Background: Although self-consistent multiconfiguration methods have been used for decades to address the description of atomic and molecular many-body systems, only a few trials have been made in the context of nuclear structure.

Purpose: This work aims at the development of such an approach to describe in a unified way various types of correlations in nuclei in a self-consistent manner where the mean-field is improved as correlations are introduced. The goal is to reconcile the usually set-apart shell-model and self-consistent mean-field methods.

Method: This approach is referred to as “variational multiparticle-multihole configuration mixing method.” It is based on a double variational principle which yields a set of two coupled equations that determine at the same time the expansion coefficients of the many-body wave function and the single-particle states. The solution of this problem is obtained by building a doubly iterative numerical algorithm.

Results: The formalism is derived and discussed in a general context, starting from a three-body Hamiltonian. Links to existing many-body techniques such as the formalism of Green's functions are established. First applications are done using the two-body D1S Gogny effective force. The numerical procedure is tested on the ${}^{12}\mathrm{C}$ nucleus to study the convergence features of the algorithm in different contexts. Ground-state properties as well as single-particle quantities are analyzed, and the description of the first $2^{+}$ state is examined.

Conclusions: The self-consistent multiparticle-multihole configuration mixing method is fully applied for the first time to the description of a test nucleus. This study makes it possible to validate our numerical algorithm and leads to encouraging results. To test the method further, we will realize in the second article of this series a systematic description of more nuclei and observables obtained by applying the newly developed numerical procedure with the same Gogny force. As raised in the present work, applications of the variational multiparticle-multihole configuration mixing method will, however, ultimately require the use of an extended and more constrained Gogny force.

The emission of $\gamma$ rays from neutron-bound and neutron-unbound states in ${}^{95}\mathrm{Mo}$, populated in the ${}^{94}\mathrm{Mo}(d,p)$ reaction, has been investigated. Charged particles and $\gamma$ radiation were detected with arrays of annular silicon and Clover-type high-purity Germanium detectors, respectively. Utilizing $p-\gamma$ and $p-\gamma -\gamma$ coincidences, the ${}^{95}\mathrm{Mo}$ level scheme was greatly enhanced with 102 new transitions and 43 new states. It agrees well with shell model calculations for excitation energies below $\approx 2$ MeV. From $p-\gamma$ coincidence data, a new method for the determination of spins of discrete levels is proposed. The method exploits the suppression of high-angular momentum neutron emission from levels with high spins populated in the $(d,p)$ reaction above the neutron separation energy. Spins for almost all ${}^{95}\mathrm{Mo}$ levels below 2 MeV (and for a few levels above) have been determined with this method.

The moment of inertia for nuclear collective rotations is derived within a semiclassical approach based on the Inglis cranking and Strutinsky shell-correction methods, improved by surface corrections within the nonperturbative periodic-orbit theory. For adiabatic (statistical-equilibrium) rotations it was approximated by the generalized rigid-body moment of inertia accounting for the shell corrections of the particle density. An improved phase-space trace formula allows to express the shell components of the moment of inertia more accurately in terms of the free-energy shell correction. Evaluating their ratio within the extended Thomas-Fermi effective-surface approximation, one finds good agreement with the quantum calculations.

We investigate even-even two-proton Borromean systems at prominent intermediate heavy waiting points for the rapid proton capture process. The most likely single-particle levels are used to calculate three-body energy and structure as a function of proton-core resonance energy. We establish a linear dependence between two- and three-body energies with the same slope, but the absolute value slightly dependent on partial wave structure. Using these relations we estimate low-lying excited states in the isotones following the critical waiting points. The capture rate for producing a Borromean bound state is described based on a full three-body calculation for temperatures about $0.1–10$ GK. In addition, a simple rate expression, depending only on a single resonance state, is found to comply with the three-body calculation for temperatures between $0.1$ and 4 GK. The rate calculations are valid for both direct and sequential capture paths. As a result the relevant path of the radiative capture reactions can be determined. We present results for $E1$ and $E2$ photon emission, and discuss occurrence preferences in general as well as relative sizes of these most likely processes. Finally, we present a method for estimating proton capture rates in the region around the critical waiting points.

The level density and $\gamma$-ray strength function ($\gamma \mathrm{SF}$) of ${}^{243}\text{Pu}$ have been measured in the quasicontinuum using the Oslo method. Excited states in ${}^{243}\text{Pu}$ were populated using the ${}^{242}\text{Pu}(d,p)$ reaction. The level density closely follows the constant-temperature level density formula for excitation energies above the pairing gap. The $\gamma \mathrm{SF}$ displays a double-humped resonance at low energy as also seen in previous investigations of actinide isotopes. The structure is interpreted as the scissors resonance and has a centroid of ${\omega }_{\mathrm{SR}}=2.42\left(5\right)$ MeV and a total strength of $B_{\mathrm{SR}}=10.1\left(15\right){\mu }_N^2$, which is in excellent agreement with sum-rule estimates. The measured level density and $\gamma \mathrm{SF}$ were used to calculate the ${}^{242}\text{Pu}(n,\gamma )$ cross section in a neutron energy range for which there were previously no measured data.

Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus and the daughter products.

Purpose: We explore the ability of dynamic mean-field methods to describe induced fission processes, using quadrupole boosts in the nuclide ${}^{240}\mathrm{Pu}$ as an example.

Methods: Following upon the work presented in Goddard et al. [Phys. Rev. C 92, 054610 (2015)], quadrupole-constrained Hartree-Fock calculations are used to create a potential energy surface. An isomeric state and a state beyond the second barrier peak are excited by means of instantaneous as well as temporally extended gauge boosts with quadrupole shapes. The subsequent deexcitation is studied in a time-dependent Hartree-Fock simulation, with emphasis on fissioned final states. The corresponding fission fragment mass numbers are studied.

Results: In general, the energy deposited by the quadrupole boost is quickly absorbed by the nucleus. In instantaneous boosts, this leads to fast shape rearrangements and violent dynamics that can ultimately lead to fission. This is a qualitatively different process than the deformation-induced fission. Boosts induced within a finite time window excite the system in a relatively gentler way and do induce fission but with a smaller energy deposition.

Conclusions: The fission products obtained using boost-induced fission in time-dependent Hartree-Fock are more asymmetric than the fragments obtained in deformation-induced fission or the corresponding adiabatic approaches.

We report the measurement of one-neutron stripping to excited-state cross sections from the weakly bound projectile ${}^6\mathrm{Li}$ to the ${}^{96}\mathrm{Zr}$ target at near-barrier energies by the online $\gamma$-ray spectroscopy method. Transitions of the ${}^{97}\mathrm{Zr}$ nucleus were clearly identified by $\gamma \text{−}\gamma$ coincidences. This cross section was found to be much smaller than the previously reported complete-fusion cross section for this system at energies above the barrier, whereas it becomes of the same magnitude around the Coulomb-barrier energy. No evidence of two-neutron transfer was found. We also performed coupled reaction channel calculations for the one-neutron stripping process. The calculation results are discussed.

We compute predictions for various low-transverse-momentum bulk observables in $\sqrt{s_{NN}}=5.023$ TeV Pb+Pb collisions at the CERN Large Hadron Collider (LHC) from the event-by-event next-to-leading-order perturbative-QCD + saturation + viscous hydrodynamics (“EKRT”) model. In particular, we consider the centrality dependence of charged hadron multiplicity, flow coefficients of the azimuth-angle asymmetries, and correlations of event-plane angles. The centrality dependencies of the studied observables are predicted to be very similar to those at 2.76 TeV, and the magnitudes of the flow coefficients and event-plane angle correlations are predicted to be close to those at 2.76 TeV. The flow coefficients may, however, offer slightly more discriminating power on the temperature dependence of QCD matter viscosity than the 2.76 TeV measurements. Our prediction for the multiplicity in the 0–5 % centrality class, obtained using the two temperature-dependent shear-viscosity-to-entropy ratios that give the best overall fit to BNL Relativistic Heavy Ion Collider (RHIC) and LHC data is $d{N}_{\mathrm{ch}}/d\eta {|}_{\left|\eta \right|\le 0.5}=1876\cdots 2046$. We also predict a power-law increase from 200 GeV Au+Au collisions at RHIC to 2.76 and 5.023 TeV Pb+Pb collisions at the LHC, $d{N}_{\mathrm{ch}}/d\eta {|}_{\left|\eta \right|\le 0.5}\propto s^{0.164\cdots 0.174}$.

Precisely measured electron-proton elastic scattering cross sections [Phys. Rev. Lett. 105, 242001 (2010)] are reanalyzed to evaluate their strength for determining the rms charge radius ($R_{\mathrm{E}}$) of the proton. More than half of the cross sections at lowest $Q^2$ are fit using two single-parameter form-factor models, with the first based on a dipole parametrization, and the second on a linear fit to a conformal-mapping variable. These low-$Q^2$ fits extrapolate the slope of the form factor to $Q^2=0$ and determine $R_{\mathrm{E}}$ values of approximately 0.84 and 0.89 fm, respectively. Fits spanning all $Q^2$, in which the single constants are replaced with cubic splines at larger $Q^2$, lead to similar results for $R_{\mathrm{E}}$. We conclude that the scattering data are consistent with $R_{\mathrm{E}}$ ranging from at least 0.84 to 0.89 fm, and therefore is consistent with both of the discrepant determinations of $R_{\mathrm{E}}$ made using muonic and electronic hydrogen-atom spectroscopy.

The clustering of $\alpha$ particles in atomic nuclei results in the self-organization of various geometrical arrangements at the femtometer scale. The one-dimensional alignment of multiple $\alpha$ particles is known as linear-chain structure, evidence of which has been highly elusive. We show via resonant elastic and inelastic $\alpha$ scattering of a radioactive ${}^{10}\mathrm{Be}$ beam that excited states in the neutron-rich nucleus ${}^{14}\mathrm{C}$ agree with recent predictions of linear-chain structure based on an antisymmetrized molecular dynamics model.

We have studied the ground-state properties (binding energy and charge radius) using relativistic mean field formalism (RMF) for Mg isotopes from the valley of stability to the drip-line region. The RMF densities have been analyzed in the context of reaction dynamics. The results for ${}^{24-40}\mathrm{Mg}+{}^{12}\mathrm{C}$ reactions at projectile energy of 240 MeV/nucleon are calculated using the Glauber model with the conjunction of densities from relativistic mean field formalism and compared with experimental data. We found nice agreement of estimated values of the reaction cross sections with the data values, except for the ${}^{37}\mathrm{Mg}$ isotope. In view of this, the halo status of ${}^{37}\mathrm{Mg}$ is examined through a higher magnitude of rms radius, one neutron removal cross section, and a small value of longitudinal momentum distribution. Finally, an effort is made to explore the structure of ${}^{37}\mathrm{Mg}$ halo candidate using Glauber many-body formalism.

The density and isospin dependencies of nonrelativistic nucleon effective mass $\left(m_N^{*}\right)$ are studied, which is a measure of the nonlocality of the single particle (s.p.) potential. It can be decoupled as the so-called $k$ mass ($m_k^{*}$, i.e., the nonlocality in space) and $E$ mass ($m_E^{*}$, i.e., the nonlocality in time). Both $k$ mass and $E$ mass are determined and compared by using the latest versions of the nonrelativistic Brueckner-Hartree-Fock (BHF) model and the relativistic Hartree-Fock (RHF) model. The latter is achieved based on the corresponding Schrödinger equivalent s.p. potential in a relativistic framework. We demonstrate the origins of different effective masses and discuss also their neutron-proton splitting in the asymmetric matter in different models. We find that the neutron-proton splittings of both the $k$ mass and the $E$ mass have the same asymmetry dependencies at the densities considered; namely, $m_{k,n}^{*}>m_{k,p}^{*}$ and $m_{E,p}^{*}>m_{E,n}^{*}$. However, the resulting splittings of nucleon effective masses could have different asymmetry dependencies in these two models because they could be dominated either by the $k$ mass (then we have $m_n^{*}>m_p^{*}$ in the BHF model), or by the $E$ mass (then we have $m_p^{*}>m_n^{*}$ in the RHF model). The isospin splitting in the BHF model is more consistent with the recent analysis from the nucleon-nucleus-scattering data, while the small $E$ mass $m_E^{*}$ in the RHF case as a result of the missing ladder summation finally leads to an opposite splitting behavior.

High-resolution laser spectroscopy was performed on ${}^{206}\mathrm{Fr}$ with the collinear resonance ionization spectroscopy (CRIS) experiment at CERN-ISOLDE. The hyperfine structure and isotope shift of the ground, first isomeric and second isomeric states were measured. The hyperfine components were unambiguously assigned to each nuclear state by means of laser-assisted nuclear decay spectroscopy. The branching ratios in the $\alpha$ decay of ${}^{206}\mathrm{Fr}$ and ${}^{202}\mathrm{At}$ were also measured for the first time with isomerically purified beams. The extracted hindrance factors allow determination of the spin of the ground, first isomeric, and second isomeric states in ${}^{202}\mathrm{At}$ and ${}^{198}\mathrm{Bi}$.

Lifetimes of yrast and nonyrast states of ${}^{102}\mathrm{Pd}$ populated via the ${}^{92}\mathrm{Zr}$(${}^{13}\mathrm{C}$, $3n$) reaction are measured by means of the recoil distance Doppler-shift technique with a Cologne plunger coupled to a GASP spectrometer. The event-by-event data accumulated at 24 plunger distances in the range of 0.1 $\mu \mathrm{m}$ to 9 mm are analyzed using the differential decay curve method. The resulting $B\left(E2\right)$ values of the $\gamma$ transitions depopulating yrast-band members up to the $I^{\pi }=8^{+}$ state are found to deviate significantly from the corresponding predictions of the E(5) critical-point symmetry.

It is well known that short-range nucleon-nucleon correlations (SRC) from the tensor components and/or the repulsive core of nuclear forces lead to a high- (low-)momentum tail (depletion) in the single-nucleon momentum distribution above (below) the nucleon Fermi surface in cold nucleonic matter. Significant progress was made recently in constraining the isospin-dependent parameters characterizing the SRC-modified single-nucleon momentum distribution in neutron-rich nucleonic matter using both experimental data and microscopic model calculations. Using the constrained single-nucleon momentum distribution in a nonlinear relativistic mean field (RMF) model, we study the equation of state (EOS) of asymmetric nucleonic matter (ANM), especially the density dependence of nuclear symmetry energy $E_{\text{sym}}\left(\rho \right)$. First, as a test of the model, the average nucleon kinetic energy extracted recently from electron-nucleus scattering experiments using a neutron-proton dominance model is well reproduced by the RMF model incorporating effects of the SRC-induced high-momentum nucleons, while it is significantly under predicted by the RMF model using a step function for the single-nucleon momentum distribution as in free Fermi gas (FFG) models. Second, consistent with earlier findings within nonrelativistic models, the kinetic symmetry energy of quasinucleons is found to be $E_{\text{sym}}^{\text{kin}}\left({\rho }_0\right)=-16.94\pm 13.66\text{MeV}$ which is dramatically different from the prediction of $E_{\text{sym}}^{\text{kin}}\left({\rho }_0\right)\approx 12.5$ MeV by FFG models at nuclear matter saturation density ${\rho }_0=0.16{\text{fm}}^{-3}$. Third, comparing the RMF calculations with and without the high-momentum nucleons using two sets of model parameters both reproducing identically all empirical constraints on the EOS of symmetric nuclear matter (SNM) and the symmetry energy of ANM at ${\rho }_0$, the SRC-modified single-nucleon momentum distribution is found to make the $E_{\text{sym}}\left(\rho \right)$ more concave around ${\rho }_0$ by softening it significantly at both subsaturation and suprasaturation densities, leading to an isospin-dependent incompressibility of ANM in better agreement with existing experimental data. Fourth, the maximum mass of neutron stars is enhanced by the increased kinetic pressure from high-momentum nucleons at suprasaturation densities in SNM.

We study the production of hadronic resonances and their interaction in the partonic and hadronic medium using the EPOS3 model, which employs the UrQMD model for the description of the hadronic phase. We investigate the centrality dependence of the yields and momentum distributions for various resonances [$\rho {\left(770\right)}^0$, $K^{*}{\left(892\right)}^0$, $\varphi \left(1020\right)$, $\mathrm{\Delta }{\left(1232\right)}^{++}$, $\mathrm{\Sigma }{\left(1385\right)}^{\pm }$, $\mathrm{\Lambda }\left(1520\right)$, $\mathrm{\Xi }{\left(1530\right)}^0$ and their antiparticles] in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. The predictions for $K^{*}{\left(892\right)}^0$ and $\varphi \left(1020\right)$ will be compared with the experimental data from the ALICE collaboration. The observed signal suppression of the $K^{*}{\left(892\right)}^0$ with increasing centrality will be discussed with respect to the resonance interaction in the hadronic medium. The mean transverse momentum and other particle ratios such as $\varphi \left(1020\right)/p$ and $(\mathrm{\Omega }+\overline{\mathrm{\Omega }})/\varphi \left(1020\right)$ will be discussed with respect to additional contributions from the hadronic medium interactions.

We obtain the critical magnetic field required for complete destruction of $S$-wave pairing in neutron matter, thereby setting limits on the pairing and superfluidity of neutrons in the crust and outer core of magnetars. We find that for fields $B\ge {10}^{17}$ G the neutron fluid is nonsuperfluid—if weaker spin 1 superfluidity does not intervene—a result with profound consequences for the thermal, rotational, and oscillatory behavior of magnetars. Because the dineutron is not bound in vacuum, cold dilute neutron matter cannot exhibit a proper BCS-BEC crossover. Nevertheless, owing to the strongly resonant behavior of the $nn$ interaction at low densities, neutron matter shows a precursor of the BEC state, as manifested in Cooper-pair correlation lengths being comparable to the interparticle distance. We make a systematic quantitative study of this type of BCS-BEC crossover in the presence of neutron fluid spin polarization induced by an ultrastrong magnetic field. We evaluate the Cooper-pair wave function, quasiparticle occupation numbers, and quasiparticle spectra for densities and temperatures spanning the BCS-BEC crossover region. The phase diagram of spin-polarized neutron matter is constructed and explored at different polarizations.

A microscopic calculation of $\alpha$-cluster preformation probability and $\alpha$-decay width in the typical $\alpha$ emitter ${}^{212}\mathrm{Po}$ is presented. Results are obtained by improving a recent approach to describe $\alpha$ preformation in ${}^{212}\mathrm{Po}$ [Phys. Rev. C 90, 034304 (2014)] implementing four-nucleon correlations (quartetting). Using the actually measured density distribution of the ${}^{208}\mathrm{Pb}$ core, the calculated $\alpha$-decay width of ${}^{212}\mathrm{Po}$ agrees fairly well with the measured one.

Shape coexistence between the strongly deformed ground state and the weakly deformed $0_2^{+}$ state in ${}^{98}\mathrm{Sr}$ has been a major topic of interest due to the energy difference of 215 keV, which is the smallest in all even-even nuclei. The electric monopole transition strength ${\rho }^2\left(E0\right)$ is an important quantity that can relate the deformation difference and the shape mixing between the two $0^{+}$ states, which are admixtures of the vibrational (S) and the rotational (D) states in a simple mixing model. In a $\beta$-decay spectroscopy experiment, the experimental ${\rho }^2\left(E0\right)$ was measured. A value of 0.053(5) is consistent with the previous measurement and was combined with known electric quadrupole transition strengths $B\left(E2\right)$ in calculations of a two-state mixing model. Based on a systematic study on neighboring Kr, Zr, and Mo isotopes, the mixing of the $0^{+}$ and $2^{+}$ states in ${}^{98}\mathrm{Sr}$ was determined to be 8.6% and 1.3%, respectively, corresponding to deformation parameters ${\beta }_{\text{D}}=0.38\left(1\right)$ and ${\beta }_{\text{S}}=-0.23\left(2\right)$. These parameters reproduce experimental transition strengths well except for the $4_1^{+}\to 2_1^{+}$ transition, which suggests a smaller D-band deformation for $J\ge 4$.