In the collective spectra of atomic nuclei, the level energy [Formula: see text] varies with atomic number [Formula: see text] and neutron number [Formula: see text]. Also the [Formula: see text]2 decay-reduced transition probability [Formula: see text] is related to the energy [Formula: see text]. The product [Formula: see text] is constant according to Grodzins product rule, independent of the vibration or rotational status of the nucleus. The product rule is often used for determining [Formula: see text] from the known [Formula: see text]. However, the variation of the product with various parameters is also suggested in the literature. Hence, a detailed global study of this rule for [Formula: see text] region is warranted. We use a novel method of displaying the linear relation of [Formula: see text] with [Formula: see text] for the isotopes of each element (Xe–Pt), instead of their variation with [Formula: see text] or [Formula: see text]. Through our work, we firmly establish the global validity of the Grodzins relation of [Formula: see text], being proportional to the moment of inertia, except for the deviation in specific cases. Our [Formula: see text] versus [Formula: see text] plots provide a transparent view of the variation of the low-energy nuclear structure. This gives a new perspective of their nuclear structure. Also the various theoretical interpretations of [Formula: see text]s and the energy [Formula: see text] are reviewed.
The consequences of some symmetries of the three-alpha system are discussed. In particular, the recent description of the low-energy spectrum of the C-12 nucleus in terms of the algebraic cluster model (ACM) is compared to that of the multichannel dynamical symmetry (MUSY), which is the intersection of the shell and cluster models. The previous one applies interactions of a D-3h geometric symmetry [D. J. Marin-Lambarri et al., Phys. Rev. Lett. 113 (2014) 012502], while the latter one has a U(3) dynamical symmetry. The available data is in line with both descriptions.
Within the cluster-core model picture using the preformed cluster model, proton rich, 2-proton emitting nuclei are studied. The experimentally established [Formula: see text]Fe, [Formula: see text]Ni, [Formula: see text]Zn and [Formula: see text]Kr are investigated in terms of simple potential energy surfaces for all possible cluster plus core configurations of the 2-proton emitting nuclei. The calculated potential energy surfaces reveal a strong minimum for 2-proton-cluster plus core configuration. In addition, the calculations are carried out for the theoretically studied 2-proton emitters such as [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text], which also reveal 2-proton cluster plus core configuration as the favorable one possessing strong minimum in the potential energy surface. Furthermore, the calculated potential energies are used to calculate the preformation probability by solving the stationary Schrödinger equation of motion in mass asymmetry coordinate. The formation yield also clearly reveals a larger formation probability for the 2-proton cluster plus core configuration for all the nuclei studied. The Q-value systematic of 1-proton, 2-proton, 4-proton and 4He is also analyzed.
In this work we present some results of the interaction of high-energy muons with emulsion nuclei. The interaction results in emission of a number of fragments as a consequence of electromagnetic dissociation of the excited target nuclei. This excitation is attributed to absorption of photons by the target nuclei due to the intense electric field of the very fast incident muon particles. The interactions take place at impact parameters that allow ultra-peripheral collisions to take place, leading to giant resonances and hence multifragmentation of emulsion targets. Charge identification, range, energy spectra, angular distribution and topological cross-section of the produced fragments are measured and evaluated.
The idea of treating the trinucleon systems as elementary entities in the elementary particle model (EPM) as an Effective Field Theory has been a success in explaining the weak charge-changing processes in nuclei. The EPM results are found to be as good as those obtained from nuclear microscopic models using two-and three-body forces. We extend this concept to investigate the validity of the elemental nature of [Formula: see text] nuclei through studies of nuclear structure of neutron-rich nuclei. By treating neutron-rich nuclei as primarily made up of tritons as its building blocks, we extract one- and two-triton separation energies of these nuclei. Calculations have been performed here within relativistic mean field (RMF) models with latest interactions. Clear evidence arises of a new shell structure with well-defined predictions of new magic nuclei. These unique predictions have been consolidated by standard one- and two-neutron separation energy calculations. The binding energy per nucleon plots of these nuclei also confirm these predictions. We make unambiguous prediction of six magic nuclei: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].
In the framework of relativistic mean-field theory, the ground state properties like binding energy, charge radius and quadrupole deformation parameter for various isotopes of zirconium from the valley of stability to drip-line region have been studied. The results are compared with the experimental data and we found reasonable agreement. The calculations are carried out for [Formula: see text]-decay energy and [Formula: see text]-decay half-life up to the drip-line. Total reaction and elastic differential cross-sections are also studied for few zirconium isotopes as projectiles with [Formula: see text] as target, using different parameter sets namely NL3*, DD-ME2 and DD-PC1 in conjunction with Glauber model.
A compact accelerator-driven neutron source (CANS) has been proposed and designed by the Peking University (PKU) RFQ group. The source is based on a compact deuteron RF accelerator that delivers an average current of a few mA of deuterons at 11[Formula: see text]MeV to the target. The accelerator consists of a short radio frequency quadrupole (RFQ) followed by efficient interdigital H-mode drift tube linac (IH-DTL) structure. The total length of the whole accelerator structure is 4.96[Formula: see text]m, including 1.76[Formula: see text]m for the 4-vane RFQ and 2.70[Formula: see text]m for the IH-DTL. The dynamic simulation results show that the beam has excellent quality, with transmission efficiency higher than 99%. The transverse and longitudinal normalized rms emittance at the DTL exit is 0.29[Formula: see text]mm⋅mrad and 0.12 MeV⋅deg, respectively. Details of the beam dynamics of the RFQ and IH-DTL are presented in this paper.
The energies of the ground, [Formula: see text] and [Formula: see text] bands as well as the associated [Formula: see text] values have been calculated using interacting boson model (IBM). We have developed a new method called “new empirical equation” for each even–even rare-earth Er–Os for [Formula: see text]. Also, the relation of the gamma energy over spin as a function of the spin [Formula: see text] (E-GOS) has been drawn. The ratio between the energies of the [Formula: see text] and [Formula: see text] states as a function of [Formula: see text] has been drawn to determine the property of the ground-state band, these curves indicated that these isotopes have a rotational property SU(3), with the [Formula: see text] property for [Formula: see text]Os isotopes. The contour plots of the potential energy surface for Er–Os for [Formula: see text] are studied using the simplified form of interacting boson model with an intrinsic coherent state. The critical points have been determined for [Formula: see text]Os isotopes. The behaviors of energy and [Formula: see text] ratios in the ground-state band are examined.
In the present study, two different density distributions of oxygen isotopes ([Formula: see text]O) that consist of the harmonic oscillator single-particle wave functions (SDHO) and the relativistic mean-field (RMF) approaches are investigated for the availability of elastic scattering cross-sections. For this purpose, the elastic scattering angular distributions of nuclear reactions with 13 target nuclei, four target nuclei and nine target nuclei are calculated for [Formula: see text]O, [Formula: see text]O and [Formula: see text]O, respectively. For these calculations, the double folding model based on the optical model is used. The optical potential parameters, volume integrals and cross-sections for all the nuclear reactions are given in this study. The comparison of theoretical results and experimental data shows very good agreement. The imaginary potential depth expressions, which will be new and more practical terms to explain the nuclear interactions of [Formula: see text]O, [Formula: see text]O and [Formula: see text]O with different nuclei, for each oxygen isotope are proposed.
The [Formula: see text] interference has been studied in the dilepton invariant mass distribution spectra in the photonuclear reaction, but that is not done for the gamma-nucleon reaction. In the recent past, the [Formula: see text] invariant mass distribution spectrum in the [Formula: see text] reaction, i.e., [Formula: see text] reaction, was measured at Jefferson Laboratory to look for the [Formula: see text] interference in the multi-GeV region. To study the mechanism of this reaction, the differential cross section of the [Formula: see text] invariant mass distribution is calculated in the quoted energy region. The reaction is assumed to proceed as [Formula: see text]; [Formula: see text], where [Formula: see text] denotes a vector meson, i.e., either [Formula: see text] or [Formula: see text] meson. The photoproduction of the vector meson is described by the Vector Meson Dominance (VMD) model which consists of diagonal and off-diagonal processes. The diagonal process is described as [Formula: see text]. The low-energy [Formula: see text] meson photoproduction data is well described by the off-diagonal process which is illustrated as [Formula: see text]. The reaction [Formula: see text] proceeds due to one pion exchange interaction. The differential cross-sections of the [Formula: see text] reaction due to the above processes of VMD model are compared, and the significance of the pion exchange interaction is investigated in the energy region of [Formula: see text] beam available at Jefferson Laboratory.
Gap equations at finite temperature are established in the isovector plus isoscalar pairing case [Formula: see text] using a path integral approach. Expressions of the various statistical quantities, i.e., the energy, the entropy and the heat capacity are then deduced. It is shown that they do generalize the ones obtained in the pure isovector ([Formula: see text]) pairing case, as well as those obtained within the conventional finite temperature Bardeen–Cooper–Schrieffer (FTBCS) theory in the pairing between like-particles case. A numerical study is then performed using the schematic one-level model. It is shown that the isoscalar n–p gap parameter [Formula: see text] behaves as a function of the temperature, like its homologues [Formula: see text] and [Formula: see text] in the conventional FTBCS approach. As for the three other gap parameters, i.e., [Formula: see text], [Formula: see text] and [Formula: see text], their behaviors are clearly modified when the isoscalar pairing is taken into account. In particular, one observes a shift of the values of the critical temperatures. Dealing with the statistical quantities, the inclusion of the isoscalar pairing, in addition to the isovector one, leads to a lowering of the energy as well as a change of the shapes of the curves of the energy, the entropy and the heat capacity as a function of the temperature.
Gap parameter of Lipkin–Nogami (LN) model is replaced by order parameter of the exact Ginzburg–landau (EGL) theory. Thermodynamic quantities such as energy, entropy and heat capacity for [Formula: see text]Mo nuclei are calculated using this modified form of the LN model (MLN). In the LN model, the gap parameter suddenly decreases to zero at critical temperature. This causes singular points in the graph of heat capacity. However, in the MLN method, the order parameter does not become zero at critical temperature and gradually decreases along with the temperature. This causes the singular points, which are predicted in the heat capacity of LN model to be eliminated. Therefore, the heat capacity as a function of temperature becomes continuous and S-shaped, which is qualitatively in agreement with the experimental data.
The power law expression [Formula: see text] offers a single-term formula with just two parameters for expressing the level energies in the spectra of even-[Formula: see text] even-[Formula: see text] nuclei. Its application to ground band spectra for a wide range of nuclei has been demonstrated in our earlier works. Here, we extend its application to the rotational bands built on an excited state of [Formula: see text] [Formula: see text]-vibration band and [Formula: see text] beta band. A novel assumption of a virtual level with spin zero for [Formula: see text]-bands is made and its validity and use is illustrated. Here, the constancy of the parameters “[Formula: see text]” and “[Formula: see text]” with spin, offers a more realistic view of the dependence of the nuclear core deformation on spin, in the excited bands. Also, it enables a spinwise view, not available in the other energy fit expressions.
The Lipkin-Meshkov-Glick is a simple, but not trivial, model of a quantum many-body system which allows us to solve the many-body Schr\"odinger equation without making any approximation. The model, which in its unperturbed case is composed only by two energy levels, includes two interacting terms. A first one, the $V$ interaction, which promotes or degrade pairs of particles, and a second one, the $W$ interaction, which scatters one particle in the upper and another in the lower energy level. In comparing this model with other approximation methods, the $W$ term interaction is often set to zero. In this paper, we show how the presence of this interaction changes the global structure of the system, generates degeneracies between the various eigenstates and modifies the energy eigenvalues structure. We present analytical solutions for systems of two and three particles and, for some specific cases, also for four, six and eight particles. The solutions for systems with more than eight particles are only numerical but their behaviour can be well understood by considering the extrapolations of the analytical results. Of particular interest it is the study of how the $W$ interaction affects the energy gap between the ground state and the first-excited state.
In this paper, a detailed study of two-particle rapidity correlation has been presented by measuring the dynamical fluctuation variable [Formula: see text] in forward and backward pseudo-rapidity window of shower particles produced in the relativistic heavy ion collision, [Formula: see text]O–AgBr interactions at 60[Formula: see text]AGeV and [Formula: see text]S–AgBr interactions at 200[Formula: see text]AGeV. Variations of [Formula: see text] with rapidity gap between forward and backward zones and with the width of each zone have been studied. For both cases, [Formula: see text] increase with increasing either width of the zone or gap between the zones. Our findings show the presence of strong long-range correlation. Comparison of experimental results with MC-RAND events confirms the present correlation to be dynamical in nature. We have also compared our results with FRITIOF and UrQMD events. Such events also show the presence of correlation, but found to fail to reproduce the experimental results both quantitatively and qualitatively. Strength of correlation is dependent on the centrality of collision for experimental events, it decreases with centrality.
An approach for the three-body force effect is used to study p-[Formula: see text] elastic scattering at energies 350–1728[Formula: see text]MeV. The multiple scattering theory of Glauber and the optical limit approximation are used in calculations of elastic scattering differential cross-section at 350, 600, 800, 1000 and 1728[Formula: see text]MeV. The inclusion of 2[Formula: see text]-exchange three-nucleon force improves the agreement with the experimental data for both approximations. The results of optical limit approximation without three-nucleon force effect are clearly smaller than the results of multiple scattering theory for [Formula: see text] due to the absence of multiple scattering terms in the first. However, with inclusion of three-nucleon force, the results of both approximations are approximately similar.
The tensor properties of the [Formula: see text] algebra generators are determined in respect to the reduction chain [Formula: see text], which defines a shell-model coupling scheme of the proton–neutron symplectic model (PNSM). They are further used to calculate the matrix elements of the basic [Formula: see text] operators of the PNSM in the space of fully symmetric representations in the [Formula: see text]-coupled basis using a generalized Wigner–Eckart theorem. The obtained results allow further the matrix elements of any physical operator of interest, such as the relevant transition operators or the collective potential, to be calculated. As an illustration, the matrix elements of the basic irreducible tensor terms which appear in the [Formula: see text] decomposition of the long-range full major-shell mixing proton–neutron quadrupole–quadrupole interaction are presented.
New transitions in neutron rich [Formula: see text]Y have been identified by analyzing the high statistics [Formula: see text]-[Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text]-[Formula: see text]-[Formula: see text] coincidence data from the spontaneous fission of [Formula: see text]Cf at the Gammasphere detector array. Shell model calculations were performed and are found in good agreement with experimental data. The ground state is nearly spherical but a new excited band has large deformation.
The lattice QCD data of pressure and the energy density have been used to extract the hadronic radius parameter of the excluded volume hadron resonance gas (EVHRG) model. The equation of state can be described well with the extracted radius parameter [Formula: see text] fm. Specific heat is also calculated in the EVHRG model. Further, two new universal descriptions of chemical freeze-out parameters have been introduced based on pressure and specific heat, respectively. It is shown that the chemical freeze-out parameters obtained at various [Formula: see text] in ideal hadron resonance gas (HRG) model approximately correspond to [Formula: see text] and [Formula: see text], respectively. These two quantities are important to describe the thermodynamic properties of the hadronic matter created in heavy-ion collision experiment. The sensitivity of universal chemical freeze-out lines on repulsive interaction is also studied. It has been observed that the behaviors of chemical freeze-out lines for [Formula: see text] and [Formula: see text] in EVHRG model remain similar to ideal HRG model for the best fit value of hadronic radii.
The present work is aimed at considering the recent forms of Bohr Hamiltonian, which are namely the hybrid model and the model combining the X(3) and E(5) symmetries, in the presence of the [Formula: see text]-dependent Morse potential. The energy spectra and the transition rates of each model have been obtained. Some nuclei, the isotopes of Ru, Pd, Xe and [Formula: see text]Ba, have been fitted by using the three-parameter solution of the combined Hamiltonian with the Morse potential. Also, a few nuclei have been fitted by using the four-parameter solution of the hybrid model. In order to evaluate our results, in addition to reporting the root mean square (rms), we compare our data for each nucleus with the corresponding results of other references.
