States In 11B Research Articles

Analysis of 11B + 13,14C scattering and 13C(11B, 10B)14C reaction data at E lab(11B) = 45 MeV using energy dependent optical model systematics for carbon isotopes

Existing data for 11B + 13,14C elastic and inelastic scattering at E lab(11B) = 45 MeV, as well as new data for the 13C(11B, 10B)14C reaction for transitions populating the ground state of 14C and the ground plus first four excited states of 10B, were analysed using the coupled-channels (CC) and coupled-reaction-channels (CRC) methods. A recently proposed energy dependent optical model (OM) potential for carbon isotopes, consisting of Woods-Saxon (WS) volume real and WS volume plus surface imaginary components, applied successfully to OM analyses of scattering from mid-mass (A > 27) and heavy target nuclei, was used to generate the distorted waves in the entrance and exit channels. The data analysed in this work cover the whole angular range, enabling the most important reaction mechanisms leading to the production of nuclei in the exit reaction channels to be established. For these light boron + carbon systems, a reasonable fit to both scattering and reaction data over the full angular range required some modification of the parameters of the OM potential extracted from the energy-dependent carbon systematics: omission of the surface imaginary part and a slight increase in the radius of the real part. Inclusion of a sufficient number of inelastic channels in a CC analysis of the 11B + 13,14C elastic scattering was shown to be important at mid-range scattering angles, while for the 13C(11B, 10B)14C reaction inclusion of two-step neutron transfers via low-lying excited states of 11B was required to give good overall agreement between the CRC calculations and the data. We suggest the analytical form of the global carbon OM potential may benefit from an additional parameterization of the radius of the real part and the depth of the surface imaginary part, dependent on the target mass number, to give better applicability to the analysis of scattering from light target nuclei.

γ-ray spectroscopic study of self-conjugate 10B nucleus with inelastic proton scattering

A γ-ray spectroscopic study of 10B is reported. Excited states in 10B were populated in inelastic proton scattering and their γ-decays were measured with the ELIFANT array, a state-of-the-art spectrometer with large volume LaBr3:Ce and CeBr3 detectors placed in anti-Compton shields and having unprecedented efficiency for high-energy γ rays. A few weak transitions were observed in the experiment, namely M3 transition between Jπ, T = 0+1, 1 isobaric analog state to the Jπ, T = 3+1,0 ground state and E2 transition between the Jπ, T = 2+1,0 state and the isobaric analog state. The results are compared to a new set of ab initio no-core shell model calculation using the newest version of the local position-space chiral N3LO nucleon-nucleon interaction, which correctly reproduces the spectrum of the excited states in 10B, a problem of the theory in previous years.

Systematic study of the relationship between nuclear structure and reactions for the 10Be nucleus

Abstract We systematically investigate the relationship between the nuclear structure and reaction in the 10Be nucleus using a theoretical framework. The structure of the 10Be nucleus is constructed with a cluster model based on a microscopic viewpoint. In this paper, the 10Be nucleus is prepared with different structures by manipulating the parameters of an effective nucleon–nucleon interaction. The nuclear structure and expectation values of physical quantities are drastically changed by the modification. We summarize such changes and show the effects on the elastic and inelastic scatterings for proton and 12C targets in the microscopic coupled-channel calculation. Of especial interest, we recently reported the visualization of the dineutron correlation in 10Be on proton inelastic scattering in [Phys. Rev. C 104, 034613 (2021)]. In this preceding work, we found that changing the degree of dineutron correlation in 10Be leads to drastic changes of the inelastic cross section for the 2$_2^+$ state. The development (or breaking) of the dineutron correlation is governed by the strength of the spin–orbit interaction of the structure calculation. However, in the previous work, some of the realistic physical points were missing, for example, the binding energy (BE). Therefore, we reconstruct the 10Be nucleus by adjusting the effective nucleon–nucleon interaction to obtain a reasonable BE of the ground state. With this improvement, we again discuss the dineutron correlation in the 10Be nucleus. We reconfirm the way to measure the degree of development (or breaking) of the dineutron cluster structure: its sensitivity to the inelastic cross section of the 2$_2^+$ state of 10Be. Subject Index cluster model, folding model, dineutron correlation, effective nucleon-nucleon interaction.

Interplay of dynamical and structure effects in the observables for 12C(p,2p) near 400 MeV with polarized and unpolarized beams

We investigate the interplay of reaction mechanism and structure effects in the calculated cross sections and polarization observables for the direct C12(p,2p) reaction near 400 MeV around the Quasi Free Scattering (QFS) kinematical condition. We do the first consistent comparison between the scattering observables obtained from solutions of three-body Faddeev/Alt-Grassberger-Sandhas (F/AGS) equations and from the Distorted-Wave Impulse Approximation (DWIA). We explore structure effects on the calculated observables, making use of one-nucleon spectroscopic overlaps obtained from the quantum Monte Carlo (QMC) many-body wave functions and using a Woods-Saxon parametrization with parameters adjusted to experimental (p,2p) data. We show, for the first time, that the two reaction formalisms exhibit a distinct behavior depending upon the kinematic conditions. We also show that the agreement between the experimental data and the theoretical results depends on the reaction formalism, kinematical conditions and optical model parametrizations in addition to the spectroscopic factors (SFs). The agreement between the data and predictions using QMC wave functions diminishes prominently for transitions to excited states of 11B.

Neutron Halos in Excited States of 12B

An experiment was done to search for states with a neutron halo in 12B. The measurements were carried out at the cyclotron of the University of Jyvaskyla (Finland) using Large Scattering Chamber (LSC). The idea of the work was to search for two states with the expected neutron halo, 1 ̄ and 2 ̄. Differential cross sections with excitation of 12B states, including abovementioned states, were observed. The preliminary calculations on halo radii by the method of asymptotic normalization coefficients for the 2 ̄ and 1 ̄ states which are in a discrete spectrum gave following values: 5.6 fm and 7.4 fm, which is much larger than the radius of the valence neutron in the ground state. But strictly the presence of a neutron halo can be confirmed only for 1 ̄ state. The 2 ̄ state can be considered only as candidate for halo. An unexpected result was obtained for the 3 ̄, 3.39 MeV state, which is in continuum 19 keV above the decay threshold 12B → 11B + n, preliminary estimation for its halo radius is ∼ 6.5 fm. This indicates that the halo can be present in this state as well. But strict conditions for neutron halo are not fulfilled in the same way as for 2 ̄ state. Until now, the neutron halo in unbound states has been observed only for the members of the rotational bands.

Analysis of spectroscopic factors in Be11 and Be12 in the Nilsson strong-coupling limit

Spectroscopic factors in 10Be, 11Be and 12Be, extracted from (d,p), one neutron knockout, and (p,d) reactions are interpreted within the rotational model. Assuming that the ground state and first excited state of 11Be can be associated with the 1/2[220] and 1/2[101] Nilsson levels, the strong coupling limit gives simple expressions that relate the amplitudes of these wavefunctions (in the spherical basis) with the measured cross-sections and derived spectroscopic factors. We obtain good agreement with both the measured magnetic moment of the ground state in 11Be and the reaction data.

The cluster states in light nuclei

The differential cross-sections of the elastic and inelastic α +11B scattering was measured at E(α) = 29 MeV. The analysis of the data by Modified Diffraction Model (MDM) showed that the root-mean- square (RMS) radius of the 11B state 3/2-, E* = 8.56 MeV is ~ 0.5 fm larger than that of the ground state. It is found that the radius of 3/2- (8.56 MeV) state in the 11B nucleus is close to the radii of the Hoyle state in 12C.

Structure and decay pattern of linear-chain states in neutron-rich Carbon isotopes

The linear-chain states of14C are studied by using the antisymmetrized molecular dynamics. The calculated properties of the linear-chain states were compared with the observed data. The results for the π-bond linear-chain states reasonably agree with the observation. It is also shown that the linear-chain states decay to the excited states of10Be. Hence, we regard that this unique decay pattern is a strong evidence of the linear-chain formation.

Rotational bands in 11B and identification of diluted states

Differential cross-sections of the 11B + α inelastic scattering at E(α) = 65 leading to the most of the known 11B states at the excitation energies up to 14 MeV were measured. The data analysis was done by DWBA and in some cases by the modified diffraction model allowing determining the radii of the excited states. The radii of the states with excitation energies less than ∼ 7 MeV with the accuracy not less than 0.1-0.15 fm coincide with the radius of the ground state. This result is consistent with the traditional view of the shell structure of the low-lying states in 11B. Most of the observed high-energy excited states are distributed among four rotational bands. The moments of inertia of band states are close to the moment of inertia of the Hoyle state of 12C. The calculated radii, related to these bands, are 0.7 - 1.0 fm larger than the radius of the ground state, and are close to the radius of the Hoyle state. These results are in agreement with existing predictions about various cluster structure of 11B at high excitation energies. The state with the excitation energy 12.56 MeV, Iπ = 1/2+, T = 1/2 and the root mean square radius R ∼ 6 fm predicted in the frame of the alpha condensate hypothesis was not found.

Investigation ofBe10and its cluster dynamics with the nonlocalized clustering approach

We extend the new concept of nonlocalized clustering to the nucleus 10Be with proton number Z=4 and neutron number N=6 (N=Z+2). The Tohsaki-Horiuchi-Schuck-R\"opke (THSR) wave function is formulated for the description of different structures of 10Be. Physical properties such as energy spectrum and root-mean-square radii are calculated for the first two 0+ states and corresponding rotational bands. With only one single THSR wave function, the calculated results show good agreement with other models and experimental values. We apply, for the first time, the THSR wave function on the chain orbit ({\sigma}-orbit) structure in the 0^+_2 state of 10Be. The ring orbit ({\pi}-orbit) and {\sigma}-orbit structures are further illustrated by calculating the density distribution of the valence neutrons. We also investigate the dynamics of ff-clusters and the correlations of two valence neutrons in 10Be.

Nature of the En = 1.24 MeV state in 12Be

I suggest that a new state (Phys. Rev. C 90, 024309 (2014)) observed in 12Be, with a neutron decay energy of 1243keV, is likely to be $ 2^{+}$ , rather than the previously suggested ( $ 2^{-}$ , ( $ 1^{-}$ )). Primary p-wave decay is then to the first excited state of 11Be, but a possible d-wave g.s. branch could be as large as about 10%.

Exclusive measurements of quasi-free proton scattering reactions in inverse and complete kinematics

Quasi-free scattering reactions of the type (p,2p) were measured for the first time exclusively in complete and inverse kinematics, using a 12C beam at an energy of ∼400 MeV/u as a benchmark. This new technique has been developed to study the single-particle structure of exotic nuclei in experiments with radioactive-ion beams. The outgoing pair of protons and the fragments were measured simultaneously, enabling an unambiguous identification of the reaction channels and a redundant measurement of the kinematic observables. Both valence and deeply-bound nucleon orbits are probed, including those leading to unbound states of the daughter nucleus. Exclusive (p,2p) cross sections of 15.8(18) mb, 1.9(2) mb and 1.5(2) mb to the low-lying 0p-hole states overlapping with the ground state (3/2−) and with the bound excited states of 11B at 2.125 MeV (1/2−) and 5.02 MeV (3/2−), respectively, were determined via γ-ray spectroscopy. Particle-unstable deep-hole states, corresponding to proton removal from the 0s-orbital, were studied via the invariant-mass technique. Cross sections and momentum distributions were extracted and compared to theoretical calculations employing the eikonal formalism. The obtained results are in a good agreement with this theory and with direct-kinematics experiments. The dependence of the proton–proton scattering kinematics on the internal momentum of the struck proton and on its separation energy was investigated for the first time in inverse kinematics employing a large-acceptance measurement.

Study of rlastic and inelastic 11 B +α scattering and search for cluster states of enlarged radius in 11B

The differential cross sections for elastic and inelastic 11B + α scattering were measured at the alpha-particle energy of 65 MeV, the inelastic-scattering processes leading to the excitation of known states of 11B up to excitation energies of about 14 MeV. Data on elastic scattering were analyzed together with those that were published earlier for lower energies. The cross sections for inelastic scattering were analyzed on the basis of the distorted-wave method. A modified diffractionmodel was used to determine the root-mean-square radii of excited states. The radii of states whose excitation energies were below about 7MeV were found to agree with radius of the ground state to within 0.1 to 0.15 fm. This result complieswith the traditional idea that the low-lying states of 11B have a shell structure. The possibility that these states belong to the predicted rotational bands, which, if any, are truncated to three states, cannot be ruled out either. The majority of the observed highly excited states are distributed among four rotational bands. The moments of inertia of these bands are close; for the band based on the 3/2− state at E* = 8.56 MeV, they are even higher than those of the Hoyle state in the 12C nucleus. The measured radii of states associated with these bands of 11B are larger than the ground-state radius by 0.7 to 1.0 fm and are also close to the radius of the Hoyle state. The results of the present study agree with the existing predictions that the cluster structure of the 11B nucleus is diverse at high excitation energies. The hypothesis that the 11B nucleus features a “giant” state of size commensurate with those in heavy nuclei was not confirmed.

Electric properties of the low-lying excited states of benzonitrile: geometry relaxation and solvent effects

Accurate calculations of the dipole moment and the polarizability for the ground and two lowest singlet and triplet excited states of benzonitrile (BN) have been performed by a variety of wave function and density functional theory (DFT) methods. Changes in molecular properties upon the electron excitation strongly depend on the character of an excited state. The vertical dipole moment change and the excess polarizability for the 11B state are smaller than those for the 21A state. In order to estimate adiabatic excited-state properties, corresponding relaxed geometries have been obtained using the PBE0 functional with the aug-cc-pVTZ basis set. The excited-state property values obtained with the long-range exchange corrected DFT methods are in general closer to the coupled cluster (CC) results, although the hybrid DFTs also provide reasonable predictions. Our CCSD adiabatic excess dipole moment value for the 11B state equal to 0.11 D is in excellent agreement with the experimental value. The 21A state appears to be more sensitive to selected method due to an important role of double-excitation effects. Solvent effects on dipole moment and polarizability of BN molecule in its ground and excited states were evaluated using both LR and cLR methods combined with the (TD-)CAMB3LYP/POL approach.

8Li+α resonant elastic scattering: a tool to study cluster states in 12B

The 8Li+4He elastic scattering excitation function was measured by using the inverse kinematic thick target method. The 8Li beam was provided by the LNS radioactive facility EXCYT at an energy of 30 MeV and it was delivered into a large scattering chamber filled with 4He gas. The detection system was made by three silicon telescopes and one MCP. This last detector was used to measure the number of incident particles as well as the time of flight allowing for the discrimination between elastic and inelastic scattering. The setup and the experimental technique will be described in details and the results, as well as the comparison of the data with an R-matrix calculation, will be shown and discussed.

Nuclear magnetic moments for J π = 2 1 + state of 10Be with ab initio Monte Carlo shell model calculation

The magnetic moment of 2 1 + state for 10Be are calculated and investigated in terms of single particle orbits for protons and neutrons under the framework of ab initio Monte Carlo shell model method in an e max = 3 model space. The reduced matrix elements of orbital and spin angular momentum are evaluated. It is found that the orientations of orbital angular momentum in different single particle orbits are consistent. Conversely, the orientations of spin in different single particle orbits tend to be chaotic. The nuclear magnetic moment of 2 1 + state for 10Be is obtained as 1.006 µ N and is discussed in regards to the contribution of orbital and spin angular momentum both for protons and neutrons. The corresponding g-factor is also given.

Elastic and inelastic scattering of 14C + 11B versus 12,13C + 11B

Complete angular distributions of the 14C + 11B elastic and inelastic scattering at the energy $ E_{lab}({}^{11}B)$ = 45 MeV were measured for the ground and excited states of 11B. The data were analyzed within the optical model and the coupled-reaction-channels method. The parameters of the 14C + 11B optical potential and 11B deformation were deduced. The contributions of one- and two-step transfers of nucleons and clusters into the 14C + 11B elastic and inelastic scattering were calculated. The isotopic differences between the 14C + 11B and 12,13C + 11B scatterings are presented and clearly show the importance of the large angle scattering data for understanding the interaction between light heavy ions.

Structures of ground and excited states in C isotopes

Structures of ground and excited states of C isotopes are theoretically investigated with the method of antisymmetrized molecular dynamics. For 14C, it is suggested that a linear-chain 3a structure can be stabilized by the excess neutrons and may construct an rotational band near the 10Be+α threshold energy. In 11C and its mirror nucleus 11B, a cluster gas state and a linear-like cluster state are suggested in excited states. Possible assignment of the cluster states in 11B with the experimental energy levels are discussed. Deformations of proton and neutron densities of the ground bands in neutron-rich C are also discussed.

Microscopic Three-Cluster Descriptions of 11B and 11C Nuclei

We investigate bound and resonance states of 11B and 11C. For this aim, we make use a three-cluster microscopic model which is a combination of the resonating group method and the hyperspherical harmonics Method. The model employs the basis of hyperspherical harmonics to enumerate channels and to describe the three-cluster continuum. The parameters of bound states and the nature of resonance states imbedded in the three-cluster continuum are investigated in detail.

Cluster structures of excited states in 11B

The cluster structure of excited states in 11B is investigated with a method of β-γ constrained antisymmetrized molecular dynamics in combination with the generator coordinate method. For negative-parity states, we identify a band with a 2α+t cluster structure. This band starts from the 3/2−3 state and may correspond to the experimental band observed recently. We find that the composision of the 3/2−3 state s quite similar to that of the 0+2 state in 12C.