Function Of Nucleon Number Research Articles

Toward Nuclear Physics from Lattice QCD on Quantum Computers

Abstract One of the ultimate missions of lattice quantum chromodynamics (QCD) is to simulate atomic nuclei from the first principles of the strong interaction. This is an extremely hard task for current computational technology, but might be reachable in the coming quantum computing era. In this paper, we discuss the computational complexities of classical and quantum simulations of lattice QCD. It is shown that the quantum simulation scales better as a function of nucleon number and thus will outperform classical simulation for large nuclei.

Microscopic formulation of the interacting boson model for reflection asymmetric nuclei

Reflection asymmetric, octupole shapes in nuclei are a prominent aspect of nuclear structure, and have been recurrently studied over the decades. Recent experiments using radioactive-ion beams have provided evidence for stable octupole shapes. A variety of nuclear models have been employed for the related theoretical analyses. We review recent studies on the nuclear octupole shapes and collective excitations within the interacting boson model. A special focus is placed on the microscopic formulation of this model by using the mean-field method that is based on the framework of nuclear density functional theory. As an illustrative example, a stable octupole deformation, and a shape phase transition as a function of nucleon number that involves both quadrupole and octupole degrees of freedom are shown to occur in light actinides. Systematic spectroscopic studies indicate enhancement of the octupole collectivity in a wide mass region. Couplings between the octupole and additional degrees of freedom are incorporated in a microscopic manner in the boson system, and shown to play a crucial role in the description of the related intriguing nuclear structure phenomena such as the shape coexistence.

Signatures for a nuclear quantum phase transition from E0 and E2 observables in Gd isotopes

Nuclei are complex quantum objects due to complex nucleon-nucleon interactions. They can undergo rather rapid changes in structure as a function of nucleon number. A well known region of such a shape transition is the rare-earth region around N = 90, where accessible nuclei range from spherical nuclei at the closed neutron shell at N = 82 to deformed nuclei. For a better understanding of this phenomenon, it is of interest to study empirical signatures like the E2 transition strength or the E0 excitation strength . The nuclide 152Gd with 88 neutrons is located close to the quantum phase transition at N = 90. The lifetime of 152Gd has been measured using fast electronic scintillation timing (FEST) with an array of HPGe- and LaBr3- detectors. Excited states of 152Gd were populated via an (α,n)-reaction on a gold-backed 149Sm target. The measured lifetime of corresponds to a reduced transition strength of W.u. and an E0 transition strength of ρ2(E0) = 39(3) · 10−3 to the ground state. This result provides experimental support for the validity of a correlation between E0 and E2 strengths that is a novel indicator for a quantum phase transition. This work was published as J. Wiederhold et al., Phys. Rev. C 94, 044302 (2016).

Lifetime measurement of neutron-rich even-even molybdenum isotopes

Background: In the neutron-rich $A\ensuremath{\approx}100$ mass region, rapid shape changes as a function of nucleon number as well as coexistence of prolate, oblate, and triaxial shapes are predicted by various theoretical models. Lifetime measurements of excited levels in the molybdenum isotopes allow the determination of transitional quadrupole moments, which in turn provides structural information regarding the predicted shape change.Purpose: The present paper reports on the experimental setup, the method that allowed one to measure the lifetimes of excited states in even-even molybdenum isotopes from mass $A=100$ up to mass $A=108$, and the results that were obtained.Method: The isotopes of interest were populated by secondary knock-out reaction of neutron-rich nuclei separated and identified by the GSI fragment separator at relativistic beam energies and detected by the sensitive PreSPEC-AGATA experimental setup. The latter included the Lund-York-Cologne calorimeter for identification, tracking, and velocity measurement of ejectiles, and AGATA, an array of position sensitive segmented HPGe detectors, used to determine the interaction positions of the $\ensuremath{\gamma}$ ray enabling a precise Doppler correction. The lifetimes were determined with a relativistic version of the Doppler-shift-attenuation method using the systematic shift of the energy after Doppler correction of a $\ensuremath{\gamma}$-ray transition with a known energy. This relativistic Doppler-shift-attenuation method allowed the determination of mean lifetimes from 2 to 250 ps.Results: Even-even molybdenum isotopes from mass $A=100$ to $A=108$ were studied. The decays of the low-lying states in the ground-state band were observed. In particular, two mean lifetimes were measured for the first time: $\ensuremath{\tau}=29.{7}_{\ensuremath{-}9.1}^{+11.3}$ ps for the ${4}^{+}$ state of $^{108}\mathrm{Mo}$ and $\ensuremath{\tau}=3.{2}_{\ensuremath{-}0.7}^{+0.7}$ ps for the ${6}^{+}$ state of $^{102}\mathrm{Mo}$.Conclusions: The reduced transition strengths $B(E2)$, calculated from lifetimes measured in this experiment, compared to beyond-mean-field calculations, indicate a gradual shape transition in the chain of molybdenum isotopes when going from $A=100$ to $A=108$ with a maximum reached at $N=64$. The transition probabilities decrease for $^{108}\mathrm{Mo}$ which may be related to its well-pronounced triaxial shape indicated by the calculations.

Novel triaxial structure in low-lying states of neutron-rich nuclei aroundA≈100

Background: In recent years, the study of triaxiality in the low-lying states of atomic nuclei with transition character or shape coexistence has been of great interest. Previous studies indicate that the neutron-rich nuclei in the $A\ensuremath{\sim}100$ mass region with $Z\ensuremath{\sim}40,N\ensuremath{\sim}60$ serve as good grounds for examining the role of triaxiality in nuclear low-lying states.Purpose: The aim of this work is to provide a microscopic study of low-lying states for nuclei in the $A\ensuremath{\sim}100$ mass regions and to examine in detail the role of triaxiality in the shape-coexistence phenomena and the variation of shape with the isospin and spin values at the beyond mean-field level.Method: The starting point of our method is a set of relativistic mean-field plus BCS wave functions generated with a constraint on triaxial deformations $(\ensuremath{\beta},\ensuremath{\gamma})$. The excitation energies and electric multipole transition strengths of low-lying states are calculated by solving a five-dimensional collective Hamiltonian (5DCH) with parameters determined by the mean-field wave functions.Results: The low-lying states of Mo isotopes and of $N=60$ isotones in the $A\ensuremath{\sim}100$ mass region are calculated. The results indicate that triaxiality is essential to reproduce the data of excitation energies and electric quadrupole transition strengths in low-lying states and plays an important role in the shape evolution as a function of nucleon number. However, the decrease of nuclear collectivity with the increase of angular momentum in neutron-rich Mo isotopes has not been reproduced.Conclusions: The evolution of nuclear collectivity in the low-lying states of neutron-rich nuclei in the $A\ensuremath{\sim}100$ mass region as a function of nucleon number is governed by the novel triaxial structure. However, the mechanism that governs the variation of nuclear shape with spin in Mo isotopes remains unclear and deserves further investigation by taking into account the effects other than the collective motions.

Shape Phase Transitions in Geometrical and Algebraic Nuclear Collective Models

Phase transitions in finite systems sound Greek to many and κινζικα (Chinese) to Greeks. In fact, evidence for phase transitions as function of nucleon number has been lurking for over 30 years, when early measurements of two nucleon transfer cross-sections and isotope shifts in Sm and Gd nuclei [1] gave clear evidence of dramatic changes in the shape of nuclei across an isotopic chain. Later theoretical investigations [2] within the framework of the interacting boson approximation (IBA) model [3] found that the transition from spherical to deformed shapes exhibits features of a first- or second-order phase transition, depending on the trajectory taken within the parameter space. These are quantum phase transitions (QPT) in the equilibrium shape of nuclei [4], occurring at zero temperature. Over the past several years, the idea of QPT has found a renewed interest, stemming from the development of critical point symmetries (CPS) [5,6], which provide very simple descriptions of behavior at the critical point of QPT, and the discovery of their empirical realizations [7,8].

Isoscalar and Isovector Giant Monopole Vibrations Described by Collective Parameters

Using a recently suggested method, where the nuclear density is parametrized directly, we investigate isoscalar and isovector monopole vibrations. The method is applicable for large amplitude motion, but in this paper it is tested in the simple case of small amplitude vibrations. The parameters are a radial scaling parameter and a surface skin-thickness parameter for each of the neutron and proton density distributions. The energy of the isoscalar (isovector) mode as function of nucleon number is obtained with an accuracy of 4% (15%) for different forces. The isoscalar state is for nuclei above 40Ca an overall scaling vibration. The isovector state for the same nuclei is mainly a scaling mode, but it contains significant contributions from the diffuseness degrees of freedom. The masses related to the two modes are found to be nearly equal. They vary from light to heavy nuclei from 100% to 60% of the total nuclear mass. The technical and physical advantages of the method are strikingly demonstrated by this successful application.

Shell model level densities in evaporation calculations

The energy and spin dependence of nuclear level densities are calculated from realistic shell model potentials in the saddle point approximation. Effective Fermi gas level density parameters are extracted and their behaviour as a function of nucleon number, excitation energy and angular momentum is examined. Evaporation residue distributions following heavy ion induced fusion reactions leading to compound nuclei near doubly magic 56Ni are predicted from Hauser-Feshbach theory with the shell model level densities. Good agreement with experimental residue cross sections is obtained, provided nuclear deformation is included.