We investigate the structure of the neutron-rich $Λ$-hypernucleus $_Λ^{10}$Li by using microscopic shell-model calculations considering a $Λ$-$Σ$ coupling effect. The calculated $Σ$-mixing probability in the $_Λ^{10}$Li ground state is found to be about 0.34 % which is coherently enhanced by the $Λ$-$Σ$ coupling configurations, leading to the energy shift 0.28 MeV which is about 3 times larger than that in $_Λ^{7}$Li. The importance of the $Σ$ configuration obtained by the $ΣN$ interaction and the potentiality of the neutron-rich environment are discussed.
We investigate theoretically production cross sections of the $J^π=$ 0$^+$ ground state of a $^4_Λ$He hypernucleus in the $^4$He($π$,~$K$) reaction with a distorted-wave impulse approximation using the optimal Fermi-averaged $πN\to KΛ$ $t$ matrix. We demonstrate the sensitivity of the production cross sections to the $Λ$ wavefunctions obtained from $3N$-$Λ$ potentials and to meson distorted waves in eikonal distortions. It is shown that the calculated laboratory cross sections of the 0$^+$ ground state in $^4_Λ$He amount to $dσ/dΩ_{\rm lab} \simeq$ 11 $μ$b/sr at $p_π=$ 1.05 GeV/$c$ in the $K$ …
Hiyama et al. [PRL 104 (2010) 212502] have recently reported on a pioneering five-body alpha-alpha-n-Lambda-Lambda cluster-model calculation of Lambda-Lambda-11Be in order to confront a possible interpretation of the KEK-E373 HIDA event. Unfortunately, a six-body alpha-alpha-n-n-Lambda-Lambda calculation of Lambda-Lambda-12Be to confront another possible interpretation is beyond reach at present. Using experimental B-Lambda values with small corrections based on recently determined Lambda-N spin-dependent interaction parameters, we obtain binding-energy shell-model estimates for both Lambda-La…
Cluster-breaking and reconfiguration effects in $_Λ^{12}\rm{B}$ hypernucleus
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；High Energy Accelerator Research Organization (KEK)（高能加速器研究机构）；SOKENDAI（日本综合研究大学院大学）；Osaka University（大阪大学）；Osaka Institute of Technology（大阪工业大学）；Hosei University（法政大学）
The missing mass spectroscopy of the $^{7}_Λ$He hypernucleus was performed, using the $^{7}$Li$(e,e^{\prime}K^{+})^{7}_Λ$He reaction at the Thomas Jefferson National Accelerator Facility Hall C. The $Λ$ binding energy of the ground state (1/2$^{+}$) was determined with a smaller error than that of the previous measurement, being $B_Λ$ = 5.55 $\pm$ 0.10(stat.) $\pm$ 0.11(sys.) MeV. The experiment also provided new insight into charge symmetry breaking in p-shell hypernuclear systems. Finally, a peak at $B_Λ$ = 3.65 $\pm$ 0.20(stat.) $\pm$ 0.11(sys.) MeV was observed and assigned as a mixture of…
The basic version of the semi-microscopic particle-hole dispersive optical model is implemented to describe main properties of the Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei. Calculation results obtained for $^{48}Ca$, $^{90}Zr$, $^{132}Sn$, and $^{208}Pb$ are compared with available experimental data.
The structure of the neutron-rich carbon nucleus ^{16}C is described by introducing a new microscopic shell model of no-core type. The model space is composed of the 0s, 0p, 1s0d, and 1p0f shells. The effective interaction is microscopically derived from the CD-Bonn potential and the Coulomb force through a unitary transformation theory. Calculated low-lying energy levels of ^{16}C agree well with the experiment. The B(E2;2_{1}^{+} \to 0_{1}^{+}) value is calculated with the bare charges. The anomalously hindered B(E2) value for ^{16}C, measured recently, is well reproduced.
In the present paper we demonstrate that there exists a fully microscopic shell-model counterpart of the Bohr-Mottelson model by embedding the latter in the microscopic shell-model theory of atomic nucleus within the framework of the recently proposed fully microscopic proton-neutron symplectic model (PNSM). For this purpose, another shell-model coupling scheme of the PNSM is considered in which the basis states are classified by the algebraic structure $SU(1,1) \otimes SO(6)$. It is shown that the configuration space of the PNSM contains a six-dimensional subspace that is closely related to t…
We calculate microscopically total and parity-projected level densities for $β$-stable even-even nuclei between Fe and Ge, using the shell model Monte Carlo methods in the complete $(pf+0g_{9/2})$-shell. A single-particle level density parameter $a$ and backshift parameter $Δ$ are extracted by fitting the calculated densities to a backshifted Bethe formula, and their systematics are studied across the region. Shell effects are observed in $Δ$ for nuclei with Z=28 or N=28 and in the behavior of $A/a$ as a function of the number of neutrons. We find a significant parity-dependence of the level d…
We use a large-scale 6 hbar Omega calculation for Li6 with microscopically derived two-body interaction to construct the 0 hbar Omega 0p-shell effective hamiltonian, electric quadrupole, and magnetic dipole operators. While the E2 and M1 6 hbar Omega operators are one-body operators with free nucleon charges, the effective operators are two-body operators with substantially different renormalization for the isoscalar and isovector matrix elements, especially for the E2 operator. We show that these operators can be very well approximated by one-body operators provided that effective proton and …
Shell-model calculations in a large model space are performed for _Λ^{16}O and_Λ^{17}O. Effective interactions with degrees of freedom of Σin addition to Λand nucleons are derived from hyperon-nucleon and nucleon-nucleon interactions within the framework of the unitary-model-operator approach. Effects of the Σdegrees of freedom and the parity-mixing intershell coupling on the Λhypernuclear structure are investigated, employing the Nijmegen NSC97a-f and NSC89 hyperon-nucleon potentials.
Energy levels and electromagnetic properties of with $N=28\sim 30$ nuclides are studied in terms of a large-scale shell model calculation, which contains no newly adjusted parameters. The Kuo-Brown $G$-matrix interaction is shown to reproduce energy levels of 205 low-lying states of these nuclei. We evaluate effective charges by incorporating the core-polarization effects caused by the coupling to GQR's. We then compute E2 moments and transition probabilities. The M1 moments and transition rates are calculated by quoting the effective $g$-factors of Towner, which are obtained by taking into ac…
$0s$-orbit $Λ$ states in $p$-shell double-$Λ$ hypernuclei ($^{\ \,A}_{ΛΛ}Z$), $^{\ \,8}_{ΛΛ}\textrm{Li}$, $^{\ \,9}_{ΛΛ}\textrm{Li}$, $^{10,11,12}_{\ \ \ \ \ ΛΛ}\textrm{Be}$, $^{12,13}_{\ \ ΛΛ}\textrm{B}$, and $^{\,14}_{ΛΛ}\textrm{C}$ are investigated. Microscopic cluster models are applied to core nuclear part and a potential model is adopted for $Λ$ particles. The $Λ$-core potential is a folding potential obtained with effective $G$-matrix $Λ$-$N$ interactions, which reasonably reproduce energy spectra of $^{A-1}_{\,Λ}Z$. System dependence of the $Λ$-$Λ$ binding energies is understood by the…
Background: Effective interactions, either derived from microscopic theories or based on fitting selected properties of nuclei in specific mass regions, are widely used inputs to shell-model studies of nuclei. Until recently, most shell-model calculations have been confined to a single oscillator shell. Recent interest in nuclei away from the stability line, requires however larger shell-model spaces. Since the derivation of microscopic effective interactions has been limited to degenerate model spaces, there are both conceptual and practical limits to present shell-model calculations that uti…
GT transitions in $N=28\sim 30$ nuclei are studied in terms of a large-scale realistic shell-model calculation, by using Towner's microscopic parameters. $B({\rm GT})$ values to low-lying final states are reproduced with a reasonable accuracy. Several gross properties with respect to the GT transitions are investigated with this set of the wavefunctions and the operator. While the calculated total GT$^-$ strengths show no apparent disagreement with the measured ones, the calculated total GT$^+$ strengths are somewhat larger than those obtained from charge-exchange experiments. Concerning the I…
An extended SU(3) shell model that for the first time explicitly includes unique-parity levels is introduced. Shell-model calculations for the isotopes of $^{64}$Ge and $^{68}$Se are performed where valence nucleons beyond the N=28=Z core occupy levels of the normal parity upper-$fp$ shell ($f_{5/2},p_{3/2},p_{1/2}$) and the unique parity $g_{9/2}$ intruder configuration. The levels of the upper-$fp$ shell are handled within the framework of an m-scheme basis as well as its pseudo-SU(3) counterpart, and respectively, the $g_{9/2}$ as a single level and as a member for the complete $gds$ shell.…
Elastic scattering observables (differential cross section and analyzing power) are calculated for the reaction $^6$He(p,p)$^6$He at projectile energies starting at 71 MeV/nucleon. The optical potential needed to describe the reaction is based on a microscopic Watson first-order folding potential, which explicitly takes into account that the two neutrons outside the $^4$He-core occupy an open p-shell. The folding of the single-particle harmonic oscillator density matrix with the nucleon-nucleon t-matrix leads for this case to new terms not present in traditional folding optical potentials for …
The shell structure of even-even isotopes in Si, S, Ar and Ca has been analysed. The theoretical calculations of shell closure parameter $D_{n} (N)$ and the differential variation of the two-neutron separation energy $dS_{2n} (Z, N )$ are carried out within the framework of Hartree-Fock-Bogoliubov theory. Calculations are carried out for different skyrme forces and their sensitivity has been tested. Same nuclides are studied by employing the relativistic mean field aproach based on meson exchange and point coupling models. Theoretically calculated estimates are in good agreement with the recen…
The advent of nucleon-nucleon potentials derived from chiral perturbation theory, as well as the so-called V-low-k approach to the renormalization of the strong short-range repulsion contained in the potentials, have brought renewed interest in realistic shell-model calculations. Here we focus on calculations where a fully microscopic approach is adopted. No phenomenological input is needed in these calculations, because single-particle energies, matrix elements of the two-body interaction, and matrix elements of the electromagnetic multipole operators are derived theoretically. This has been …
The radiative thermal neutron capture cross sections over the range of thermal energies from 1 keV to 1 MeV are studied in statistical Hauser-Feshbach formalism. The optical model potential is constructed by folding the density dependent M3Y nucleon-nucleon interaction with radial matter densities of target nuclei obtained from relativistic-mean-field (RMF) theory. The standard nuclear reaction code TALYS1.8 is used for calculation of cross sections. The nuclei studied in the present work reside near the $Z=28$ proton shell closure and are of astrophysical interests taking part in p-, s-, and …
A microscopic model of the electromagnetic form factor of the nucleon is developed in a hadronic framework, including pions, nucleons and the Delta-resonance explicitly. The space like on-shell form factors are reproduced and predictions for the half off-shell dependence are made. The impact of this off-shell dependence in the time like sector (q^2 < 1 GeV^2, thus including the region of vector meson dominance) is of main interest in this investigation.
The ground-state energy of the doubly magic nuclei 4He and 16O has been calculated within the framework of the Goldstone expansion starting from modern nucleon-nucleon potentials. A low-momentum potential V-low-k has been derived from the bare potential by integrating out its high-momentum components beyond a cutoff Lambda. We have employed a simple criterion to relate this cutoff momentum to a boundary condition for the two-nucleon model space spanned by a harmonic-oscillator basis. Convergence of the results has been obtained with a limited number of oscillator quanta.
The shell model Monte Carlo (SMMC) method enables calculations in model spaces that are many orders of magnitude larger than those that can be treated by conventional methods, and is particularly suitable for the calculation of level densities in the presence of correlations. We review recent advances and applications of SMMC for the microscopic calculation of level densities. Recent developments include (i) a method to calculate accurately the ground-state energy of an odd-mass nucleus, circumventing a sign problem that originates in the projection on an odd number of particles, and (ii) a me…
The RPA long range correlations are known to play a significant role in understanding the depletion of single particle-hole states observed in (e, e') and (e, e'p) measurements. Here the Random Phase Approximation (RPA) theory, implemented using the D1S force is considered for the specific purpose of building correlated ground states and related one-body density matrix elements. These may be implemented and tested in a fully microscopic optical model for NA scattering off doubly-closed-shell nuclei. A method is presented to correct for the correlations overcounting inherent to the RPA formalis…
An approximate but straight forward projection method to molecular many alpha-particle states is proposed and the overlap to the shell model space is determined. The resulting space is in accordance with the shell model, but still contains states which are not completely symmetric under permutations of the alpha-particles, which is one reason to call the construction semi-microscopic. A new contribution is the construction of the 6- and 7-$α$-particle spaces. The errors of the method propagate toward larger number of alpha-particles and larger shell excitations. In order to show the effectiven…
We formulate theory of the two-proton radioactivity based on the real-energy continuum shell model. This microscopic approach is applied to describe the two-proton decay of the $1^-_2$ state in $^{18}$Ne.
The damping of collective rotational motion is studied microscopically, making use of shell model calculations based on the cranked Nilsson deformed mean-field and on residual two-body interactions, and focusing on the shape of the gamma-gamma correlation spectra and on its systematic behavior. It is shown that the spectral shape is directly related to the damping width of collective rotation, \Gammarot, and to the spreading width of many-particle many-hole configurations, \Gammamu. The rotational damping width is affected by the shell structure, and is very sensitive to the position of the Fe…
The quadrupole collectivity in Nd, Sm, Gd, Dy, Er, Yb, Hf and W nuclei with neutron numbers 122 $\le$ N $\le$ 156 is studied, both at the mean field level and beyond, using the Gogny energy density functional. Besides the robustness of the N=126 neutron shell closure, it is shown that the onset of static deformations in those isotopic chains with increasing neutron number leads to an enhanced stability and further extends the corresponding two-neutron driplines far beyond what could be expected from spherical calculations. Independence of the mean field predictions with respect to the particul…
Quantum shell effects drive many aspects of many-body quantal systems and their interactions. Among these are the quasifission reactions that impede the formation of a compound nucleus in superheavy element (SHE) searches. Fragment production in quasifission is influenced by shell effects as a nontrivial manifestation of microscopic dynamics hindering the full equilibration of the composite system to form the compound nucleus. In this Letter, we use the microscopic time-dependent Hartree-Fock (TDHF) theory to study 48Ca+249Bk collisions to investigate the influence of the tensor component of t…
We perform three-body model calculations for a $sd$-shell hypernucleus $^{19}_Λ$F ($^{17}_Λ{\rm O}+p+n$) and its core nucleus $^{18}$F ($^{16}{\rm O}+p+n$), employing a density-dependent contact interaction between the valence proton and neutron. We find that the $B(E2)$ value from the first excited state (with spin and parity of $I^π=3^+$) to the ground state ($I^π=1^+$) is slightly decreased by the addition of a $Λ$ particle, which exhibits the so called shrinkage effect of $Λ$ particle. We also show that the excitation energy of the $3^+$ state is reduced in $^{19}_Λ$F compared to $^{18}$F,…
We develop the microscopic description of the two-nucleon radioactivity in the framework of the Shell Model Embedded in the Continuum. This approach is applied for the description of spontaneous two-proton radioactivity in $^{45}$Fe, $^{48}$Ni and $^{54}$Zn.
Constructing microscopic effective interactions (`optical potentials') for nucleon-nucleus (NA) elastic scattering requires in first order off-shell nucleon-nucleon (NN) scattering amplitudes between the projectile and the struck target nucleon and nonlocal one-body density matrices. While the NN amplitudes and the {\it ab intio} no-core shell-model (NCSM) calculations always contain the full spin structure of the NN problem, one-body density matrices used in traditional microscopic folding potential neglect spin contributions inherent in the one-body density matrix. Here we derive and show th…
We review an extension of Migdal's Theory of Finite Fermi Systems which has been developed and applied to collective vibrations in closed shell nuclei in the past ten years. This microscopic approach is based on a consistent use of the Green function method. Here one considers in a consistent way more complex 1p1h$\otimes$phonon configurations beyond the RPA correlations. Moreover, these configurations are not only included in the excited states but also explicitly in the ground states of nuclei. The method has been applied to the calculation of the strength distribution and transition densiti…
The quest to build a mass formula which have in it the most relevant microscopic contributions is analyzed. Inspired in the successful Duflo-Zuker mass description, the challenges to describe the shell closures in a more transparent but equally powerful formalism are discussed.
Microscopic investigation of magnetic and antimagnetic rotational motion in atomic nuclei
University of Kashmir（克什米尔大学）；Govt. Degree College Kulgam（库尔加姆政府学位学院）；Indian Institute of Technology Bombay（孟买印度理工学院）；University of Engineering and Management（工程与管理大学）；GDC Shopian（肖皮安政府学位学院）；Islamic University of Science and Technology（伊斯兰科学技术大学）
The semi-classical Wigner-Kirkwood $\hbar$ expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in $\hbar$. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme, are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a…
The shell-model coupling scheme of the proton-neutron symplectic model (PNSM), defined by the following dynamical symmetry chain $Sp(12,R) \supset SU(1,1) \otimes SO(6) \supset U(1) \otimes SU_{pn}(3) \otimes SO(2) \supset SO(3)$, is considered. It is shown that it corresponds to a microscopic version of the Bohr-Mottelson collective model which captures the original relationships between its exactly solvable submodel limits. This variant of the PNSM provides an interesting and relevant shell-model symplectic-based framework for exploring the nuclear collective dynamics. Some simple applicatio…
The competition between the isovector (T=1) and isoscalar (T=0) proton-neutron ($p-n$) correlations in $N=Z$ nuclei is investigated by calculating their correlation energies with a realistic effective interaction which reproduces observed nuclear properties very well, in a strict shell model treatment. It is shown in the realistic shell model that the double-differences of binding energies $(B(A+pn:T) + B(A) - B(A+p) - B(A+n))$ ($B(A)$ being the binding energy) are good indicators of the T=1 and T=0 $p-n$ correlations. Each of them, however, originates in plural kinds of correlations with T=1 …
The nuclear structure dependence of direct reactions that remove a pair of like or unlike nucleons from a fast $^{12}$C projectile beam are considered. Specifically, we study the differences in the two-nucleon correlations present and the predicted removal cross sections when using $p$-shell shell-model and multi-$\hbarω$ no-core shell-model (NCSM) descriptions of the two-nucleon overlaps for the transitions to the mass $A$=10 projectile residues. The NCSM calculations use modern chiral two-nucleon and three-nucleon (NN+3N) interactions. The $np$-removal cross sections to low-lying $T$=0, $^{1…
The decay dynamical path is determined within the macroscopic-microscopic model for the emission of 24Ne from 232U. The nuclear shape parametrization is characterized five degrees of freedom. The single particle energies and the nucleon wave functions are obtained within the superasymmetric Woods-Saxon two center shell model. It turns out that the cluster decay follows a potential magic valley, starting from the ground state of the parent and reaching a configuration of two touching nuclei at scission. A small pocket in the potential barrier is evidenced, as a result of large shell effects in …
The neutron capture cross sections have been studied near the $Z=50$ closed shell for a number of nuclei those take part in heavy element nucleosynthesis, the slow and the rapid neutron capture processes and the proton capture process. An optical model potential is constructed in theoretical approach by folding the density dependent M3y purely real nucleon-nucleon interaction with the target radial matter density in relativistic mean field (RMF) approach. The standard code TALYS1.8 is used for cross-section calculation. We have presented the Maxwellian-averaged capture cross-section (MACS) val…
Elastic scattering of pions from finite nuclei is investigated utilizing a contemporary, momentum--space first--order optical potential combined with microscopic estimates of second--order corrections. The calculation of the first--order potential includes:\ \ (1)~full Fermi--averaging integration including both the delta propagation and the intrinsic nonlocalities in the $π$-$N$ amplitude, (2)~fully covariant kinematics, (3)~use of invariant amplitudes which do not contain kinematic singularities, and (4)~a finite--range off--shell pion--nucleon model which contains the nucleon pole term. The…
The 0+-spectrum in rare earth nuclei within the pseudo-SU(3) shell model
Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Frankfurt Institute for Advanced Studies, J.W. von Goethe Univeristy（法兰克福先进研究所，约翰·沃尔夫冈·冯·歌德大学）；Maharishi Markandeshwar, Deemed to be University（玛哈里希·马克丹什瓦尔认定大学）
In view of the recent experiments on neutrino oscillations performed by the LSND and KARMEN collaborations as well as of future experiments, we present new theoretical results of the flux averaged $^{12}C(ν_e,e^-)^{12}N$ and $^{12}C(ν_μ,μ^-)^{12}N$ cross sections. The approaches used are charge-exchange RPA, charge-exchange RPA among quasi-particles (QRPA) and the Shell Model. With a large-scale shell model calculation the exclusive cross sections are in nice agreement with the experimental values for both reactions. The inclusive cross section for $ν_μ$ coming from the decay-in-flight of $π^+…
The microscopic structure of neutron-rich sd-shell nuclei is investigated by using the spherical shell-model in the sd-pf valence space with the extended pairing plus quadrupole-quadrupole forces accompanied by the monopole interaction (EPQQM). The calculation reproduces systematically the known energy levels for even-even and odd-mass nuclei including the recent data for 43S, 46S and 47Ar. In particular, the erosion of the N=28 shell closure in 42Si can be explained. Our EPQQM results are compared with other shell-model calculations with the SDPF-NR and SDPF-U effective interactions.
Shell model wave functions have been used to form microscopic g-folding optical potentials with which elastic scattering data from 8He, 10,11C, and 18,20,22O scattering on hydrogen has been analyzed. Those potentials, the effective two-nucleon interaction used in their formation, and the shell model details, then have been used in distorted wave approximation calculations of differential cross sections from inelastic scattering to the first excited states of five of those radioactive ions.
