Nuclear Theory

In this work we present the first beyond closure calculation for the neutrinoless double beta decay ( 0νββ ) of 76 Ge to the first 2 + states of 76 Se. The isospin symmetry restored Quasi-particle random phase approximation (QRPA) method with the CD-Bonn realistic force is adopted for the nuclear structure calculations. We analyze the structure of the two nucleon mechanism nuclear matrix elements, and estimate the uncertainties from the nuclear many-body calculations. We find g pp plays an important role for the calculations and if quenching is included, suppression for the transition matrix element M λ is found. Our results for the transition matrix elements are about one order of magnitude larger than previous projected Hatree-Fock-Boglyubov results with the closure approximation.

The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While various options for the computational basis are available, perturbatively constructed natural orbitals recently have been shown to lead to significant improvement in many-body applications yielding faster model-space convergence and lower sensitivity to basis set parameters in large-scale no-core shell model diagonalizations. This work provides a detailed comparison of single-particle basis sets and a systematic benchmark of natural orbitals in nonperturbative many-body calculations using the in-medium similarity renormalization group approach. As a key outcome we find that the construction of natural orbitals in a large single-particle basis enables for performing the many-body calculation in a reduced space of much lower dimension, thus offering significant computational savings in practice that help extend the reach of ab initio methods towards heavier masses and higher accuracy.

Phase shifts and inelasticity parameters for NN scattering in the partial-wave channels 3 S 1 -- 3 D 1 and 1 S 0 at energies T lab from zero to about 1 GeV are described within a unified NN potential model assuming the formation of isoscalar and isovector dibaryon resonances near the N N ∗ (1440) threshold. Evidence for these near-threshold resonances is actually found in the recent WASA experiments on single- and double-pion production in NN collisions. There, the excitation of the Roper resonance N ∗ (1440) exhibits a structure in the energy dependence of the total cross section, which corresponds to the formation of dibaryon states with I( J π )=0( 1 + ) and 1( 0 + ) at the N N ∗ (1440) threshold. These two S -wave dibaryon resonances may provide a new insight into the nature of the strong NN interaction at low and intermediate energies.

The nature of the Λnn and 3 Λ H ∗ ( J π =3/ 2 + , I=0) states is investigated within a pionless effective field theory at leading order, constrained by the low energy ΛN scattering data and hypernuclear 3- and 4-body data. Bound state solutions are obtained using the stochastic variational method, the continuum region is studied by employing two independent methods - the inverse analytic continuation in the coupling constant method and the complex scaling method. Our calculations yield both the Λnn and 3 Λ H ∗ states unbound. We conclude that the excited state 3 Λ H ∗ is a virtual state and the Λnn pole located close to the three-body threshold in a complex energy plane could convert to a true resonance with Re (E)>0 for some considered ΛN interactions. Finally, the stability of resonance solutions is discussed and limits of the accuracy of performed calculations are assessed.

We study the inclusive strange vector meson K ∗ (892 ) + production in π − A reactions at near-threshold laboratory incident pion momenta of 1.4--2.0 GeV/c within a nuclear spectral function approach. The approach accounts for incoherent primary π − meson--proton π − p→ K ∗ (892 ) + Σ − production processes as well as the influence of the scalar K ∗ (892 ) + --nucleus potential (or the K ∗ (892 ) + in-medium mass shift) on these processes. We calculate the absolute differential and total cross sections for the production of K ∗ (892 ) + mesons off carbon and tungsten nuclei at laboratory angles of 0 ∘ --45 ∘ and at these momenta within five scenarios for the above shift. We show that the K ∗ (892 ) + momentum distributions and their excitation functions (absolute and relative) possess a high sensitivity to changes in the in-medium K ∗ (892 ) + mass shift in the low-momentum region of 0.1--0.6 GeV/c. Therefore, the measurement of such observables in a dedicated experiment at the GSI pion beam facility in the near-threshold momentum domain will allow to get valuable information on the K ∗ (892 ) + in-medium properties.

Alternative methods to calculate neutron capture cross sections on radioactive nuclei are reported using the theory of Inclusive Non-Elastic Breakup (INEB) developed by Hussein and McVoy [1]. The statistical coupled-channels theory proposed in Ref. [2] is further extended in the realm of random matrices. The case of reactions with the projectile and the target being two-cluster nuclei is also analyzed and applications are made for scattering from a deuteron target [3]. An extension of the theory to a three-cluster projectile incident on a two-cluster target is also discussed. The theoretical developments described here should open new possibilities to obtain information on the neutron capture cross sections of radioactive nuclei using indirect methods.

The location of the neutron drip line, currently known for only the lightest elements, remains a fundamental question in nuclear physics. Its description is a challenge for microscopic nuclear energy density functionals, as it must take into account in a realistic way not only the nuclear potential, but also pairing correlations, deformation effects and coupling to the continuum. The recently developed deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) aims to provide a unified description of even-even nuclei throughout the nuclear chart. Here, the DRHBc with the successful density functional PC-PK1 is used to investigate whether and how deformation influences the prediction for the neutron drip-line location for even-even nuclei with 8<=Z<=20, where many isotopes are predicted deformed. The results are compared with those based on the spherical relativistic continuum Hartree-Bogoliubov (RCHB) theory and discussed in terms of shape evolution and the variational principle. It is found that the Ne and Ar drip-line nuclei are different after the deformation effect is included. The direction of the change is not necessarily towards an extended drip line, but rather depends on the evolution of the degree of deformation towards the drip line. Deformation effects as well as pairing and continuum effects treated in a consistent way can affect critically the theoretical description of the neutron drip-line location.

Because of the development of many-body theories of nuclear matter, the long-standing, open problem of the equation of state (EOS) of dense matter may be understood in the near future through the confrontation of theoretical calculations with laboratory measurements of nuclear properties \& reactions and increasingly accurate observations in astronomy. In this review, we focus on the following six aspects: 1) providing a survey of the quark mean-field (QMF) model, which consistently describes a nucleon and many-body nucleonic system from a quark potential; 2) applying QMF to both nuclear matter and neutron stars; 3) extending QMF formalism to the description of hypernuclei and hyperon matter, as well as hyperon stars; 4) exploring the hadron-quark phase transition and hybrid stars by combining the QMF model with the quark matter model characterized by the sound speed; 5) constraining interquark interactions through both the gravitational wave signals and electromagnetic signals of binary merger event GW170817; and 6) discussing further opportunities to study dense matter EOS from compact objects, such as neutron star cooling and pulsar glitches.

A quark-meson coupling model based on the quark model proposed by Bogoliubov for the description of the quark dynamics is developed and applied to the description of neutron stars. Starting from a su(3) symmetry approach, it is shown that this symmetry has to be broken in order to satisfy the constraints set by the hypernuclei and by neutron stars. The model is able to describe observations such as two solar mass stars or the radius of canonical neutron stars within the uncertainties presently accepted. If the optical potentials for Λ and Ξ hyperons in symmetric nuclear matter at saturation obtained from laboratory measurements of hypernuclei properties are imposed the model predicts no strangeness inside neutron stars.

Based on the realistic nuclear force of the high-precision CD-Bonn potential, we have performed comprehensive calculations for neutron-rich calcium isotopes using the Gamow shell model (GSM) which includes resonance and continuum. The realistic GSM calculations produce well binding energies, one- and two-neutron separation energies, predicting that 57 Ca is the heaviest bound odd isotope and 70 Ca is the dripline nucleus. Resonant states are predicted, which provides useful information for future experiments on particle emissions in neutron-rich calcium isotopes. Shell evolutions in the calcium chain around neutron numbers \textit{N} = 32, 34 and 40 are understood by calculating effective single-particle energies, the excitation energies of the first 2 + states and two-neutron separation energies. The calculations support shell closures at 52 Ca (\textit{N} = 32) and 54 Ca (\textit{N} = 34) but show a weakening of shell closure at 60 Ca (\textit{N} = 40). The possible shell closure at 70 Ca (\textit{N} = 50) is predicted.