit the inverse relation; the $^8$C radius is smaller than the $^8$He radius. This is due to the Coulomb barrier of the valence protons around the $^4$He cluster core in $^8$C, which breaks the mirror symmetry of the radius in the two nuclei. A similar variation in the radius is obtained in the mirror nuclei, $^6$He and $^6$Be. A very large spatial extension of valence nucleons is observed in the $0^+_2$ states of $^8$He and $^8$C. This property is related to the dominance of the $(p_{3/2})^2(p_{1/2})^2$ configuration for four valence nucleons, which is understood from the reduction in the strength of the couplings to other configurations by involving the spatially extended components of valence nucleons.
We apply the complex scaling method to the calculation of scattering phase shifts and extract the contributions of resonances in a phase shift and a cross section. The decomposition of the phase shift is shown to be useful to understand the roles of resonant and non-resonant continuum states. As examples, we apply this method to several two-body systems: (i) a schematic model with the Gyarmati potential which produces many resonances, (ii) the alpha-alpha system which has a Coulomb barrier potential in addition to an attractive nuclear interaction, and (iii) the alpha-n system which has no barrier potential. Using different kinds of potentials, we discuss the reliability of this method to investigate the resonance structure in the phase shifts and cross sections.
We study the resonance spectroscopy of the proton-rich nucleus 8C in the alpha+p+p+p+p cluster model. Many-body resonances are treated on the correct boundary condition as the Gamow states using the complex scaling method. We obtain the ground state of 8C as a five-body resonance for the first time, which has dominantly the sub-closed (p_{3/2})^4 configuration and agrees with the recent experiment for energy and decay width. We predict the second 0+ state with the excitation energy of 5.6 MeV, which corresponds to the $2p2h$ state from the ground state. We evaluate the occupation numbers of four valence-protons in the 8C states and also the J^πdistribution of proton-pair numbers of the two 0+ states of 8C. The ground state involves a large amount of the 2+ proton-pair fraction, while the excited 0+_2 state almost consists of two of the 0+ proton pairs, which can be understood from the (p_{3/2})^2(p_{1/2})^2 configuration. We also discuss the mirror symmetry between 8C and 8He with an alpha+four nucleon picture. It is found that the 0+ states retain the mirror symmetry well for the configuration properties of two nuclei.
We investigate the three-body Coulomb breakup of a two-neutron halo nucleus $^{11}$Li. We use the coupled-channel $^9$Li + $n$ + $n$ three-body model, which includes the coupling between last neutron states and the various $2p$-$2h$ configurations in $^9$Li due to the tensor and pairing correlations. The three-body scattering states of $^{11}$Li are described by using the combined methods of the complex scaling and the Lippmann-Schwinger equation. The calculated breakup cross section successfully reproduces the experiments. The large mixing of the s-state in the halo ground state of $^{11}$Li is shown to play an important role in explanation of shape and strength of the breakup cross section. In addition, we predict the invariant mass spectra for binary subsystems of $^{11}$Li. It is found that the two kinds of virtual s-states of $^9$Li-$n$ and $n$-$n$ systems in the final three-body states of $^{11}$Li largely contribute to make low-lying peaks in the invariant mass spectra. On the other hand, in the present analysis, it is suggested that the contributions of the p-wave resonances of $^{10}$Li is hardly confirmed in the spectra.
The paper considers the chains of successive electron capture reactions by nuclei of the iron group which take place in the crystal structures of neutron star envelopes. It is shown that as a result of such reactions the daughter nuclei in excited states accumulate within certain layers of neutron star crusts. The phonon model of interactions is proposed between the excited nuclei in the crystalline structure, as well as formation of highly excited nuclear states which emit neutrons and higher energy photons.