Physics with loosely bound nuclei

The essential aspect of contemporary physics is to understand properties of nucleonic matter that constitutes the world around us. Over the years research in nuclear physics has provided strong guidance in understanding the basic principles of nuclear interactions. But, the scenario of nuclear physics changed drastically as the new generation of accelerators started providing more and more rare isotopes, which are away from the line of stability. These weakly bound nuclei are found to exhibit new forms of nuclear matter and unprecedented exotic behaviour. The low breakup thresholds of these rare nuclei are posing new challenges to both theory and experiments. Fortunately, nature has provided a few loosely bound stable nuclei that have been studied thoroughly for decades Attempts are being made to find a consistent picture for the unstable nuclei starting from their stable counterparts. Some significant differences in the structure and reaction mechanisms are found.     

Effective-range expansion for two coupled channels and properties of bound states

The S matrix and the scattering-amplitude matrix (F matrix) are considered for the case of two coupled elastic-scattering channels differing by the values of the orbital angular momentum (l ₁ and l ₂ = l ₁ + 2). The matrix elements of the S and F matrices in the absence of Coulomb interaction are expressed in terms of the matrix elements of the matrix K ⁻¹ inverse to the reaction K matrix. The elements of the K ⁻¹ matrix are written in the form of expansions that are generalizations of the single-channel effective-range expansion. If there is a bound state in the system of colliding particles, then an analytic continuation of these expansions to the region of negative energies makes it possible to obtain both the position of the pole corresponding to this bound state and the residues of scattering amplitudes at this pole, the respective vertex constants and asymptotic normalization coefficients being expressed in terms of these residues. By way of example, the developed formalism is applied to describing triplet neutron-proton scattering.     

Compact and loosely bound structures in light nuclei

The role of various components in the wave function of loosely bound light nuclei is considered in terms of the cluster model by taking into account orbital polarization. We show that several structures corresponding to particular modes of nucleon motion can be concurrently important for such structures. Specific examples of simple and fairly flexible trial wave functions are given for the ⁸Be and ⁶He nuclei. Explicit expressions are derived for the microscopic wave functions of these nuclei and employed to calculate basic nuclear parameters for commonly used central exchange NN potentials.     

Shell-model calculations for the zinc isotopes

Shell-model calculations for the zinc isotopes have been carried out with active particles distributed in the $\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{, 0}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbits outside a closed “⁵⁶Ni” core. The effective Hamiltonian used was one obtained by Koops and Glaudemans from a fit to Ni and Cu level energies. An average absolute deviation of 0.19 MeV between the calculated and experimental ground-state binding energies is obtained for the A = 62?68 Zn isotopes. Good agreement is also found between most calculated and experimental excitation energies and spectroscopic factors for single-nucleon transfer for the low-lying levels in these nuclei. Experimentally known B(E2) values are generally well reproduced by the present model with effective charges of 1.0 ± 0.1 and 1.6 ± 0.2 for the neutron and proton, respectively. Magnetic dipole as well as Gamow-Teller transitions are not well accounted for by these calculations and seem to be sensitive to excitations of the ⁵⁶Ni core.     

Dynamic polarization in the Coulomb breakup of loosely bound F

Angular distributions of the Coulomb breakup of radioactive ¹⁷F were measured by impinging a 10 MeV/nucleon beam on ²⁰⁸Pb and on ⁵⁸Ni to study the dynamic polarization effects. The breakup products, oxygen and a proton, were detected in coincidence. First-order perturbation theory significantly overpredicts the breakup cross section for the ²⁰⁸Pb target. Dynamical calculations with a dynamic polarization as the leading order correction were performed. The calculations reproduce the data for ¹⁷F on ⁵⁸Ni but overpredict the breakup of ¹⁷F on ²⁰⁸Pb by a factor of two at forward angles.     

Disappearance of the hindrance ofE1-transition involving loosely bound nucleon

AlthoughE1-transition between levels below giant dipole resonance are almost always strongly hindered, there are several exceptions as observed in¹¹Be and¹³C. These fastE1-transitions are studied by adopting a simple “cutoff” model, in which the behavior of single particle wave functions only outside of the nucleus contribute. The results are compared with the particle-GDR coupling model. The reason why theE1-hindrance disappears is explained. We also investigate the direct capture of thermal neutron by⁴⁰Ca andN=82 nuclei, where similar situation is observed. Further, the implication of the direct capture in multiple neutron capture is discussed.     

He-LiH体系束缚态能级的理论计算

在CCSD(T) 势能面的基础上,采用严格的量子力学方法计算得到了He-LiH体系束缚态振转能级和波函数,结果表明该体系存在10个振转束缚态.从波函数的分布图中可以知道,与J=0的第一个能级对应的本征态是靠近Li端较深势阱的一个束缚态;第二个能级为伸展激发振动能级;基本上存在于深势阱内,但H端的浅势阱通过隧道效应,对该能级的几率分布产生了影响.     

Microscopic calculations for Be isotopes within real-time evolution method

The European Physical Journal A - This paper is a write-up of the ideas that were presented, developed and discussed at the third International Workshop on QCD Challenges from pp to A–A,...     

Reactions involving loosely bound cluster nuclei: Heavy ions and new technologies

Experimental results on excitation functions for complete-fusion and transfer reactions in the interaction of ⁶He and ^6,8,9Li nuclei with various target nuclei are presented. Data on fusion-reaction cross sections in the case of ⁶He differ strongly from the predictions of the statistical model. A strong enhancement of the cross section at barrier energies is observed for this reaction channel. Also, an increase in the cross sections for neutron-transfer reactions (in the case of ⁶He and ^8,9Li beams) and deuteron-transfer reactions (in the case of ⁶Li) is observed in the deep-subbarrier energy region. The results are discussed from the point of view of the effect of the cluster structure of nuclei on the probability of interaction at barrier energies. The results of employing heavy-ion beams in new technologies are presented.     

Sub- and above-barrier fusion of loosely bound 6Li with 28Si

Fusion excitation functions are measured for the system ⁶Li + ²⁸Si using the characteristic $ \gamma$ -ray method, encompassing both the sub-barrier and above-barrier regions, viz, E _lab = 7-24 MeV. Two separate experiments were performed, one for the above-barrier region ( E _lab = 11-24 MeV) and another for the below-barrier region ( E _lab = 7-10 MeV). The results were compared with our previously measured fusion cross-section for the ⁷Li + ²⁸Si system. We observed the enhancement of the fusion cross-section at sub-barrier regions for both ⁶Li and ⁷Li , but the yield was substantially larger for ⁶Li . However, for well-above-barrier regions, a similar type of suppression was identified for both the systems.     

Diffractive scattering of loosely bound nuclei involving two charged clusters on nuclei

The theory of diffractive interaction between loosely bound nuclei featuring two charged clusters and nuclei is developed with allowance for Coulomb interaction. The differential cross sections for the scattering of ⁶Li, ⁷Be, and ⁸B nuclei on ¹²C nuclei are calculated, and the results of these calculations are compared with data from recent experiments.     

IBA calculations on the even-even Pt isotopes

By performing least-squares-fit calculations on the energy spectra of the even-even ^186–196Pt isotopes, the IBA model I and the IBA model II are compared on an equal footing. It is found that both model I and model II can fit energy spectra and absolute B(E2) transition rates reasonably well. Model II shows a distinct improvement in the energy spectra of β-bands of heavier nuclei in the isotope series. It is suggested that for regions far from the closed shells model I may be used to simulate model II as a useful phenomenological probing tool.     

Shell-model calculations on Ni and Cu isotopes

Binding energies, excitation energies and spectroscopic factors have been calculated for^57–67Ni and^58–68Cu in an unrestricted (2p_3/2, lf _5/2,2p_1/2) shell-model space. The effective two-body matrix elements are obtained from the modified surface delta interaction (MSDI) and from a least-squares fit to experimental binding and excitation energies (ASDI). The average deviation between about 100 experimental and calculated energies is 0.14MeV for MSDI and 0.08 MeV for ASDI. Excitation energies of high-spin states are given also. Spectroscopic factors have been calculated for all single-nucleon transfer reactions on stable Ni or Cu targets leading to Ni or Cu isotopes. For spectroscopic factors larger than 0.4 the average deviation between theory and experiment is about 30%. The experimentally observed and calculated spectroscopic strengths are compared by using sum rules and are found to be consistent. An extensive compilation has been made of experimental data on energies,J ^π assignments and spectroscopic factors.     

The interacting boson model: Microscopic calculations for the mercury isotopes

Microscopic calculations of the parameters of the proton-neutron interacting boson model (IBM-2) appropriate to the even Hg isotopes are reported. The calculations are based on the Otsuka-Armia-Iachello boson mapping procedure, which is briefly reviewed. Renormalization of the parameters due to exclusion of the l=4 g boson is treated perturbatively. The calculations employ a semi-realistic shell-model Hamiltonian with no adjustable parameters. The calculated parameters of the IBM-2 Hamiltonian are used to generate energy spectra and electromagnetic transition probabilities, which are compared with experimental data and with the result of phenomenological fits. The overall agreement is reasonable with some notable exceptions, which are discussed. Particular attention is focused on the parameters of the Majorana interaction and on the F-spin character of low-lying levels.     

Interaction of loosely bound radioactive 7Be and stable 7Li with 9Be

Quasielastic scattering angular distributions have been measured for the ⁷Be + ⁹Be system at E _lab = 17 , 19 and 21MeV in the angular range $ \theta_{{cm}}^{}$ = 24^° - 57^° . An optical model (OM) analysis of these data has been carried out in order to extract optical potential parameters and reaction cross-sections. One-proton stripping cross-sections were also measured for this system at E _lab = 19 and 21MeV. These transfer angular-distribution data were compared with the finite-range distorted-wave Born approximation (FRDWBA) calculations. For the ⁷Li + ⁹Be system quasielastic scattering angular distributions were measured and emitted light charged particles were detected at E _lab = 15.75 , 24.00 and 30.00MeV in the angular range $ \theta_{{cm}}^{}$ = 7^° - 70^° . Fusion cross-sections were obtained by reproducing the measured $ \alpha$ -evaporation spectra from the compound nucleus at backward angles with the statistical model calculations. The ratios of the experimental fusion cross-sections to the total reaction cross-sections (obtained from OM analysis) were found to be small. This result suggests that the break-up process has a strong influence on the fusion process leading to a reduction in the fusion cross-section.     

Fine-grid calculations for stellar electron and positron capture rates on Fe isotopes

The acquisition of precise and reliable nuclear data is a prerequisite to success for stellar evolution and nucleosynthesis studies. Core-collapse simulators find it challenging to generate an explosion from the collapse of the core of massive stars. It is believed that a better understanding of the microphysics of core-collapse can lead to successful results. The weak interaction processes are able to trigger the collapse and control the lepton-to-baryon ratio (Y _e ) of the corematerial. It is suggested that the temporal variation of Y _e within the core of a massive star has a pivotal role to play in the stellar evolution and a fine-tuning of this parameter at various stages of presupernova evolution is the key to generate an explosion. During the presupernova evolution of massive stars, isotopes of iron, mainly ^54–56Fe, are considered to be key players in controlling Y _e ratio via electron capture on these nuclides. Recently an improved microscopic calculation of weak-interaction-mediated rates for iron isotopes was introduced using the proton-neutron quasiparticle random-phase-approximation (pn-QRPA) theory. The pn-QRPA theory allows a microscopic state-by-state calculation of stellar capture rates which greatly increases the reliability of calculated rates. The results were suggestive of some fine-tuning of the Y _e ratio during various phases of stellar evolution. Here we present for the first time the fine-grid calculation of the electron and positron capture rates on ^54–56Fe. The sensitivity of the pn-QRPA calculated capture rates to the deformation parameter is also studied in this work. Core-collapse simulators may find this calculation suitable for interpolation purposes and for necessary incorporation in the stellar evolution codes.     

Positive energy bound states in resonating group calculations

Spurious resonances occuring in numerical resonating group calculations off the oscillator limit are explained as being due to positive energy bound states. A generalization of Swan's version of the Levinson theorem is given which takes into account these states.