$0^+$, $1^-$, $2^+$, and $3^-$ excitations of $^{28}\textrm{Si}$ are investigated via proton and $α$ inelastic scattering off $^{28}\textrm{Si}$. The structure calculation of $^{28}\textrm{Si}$ is performed with the energy variation after total angular momentum and parity projections in the framework of antisymmetrized molecular dynamics (AMD). As a result of the AMD calculation, the oblate ground and prolate bands, $0^+$ and $3^-$ excitations, and the $1^-$ and $3^-$ states of the $K^π=0^-$ band are obtained. Using the matter and transition densities of $^{28}\textrm{Si}$ obtained by AMD, microscopic coupled-channel calculations of proton and $α$ scattering off $^{28}\textrm{Si}$ are performed. The proton-$^{28}\textrm{Si}$ potentials in the reaction calculation are microscopically derived by folding the Melbourne $g$-matrix $NN$ interaction with the AMD densities of $^{28}\textrm{Si}$. The $α$-$^{28}\textrm{Si}$ potentials are obtained by folding the nucleon-$^{28}\textrm{Si}$ potentials with an $α$ density. The calculation reasonably reproduces the observed elastic and inelastic cross sections of proton and $α$ scattering. Transition properties are discussed by combining the reaction analysis of proton and $α$ scattering and structure features such as transition strengths and form factors. The isoscalar monopole and dipole transitions are focused.
The experimental data on elastic and inelastic scattering of 270 MeV 3He particles to several low lying states in 90Zr, 116Sn and 208Pb are analyzed within the double folding model (DFM). Fermi density distribution (FDD) of target nuclei is used to obtain real potentials with different powers. DF results are introduced into modified DWUCK4 code to calculate the elastic and inelastic scattering cross sections. Two choices of potentials form factors; Woods Saxon (WS) and Woods Saxon Squared (WS2) for real potential are used, while the imaginary part is taken as phenomenological Woods Saxon (PWS)…
The proton inelastic scattering of $^{24}$O($p,p'$) at 62 MeV/nucleon is described by a self-consistent microscopic calculation with the continuum particle-vibration coupling (cPVC) method. The SLy5, SkM*, and SGII parameters are adopted as an effective nucleon-nucleon interaction. For all the parameters, the cPVC calculation reproduces very well the first peak at 4.65 MeV in the $^{24}$O excitation energy spectrum as well as its angular distribution. The role of the cPVC self-energy strongly depends on the effective interactions. The higher-lying strength around 7.3 MeV is suggested to be a s…
[Background:] The band structure of the negative-parity states of $^{24}$Mg has not yet been clarified. The $K^π=0^-$, $K^π=1^-$, and $K^π=3^-$ bands have been suggested, but the assignments have been inconsistent between experiments and theories. [Purpose:] Negative-parity states of $^{24}$Mg are investigated by microscopic structure and reaction calculations via proton and alpha inelastic scattering to clarify the band assignment for the observed negative-parity spectra. [Method:] The structure of $^{24}$Mg was calculated using the antisymmetrized molecular dynamics~(AMD). Proton and alpha i…
The $K^π=0^+_1$, $K^π=2^-$, and $K^π=0^-_1$ bands of $^{20}$Ne are investigated with microscopic structure and reaction calculations via proton and $α$ inelastic scattering off $^{20}$Ne. Structures of $^{20}$Ne are calculated with variation after parity and total angular momentum projections in the antisymmetrized molecular dynamics(AMD). The $K^π=0^+_1$ and $K^π=0^-_1$ bands have $^{16}\textrm{O}+α$ cluster structures, whereas the $K^π=2^-$ band shows a $^{12}\textrm{C}+2α$-like structure. Microscopic coupled-channel calculations of proton and $α$ scattering off $^{20}$Ne are performed by us…
Isospin characters of nuclear excitations in $^{26}$Mg and $^{10}$Be are investigated via proton($p$) and alpha($α$) inelastic scattering. A structure model of antisymmetrized molecular dynamics (AMD) is applied to calculate the ground and excited states of $^{26}$Mg and $^{10}$Be. The calculation describes the isoscalar feature of the ground-band $2^+_1$($K^π=0^+_1$) excitation and predicts the neutron dominance of the side-band $2^+_2$($K^π=2^+$) excitation in $^{26}$Mg and $^{10}$Be. The $p$ and $α$ inelastic scattering off $^{26}$Mg and $^{10}$Be is calculated by microscopic coupled-channe…
Aspects of nuclear structure in alpha-conjugate nuclei have long been associated with alpha clustering, including the existence of superdeformed bands. In this paper, an alpha-particle inelastic scattering experiment investigating the location of $0^+$ states in $^{28}$Si is reported in an attempt to locate possible cluster states. The results are compared to a semi-microscopic model which shows good agreement with the data, and supports the assignment of a newly discovered $0^+$ state as the band-head of a previously observed superdeformed band in $^{28}$Si
To discuss a possible observation of large-amplitude nuclear shape mixing by nuclear reaction, we employ a simple collective model and evaluate transition densities, with which the differential cross sections are obtained through the microscopic coupled-channel calculation. Assuming the spherical-to-prolate shape transition, we focus on large-amplitude shape mixing associated with the softness of the collective potential in the $β$ direction. We introduce a simple model based on the five-dimensional quadrupole collective Hamiltonian, which simulates a chain of isotopes that exhibit spherical-t…
Nuclear excitation cross section of $^{229}$Th from the ground state to the low-lying isomeric state via inelastic electron scattering is calculated, on the level of Dirac distorted wave Born approximation. With electron energies below 100 eV, inelastic scattering is very efficient in the isomeric excitation, yielding excitation cross sections on the order of 10$^{-27}$ to 10$^{-26}$ cm$^2$. Systematic analyses are presented on elements affecting the excitation cross section, including the ion-core potential, the relativistic effect, the knowledge of the reduced nuclear transition probabilitie…
0.8 GeV proton inelastic scatterings from $^{40}$Ar nucleus are analyzed using an optical potential model in the Dirac coupled channel formalism. A rotational collective model is used to obtain the transition optical potentials for the low lying excited states of the rotational band. The optical potential parameters of a Woods-Saxon shape and the deformation parameters of the excited states are searched phenomenologically to reproduce the experimental differential cross-section data by using the sequential iteration method. The effect of a multistep process is investigated by including the cha…
A compact approach based on the folding model is suggested for the determination of the isoscalar and isovector transition strengths of the low-lying ($ΔS=ΔT=0$) excitations induced by inelastic proton scattering measured with exotic beams. Our analysis of the recently measured inelastic $^{18,20}$O+p scattering data at $E_{\rm lab}=30$ and 43 MeV/nucleon has given for the first time an accurate estimate of the isoscalar $β_0$ and isovector $β_1$ deformation parameters (which cannot be determined from the (p,p') data alone by standard methods) for 2$^+_1$ and $3^-_1$ excited states in $^{18,20…
Longitudinal and transverse form factors are calculated for the transition into the low lying excited T=0 and T=1 states of 6Li in the framework of the resonating group model. All form factors are reproduced simultaneously using three cluster-wavefunctions. Meson exchange currents yield only minor corrections and do not lead to any specific structures at large momentum transfers.
The molecular algebraic model based on three and four alpha clusters is used to describe the inelastic scattering of alpha particles populating low-lying states in $^{12}$C and $^{16}$O. Optical potentials and inelastic formfactors are obtained by folding densities and transition densities obtained within the molecular model. One-step and multi-step processes can be included in the reaction mechanism calculation. In spite of the simplicity of the approach the molecular model with rotations and vibrations provides a reliable description of reactions where $α$-cluster degrees of freedom are invo…
Cross-section and analyzing power data from 197 MeV $(p,p')$ scattering and longitudinal and transverse form factors for electron scattering to low lying states in $^{10}$B have been analyzed as tests of the structure of the nuclear states when they are described using a no-core $(0+2)\hbarω$ shell model. While the results obtained from the shell model clearly show the need of other elements, three-body forces in particular, to explain the observed spectrum, the reasonable level of agreement obtained in the analyses of the scattering data suggest that the wavefunctions from our shell model usi…
Electron scattering is a tool that can provide relatively clean view of the nuclear structure in both ground and excited states, as it depends on the well-known electromagnetic interaction. But since the common expressions for its cross section were derived with certain assumptions, in this paper we describe several nontrivial steps necessary for a proper theoretical calculation within the current density-functional framework, namely with Skyrme QRPA for axial nuclei, with aim to enable comparison of the theoretically predicted low-lying $1^-$ toroidal modes with future (e,e') experiments.
Dirac phenomenological coupled channel analyses are performed using an optical potential model for the high-lying excited vibrational states at 800 MeV unpolarized proton inelastic scatterings from $^{22}$Ne nucleus. Lorentz-covariant scalar and time-like vector potentials are used as direct optical potentials and the first-order vibrational collective model is used for the transition optical potentials to describe the high-lying excited vibrational collective states. The complicated Dirac coupled channel equations are solved phenomenologically using a sequential iteration method by varying th…
Dirac coupled channel calculations are performed phenomenologically for the high-lying excited states that belong to the 2$^+$ gamma vibrational band at the 800-MeV polarized proton inelastic scatterings from the s-d shell nuclei, $^{24}$Mg and $^{26}$Mg. Optical potential model is used and scalar and time-like vector potentials are considered as direct potentials. First-order vibrational collective models are used to obtain the transition optical potentials in order to accommodate the high-lying excited vibrational collective states. The complicated Dirac coupled channel equations are solved …
The low-lying states of the $^{9}$Li nucleus are investigated with a unified framework of microscopic structure and reaction models. In the structure model, the wave function is fully antisymmetrized and the $^{9}$Li nucleus is described as an $α$ + $t$ + $n$ + $n$ four-body system, and low-lying 1/2$^{-}$, 3/2$^{-}$, 5/2$^{-}$, and 7/2$^{-}$ states are obtained by the stochastic multi-configuration mixing method. Using these wave functions, the quasi-elastic cross section at $E/A$ = 60 MeV and the elastic and inelastic cross sections at $E/A$ = 50 MeV on the $^{12}$C target are calculated in …
We systematically derive a length scale characterizing the size of a low-lying, beta stable nucleus from empirical data for the diffraction peak angle in the proton inelastic differential cross section of incident energy of \sim 1 GeV. In doing so, we assume that the target nucleus in the ground state is a completely absorptive "black" sphere of radius a. The cross section πa^2, where a is determined in such a way as to reproduce the empirical proton diffraction peak angle in the elastic channel, is known to agree with empirical total reaction cross sections for incident protons to within erro…
Inelastic neutron scattering was used to study the low-lying nuclear structure of $^{132}$Xe. A comprehensive level scheme is presented, as well as new level lifetimes, multipole mixing ratios, branching ratios, and transition probabilities. Comparisons of these data as well as previously measured $E2$ strengths and $g$ factors are made with new shell-model calculations for $^{132,134,136}$Xe to explore the emergence of collectivity in the Xe isotopes with $N$ < 82 near the closed shell.
Excitation of the anomalously low lying nuclear isomer $^{229m}$Th$(3/2^+, 8.28 \pm 0.17$ eV) in the process of inelastic electron scattering is studied theoretically in the framework of the perturbation theory for the quantum electrodynamics. The calculated cross sections of $^{229m}$Th by the extremely low energy electrons in the range 9 eV--12 eV for the Th atom and Th$^{1+,4+}$ ions lie in the range $10^{-25}$--$10^{-26}$ cm$^2$. Being so large, the cross section opens up new possibilities for the effective non-resonant excitation of $^{229m}$Th in experiments with an electron beam or elec…
In the frame of the algebraic Riemann Rotational Model one computes the longitudinal, transverse and toroidal multipoles corresponding to the excitations of low-lying levels in the ground state band of several even-even nuclei by inelastic electron scattering (e,e'). Related to these transitions a new quantity, which accounts for the deviations from the Siegert theorem, is introduced. The intimate connection between the nuclear vorticity and the dynamic toroidal quadrupole moment is underlined. Inelastic differential cross-sections calculated at backscattering angles shows the dominancy of tor…
We study fusion reactions of $^{16}$O with $^{154}$Sm, $^{186}$W and $^{238}$U at sub-barrier energies by a coupled-channels framework. We focus especially on the effects of $β_{6}$ deformation and low-lying vibrational excitations of the target nucleus. It is shown that the inclusion of $β_{6}$ deformation leads to a considerable improvement of the fit to the experimental data for all of these reactions. For the $^{154}$Sm and $^{238}$U targets, the octupole vibration significantly affects the fusion barrier distribution. The effect of $β$ band is negligible in all the three reactions, while …
The description of the inelastic proton -- nucleus cross section at very high energies is still an open question. The current theoretical uncertainty has direct impact on the predictions of the cosmic ray and neutrino physics observables. In this paper we consider different models for the treatment of $σ_{inel}^{pA}$, compare its predictions at ultrahigh cosmic ray energies and estimate the prompt neutrino flux at the neutrino energies that have been probed by the IceCube Observatory. We demonstrate that depending of the model used to describe $σ_{inel}^{pA}$, the predictions for the prompt ne…
The energetic beam of (spin and isospin zero) $α$-particles remains a very efficient probe for the nuclear isoscalar giant resonances. In the present work, a microscopic folding model study of the isoscalar giant resonances in $^{208}$Pb induced by inelastic \aPb scattering at $E_{\rm lab}=240$ and 386 MeV has been performed using the (complex) CDM3Y6 interaction and nuclear transition densities given by both the collective model and Random Phase Approximation (RPA) approach. The fractions of energy weighted sum rule around the main peaks of the isoscalar monopole, dipole and quadrupole giant …
We consider the potential benefits of searching for supersymmetric dark-matter through its inelastic excitation, via the "scalar current", of low-lying collective nuclear states in a detector. If such states live long enough so that the gamma radiation from their decay can be separated from the signal due to nuclear recoil, then background can be dramatically reduced. We show how the kinematics of neutralino-nucleus scattering is modified when the nucleus is excited and derive expressions for the form factors associated with exciting collective states. We apply these results to two specific ca…
Unpolarized 800 MeV proton inelastic scatterings from an s-d shell nucleus $^{22}$Ne are analyzed using phenomenological optical potentials in the Dirac coupled channel formalism. The first-order rotational collective model is used to obtain the transition optical potentials for the low lying excited collective states that belong to the ground state rotational band of the nucleus. The optical potential parameters of Woods-Saxon shape and the deformation parameters of the excited states are varied phenomenologically using the sequential iteration method to reproduce the experimental differentia…
Neutrinos with energy of order 10~MeV, such as from pion decay-at-rest sources, are an invaluable tool for studying low-energy neutrino interactions with nuclei -- previously enabling the first measurement of coherent elastic neutrino-nucleus scattering. Beyond elastic scattering, neutrinos and dark matter in this energy range also excite nuclei to its low-lying nuclear states, providing an additional physics channel. Here, we consider neutral-current inelastic neutrino-nucleus and dark matter(DM)-nucleus scattering off $^{40}$Ar, $^{133}$Cs, and $^{127}$I nuclei that are relevant to a number …
The $^9$C nucleus and related capture reaction, ${^8\mathrm{B}}(p,γ){^9\mathrm{C}}$, have been intensively studied with an astrophysical interest. Due to the weakly-bound nature of $^9$C, its structure is likely to be described as the three-body (${^7\mathrm{Be}}+p+p$). Its continuum structure is also important to describe reaction processes of $^9$C, with which the reaction rate of the ${^8\mathrm{B}}(p,γ){^9\mathrm{C}}$ process have been extracted indirectly. We perform three-body calculations on $^9$C and discuss properties of its ground and low-lying states via breakup reactions. We employ…
Direct dark matter detection focuses on elastic scattering of dark matter particles off nuclei. In this study, we explore inelastic scattering where the nucleus is excited to a low-lying state of 10-100 keV, with subsequent prompt de-excitation. We calculate the inelastic structure factors for the odd-mass xenon isotopes based on state-of-the-art large-scale shell-model calculations with chiral effective field theory WIMP-nucleon currents. For these cases, we find that the inelastic channel is comparable to or can dominate the elastic channel for momentum transfers around 150 MeV. We calculate…
In the QCD evolution of transverse momentum dependent parton distribution and fragmentation functions, the Collins-Soper evolution kernel includes both a perturbative short-distance contribution as well as a large-distance non-perturbative, but strongly universal, contribution. In the past, global fits, based mainly on larger $Q$ Drell-Yan-like processes, have found substantial contributions from non-perturbative regions in the Collins-Soper evolution kernel. In this article, we investigate semi-inclusive deep inelastic scattering measurements in the region of relatively small $Q$, of the orde…
Motivation: Detailed experimental knowledge of the level structure of light weakly bound nuclei is necessary to guide the development of new theoretical approaches that combine nuclear structure with reaction dynamics. Purpose: The resonant structure of 8B is studied in this work. Method: Excitation functions for elastic and inelastic 7Be+p scattering were measured using a 7Be rare isotope beam. Excitation energies ranging between 1.6 and 3.4 MeV were investigated. An R-matrix analysis of the excitation functions was performed. Results: New low-lying resonances at 1.9, 2.5, and 3.3 MeV in 8B a…
