Medium-heavy Nuclei Research Articles

Incompressibility of finite fermionic systems: Stable and exotic atomic nuclei

The incompressibility of finite fermionic systems is investigated using analytical approaches and microscopic models. The incompressibility of a system is directly linked to the zero-point kinetic energy of constituent fermions, and this is a universal feature of fermionic systems. In the case of atomic nuclei, this implies a constant value of the incompressibility in medium-heavy and heavy nuclei. The evolution of nuclear incompressibility along Sn and Pb isotopic chains is analyzed using global microscopic models, based on both non-relativistic and relativistic energy functionals. The result is an almost constant incompressibility in stable nuclei and systems not far from stability, and a steep decrease in nuclei with pronounced neutron excess, caused by the emergence of a soft monopole mode in neutron-rich nuclei.

Quantitative study of coherent pairing modes with two-neutron transfer: Sn isotopes

Pairing rotations and pairing vibrations are collective modes associated with a field, the pair field, which changes the number of particles by two. Consequently, they can be studied at profit with the help of two-particle transfer reactions on superfluid and in normal nuclei, respectively. The advent of exotic beams has opened, for the first time, the possibility to carry out such studies in medium heavy nuclei, within the same isotopic chain. In the case studied in the present paper that of the Sn-isotopes (essentially from closed (Z=N=50) to closed (Z=50,N=82) shells). The static and dynamic off-diagonal, long range order phase coherence in gauge space displayed by pairing rotations and vibrations respectively, leads to coherent states which behave almost classically. Consequently, these modes are amenable to an accurate nuclear structure description in terms of simple models containing the right physics, in particular BCS plus QRPA and HF mean field plus RPA respectively. The associated two- nucleon transfer spectroscopic amplitudes predicted by such model calculations can thus be viewed as essentially "exact". This fact, together with the availability of optical potentials for the different real and virtual channels involved in the reactions considered, namely (A+2)Sn+p, (A+1)Sn+d and (A)Sn+t, allows for the calculation of the associated absolute cross sections without, arguably, free parameters. The numerical predictions of the absolute differential cross sections, obtained making use of the above mentioned nuclear structure and optical potential inputs, within the framework of second order DWBA, taking into account simultaneous, successive and non-orthogonality contributions provide, within experimental errors an overall account of the experimental findings for all of the measured (A+2)Sn(p,t)(A)Sn(gs) reactions, for which absolute cross sections have been reported to date.

Damping of high-energy particle-hole-type nuclear excitations: A semimicroscopic model

A semimicroscopic model (particle-hole dispersive optical model) is formulated to describe the main relaxation modes of high-energy particle-hole-type excitations in medium-heavy mass nuclei. Within this model, Landau damping and the single-particle continuum are considered microscopically, while the spreading effect is treated phenomenologically, employing a statistical assumption. Description of direct nucleon decay of the above-mentioned excitations (including giant resonances) is a unique feature of the proposed model, which in applying to closed-shell nuclei is arranged for practical implementations. The methodical similarity of formulations of the single-quasiparticle and particle-hole optical models is emphasized.

Pygmy and giant electric dipole responses of medium-heavy nuclei in a self-consistent random-phase approximation approach with a finite-range interaction

The pygmy dipole resonance (PDR) is studied in various medium-heavy nuclei by using a Gogny interaction in a self-consistent Hartree-Fock plus random phase approximation method. We compare the details of the PDR structure with those of the giant dipole resonance (GDR). In the PDR protons and neutrons vibrate in phase, and the main contributions are given by particle-hole excitations involving the neutrons in excess. On the contrary, in the GDR protons and neutrons vibrate out of phase, and all the nucleons are involved in the excitation. The values of the parameters we used to define the collectivity of an excitation indicate that the PDR is less collective than the GDR. We also investigate the role of the residual interaction in the appearance of the PDR and we find a subtle interplay with the shell structure of the nucleus.

Electron-capture and its role to explosive neutrino-nucleosynthesis

In explosive nucleosynthesis, among other reactions, prominent position posses the electron capture by nucleons and nuclei. This process plays important role in the core-collapse of massive stars by modifying the quantity Ye. From a nuclear theory point of view, this process may be studied by using the same nuclear methods (e.g. the quasi-particle random phase approximation, QRPA, employed in the present work) with the one-body charge changing nuclear processes (β-decay modes, charged-current electron-neutrino absorption by nuclei, etc). In this work we concentrate on a detailed study of the orbital e-capture by medium-heavy nuclei (Fe region) which play fundamental role in the evolution of massive stars and in the so called explosive neutrino nucleosynthesis. We study extensively the cross sections and rates of e-capture process by "iron group peaked nuclei", isotopes that are important for investigating the neutrino nucleosynthesis and other related phenomena.

A search for ϕ meson nucleus bound state using antiproton annihilation on nucleus

The mass shift of the vector mesons in nuclei is known to be a powerful tool for investigating the mechanism of generating hadron mass from the QCD vacuum. The mechanism is known to be the spontaneous breaking of chiral symmetry. In 2007, KEK-PS E325 experiment reported about 3.4 % mass reduction of the ϕ meson in medium-heavy nuclei (Cu). This result is possibly one of the indications of the partial restoration of chiral symmetry in nuclei, however, unfortunately it is hard to make strong conclusions from the data. One of the ways to conclude the strength of the ϕ meson mass shift in nuclei will be by trying to produce only slowly moving ϕ mesons where the maximum nuclear matter effect can be probed. The observed mass reduction of the ϕ meson in the nucleus can be translated as the existence of an attractive force between ϕ meson and nucleus. Thus, one of the extreme conditions that can be achieved in the laboratory is indeed the formation of a ϕ-nucleus bound state, where the ϕ meson is “trapped” in the nucleus. The purpose of the experiment is to search for a ϕ-nucleus bound state and measure the binding energy of the system. We will demonstrate that a completely background-free missing-mass spectrum can be obtained efficiently by \((\bar{p}, \phi)\) spectroscopy together with K + Λ tagging, using the primary reaction channel \(\bar{p} p \rightarrow \phi \phi\). This paper gives an overview of the physics motivation and the detector concept, and explains the direction of the initial research and development effort.

Gamow-Teller strengths and electron-capture rates forpf-shell nuclei of relevance for late stellar evolution

Background: Electron-capture reaction rates on medium-heavy nuclei are an important ingredient for modeling the late evolution of stars that become core-collapse or thermonuclear supernovae. The estimation of these rates requires the knowledge of Gamow-Teller strength distributions in the ${\ensuremath{\beta}}^{+}$ direction. Astrophysical models rely on electron-capture rate tables largely based on theoretical models, which must be validated and tested against experimental results.Purpose: This paper presents a systematic evaluation of the ability of theoretical models to reproduce experimental Gamow-Teller transition strength distributions measured via ($n$,$p$)-type charge-exchange reactions at intermediate beam energies. The focus is on transitions from stable nuclei in the $pf$ shell ($45\ensuremath{\le}A\ensuremath{\le}64$). In addition, the impact of deviations between experimental and theoretical Gamow-Teller strength distributions on derived stellar electron-capture rates is investigated.Method: Data on Gamow-Teller transitions from 13 nuclei in the $pf$ shell measured via charge-exchange reactions and supplemented with results from $\ensuremath{\beta}$-decay experiments where available, were compiled and compared with strength distributions calculated in shell models (using the GXPF1a and KB3G effective interactions) and quasiparticle random-phase approximation (QRPA) using ground-state deformation parameters and masses from the finite-range droplet model. Electron-capture rates at relevant stellar temperatures and densities were derived for all distributions and compared.Results: With few exceptions, shell-model calculations in the $pf$ model space with the KB3G and GXPF1a interactions qualitatively reproduce experimental Gamow-Teller strength distributions of 13 stable isotopes with $45\ensuremath{\le}A\ensuremath{\le}64$. Results from QRPA calculations exhibit much larger deviations from the data and overestimate the total experimental Gamow-Teller strengths. For stellar densities in excess of ${10}^{7}$ g/cm${}^{3}$, ground-state electron-capture rates derived from the shell-model calculations using the KB3G (GXPF1a) interaction deviate on average less than 47$%$ (31$%$) from those derived from experimental data for which the location of daughter states at low excitation energies are well established. For electron-capture rates derived from Gamow-Teller strengths calculated in QRPA, the deviations are much larger, especially at low stellar densities.Conclusions: Based on the limited set of test cases available for nuclei in the $pf$ shell, shell-models using the GXPF1a and KB3G interactions can be used to estimate electron-capture rates for astrophysical purposes with relatively good accuracy. Measures of the uncertainties in these rates can serve as input for sensitivity studies in stellar evolution models. Ground-state electron-capture rates based on the QRPA formalism discussed in the paper exhibit much larger deviations than those based on the shell-model calculations and should be used with caution, especially at low stellar densities.

G-factor measurements of short lived states in the mass region 50 < A < 110

Magnetic moments provide important nuclear structure information. This contribution will present the experimental tools and challenges of measuring magnetic properties of excited nuclear states, especially of the short lived picosecond states. Our understanding of the transient field and its applicability will be discussed using examples and results of recent measurements on medium heavy nuclei (A~100).

Effect of tensor interaction on deformation and shell structure of medium-heavy and superheavy nuclei

The effect of tensor interaction is studied on deformation and shell structure of various nuclei within the deformed Skyrme Hartree–Fock+BCS model. We discuss first the effect of tensor interaction on the deformations of Kr isotopes and 80Zr. Second, the same model is applied to investigate the role of tensor correlations on the evolution of shell structure in superheavy nuclei. To this end, we adopt four different Skyrme interactions: SLy5 without tensor interaction, and SLy5+T, T24 and T44 with tensor interaction. It is shown that the SLy5+T interaction gives the shape changes of the lowest configurations of Kr isotopes similar to experimental observations. The importance of the tensor correlations is also pointed out for the single-particle spectra of protons and neutrons in 249Bk and 251Cf, respectively. The large shell gaps of superheavy nuclei are found at Z = 114 and Z = 120 for protons and N = 184 for neutrons with the spherical shape irrespective of the tensor correlations. It is also shown that Z = 114 and N = 164 shell gaps are more pronounced by the tensor correlations of SLy5+T interaction. The effect of time-odd components of Skyrme energy density functionals is examined on the deformation and the stability of superheavy elements.

The Investigation of 130,132Te by IBM-2

In this study, we determined the most appropriate Hamiltonian that is needed for present calculations of nuclei in the A 130 region by interacting boson model. The second version of interacting boson model (IBM-2) has been widely used for describing the quadrupole collective states of the medium heavy nuclei. The proton and neutron variables are distinguished when this version of the model is applied. Because it is important to describe the proton and neutron variables explicitely. Using the best-fitted values of parameters in the Hamiltonian of the IBM-2, we have calculated energy levels and B(E2) values for 130,132Te. The results were compared with the previous experimental and theoretical data and it is observed that they are in good agreement. Some B(E2) values that are still not known so far are stated and the set of parameters used in these calculations is the best approximation that has been carried out so far. It has turned out that the interacting boson approximation (IBA) is fairly reliable for the calculation of spectra in the entire set of such Te isotopes.

Robust Regularity inγ-Soft Nuclei and Its Microscopic Realization

γ softness in atomic nuclei is investigated in the framework of energy density functionals. By mapping constrained microscopic energy surfaces for a set of representative nonaxial medium-heavy and heavy nuclei to a Hamiltonian of the proton-neutron interacting boson model (IBM-2) containing up to three-body interactions, low-lying collective spectra and transition rates are calculated. Observables are analyzed that distinguish between the two limiting geometrical pictures of nonaxial nuclei: the rigid-triaxial rotor and the γ-unstable rotor. It is shown that neither of these pictures is realized in actual nuclei, and that a microscopic description leads to results that are almost exactly in between the two geometrical limits. This finding points to the optimal choice of the IBM Hamiltonian for γ-soft nuclei.

On the direct and semidirect neutron radiative capture by medium-heavy mass nuclei

The new semimicroscopic model (particle-hole dispersive optical model) recently developed for de- scribing high-energy particle-hole-type excitations in medium-heavy mass nuclei is applied for the description of the simplest photonuclear reactions accompanied by excitation of the isovector giant dipole and quadrupole resonances. The calculated reaction cross sections and their derivatives are compared with corresponding experi- mental data and also with the similar results obtained within the previously developed semimicroscopic approach to the description of the giant resonances.

Damping of high-energy particle-hole-type nuclear excitations: a semi-microscopic model

A semi-microscopic model (particle-hole dispersive optical model) is formulated to describe the main relaxation modes of high-energy particle-hole-type excitations in medium-heavy mass nuclei. Within this model Landau damping and the single-particle continuum are considered microscopically, while the spreading effect is treated phenomenologically with taking a statistical assumption into account. Description of direct-nucleon-decay properties of the above-mentioned excitations (including giant resonances) is a unique feature of the proposed model, which in applying to closed-shell nuclei is arranged for practical implementations.

On direct proton decay of the Gamow-Teller giant resonance

The semi-microscopic approach to the description of giant resonances in medium-heavy mass closed-shell nuclei is implemented to treat partial probabilities of direct-proton decay of the Gamow-Teller giant resonance (GTGR) in 208 Bi. The corresponding experimental data are reasonably explained.

Symmetry Energy Effects in a Statistical Multifragmentation Model

The symmetry energy effects on the nuclear disintegration mechanisms of the neutron-rich system (A0 = 200, Z0 = 78) are studied in the framework of the statistical multifragmentation model (SMM) within its micro-canonical ensemble. A modified symmetry energy term with consideration of the volume and surface asymmetry is adopted instead of the original invariable value in the standard SMM model. The results indicate that as the volume and surface asymmetries are considered, the neutron-rich system translates to a fission-like process from evaporation earlier than the original standard SMM model at lower excitation energies, and its mass distribution has larger probabilities in the medium-heavy nuclei range so that the system breaks up more averagely. When the excitation energy becomes higher, the volume and surface asymmetry lead to a smaller average multiplicity.

A new algorithm for large scale shell model calculations and its applicability to medium-heavy and neutron rich nuclei

An upgraded version of an algorithm developed few years ago for diagonalizing large matrices has been implemented for the nuclear shell model eigenvalue problem. The use of a spin uncoupled basis yields a quite sparse Hamiltonian matrix. Its dimensions are further reduced effectively by an importance sampling specific of the method. Some numerical examples enphasizes the potential of the revised algorithm.

Peculiarities of sub-barrier reactions with heavy ions

With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed and spherical nuclei at sub-barrier energies. The calculated results are in a good agreement with existing experimental data. With decreasing bombarding energy under the barrier the external turning point of the nucleus-nucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is expected at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum of captured system on the bombarding energy. From the comparison of calculated capture cross sections and experimental capture (fusion) cross sections, the importance of quasifission near the entrance channel is shown for the actinide-based reactions and reactions with medium-heavy nuclei at sub-barrier energies.

Sub-barrier capture with quantum diffusion approach

With the quantum diffusion approach the behavior of capture cross sections and mean-square angular momenta of captured systems are revealed in the reactions with deformed and spherical nuclei at sub-barrier energies. With decreasing bombarding energy under the barrier the external turning point of the nucleus-nucleus potential leaves the region of short-range nuclear interaction and action of friction. Because of this change of the regime of interaction, an unexpected enhancement of the capture cross section is found at bombarding energies far below the Coulomb barrier. This effect is shown its worth in the dependence of mean-square angular momentum on the bombarding energy. From the comparison of calculated capture cross sections and experimental capture or fusion cross sections the importance of quasifission near the entrance channel is demonstrated for the actinidebased reactions and reactions with medium-heavy nuclei at extreme sub-barrier energies.

An upgraded algorithm for shell model calculations and its implementation in medium-heavy nuclei

A matrix diagonalization algorithm we developed in the past years has been revised and implemented for large scale shell model calculations using a spin uncoupled basis so as to obtain a sparse Hamiltonian matrix. The dimensions of such a matrix are reduced drastically by a procedure that combines an effective projection of the good angular momentum with an importance sampling specific of the method. Its numerical implementation on 116Sn illustrates the simplicity of the method and the fast convergence of the iterative procedure.

Proton resonance elastic scattering in inverse kinematics on the medium heavy nucleus 68Zn

An isobaric analog resonance of 69Zn was studied by the resonance elastic scattering of p ( 68Zn , p with a 5.5MeV/nucleon 68Zn beam and a thick polyethylene target. The excitation function of the differential cross-section of proton elastic scattering was measured around 0 degrees in the laboratory frame by the thick target inverse kinematics method. The angular momentum, and proton and total widths of the resonance assigned using an R -matrix calculation are in good agreement with earlier measurements performed using normal kinematics, demonstrating that the thick target inverse kinematics method is a useful tool for studying the single-particle structures of neutron-rich nuclei.