Translation-invariant Shell Model Research Articles

Role of the Center of Mass Correction in Magnetic Form Factors for 19O and 21Na Exotic Nuclei with Different Interactions

The transverse magnetic electron scattering form factors of 19O and 21Na exotic nuclei were studied in the plane wave Born approximation (PWBA). The shell model calculations with three sd-shell interactions, USDA, USDB, and Wildenthal, were carried out for the ground and low-lying excited states. The exact center of mass correction in the Born approximation picture through the translation-invariant shell model (TISM) was included to modify the transverse form factors. The measured magnetic dipole moments were well reproduced with the core polarization (CP) effect introduced through the effective g-factors. The occupancies percentage with respect to the valence nucleons was also calculated.

Реакція 10В(15N,14С)11С при енергії 81 МеВ, спектроскопічні фактори реакції та взаємодія ядер 14С + 11С

New experimental data of angular distribution cross-sections for the 10В(15N,14С)11С reaction at the energy Еlab(15N) = 81 MeV were obtained for the ground states of 14С, 11С nuclei and 2.00 MeV (1/2-), 4.31 MeV (5/2-), 4.31 MeV (3/2-) excited states of 11С nucleus. The experimental data were analyzed within the coupled-reaction-channels (CRC) method. In the CRC calculations, the 15N + 10В Woods - Saxon (WS) optical potential obtained from the CRC analysis of the experimental elastic and inelastic data of these nuclei was used and parameters of the 14С + 11С WS optical potential were deduced from the analysis of the 10В(15N,14С)11С reaction experimental data. Spectroscopic amplitudes of nucleons and cluster transfers were calculated within the translation-invariant shell model.

Reaction 14C(11B, 12C)13B at Elab(11B) = 45 MeV, interaction of 13B + 12C versus that of 10,11,12B + 12C

New experimental data for differential cross-sections of the 14C(11B, 12C)13B reaction obtained recently at the energy Еlab(11B) = 45 MeV for the ground states of 13B and 12C were analyzed within the coupled reaction channels (CRC) method that included the 11B + 14C elastic scattering channel as well as channels for one- and two-step transfers of nucleons in the coupling scheme. The necessary 11B + 14C Woods - Saxon (WS) optical potential parameters for the entrance reaction channel were obtained from 11B elastic scattering in the previous work, while those for 12C + 13B interaction were deduced from fitting the CRC calculations to the 14C(11B, 12C)13B reaction data. Needed spectroscopic amplitudes of transferred nucleons and clusters were calculated within the translational-invariant shell model. The data are well described by the direct transfer of a proton while contributions from two-step transfers were found to be negligible. The deduced 13B + 12C WS optical potential parameters are compared with those of the 10,11,12B + 12C nuclei interactions. The effect of isotopic differences in these interactions was observed.

Механізми реакції 6Li(10B,9Be)7Be при енергії 51 МеВ. Структура та взаємодія ядер 9Be + 7Be

New experimental data of angular distributions for the 6Li(10B,9Be)7Be reaction were measured at the energy Elab(10B) = 51 MeV for the ground states of nuclei and excited 0.429 - 7.2 MeV states of 7Be. The reaction experimental data were analyzed within coupled-reaction-channels method (CRC) for many types of the nucleon and cluster transfers which spectroscopic amplitudes (factors) in the 9Be and 7Be nuclei were calculated using translation invariant shell model. The Woods - Saxon potential was used for CRC-calculations. The 6Li + 10B potential parameters were deduced before from the analysis of experimental data of 10B ions scattering by 6Li nuclei at the energy Elab(10B) = 51 MeV, and the 9Be + 7Be potential parameters for exit reaction channel were deduced from the CRC calculations fitting to the reaction experimental data. Thus, the information about the 9Be + 7Be optical potential, the basic reaction mechanisms and the 9Be and 7Be nuclei structures were deduced.

Ground and excited state characteristics of the nuclei with A = 6

The binding energy, the root-mean-square radius, the magnetic dipole moment, the electric quadrupole moment, and the moment of inertia of the nucleus 6Li are calculated by applying different models. The translation invariant shell model is applied to calculate the binding energy, the root-mean-square radius, and the magnetic dipole moment by using two- and three-body interactions. Also, the spectra of the nuclei with A = 6 are calculated by using the translation-invariant shell model. Moreover, the ft-value of the allowed transition: 6He(Jπ=0+;T=1)β- → 6Li(Jπ=1+;T'=1) is also calculated. Furthermore, the concept of the single-particle Schrodinger fluid for axially symmetric deformed nuclei is applied to calculate the moment of inertia of 6Li. Also, we calculated the magnetic dipole moment and the electric quadrupole moment of the nucleus 6Li in this case of axially symmetric shape. Moreover, the nuclear superfluidity model is applied to calculate the moment of inertia of 6Li, based on a single-particle deformed anisotropic oscillator potential added to it a spin-orbit term and a term proportional to the square of the orbital angular momentum, as usual in this case. The single-particle wave functions obtained in this case are used to calculate the magnetic dipole moment and the electric quadrupole moment of 6Li.

Effect of the Exact Center of Mass Correction on the Longitudinal Form Factors for Neutron Rich 12,14,18N Isotopes

The nuclear structure of the ground state for even 12,14,18N isotopes are studied within the shell model framework through the longitudinal elastic electron scattering. The generate wave functions from two-body interaction of Cohen and Kurath in the p-shell for 12,14N, and psdsu3 interaction for 18N nucleus. The exact value of the center of mass correction in the translation invariant shell model (TISM) are re-examined for longitudinal form factors. The contribution of a higher 2p-shell configuration resolves some discrepancies with the experiments for the form factors at q-values. The inclusion of the core polarization effects through an effective nucleon charge gives a reasonable agreement for the present results with available data. The occupancy percentage with respect to the valance nucleons is also calculated.

МЕХАНІЗМИ РЕАКЦІЇ 14C(11B,10В)15С ЗА ЕНЕРГІЇ 45 МеВ ДЛЯ ОСНОВНИХ І ЗБУДЖЕНИХ СТАНІВ ЯДЕР 10В І 15С

New experimental data for differential cross-sections of the reaction 14C(11B,10B)15C at Еlab(11B) = 45 MeV were obtained for transitions to the ground and excited states of the exit reaction channel nuclei. The experimental data were analyzed within the coupled-reaction-channels method (CRC). The 14C + 11B elastic scattering channel as well as channels for one- and two-step transfers of nucleons and clusters were included in the coupling scheme. The Woods - Saxon (WS) potential was used in the CRC-calculations for the entrance reaction channel with the parameters deduced previously from the analysis of the experimental data of 11B + 14C elastic and inelastic scattering, whereas the WS potential for the exit 15C + 10B reaction channel was deduced from the fit of CRC cross-sections to the 14C(11B,10B)15C reaction experimental data. Needed for CRC-calculations spectroscopic amplitudes (factors) of the nucleons and clusters transferred in the reaction were calculated within the translational-invariant shell model. The mechanisms for one- and two-step transfers of nucleons and clusters were investigated in this reaction. The 15C + 10B potential parameters were deduced, and comparisons of the CRC reaction cross-sections calculated with the 15C + 10B and 12,13C + 10B potential parameters were performed. The differences between these CRC calculations were observed, e.g. "isotopic effects" were observed for the potentials of 10B interaction with 12,13,15C carbon isotopes.

Short-Range NN Correlations in the Reaction 12C + p → 10A + pp + N

The exclusive reaction 12C(p,pNN)10A of the quasi-elastic knockout of a nucleon from short-range correlated nucleon pair $$\langle NN\rangle $$ in the 12С nucleus by a proton with an energy of several gigaelectronvolts is considered in the plane-wave approximation. The translational invariant shell model with intermediate coupling is used to calculate two-nucleon spectroscopic factors for the $$\langle NN\rangle $$ pairs. Relativistic effects in the p + $$\langle NN\rangle $$ → p + N + N process are considered within light front dynamics.

12C(15N, 14C)13N reaction at 81 MeV. Competition between one and two particle transfers

Angular distributions at both forward and backward angles for the 12C(15N, 14C)13N reaction were measured at the energy Elab(N15)=81 MeV for ground and exited states of 14C and 13N nuclei by detecting both particles at forward angles. Coupled-reaction-channels (CRC) calculations using spectroscopic amplitudes calculated within the translational invariant shell model (TISM) for transferring nucleons and clusters were carried out. These calculations describe the origin of the observed highly oscillatory large angle data as two neutron transfer while the less structured forward angle data is by proton transfer. Multi-step and other nucleon transfers were found to give small contributions to the current data.

Formation of Hyper Hydrogen isotopes in light p-shell nuclei

Recent experiment by A1 Collaboration at Mainz, namely identification of Λ4H hyperfragment from primary Λ9Li hypernucleus produced in reaction (e, e′K+), stirred renewed interest in baryonic decay of hypernuclei. The important role of s−1sΛ excitation in p-shell hypernuclei as well as the existence of selection rules connected with [f] (Young diagram) was noted earlier within Translational Invariant Shell Model (TISM). The particular conditions of the present experiment (reaction is not selective and produces highly excited states) dictate extension of the simplest TISM: expansion of the harmonic oscillator basis space and compression of multiplets (to only (λμ) for L and [f] for S, T). Such modified TISM explains abundance production of Λ4H hyperfragment and predicts production of another Hyper Hydrogen Λ6H.

The 7Li(18O, 16N)9Be reaction and optical potential of 16N + 9Be versus 16O + 9Be

Abstract Angular distributions for the 7Li(18O, 16N)9Be reaction at an energy of E lab ( O 18 ) = 114 MeV for the ground and excited states of 9Be and 16N were measured. The data were analyzed within the coupled-reaction-channels method for one- and two-step transfers of nucleons and clusters. The 7Li + 18O optical potential fitted to the 7Li + 18O elastic and inelastic scattering data was used in the reaction calculations. The needed spectroscopic amplitudes for transferred nucleons and clusters were calculated within the translational-invariant shell model. The 9Be + 16N potential parameters were deduced by fitting 7Li(18O, 16N)9Be reaction data for ground and excited states of 9Be and 16N. The reaction is dominated by deuteron transfer. The 9Be + 16N potential is compared with the 9Be + 16O potential deduced by fitting previously reported 9Be + 16O elastic scattering data at energies E c.m. = 5.4 – 100.9 MeV and found to be less strongly absorbing.

CLUSTER–CLUSTER POTENTIALS FOR THE LITHIUM NUCLEI

Two types of cluster–cluster potentials are obtained for the lithium nuclei. The first is an attractive one and the second is a superposition of repulsive and attractive Gaussian forces. The ground-state wave functions of the lithium nuclei 6 Li , 7 Li , 8 Li , and 9 Li are expanded in terms of products of two wave functions: the first represents the set of A-4 nucleons and the second represents the set of the last four nucleons. In the construction of these wave functions, we have used the basis functions of the translation-invariant shell model. The expansion coefficients of the factorizations of these wave functions are products of four-particle orbital and spin-isospin fractional parentage coefficients. Two least-square formulas for the cluster–cluster potentials, which depend on the mass number A, are fitted for the lithium nuclei.

Hyperspherical harmonics with orthogonal symmetry in the shell model approach and its application to light nuclei

A method is proposed for constructing fully antisymmetric $A$-body hyperspherical harmonics with well-defined orthogonal symmetry. These hyperspherical harmonics are obtained by diagonalizing the matrix of the second Casimir operator for the orthogonal group, calculated in the hyperspherical basis constructed with the help of the Slater determinants of the oscillator translation-invariant shell model. The introduction of orthogonal symmetry has computational benefits and also provides a physical insight into collective modes of motion of atomic nuclei. Numerical applications have been performed for $^{3\char21{}5,7}\mathrm{H}$ and $^{4\char21{}10}\mathrm{He}$.

SHELL MODEL CALCULATIONS OF 3T, 5He AND 6Li NUCLEI

The bases of the translation invariant shell model are used to construct the ground-state wave functions of 3 T , 5 He and 6 Li . For 3 T the bases used correspond to the number of quanta of excitation N up to ten. For 5 He and 6 Li the bases used correspond to the number of quanta of excitation N up to six. The model is applied to calculate the binding energy and the root mean square radius for 3 T , 5 He and 6 Li nuclei. The residual interactions used consist of central, tensor, spin-orbit and quadratic spin-orbit terms with Gaussian radial dependence. The parameters of these interactions are chosen in such away that they represent the long range attraction and the short range repulsion of nucleon interactions. It was found that this potential is more suitable for calculating the characteristics of these nuclei, and better than other potentials, such as our previous potentials which were represented by the parameters of long range attraction forces only. For 3T we obtained good agreement between calculated and experimental values of both the ground state binding energy and the root mean square radius. For 5 He and 6 Li nuclei we obtained an acceptable improvement with these calculations over other potentials.

Blokhintsev fluctuon in the deuteron within the cluster approximation

We develop an early suggested idea that the six-quark component of NN-states in nuclei (analog of the Blokhintsev fluctuon) may turn to be a physical cause for the core on the NN-interaction. Using the quark-cluster approach and the quark translationalinvariant shell model (TISM) with oscillator potential we calculate the weight of the 6q-component in a deuteron for the configurations s6 ands4p2. How our results correspond to the earlier estimates and experimental restrictions is discussed.