Incomplete fusion processes and estimation of strength of incomplete fusion in heavy ion induced nuclear reactions have been explored for several combinations of projectile-target nuclei. Dynamics of these reactions is explained using an optical model. Parameters of the optical model affect the shape and depth of nuclear potential and hence influence the theoretical predictions. For heavy ion induced reactions, the optical model potential parameters are not unique and different sets of these parameters may be used for different ranges of mass number $A$ and incident energy $E$. To explore the effect of optical model potential parameters, a comparative study of available experimental data for excitation functions of four systems, ${}^{16}\mathrm{O}+{}^{181}\mathrm{Ta}, {}^{12}\mathrm{C}+{}^{165}\mathrm{Ho}, {}^{14}\mathrm{N}+{}^{163}\mathrm{Dy}$, and ${}^{16}\mathrm{O}+{}^{74}\mathrm{Ge}$, with corresponding theoretically predicted excitation functions, made by PACE4 using different sets of optical model potential parameters, has been done. It has been observed that a single set of optical model potential parameters is not adequate for all the systems. The variations in these parameters change the theoretical cross-section predictions for various channels considerably, which in turn, change the correspondingly estimated fraction of incomplete fusion $\left(F_{\mathrm{ICF}}\right)$. The effect of deformation of target nuclei on fractional incomplete fusion has also been investigated for the above mentioned systems. $F_{\mathrm{ICF}}$ has been plotted as a function of deformation parameter $\left({\beta }_2\right)$ of the target nuclei and it is found to increase as the deformation parameter of the corresponding target nuclei increases on either side of the intrinsic spherical symmetry.

In order to study incomplete fusion (ICF) reaction dynamics, the present work manifests the role of a non-$\alpha$-cluster ${}^{14}\mathrm{N}$ projectile on ${}^{181}\mathrm{Ta}$ target at energies $\approx \mathrm{4–7}$ MeV/nucleon using the offline $\gamma$-ray spectroscopy. The excitation functions for 15 reaction residues populated in ${}^{14}\mathrm{N}+{}^{181}\mathrm{Ta}$ system have been measured and analyzed within the framework of statistical model code PACE4. The experimentally measured excitation functions of evaporation residues populated via xn/pxn channels are found to be well reproduced by the predictions of code PACE4, which confirms their production solely via complete fusion process. However, an enhancement in the measured excitation function as compared to PACE4 calculations, particularly in tail portion of ${}^{192}\mathrm{Hg}$ residue ($3n$ channel) has been observed indicating the presence of precompound emission. A significant contribution from precursor decay in pxn channels has also been observed. An enhancement in the measured excitation functions for $\alpha$-emitting channels as compared to the PACE4 predictions has been observed and attributed to the incomplete fusion process. Further, the contribution from incomplete fusion process in the ${}^{14}\mathrm{N}+{}^{181}\mathrm{Ta}$ system has also been deduced in terms of strength function ($F_{\mathrm{ICF}}$). The results have been discussed in terms of the parameters which influence the dynamics of ICF process. The $F_{\mathrm{ICF}}$ is found to depend strongly on projectile energies, the product of projectile and target charges, and $\alpha -Q$ value of the projectile.

We develop a flexible, relativistically covariant parametrization of the dense nuclear matter equation of state suited for inclusion in computationally demanding hadronic transport simulations. Within an implementation in the hadronic transport code smash, we show that effects due to bulk thermodynamic behavior are reproduced in dynamic hadronic systems, demonstrating that hadronic transport can be used to study critical behavior in dense nuclear matter, both at and away from equilibrium. We also show that two-particle correlations calculated from hadronic transport simulation data follow theoretical expectations based on the second-order cumulant ratio, and constitute a clear signature of the crossover region above the critical point.

We report on a study of the Gamow-Teller matrix element contributing to ${}^6\mathrm{He}\beta$ decay with similarity renormalization group (SRG) versions of momentum- and configuration-space two-nucleon interactions. These interactions are derived from two different formulations of chiral effective field theory ($\chi \mathrm{EFT})$—without and with the explicit inclusion of $\mathrm{\Delta }$ isobars. We consider evolution parameters ${\mathrm{\Lambda }}_{\mathrm{SRG}}$ in the range between 1.2 and 2.0 ${\mathrm{fm}}^{-1}$ and, for the $\mathrm{\Delta }$-less case, also the unevolved (bare) interaction. The axial current contains one- and two-body terms, consistently derived at tree level (no loops) in the two distinct $\chi \mathrm{EFT}$ formulations we have adopted here. The ${}^6\mathrm{He}$ and ${}^6\mathrm{Li}$ ground-state wave functions are obtained from hyperspherical-harmonics (HH) solutions of the nuclear many-body problem. In $A=6$ systems, the HH method is limited at present to treat only two-body interactions and non-SRG evolved currents. Our results exhibit a significant dependence on ${\mathrm{\Lambda }}_{\text{SRG}}$ of the contributions associated with two-body currents, suggesting that a consistent SRG-evolution of these is needed in order to obtain reliable estimates. We also show that the contributions from one-pion-exchange currents depend strongly on the model (chiral) interactions and on the momentum- or configuration-space cutoffs used to regularize them. These results might prove helpful in clarifying the origin of the sign difference recently found in no-core-shell-model and quantum Monte Carlo calculations of the ${}^6\mathrm{He}$ Gamow-Teller matrix element.

A systematic analysis of the experimental cross-section data in odd mass number $\left(A\right)$ and odd atomic number $\left(Z\right)$ nuclei is reported to reveal a novel mass-energy systematics for the pre-compound emission of fast neutrons in $\alpha$-induced reactions at low energies. The experimental excitation functions have been analyzed within the framework of statistical model predictions to get information regarding pre-compound emission. The present analysis establishes for first time an interesting systematics, emphasizing that accessible excitation energy on peripheral nucleons of the systems is an exponential function of atomic mass number ($A$) of target nuclei. One of the most important features of this systematics is to provide a precise estimation of the pre-compound contribution for any nuclei, except closed-shell ones, over a wide range of mass number $63\le A\le 109$ in the nuclear landscape. New results of the present analysis emphasize an additional subtle interconnection between the structure of nuclei and the nuclear reaction mechanism of the pre-compound emission process at low energies, where the compound nucleus process is more likely to be dominant.

Recent experiments have succeeded in isolating processes for which short-range correlation (SRC) physics is dominant and well accounted for by SRC phenomenology. But an alternative and compelling picture emerges from renormalization group (RG) evolution to low RG resolution. At high RG resolution, SRCs are identified as components in the nuclear wave function with relative pair momenta greater than the Fermi momentum. Scale separation results in wave-function factorization that can be exploited with phenomenologies such as the generalized contact formalism or the low-order correlation operator approximation. Evolution to lower resolution shifts SRC physics from nuclear structure to the reaction operators without changing the measured observables. We show how the features of SRC phenomenology manifested at high RG resolution are cleanly identified at low RG resolution using simple two-body operators and local-density approximations with uncorrelated wave functions, all of which can be systematically generalized. We verify that the experimental consequences to date follow directly at low resolution from well-established properties of nucleon-nucleon interactions such as the tensor force. Thus the RG reconciles the contrasting pictures of the same experiment and shows how to get correct results using wave functions without SRC components. Our demonstration has implications for the analysis of knockout reactions for which SRC physics is not cleanly isolated.

We study the thermodynamic properties of a relativistic magnetized neutral vector boson gas at any temperature. By comparing the results with the low temperature and the nonrelativistic descriptions of this gas, we found that the fully relativistic case can be separated in two regimes according to temperature. For low temperatures, magnetic field effects dominate and the system shows a spontaneous magnetization, its pressure splits into two components, and, eventually, a transversal magnetic collapse might occur. In the high temperature region, the gas behavior is led by pair production. The presence of antiparticles preserves the isotropy in the pressure, and increases the magnetization and the total pressure of the system by several orders. Astrophysical implications of those behaviors are discussed.

Background: Light ($30\le Z\le 45$) neutron-rich isotopes are thought to be synthesized in the neutrino-driven ejecta of core-collapse supernovae explosions via the weak $r$ process. Recent nucleosynthesis studies have demonstrated that $(\alpha ,xn)$ reactions play a particularly important role in the production of these isotopes. $\alpha$-nucleus optical model potentials ($\alpha$-OMPs) are used to model this nucleosynthesis scenario.

Purpose: The different $\alpha$-OMP model parameters can affect the calculated cross sections by more than an order of magnitude in the relevant energy regions, which affects the production of light neutron-rich isotopes. Consequently, to constrain the astrophysical conditions characterizing the supernovae ejecta, the uncertainty of the nuclear physics input has to be reduced.

Methods: The cross section of the ${}^{100}\mathrm{Mo}(\alpha ,n){}^{103}\mathrm{Ru}$ reaction was measured by means of the activation method. 0.5 mm thick molybdenum disks were irradiated with $E_{\alpha }$ = 7.0 to $E_{\alpha }$ = 13.0 MeV $\alpha$ beams. Thick target yields and reaction cross sections were determined via $\gamma$-ray spectroscopy.

Results: Cross sections at several energies below the Coulomb barrier were measured, reaching the astrophysically relevant energy region. Large discrepancies between the experimental values and statistical model predictions calculated using the well-known $\alpha$-OMPs were found. The measured cross section data could be excellently described by the Atomki-V2 potential. Therefore, this $\alpha$-OMP was used to derive the astrophysical reaction rates as a function of temperature.

Conclusions: The successful reproduction of the measured cross sections in a wide energy region confirm the reliability of the Atomki-V2 potential. The usage of the new ${}^{100}\mathrm{Mo}(\alpha ,n){}^{103}\mathrm{Ru}$ experimental data along with the Atomki-V2 potential reduces the nuclear uncertainties of the weak $r$-process production yields of nuclei with $36\le Z\le 50$ to a marginal level.

An experimental study on the temperature ($T$) dependence of giant dipole resonance (GDR) width was performed for the medium mass nucleus ${}^{74}\mathrm{Kr}$ in the range of $T\approx 2–2.5$ MeV at an average angular momentum of $26\hslash$ using the ${}^{16}\mathrm{O}+{}^{58}\mathrm{Ni}$ fusion reaction. The emitted high-energy $\gamma$ rays and evaporated neutrons were measured in coincidence with low-energy discrete $\gamma$-ray multiplicities. The GDR parameters, nuclear level density parameter, and nuclear temperature were determined by the statistical model analysis of the high-energy $\gamma$-ray spectra as well as evaporated neutron spectra. The measured GDR width is found to increase monotonically with temperature, in contradiction with the recent observation of the width saturation in ${}^{88}\mathrm{Mo}$. Comparisons of the measured data with predictions of the adiabatic thermal shape fluctuation model and its refined version, the critical temperature included fluctuation model, are presented and discussed.

We present predictions for the neutron matter equation of state, from leading to fourth order of chiral effective field theory, using recently developed, accurate chiral nucleon-nucleon potentials. For the many-body method, we employ the nonperturbative particle-particle ladder approximation, that is, we solve the $G$-matrix equation. We find the impact of subleading three-neutron forces to be mild and attractive. We also show order-by-order predictions for the symmetry energy, and discuss its density dependence in relation to empirical constraints. For the nuclear matter equation of state, in this work we adopt an empirical parametrization with good saturation properties. This is to highlight, specifically, the energy and pressure in neutron matter, particularly when comparing with empirical constraints.

Background: The ${}^{136}\mathrm{Ba}$ isotope is the daughter nucleus in ${}^{136}\mathrm{Xe}\beta \beta$ decay. It also lies in a shape transitional region of the nuclear chart, making it a suitable candidate to test a variety of nuclear models.

Purpose: To obtain spectroscopic information on states in ${}^{136}\mathrm{Ba}$, which will allow a better understanding of its low-lying structure. These data may prove useful to constrain future ${}^{136}\mathrm{Xe}\to {}^{136}\mathrm{Ba}$ neutrinoless $\beta \beta$ decay matrix element calculations.

Methods: A ${}^{138}\mathrm{Ba}(p,t)$ reaction was used to populate states in ${}^{136}\mathrm{Ba}$ up to approximately 4.6 MeV in excitation energy. The tritons were detected using a high-resolution Q3D magnetic spectrograph. A distorted wave Born approximation analysis was performed for the measured triton angular distributions.

Results: 102 excited states in ${}^{136}\mathrm{Ba}$ were observed, out of which 52 are reported for the first time. Definite spin-parity assignments are made for 26 newly observed states, while previously ambiguous assignments for ten other states are resolved. Together with other available data, the results are used to determine level densities in ${}^{136}\mathrm{Ba}$. These were compared with theory predictions, obtained using shell model calculations with Hamiltonians previously used for ${}^{136}\mathrm{Xe}$ neutrinoless $\beta \beta$ decay matrix element evaluations.

Conclusions: The shell model predicted level densities agree reasonably well for the two Hamiltonians. However the results for theory and experiment are found to agree only at lower energies, diverging from one another for the higher lying states, with the discrepancy increasing with energy. This is presumably because of lower production cross sections for a majority of the higher-lying predicted states and the experimental limitations in resolving a large number of nearly degenerate states predicted by the theory.

Excited states in ${}^{55}\mathrm{Cr}$ have been populated via the fusion-evaporation reaction ${}^{48}\mathrm{Ca}({}^{11}\mathrm{B},p3n){}^{55}\mathrm{Cr}$ at a beam energy of 32 MeV. The Cologne plunger device surrounded by a $\gamma$-ray detector array was employed to determine lifetimes with the recoil-distance Doppler-shift method. $\gamma$ rays were observed by one Ge EUROBALL cluster detector and five HPGe detectors. $\gamma \gamma$-coincidence data were analyzed with help from the differential decay-curve method, and precise lifetimes for the first excited states were extracted from the $5/2^{-}\to 3/2^{-}$ and the $9/2^{-}\to 5/2^{-}$ transitions. Reduced transition strengths $B\left(\sigma \lambda \right)$ were determined and compared to shell-model calculations employing four interactions KB3G, FPD6, GXPF1A, and GXPF1Br. The calculations were also performed for the $N=31$ isotonic chain from ${}^{53}\mathrm{Ti}$ to ${}^{61}\mathrm{Zn}$. Inspection of the wave functions as well as particle-plus-rotor model calculations allow for a detailed understanding of the excited states and the reduced transition strength in ${}^{55}\mathrm{Cr}$. The interactions GXPF1A and GXPF1Br reproduce well the experimental findings in ${}^{55}\mathrm{Cr}$ and in other isotones.

Background: Information from differential nuclear-physics experiments and theory is often too uncertain to accurately define nuclear-physics observables such as cross sections or energy spectra. Integral experimental data, representing the applications of these observables, are often more precise but depend simultaneously on too many of them to unambiguously identify issues in the observable with human expert analysis alone.

Purpose: We explore how we can leverage physics knowledge gained from differential experimental data, nuclear theory, integral experiments, and neutron-transport calculations to better understand nuclear-physics observables in the context of the application area represented by integral experiments. We support this task with machine-learning methods to discern trends in a large amount of convoluted data.

Methods: Differential and integral information was used in an analysis augmented by the random forest and the Shapley additive explanations metric. We chose as an application area one that is represented by criticality measurements and pulsed-sphere neutron-leakage spectra.

Results: We show one representative example (${}^{241}\mathrm{Pu}$ fission observables) where the combination of differential and integral information allowed to resolve issues in data representing these observables. As a starting point, the machine learning (ML) algorithms highlighted several observables as leading potentially to bias in simulating integral experiments. Differential information, paired with sensitivity to integral quantities, allowed us then to pinpoint one specific observable (${}^{241}\mathrm{Pu}$ fission cross section) as the main driver of bias. The comparison to integral experiments, on the other hand, allowed us to indicate a likely reliable experiment among several discrepant ones for this observables. In other cases (e.g., ${}^{239}\mathrm{Pu}$ observables), we were not able to resolve the confounding introduced by integral experiments but instead highlighted the need for targeted new experiments and theory developments to better constrain the nuclear-physics space for the application area represented by integral experiments.

Conclusions: We were able to combine information from differential experimental data, nuclear-physics theory, integral experiments, and neutron-transport simulations of the latter experiments with the help of the random forest algorithm and expert judgment. This combination of knowledge allows to improve our description of nuclear-physics observables as applied to a particular application area.

Background: The ${}^9\mathrm{C}$ nucleus and related capture reaction, ${}^8\mathrm{B}(p,\gamma ){}^9\mathrm{C}$, have been intensively studied with an astrophysical interest. Due to the weakly bound nature of ${}^9\mathrm{C}$, 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 ${}^9\mathrm{C}$, with which the reaction rate of the ${}^8\mathrm{B}(p,\gamma ){}^9\mathrm{C}$ process have been extracted indirectly.

Purpose: We preform three-body calculations on ${}^9\mathrm{C}$ and discuss properties of its ground and low-lying states via breakup reactions.

Methods: We employ the three-body model of ${}^9\mathrm{C}$ using the Gaussian-expansion method combined with the complex-scaling method. This model is implemented in the four-body version of the continuum-discretized coupled-channels method, by which breakup reactions of ${}^9\mathrm{C}$ are studied. The intrinsic spin of ${}^7\mathrm{Be}$ is disregarded.

Results: By tuning a three-body interaction in the Hamiltonian of ${}^9\mathrm{C}$, we obtain the low-lying $2^{+}$ state with the resonant energy 0.781 MeV and the decay width 0.137 MeV, which is consistent with the available experimental information and a relatively high-lying second $2^{+}$ wider resonant state. Our calculation predicts also sole $0^{+}$ and three $1^{-}$ resonant states. We discuss the role of these resonances in the elastic breakup cross section of ${}^9\mathrm{C}$ on ${}^{208}\mathrm{Pb}$ at 65 and 160 MeV/nucleon.

Conclusions: The low-lying $2^{+}$ state is probed as a sharp peak of the breakup cross section, while the $1^{-}$ states enhance the cross section around 3 MeV. Our calculations will further support the future and ongoing experimental campaigns for extracting astrophysical information and evaluating the two-proton removal cross sections.

We investigated the development and breaking of the dineutron correlation in ${}^{10}\mathrm{Be}$ by analyzing the elastic and inelastic scatterings with a framework combining the microscopic structure and reaction models. For studying the structure, the ${}^{10}\mathrm{Be}$ nucleus was constructed under the assumption of a four-body ($\alpha +\alpha +n+n$) cluster model. In this paper, we focused on the change in the inner structure for the $0_1^{+}$, $2_1^{+}$, and $2_2^{+}$ states when the strength of the spin-orbit interaction is varied. The inner structure, including various physical quantities such as energy, radius, and transition strength, is drastically influenced by the strength of the spin-orbit interaction. In particular, the development and breaking of the dineutron correlation are governed by the spin-orbit strength. The differences in the inner structure can be manifested by applying the obtained wave functions to elastic and inelastic scatterings with a proton target at $E/A=$ 59.4 and 200 MeV. Although the $0_1^{+}$ and $2_1^{+}$ states are significantly influenced by the spin-orbit strength of the nuclear structure calculation, the elastic and inelastic cross sections are not much affected. On the other hand, the inelastic cross section of the $2_2^{+}$ state depends greatly on the spin-orbit strength of the structure calculation. Thus, we discovered a way to measure the degree of the development of the dineutron cluster structure based on its sensitivity to the inelastic cross section of the $2_2^{+}$ state of ${}^{10}\mathrm{Be}$.

Model uncertainties arising due to suppression of target excitations in the description of deuteron scattering and resulting in a modification of the two-body interactions in a three-body system are investigated for several $(d,p)$ reactions serving as indirect tools for studying the astrophysical $(p,\gamma )$ reactions relevant to $rp$ process. The three-body nature of the deuteron-target potential is treated within the adiabatic distorted-wave approximation (ADWA) which relies on a dominant contribution from the components of the three-body deuteron-target wave function with small $n\text{−}p$ separations. This results in a simple prescription for treating the explicit energy dependence of two-body optical potentials in a three-body system requiring nucleon optical potentials to be evaluated at a shifted energy with respect to the standard value of half the deuteron incident energy. In addition, the ADWA allows for leading-order multiple-scattering effects to be estimated, which leads to a simple renormalization of the adiabatic potential's imaginary part by a factor of two. These effects are assessed using both nonlocal and local optical potential systematics for ${}^{26}\mathrm{Al}$, ${}^{30}\mathrm{P}$, ${}^{34}\mathrm{Cl}$, and ${}^{56}\mathrm{Ni}$ targets at a deuteron incident energy of 12 MeV, which is typical for experiments with radioactive beams in inverse kinematics. The model uncertainties induced by the three-body nature of deuteron-target scattering are found to be within $40\%$ both in the main peak of angular distributions and in total $(d,p)$ cross sections. At higher deuteron energies, around 60 MeV, model uncertainties can reach 100% in the total cross sections. A few examples of application to astrophysically interesting proton resonances in ${}^{27}\mathrm{Si}$ and ${}^{57}\mathrm{Cu}$ obtained using $(d,p)$ reactions and mirror symmetry are given.

Collisional energy loss of a fast particle in a medium is mostly due to the medium polarization by the electromagnetic fields of the particle. A small fraction of energy is carried away by the Cherenkov radiation. In chiral medium there is an additional contribution to the energy loss due to induction of the anomalous current proportional to the magnetic field. It causes the particle to lose energy mostly in the form of the chiral Cherenkov radiation. We employ classical electrodynamics, adequate in a wide range of particle energies, to compute the collisional energy loss by a fast particle in a homogenous chiral plasma and apply the results to quark-gluon plasma and a Weyl semimetal. In the latter case photon spectrum is strongly enhanced in the ultraviolet and x-ray regions which makes it amenable to experimental investigation. Our main observation is that while the collisional energy loss in a nonchiral medium is a slow, at most logarithmic, function of energy $\varepsilon$, the chiral Cherenkov radiation is proportional to ${\varepsilon }^2$ when the recoil is neglected and to $\varepsilon$ when it is taken into account.

This paper presents a method for estimating the pressure variance at the inner edge of a neutron star crust. The obtained results quantify uncertainty in the estimation of pressure at the core-crust interface, implying that they depend on the selected equation of state and the neutron star's mass distribution function. The quality of the transition pressure determination depends on the neutron star's mass, with a significant decrease in accuracy for configurations with masses close to $2\mathrm{M}\odot$. The method used makes it possible to control the theoretical part of the core-crust pressure dispersion in determining the observational quantities.

In the heaviest elements, the instability of atomic nuclei against spontaneous fission leads to ever shorter nuclear half-lives. Upon falling below a timescale of ${10}^{-14}$ s, the border of existence of isotopes is crossed because this is the timescale on which the formation of atomic shells occurs. Analysis of the experimental data on the spontaneous fission half-lives of Rf isotopes in relation with their expected single-particle orbitals hint at a potentially abrupt decrease in half-lives of unknown neutron-deficient Rf isotopes with neutron numbers $<149$, which suggests that the isotopic border is already almost reached. However, this conjecture, which cannot be explained within the current knowledge, was directly related to uncertainty in the experimental data on ${}^{253}\mathrm{Rf}$. We revisited the decay of ${}^{253}\mathrm{Rf}$ and identified two fission activities, which are attributed to decays of the two different states with half-lives of $12.8_{-3.4}^{+7.0}$ ms and ${44}_{-10}^{+17}\mu \mathrm{s}$. In addition, hitherto unknown $\alpha$ decay in ${}^{253}\mathrm{Rf}$, which is followed by $\alpha$ decay of the new isotope ${}^{249}\mathrm{No}$ with a half-life of ${15}_{-7}^{+74}$ ms, was observed. Based on our new data, no abrupt decreases in half-lives of the neutron-deficient No and Rf isotopes are expected, which is in line with theoretical predictions. Fission half-lives of the two different states in ${}^{253}\mathrm{Rf}$ are benchmark cases for the theoretical description of the single-particle orbital influence on the fission process.

A characteristic feature of collective and particle-hole excitations in neutron-rich nuclei is that many of them couple to an unbound neutron in continuum single-particle orbits. The continuum random-phase approximation (cRPA) is a powerful many-body method that describes such excitations, and it provides a scheme to evaluate transition strengths from the ground state. In an attempt to apply cRPA to the radiative neutron-capture reaction, we formulate in the present study an extended scheme of cRPA that describes $\gamma$ transitions from the excited states under consideration, which decay to low-lying excited states as well as the ground state. This is achieved by introducing a nonlocal one-body operator which causes transitions to a low-lying excited state, and describing a density-matrix response against this operator. As a demonstration of this new scheme, we perform numerical calculation for dipole, quadrupole, and octupole excitations in ${}^{140}\mathrm{Sn}$, and discuss $E1$ and $E2$ transitions decaying to low-lying $2_{1,2}^{+}$ and $3_1^{-}$ states. The results point to cases where the branching ratio to the low-lying states is larger than or comparable with that to the ground state. We discuss key roles of collectivity and continuum orbits in both initial and final states.