Nuclear Theory·nucl-th

Monday·January 16, 2023

5 papers—4 primary·1 cross-listed

01
Possible interpretation of the complex expectation values associated with resonances
Takayuki Myo · Kiyoshi Kato
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.
nucl-thhep-phquant-phPRC(2023)·14 citations
02
Imprints of $α$ clustering in the density profiles of $^{12}$ C and $^{16}$ O
W. Horiuchi · N. Itagaki
The $^{4}$ He nucleus is a well bound and highly correlated four-nucleon system that is also found in form of $α$ -clusters as substructure in nuclear many-body systems. The standard single-particle shell model cannot represent these four-body correlations. It is highly desirable to find a simple way to identify and distinguish these fundamental structures without large-scale computations. In this paper, we investigate with intrinsic Slater determinants as trial states in how far these two competing pictures prevail in the ground states of $^{12}$ C and $^{16}$ O. The trial states can describe both the $j$ - $j$ coupling shell-model and $α$ -cluster configurations in a unified way. One-body density distributions of the trial states are calculated and compared to elastic scattering cross section data. The parameters of the trial state are chosen to reproduce the experimental charge radii. A well developed cluster structure is characterized by an enhancement of the differential elastic scattering cross sections, as well as the elastic charge form factors around the first peak positions. The density profiles of the internal regions can also be probed at higher momentum transfer regions beyond the second minimum. With these trial states one can visualize the competition between cluster and shell structure in an intuitive and simple way.
nucl-thPRC(2023)·13 citations
03
Gamow Shell Model description of $^{40}$ Ca(d,p) transfer reaction
A. Mercenne🇺🇸 · N. Michel🇨🇳 · J.P. Linares Fernández🇫🇷 · M. Płoszajczak🇫🇷
Transfer reactions are essential to determine spectroscopic factors and astrophysical reaction rates. However, their theoretical evaluation is typically effected using standard reaction theory, from which structure degrees of freedom are absent. While reaction cross sections have been implemented in the frame of the no-core shell model with continuum, this model can be applied in practice only to the lightest nuclei. The use of the core + valence nucleon picture is then necessary to include inter-nucleon correlations in reaction cross sections involving medium nuclei. For this, we will use the recently developed coupled-channel Gamow Shell Model (GSM-CC) for direct reactions and extend it to the evaluation of transfer cross sections. As an example, we will study the $^{40}$ Ca(d,p) transfer reaction with GSM-CC. Experimental data can be successfully reproduced, but at the price of the use of a very phenomenological Hamiltonian.
nucl-thPRC(2023)·4 citations
04
Contribution of Nuclear Excitation Electromagnetic Form Factors in $^{12} C$ and $^{16} O$ to the Coulomb Sum Rule
A. Bodek · M. E. Christy
We report on empirical parameterizations of longitudinal and transverse nuclear excitation electromagnetic form factors in $^{12} C$ and $^{16} O$ . We extract the contribution of nuclear excitations to the Normalized Inelastic Coulomb Sum Rule (\csr) as a function of momentum transfer $q$ and find that it is significant (0.29 $\pm$ 0.030 at $q$ = 0.22 GeV). The total contributions of nuclear excitations to $S_{L} (q)$ in $^{12} C$ and $^{16} O$ are found to be equal within the uncertainties. Since the cross sections for nuclear excitations are significant, the radiative tails from nuclear excitations should be included in precise calculations of radiative corrections to quasielastic electron scattering at low $q$ and deep-inelastic electron scattering at large energy transfers $ν$ . The parameterizations also serve as a benchmark in testing theoretical modeling of cross sections for excitation of nuclear states in electron and neutrino interactions on nuclear targets at low energies.
nucl-thhep-phnucl-exPRC(2023)·9 citations
05
U(5) Nambu-Jona-Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses
Willian F. de Sousa🇧🇷 · Fabio L. Braghin🇧🇷
By considering the background field method we calculate one-loop polarization corrections to the coupling constant of the flavor-U(5) Nambu-Jona-Lasinio (NJL) model with degenerate up and down quarks. They break flavor and chiral symmetries, and they can be written as $G_{ij}^{Γ} (ψ ˉ λ_{i} Γ ψ) (ψ ˉ λ_{j} Γ ψ)$ , for the scalar and pseudoscalar channels ( $Γ = I, i γ_{5}$ ) and $i, j = 0, 1, ..., N_{f}^{2} - 1$ . Therefore, these coupling constants do not introduce further free parameters in the model which amount to five, six or seven in total. Their contributions to different observables are computed. The non-covariant three-dimensional regularization scheme is employed. Besides that, flavor dependence of cutoffs is implemented in an unambiguous way. It turns out that only two UV cutoffs ( $Λ_{f}$ ) are best suitable. Nevertheless, the best results are obtained for nearly flavor-independent cutoffs. A quantum mixing due to the representations of the flavor group leads to different interactions for the quarks and for the meson states, respectively denoted by $G_{f f}$ and $G_{ij}$ . This quantum mixing effect is responsible for a lowering of quark effective masses and a slight improvement of predictions of observables. A quite surprisingly good description of almost all the pseudoscalar meson masses (within nearly $5%$ ) and most of the scalar meson masses -is obtained within nearly 10 $%$ . Some problems to describe light scalar mesons masses still remain. The NJL-gap equations seems to overestimate the heavy quark condensates at the usual mean field level usually adopted for model. In spite of the good description of the meson masses, the pseudoscalar meson weak decay constant cannot be described by the NJL model with relativistic heavy quark propagators without further interactions or effects.
↳ hep-phnucl-thEPJA(2023)·7 citations

Affiliations

first authorsco-authorsvia INSPIRE

Possible interpretation of the complex expectation values associated with resonances

Imprints of α clustering in the density profiles of 12C and 16O

Gamow Shell Model description of 40Ca(d,p) transfer reaction

Contribution of Nuclear Excitation Electromagnetic Form Factors in 12C and 16O to the Coulomb Sum Rule

U(5) Nambu-Jona-Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses

Affiliations

Imprints of $α$ clustering in the density profiles of $^{12}$ C and $^{16}$ O

Gamow Shell Model description of $^{40}$ Ca(d,p) transfer reaction

Contribution of Nuclear Excitation Electromagnetic Form Factors in $^{12} C$ and $^{16} O$ to the Coulomb Sum Rule