2018 Vol. 35, No. 4
Special Issue on the 17th National Conference on Nuclear Structure in China(NCNS2018)
Display Method:
2018, 35(4): 1-5.
Abstract:
2018, 35(4): 339-349.
doi: 10.11804/NuclPhysRev.35.04.339
Abstract:
The Institute of Modern Physics, Chinese Academy of Sciences, proposed the Major National Science and Technology Infrastructure Facility named as High Intensity Heavy-ion Accelerator Facility (HIAF) in 2010. After a series of assessments charged by the National Development and Reform Commission of China, HIAF was officially approved by China government in December, 2015. HIAF will be constructed in Huizhou, Guangdong Province, and the groundbreaking ceremony of construction is scheduled around the end in the year of 2018. HIAF is composed of a superconducting Linac, a booster ring, a high-energy radioactive beam line, a storage ring, and a number of experiment setups. The total investment of HIAF is about 2.5 billion Chinese Yuan. The major goals for HIAF are to explore the hitherto unknown territories in nuclear chart, to approach the experimental limits, to open new domains of physics researches in experiments, and to develop new ideas and heavy-ion applications beneficial to the societies. In this paper, the accelerator complex of HIAF is briefly introduced, and the experimental setups and associated physics research program are presented.
The Institute of Modern Physics, Chinese Academy of Sciences, proposed the Major National Science and Technology Infrastructure Facility named as High Intensity Heavy-ion Accelerator Facility (HIAF) in 2010. After a series of assessments charged by the National Development and Reform Commission of China, HIAF was officially approved by China government in December, 2015. HIAF will be constructed in Huizhou, Guangdong Province, and the groundbreaking ceremony of construction is scheduled around the end in the year of 2018. HIAF is composed of a superconducting Linac, a booster ring, a high-energy radioactive beam line, a storage ring, and a number of experiment setups. The total investment of HIAF is about 2.5 billion Chinese Yuan. The major goals for HIAF are to explore the hitherto unknown territories in nuclear chart, to approach the experimental limits, to open new domains of physics researches in experiments, and to develop new ideas and heavy-ion applications beneficial to the societies. In this paper, the accelerator complex of HIAF is briefly introduced, and the experimental setups and associated physics research program are presented.
2018, 35(4): 350-355.
doi: 10.11804/NuclPhysRev.35.04.350
Abstract:
Exploiting special symmetries to unmask simplicity within complexity that remains the "holy grail" of nuclear theory is re-examined within the framework of its historical context and current ab initio nocore shell-model approaches that exploit high-performance computing resources and applied math methodologies. Examples using the symmetry-adapted no-core shell model (SA-NCSM) that clearly demonstrate the important role group theory plays in this evolving story will serve to elucidate current state-of-the-art developments in this arena, including comparisons of excitation spectra and transition rates with experimental results for light and medium-mass nuclei. An interesting extension of the SA-NCSM, an advanced method with a novel twist that enables one to incorporate deformation from the onset, will be proffered as a further way to manage the combinatorial growth of model-space dimensionalities that remains the nemesis of all theories that seek an ab initio understanding of nuclear collectivity, and in so doing extends applicability of the theory to heavier and more exotic nuclear species.
Exploiting special symmetries to unmask simplicity within complexity that remains the "holy grail" of nuclear theory is re-examined within the framework of its historical context and current ab initio nocore shell-model approaches that exploit high-performance computing resources and applied math methodologies. Examples using the symmetry-adapted no-core shell model (SA-NCSM) that clearly demonstrate the important role group theory plays in this evolving story will serve to elucidate current state-of-the-art developments in this arena, including comparisons of excitation spectra and transition rates with experimental results for light and medium-mass nuclei. An interesting extension of the SA-NCSM, an advanced method with a novel twist that enables one to incorporate deformation from the onset, will be proffered as a further way to manage the combinatorial growth of model-space dimensionalities that remains the nemesis of all theories that seek an ab initio understanding of nuclear collectivity, and in so doing extends applicability of the theory to heavier and more exotic nuclear species.
2018, 35(4): 356-361.
doi: 10.11804/NuclPhysRev.35.04.356
Abstract:
We discuss the quantum self-organization introduced recently as one of the major underlying mechanisms of the quantum many-body systems. Atomic nuclei are actually a good example, because two types of the motion of nucleons, single-particle states and collective modes, interplay in determining their structure. The collective mode appears as a consequence of the balance between the effect of the mode-driving force (e.g., quadrupole force for the ellipsoidal deformation) and the resistance power against it. The single-particle energies are one of the sources to bring about such resistance power:a coherent collective motion is more hindered by larger spacings between relevant single particle states. Thus, the single-particle state and the collective mode are "enemies" against each other in the usual understanding. However, the nuclear forces are rich and complicated enough so as to enhance relevant collective mode by reducing the resistance power by changing single-particle energies for each eigenstate through monopole interactions. This will be demonstrated with the concrete example taken from Zr isotopes. In this way, the quantum self-organization occurs:single-particle energies can be self-organized by (i) two quantum liquids, e.g., protons and neutrons, (ii) monopole interaction (to control resistance). Thus, atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naïve Fermi liquid picture a la Landau. Type Ⅱ shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger.
We discuss the quantum self-organization introduced recently as one of the major underlying mechanisms of the quantum many-body systems. Atomic nuclei are actually a good example, because two types of the motion of nucleons, single-particle states and collective modes, interplay in determining their structure. The collective mode appears as a consequence of the balance between the effect of the mode-driving force (e.g., quadrupole force for the ellipsoidal deformation) and the resistance power against it. The single-particle energies are one of the sources to bring about such resistance power:a coherent collective motion is more hindered by larger spacings between relevant single particle states. Thus, the single-particle state and the collective mode are "enemies" against each other in the usual understanding. However, the nuclear forces are rich and complicated enough so as to enhance relevant collective mode by reducing the resistance power by changing single-particle energies for each eigenstate through monopole interactions. This will be demonstrated with the concrete example taken from Zr isotopes. In this way, the quantum self-organization occurs:single-particle energies can be self-organized by (i) two quantum liquids, e.g., protons and neutrons, (ii) monopole interaction (to control resistance). Thus, atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naïve Fermi liquid picture a la Landau. Type Ⅱ shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger.
2018, 35(4): 362-368.
doi: 10.11804/NuclPhysRev.35.04.362
Abstract:
Charge radius is one of the most fundamental observables of atomic nuclei, reflecting the proton distributions in nuclei. Their precision measurements have severed as a key tool to study nuclear structure. Recently, a novel method to deduce charge radii has been developed via precise measurements of charge-changing cross sections(CCCS) of exotic nuclei at relativistic energies. This method is in particular suitable for investigation of exotic nuclei with low production yield. In 2013, we proposed to make such measurements for exotic nuclei lighter than oxygen based on the RIBLL2 beam line. Since then, the TOF-△E detector system for particleidentification(PID) and the CCCS platform have been constructed, continuously optimized and tested. So far CCCS measurements on a carbon target have been performed for more than 20 isotopes. In this contribution, we will introduce the progress of detector development, the progress in PID, and our experimental progress and plan.
Charge radius is one of the most fundamental observables of atomic nuclei, reflecting the proton distributions in nuclei. Their precision measurements have severed as a key tool to study nuclear structure. Recently, a novel method to deduce charge radii has been developed via precise measurements of charge-changing cross sections(CCCS) of exotic nuclei at relativistic energies. This method is in particular suitable for investigation of exotic nuclei with low production yield. In 2013, we proposed to make such measurements for exotic nuclei lighter than oxygen based on the RIBLL2 beam line. Since then, the TOF-△E detector system for particleidentification(PID) and the CCCS platform have been constructed, continuously optimized and tested. So far CCCS measurements on a carbon target have been performed for more than 20 isotopes. In this contribution, we will introduce the progress of detector development, the progress in PID, and our experimental progress and plan.
2018, 35(4): 369-373.
doi: 10.11804/NuclPhysRev.35.04.369
Abstract:
Up to now, the N* production from e+e- annihilations has been studied only around charmonium region. Charmonium decays to N*s are analogous to (time-like) EM form factors in that the charm quark annihilation provides a nearly pointlike (ggg) current. Complementary to other sources, such as πN, eN and γN reactions, this new source for N* spectroscopy has a few advantages, such as an isospin filter and a low spin filter. The experimental results on N* from e+e- annihilations and their phenomenological implications are reviewed. Possible new sources on N* production from e+e- annihilations are discussed.
Up to now, the N* production from e+e- annihilations has been studied only around charmonium region. Charmonium decays to N*s are analogous to (time-like) EM form factors in that the charm quark annihilation provides a nearly pointlike (ggg) current. Complementary to other sources, such as πN, eN and γN reactions, this new source for N* spectroscopy has a few advantages, such as an isospin filter and a low spin filter. The experimental results on N* from e+e- annihilations and their phenomenological implications are reviewed. Possible new sources on N* production from e+e- annihilations are discussed.
2018, 35(4): 374-381.
doi: 10.11804/NuclPhysRev.35.04.374
Abstract:
Within the framework of the relativistic BUU approach, we investigate the effect of energy-, density-, and especially isospin-dependent medium modifications on △ production cross sections of both hard (NN → N△) and soft (Nπ → △) processes as well as its decay width. It is found that, similar to the nucleon-nucleon elastic scattering, the △ production cross section from the hard process is strongly dependent on both density and the mass splitting effect in the isospin asymmetric matter. While the dependence is relative weak from the soft one, and so is the △ decay width. Further, in the hard (soft) process, the splitting effect is largest (smallest) and of opposite sign for the △++ and △- states.
Within the framework of the relativistic BUU approach, we investigate the effect of energy-, density-, and especially isospin-dependent medium modifications on △ production cross sections of both hard (NN → N△) and soft (Nπ → △) processes as well as its decay width. It is found that, similar to the nucleon-nucleon elastic scattering, the △ production cross section from the hard process is strongly dependent on both density and the mass splitting effect in the isospin asymmetric matter. While the dependence is relative weak from the soft one, and so is the △ decay width. Further, in the hard (soft) process, the splitting effect is largest (smallest) and of opposite sign for the △++ and △- states.
2018, 35(4): 382-389.
doi: 10.11804/NuclPhysRev.35.04.382
Abstract:
High-precision laser spectroscopy technique is used to determine the ground state properties of exotic nuclei by probing its electronic hyperfine structure and isotope shift. It provides a model-independent measurement of nuclear spin, magnetic moment, electric quadrupole moment and charge radii. These nuclear parameters can be used to investigate the nuclear structure evolution and the nuclear shapes. With the development of accelerators and isotope separators, exotic isotopes far from β stability became accessible experimentally, which enhanced the capability of the laser spectroscopy technique being applied in the field of nuclear physics. A brief introduction to experimental principle is given, followed by a review of several typical examples for the experimental investigations in the different regions of nuclear chart. This aims to demonstrate the contributions of ground state properties measurement by using laser spectroscopy technique to the nuclear structure study of exotic isotopes. This discussion involves several different nuclear theory models in order to interpret the exotic phenomena observed in the neutron-rich isotopes, such as halo structure, shell evolution, shape coexistence and so on.
High-precision laser spectroscopy technique is used to determine the ground state properties of exotic nuclei by probing its electronic hyperfine structure and isotope shift. It provides a model-independent measurement of nuclear spin, magnetic moment, electric quadrupole moment and charge radii. These nuclear parameters can be used to investigate the nuclear structure evolution and the nuclear shapes. With the development of accelerators and isotope separators, exotic isotopes far from β stability became accessible experimentally, which enhanced the capability of the laser spectroscopy technique being applied in the field of nuclear physics. A brief introduction to experimental principle is given, followed by a review of several typical examples for the experimental investigations in the different regions of nuclear chart. This aims to demonstrate the contributions of ground state properties measurement by using laser spectroscopy technique to the nuclear structure study of exotic isotopes. This discussion involves several different nuclear theory models in order to interpret the exotic phenomena observed in the neutron-rich isotopes, such as halo structure, shell evolution, shape coexistence and so on.
2018, 35(4): 390-400.
doi: 10.11804/NuclPhysRev.35.04.390
Abstract:
Tensor force is one of the most important components of the nucleon-nucleon interaction. It plays a critical role in understanding the shell evolution in exotic nuclei. However, there are still several puzzles concerning the tensor force and its effects in the nuclear medium. In this paper, we mainly focus on the studies of tensor force in the effective interactions and its effects in finite nuclear systems within the scheme of nuclear density functional theory. In particular, we highlight the recent developments, including the quantitative analysis of tensor effects in the relativistic Hartree-Fock theory by taking the evolution of proton magic shells in the isotopic chains as an example, and the "meta-data" of tensor effects provided by the ab initio relativistic Brueckner-Hartree-Fock theory by taking the evolution of spin-orbit splitting in the single-particle spectra of neutron drops as an example. Perspectives are focused on the possible strategies for the future developments of nuclear density functional theory.
Tensor force is one of the most important components of the nucleon-nucleon interaction. It plays a critical role in understanding the shell evolution in exotic nuclei. However, there are still several puzzles concerning the tensor force and its effects in the nuclear medium. In this paper, we mainly focus on the studies of tensor force in the effective interactions and its effects in finite nuclear systems within the scheme of nuclear density functional theory. In particular, we highlight the recent developments, including the quantitative analysis of tensor effects in the relativistic Hartree-Fock theory by taking the evolution of proton magic shells in the isotopic chains as an example, and the "meta-data" of tensor effects provided by the ab initio relativistic Brueckner-Hartree-Fock theory by taking the evolution of spin-orbit splitting in the single-particle spectra of neutron drops as an example. Perspectives are focused on the possible strategies for the future developments of nuclear density functional theory.
2018, 35(4): 401-408.
doi: 10.11804/NuclPhysRev.35.04.401
Abstract:
Resonance is an interesting phenomenon in nature. In nuclear physics, resonance plays an important role in the formation of many exotic phenomena. This paper introduces the recently developed RMF-CSM, RMFCGF, and RMF-CMR methods and their researches on nuclear single-particle resonances. The energies and widths of the single-particle resonant states in 120Sn and 31Ne and their evolution to mass number and deformation are given. In addition, the physical mechanism of the halo formation in 19C, 31Ne and 39Mg and the cause of energy level inversion near N=20 are analyzed. In particular, the newly developed RMF-CMR approach has been successful in describing stable and exotic nuclei and supports the prediction that Zr isotopes exist in a giant halo.
Resonance is an interesting phenomenon in nature. In nuclear physics, resonance plays an important role in the formation of many exotic phenomena. This paper introduces the recently developed RMF-CSM, RMFCGF, and RMF-CMR methods and their researches on nuclear single-particle resonances. The energies and widths of the single-particle resonant states in 120Sn and 31Ne and their evolution to mass number and deformation are given. In addition, the physical mechanism of the halo formation in 19C, 31Ne and 39Mg and the cause of energy level inversion near N=20 are analyzed. In particular, the newly developed RMF-CMR approach has been successful in describing stable and exotic nuclei and supports the prediction that Zr isotopes exist in a giant halo.
2018, 35(4): 409-419.
doi: 10.11804/NuclPhysRev.35.04.409
Abstract:
The beyond-mean-field Skyrme-Hartree-Fock approach is adopted to investigate the properties of ∧9Be, ∧∧10Be, ∧13C and ∧21Ne. The nucleon-nucleon (NN) interaction SLy4 and the nucleon-hyperon(N∧) interaction Skyrme-type SLL4 are used. The spin-orbit force of hyperon is included to show the spin-orbit splitting and non-crossing effect with BCS method to deal with pairing force. Energies of different configurations, such as 12C⊗∧[000]1/2+, 12C⊗∧[110]1/2-, 12C⊗∧[101]3/2-, 12C⊗∧[101]1/2-, 8Be⊗∧[000]1/2+, 8Be⊗∧[110]1/2-, 8 Be⊗∧[101]3/2- and 8Be⊗∧[101]1/2- are given and used to study the effects of ∧ occupying different orbitals. The calculated energy spectra, including both positive-and negative-parity levels, are given and compared to the experimental data. The observed positive-parity spin-doublet (3/2+,5/2+) are successfully reproduced, but the energy difference needs further investigation. The two well known band structures corresponding to the genuine hypernuclear states and the 9Be-analog states are also obtained and compared with the observed ones. The shrinkage effect of ∧ occupying ∧[000]1/2+ is investigated through the density distributions of nuclear core. And finally the calculation results of ∧21Ne are given and compared with the results of RMF method, which are nearly the same but with differences in some details.
The beyond-mean-field Skyrme-Hartree-Fock approach is adopted to investigate the properties of ∧9Be, ∧∧10Be, ∧13C and ∧21Ne. The nucleon-nucleon (NN) interaction SLy4 and the nucleon-hyperon(N∧) interaction Skyrme-type SLL4 are used. The spin-orbit force of hyperon is included to show the spin-orbit splitting and non-crossing effect with BCS method to deal with pairing force. Energies of different configurations, such as 12C⊗∧[000]1/2+, 12C⊗∧[110]1/2-, 12C⊗∧[101]3/2-, 12C⊗∧[101]1/2-, 8Be⊗∧[000]1/2+, 8Be⊗∧[110]1/2-, 8 Be⊗∧[101]3/2- and 8Be⊗∧[101]1/2- are given and used to study the effects of ∧ occupying different orbitals. The calculated energy spectra, including both positive-and negative-parity levels, are given and compared to the experimental data. The observed positive-parity spin-doublet (3/2+,5/2+) are successfully reproduced, but the energy difference needs further investigation. The two well known band structures corresponding to the genuine hypernuclear states and the 9Be-analog states are also obtained and compared with the observed ones. The shrinkage effect of ∧ occupying ∧[000]1/2+ is investigated through the density distributions of nuclear core. And finally the calculation results of ∧21Ne are given and compared with the results of RMF method, which are nearly the same but with differences in some details.
2018, 35(4): 420-428.
doi: 10.11804/NuclPhysRev.35.04.420
Abstract:
The E2 transition strength, B(E2), gives particularly precise information on the competition between the collective and single-particle degree of freedom. An important observable to study the development of collectivity is the B(E2; 41+ →21+)/B(E2; 21+ →g.s.) (B4/2). The B4/2 ratio is usually greater than unity. These values are 1.4 and 2.0 for an ideal rotor and a vibrator, respectively. Whereas the seniority scheme usually leads to different behaviours. In this contribution I will show examples that contrast with our standard understanding. The yrast spectra of Te isotopes show a vibrational-like equally-spaced pattern but the few known E2 transitions show anomalous rotational-like behaviour, which cannot be reproduced by collective models. Large-scale shell model calculations reproduce well the equally-spaced spectra of those isotopes as well as the constant behaviour of the B(E2) values in 114Te. For nuclei involving protons or neutrons in j=9/2 orbitals, the partial conservation of seniority can lead to dramatic changes to the E2 decay pattern that have never been seen before. The B4/2 ratios in quantum phase transitional nuclei around N=90 also show a similar exotic feature.
The E2 transition strength, B(E2), gives particularly precise information on the competition between the collective and single-particle degree of freedom. An important observable to study the development of collectivity is the B(E2; 41+ →21+)/B(E2; 21+ →g.s.) (B4/2). The B4/2 ratio is usually greater than unity. These values are 1.4 and 2.0 for an ideal rotor and a vibrator, respectively. Whereas the seniority scheme usually leads to different behaviours. In this contribution I will show examples that contrast with our standard understanding. The yrast spectra of Te isotopes show a vibrational-like equally-spaced pattern but the few known E2 transitions show anomalous rotational-like behaviour, which cannot be reproduced by collective models. Large-scale shell model calculations reproduce well the equally-spaced spectra of those isotopes as well as the constant behaviour of the B(E2) values in 114Te. For nuclei involving protons or neutrons in j=9/2 orbitals, the partial conservation of seniority can lead to dramatic changes to the E2 decay pattern that have never been seen before. The B4/2 ratios in quantum phase transitional nuclei around N=90 also show a similar exotic feature.
2018, 35(4): 429-438.
doi: 10.11804/NuclPhysRev.35.04.429
Abstract:
We present a comprehensive introduction in our newly developed Variation After Projection (VAP) calculations for the low-lying nuclear states. First, we discussed the VAP calculation with a fully JTA-projected wavefunction for the ground state in even-even nucleus. This leads to the conclusion that the spin projection plays a key role in obtaining a good shell model approximation. With this conclusion, we simplified the VAP with a time-odd Hartree-Fock mean field, on which only spin projection is required. Due to the time reversal symmetry breaking, this VAP now can be applied to the yrast states in all kinds of nuclei. It turns out that our VAP yrast energies as well as the corresponding VAP wavefunctions are very close the exact ones from the full shell model calculations. Such good approximation encourages us to extend the VAP calculations further to the non-yrast nuclear states. For this purpose, we proposed a new algorithm in our VAP based on the Cauchy's interlacing theorem. This theorem ensures that the sum of the calculated lowest projected energies with the same quantum numbers can be safely minimized. After minimization, all the calculated states can be determined simultaneously. Again, all the calculated VAP energies are very close to the exact shell model results. Recently, we have added the parity projection into the VAP, and the yrast states with both parity in 12C have been calculated in the psd model space. This time, we still have good shell model approximation for both parity states. Finally, we should point out that the present algorithm should be applicable to the low-lying states in different quantum many-body systems.
We present a comprehensive introduction in our newly developed Variation After Projection (VAP) calculations for the low-lying nuclear states. First, we discussed the VAP calculation with a fully JTA-projected wavefunction for the ground state in even-even nucleus. This leads to the conclusion that the spin projection plays a key role in obtaining a good shell model approximation. With this conclusion, we simplified the VAP with a time-odd Hartree-Fock mean field, on which only spin projection is required. Due to the time reversal symmetry breaking, this VAP now can be applied to the yrast states in all kinds of nuclei. It turns out that our VAP yrast energies as well as the corresponding VAP wavefunctions are very close the exact ones from the full shell model calculations. Such good approximation encourages us to extend the VAP calculations further to the non-yrast nuclear states. For this purpose, we proposed a new algorithm in our VAP based on the Cauchy's interlacing theorem. This theorem ensures that the sum of the calculated lowest projected energies with the same quantum numbers can be safely minimized. After minimization, all the calculated states can be determined simultaneously. Again, all the calculated VAP energies are very close to the exact shell model results. Recently, we have added the parity projection into the VAP, and the yrast states with both parity in 12C have been calculated in the psd model space. This time, we still have good shell model approximation for both parity states. Finally, we should point out that the present algorithm should be applicable to the low-lying states in different quantum many-body systems.
2018, 35(4): 439-444.
doi: 10.11804/NuclPhysRev.35.04.439
Abstract:
Isochronous mass spectrometry has been applied to 112Sn projectile fragments at the HIRFL-CSR facility in Lanzhou. To produce short-lived nuclei of interest, we used projectile fragmentation of 112Sn35+ primary beams in a~10 mm thick 9Be production target. The fragments were selected and analyzed by RIBLL2 and injected into the experimental storage ring(CSRe) every 25 s. To measure revolution times of stored ions,we used a Time-Of-Flight detector installed in CSRe. A new particle identification method was developed to distinguish ions on the measured revolution time spectrum for each injection. Based on this method, the shifts of the revolution time due to instable dipole magnet fields can be corrected and the ground and isomeric states of 101In have been well-resolved. The measured excitation energy is consistent with the theoretical value in the error range of 112 keV. The lifetime of the isomeric states of 101In is more than 200 μs.
Isochronous mass spectrometry has been applied to 112Sn projectile fragments at the HIRFL-CSR facility in Lanzhou. To produce short-lived nuclei of interest, we used projectile fragmentation of 112Sn35+ primary beams in a~10 mm thick 9Be production target. The fragments were selected and analyzed by RIBLL2 and injected into the experimental storage ring(CSRe) every 25 s. To measure revolution times of stored ions,we used a Time-Of-Flight detector installed in CSRe. A new particle identification method was developed to distinguish ions on the measured revolution time spectrum for each injection. Based on this method, the shifts of the revolution time due to instable dipole magnet fields can be corrected and the ground and isomeric states of 101In have been well-resolved. The measured excitation energy is consistent with the theoretical value in the error range of 112 keV. The lifetime of the isomeric states of 101In is more than 200 μs.
2018, 35(4): 445-449.
doi: 10.11804/NuclPhysRev.35.04.445
Abstract:
Beijing Radioactive Ion-beam Facility(BRIF) has been commissioned as the national Radioactive Ion Beam(RIB) facility based on the Isotope Separator On Line(ISOL) technique since 2016. At BRIF, the radioactive nuclides are produced by the proton beam of 100 MeV bombarding a thick-target, the reaction products diffusing out of the target are ionized by an ion source and delivered to the online mass separator. In addition to the post-accelerated radioactive ion beams, BRIF can provide low-energy ISOL beams of 100 to 300 keV with a mass resolution of 20 000. A general-purpose decay station has been built including the ISOL beam transport line, a conventional reaction chamber, charge-particle and γ detectors with integrated electronics and data acquisition system. An intense 20Na ISOL beam up to 1×105 pps was produced by using the 100 MeV proton beam bombarding a MgO thick target. With high-efficiency measurements of β, γ and α simultaneously, very rare β-γ-α decay mode in 20Na has been directly observed for the first time in the present work.
Beijing Radioactive Ion-beam Facility(BRIF) has been commissioned as the national Radioactive Ion Beam(RIB) facility based on the Isotope Separator On Line(ISOL) technique since 2016. At BRIF, the radioactive nuclides are produced by the proton beam of 100 MeV bombarding a thick-target, the reaction products diffusing out of the target are ionized by an ion source and delivered to the online mass separator. In addition to the post-accelerated radioactive ion beams, BRIF can provide low-energy ISOL beams of 100 to 300 keV with a mass resolution of 20 000. A general-purpose decay station has been built including the ISOL beam transport line, a conventional reaction chamber, charge-particle and γ detectors with integrated electronics and data acquisition system. An intense 20Na ISOL beam up to 1×105 pps was produced by using the 100 MeV proton beam bombarding a MgO thick target. With high-efficiency measurements of β, γ and α simultaneously, very rare β-γ-α decay mode in 20Na has been directly observed for the first time in the present work.
2018, 35(4): 450-454.
doi: 10.11804/NuclPhysRev.35.04.450
Abstract:
About a half of the abundances of elements heavier than iron comes from the so-called slowneutron capture process (s-process) in Asymptotic Giant Branch (AGB) stars, with the 22Ne(α, n)25Mg reaction as one of the main neutron sources. In the beginning phase of AGB thermal pulse, 22Ne is produced by the 14N(α, γ)18F(β+)18O(α, γ)22Ne reaction sequence, in which the 18O(α, γ)22Ne reaction plays a key role. While the reaction rate of the 18O(α, γ)22Ne is mainly affected by several resonant states lying closely to the α threshold in 22Ne, up to now, the relevant 22Ne parameters are fragmentary in the energy region corresponding to the typical temperatures of s-process. The direct measurement of the 18O(α, γ)22Ne reaction rate is extremely difficult due to the very low cross section. In this work, we investigated the 22Ne resonant states via the 18O(6Li, d)22Ne reaction at the Beijing HI-13 tandem accelerator of China Institute of Atomic Energy. Based on the DWBA analysis, preliminary results showed that the spin-parity of 22Ne Eα=470 keV resonant states was assigned as 0+, which would make contributions to subsequent calculation for the reaction rate of the 18O(α, γ)22Ne.
About a half of the abundances of elements heavier than iron comes from the so-called slowneutron capture process (s-process) in Asymptotic Giant Branch (AGB) stars, with the 22Ne(α, n)25Mg reaction as one of the main neutron sources. In the beginning phase of AGB thermal pulse, 22Ne is produced by the 14N(α, γ)18F(β+)18O(α, γ)22Ne reaction sequence, in which the 18O(α, γ)22Ne reaction plays a key role. While the reaction rate of the 18O(α, γ)22Ne is mainly affected by several resonant states lying closely to the α threshold in 22Ne, up to now, the relevant 22Ne parameters are fragmentary in the energy region corresponding to the typical temperatures of s-process. The direct measurement of the 18O(α, γ)22Ne reaction rate is extremely difficult due to the very low cross section. In this work, we investigated the 22Ne resonant states via the 18O(6Li, d)22Ne reaction at the Beijing HI-13 tandem accelerator of China Institute of Atomic Energy. Based on the DWBA analysis, preliminary results showed that the spin-parity of 22Ne Eα=470 keV resonant states was assigned as 0+, which would make contributions to subsequent calculation for the reaction rate of the 18O(α, γ)22Ne.
2018, 35(4): 455-462.
doi: 10.11804/NuclPhysRev.35.04.455
Abstract:
The stability of superheavy nuclei (SHN) is controlled mainly by spontaneous fission and α decay processes. To investigate whether long lived SHN could really exist around 270Ds, the competition between α decay and spontaneous fission in the region 104 ≤ Z ≤ 112 are studied systematically. The α decay half-lives are investigated by employing a generalized liquid drop model (GLDM) and phenomenological analytical formula. Calculations of spontaneous fission half-lives for the same SHN are carried out based on the Wenzel-Kramers-Brillouin(WKB) approximation with both the shell effect and the isospin effect included. Decay modes are predicted for the unknown nuclei 274-276,279Cn and 267-269Ds.
The stability of superheavy nuclei (SHN) is controlled mainly by spontaneous fission and α decay processes. To investigate whether long lived SHN could really exist around 270Ds, the competition between α decay and spontaneous fission in the region 104 ≤ Z ≤ 112 are studied systematically. The α decay half-lives are investigated by employing a generalized liquid drop model (GLDM) and phenomenological analytical formula. Calculations of spontaneous fission half-lives for the same SHN are carried out based on the Wenzel-Kramers-Brillouin(WKB) approximation with both the shell effect and the isospin effect included. Decay modes are predicted for the unknown nuclei 274-276,279Cn and 267-269Ds.
2018, 35(4): 463-469.
doi: 10.11804/NuclPhysRev.35.04.463
Abstract:
In the present work, the α decay preformation factors Pα are systematically studied within the cluster-formation model (CFM) for nuclei around Z=82, N=126 closed shells. The calculations show that the Pα calculated by CFM is linearly dependent on the product of valance protons (holes) and valance neutrons (holes) Np Nn. It is consistent with our previous works[SUN X D, et al. Phys Rev C, 2016, 94 (2):024338; DENG J G, et al. Phys Rev C, 2017, 96 (2):024318], which Pα are model-dependent and extracted from the ratios of calculated α decay half-lives to experimental data. Combining with our previous works, we confirm that the Pα is linearly dependent on the NpNn for nuclei around Z=82, N=126 shell closures. In addition, the valance proton-neutron interaction plays a key role in the α preformation.
In the present work, the α decay preformation factors Pα are systematically studied within the cluster-formation model (CFM) for nuclei around Z=82, N=126 closed shells. The calculations show that the Pα calculated by CFM is linearly dependent on the product of valance protons (holes) and valance neutrons (holes) Np Nn. It is consistent with our previous works[SUN X D, et al. Phys Rev C, 2016, 94 (2):024338; DENG J G, et al. Phys Rev C, 2017, 96 (2):024318], which Pα are model-dependent and extracted from the ratios of calculated α decay half-lives to experimental data. Combining with our previous works, we confirm that the Pα is linearly dependent on the NpNn for nuclei around Z=82, N=126 shell closures. In addition, the valance proton-neutron interaction plays a key role in the α preformation.
2018, 35(4): 470-474.
doi: 10.11804/NuclPhysRev.35.04.470
Abstract:
In the present work, the α decay half-lives are systematically studied within the two-potentialapproach for even-even nuclei, odd-A nuclei and odd-odd nuclei. To describe the deviations between experimental half-lives and calculated results due to the nuclear shell structure, α preformation factor and hindrance factor related with α cluster preformation probability are introduced. It is consistent with our previous works[X. D. Sun et al., Phys. Rev. C 93, 034316 (2016); X. D. Sun et al., Phys. Rev. C 95, 014319 (2017); X. D. Sun et al., Phys. Rev. C 95, 044303 (2017)]. Considering the shell effect on the preformation of α and by analyzing the experimental data of the α decay half-lives, the parameters of the α preformation factor/hindrance factor correction formula are obtained. we confirm that the shell effect and the proton-neutron correlation play key roles in the α preformation where the preformation probability near the shell is less than the preformation probability far from the shell.
In the present work, the α decay half-lives are systematically studied within the two-potentialapproach for even-even nuclei, odd-A nuclei and odd-odd nuclei. To describe the deviations between experimental half-lives and calculated results due to the nuclear shell structure, α preformation factor and hindrance factor related with α cluster preformation probability are introduced. It is consistent with our previous works[X. D. Sun et al., Phys. Rev. C 93, 034316 (2016); X. D. Sun et al., Phys. Rev. C 95, 014319 (2017); X. D. Sun et al., Phys. Rev. C 95, 044303 (2017)]. Considering the shell effect on the preformation of α and by analyzing the experimental data of the α decay half-lives, the parameters of the α preformation factor/hindrance factor correction formula are obtained. we confirm that the shell effect and the proton-neutron correlation play key roles in the α preformation where the preformation probability near the shell is less than the preformation probability far from the shell.
2018, 35(4): 475-481.
doi: 10.11804/NuclPhysRev.35.04.475
Abstract:
α condensates are exotic states in nuclear many-body systems, and can be viewed as the generalization of the Bose-Einstein condensate in nuclear physics. It is widely believed that, α condensates exist not only in 12C, but also in heavier self-conjugate nuclei such as 16O, 20Ne, 24Mg, 28Si, etc. It is important to understand the physical properties of these α condensates in heavy self-conjugate nuclei from the theoretical perspective, and the theoretical results could be a useful reference for the experimental studies. This work reviews the basic frameworks to study α condensates, including the Tohsaki-Horiuchi-Schuck-Röpke wave function, the Yamada-Schuck model, and the recently proposed semi-analytic approximation. The impacts of the four-body interactions of α particles on the physical properties of α condensates are reported. The breakup of α condensates and the one-dimensional α condensates are discussed briefly as the possible future directions in this field.
α condensates are exotic states in nuclear many-body systems, and can be viewed as the generalization of the Bose-Einstein condensate in nuclear physics. It is widely believed that, α condensates exist not only in 12C, but also in heavier self-conjugate nuclei such as 16O, 20Ne, 24Mg, 28Si, etc. It is important to understand the physical properties of these α condensates in heavy self-conjugate nuclei from the theoretical perspective, and the theoretical results could be a useful reference for the experimental studies. This work reviews the basic frameworks to study α condensates, including the Tohsaki-Horiuchi-Schuck-Röpke wave function, the Yamada-Schuck model, and the recently proposed semi-analytic approximation. The impacts of the four-body interactions of α particles on the physical properties of α condensates are reported. The breakup of α condensates and the one-dimensional α condensates are discussed briefly as the possible future directions in this field.
2018, 35(4): 482-486.
doi: 10.11804/NuclPhysRev.35.04.482
Abstract:
An extension of the original interacting boson model to the multi-level case including negative parity f-and p-bosons is made. An affinealgebraic approach is applied to solve the multi-level pairing problem numerically via the dual algebraic structure. The duality relation is explicitly used to construct the number-conserving unitary and number-nonconserving quasi-spin algebra, related with the Hamiltonian and the corresponding bases. After fitting to the experimental level energies of even-even 106-116Cd, several order parameters to signify the shape (phase) transition, such as occupation numbers of the bosons in the ground and a few lowest excited states, the level energy staggering in the (quasi)-γ band, are calculated to demonstrate the shape (phase) transitional behavior of these medium mass transitional nuclei.
An extension of the original interacting boson model to the multi-level case including negative parity f-and p-bosons is made. An affinealgebraic approach is applied to solve the multi-level pairing problem numerically via the dual algebraic structure. The duality relation is explicitly used to construct the number-conserving unitary and number-nonconserving quasi-spin algebra, related with the Hamiltonian and the corresponding bases. After fitting to the experimental level energies of even-even 106-116Cd, several order parameters to signify the shape (phase) transition, such as occupation numbers of the bosons in the ground and a few lowest excited states, the level energy staggering in the (quasi)-γ band, are calculated to demonstrate the shape (phase) transitional behavior of these medium mass transitional nuclei.
2018, 35(4): 487-492.
doi: 10.11804/NuclPhysRev.35.04.487
Abstract:
In this work, a phenomenological analysis of the excited-state quantum phase transitions (ESQPTs) in the finite-N boson system has been carried out within the interacting boson model in order to reveal the possibility of finding ESQPTs in nuclear systems. Particularly, the angular momentum and finite-N effects on the ESQPTs in the U(5)-SU(3) and SU(3)-O(6) transitional regions have been systematically investigated. The results indicate that the main features of ESQPTs can be well preserved even at a realistic boson number for small angular momentum but will gradually disappear as the angular momentum increases.
In this work, a phenomenological analysis of the excited-state quantum phase transitions (ESQPTs) in the finite-N boson system has been carried out within the interacting boson model in order to reveal the possibility of finding ESQPTs in nuclear systems. Particularly, the angular momentum and finite-N effects on the ESQPTs in the U(5)-SU(3) and SU(3)-O(6) transitional regions have been systematically investigated. The results indicate that the main features of ESQPTs can be well preserved even at a realistic boson number for small angular momentum but will gradually disappear as the angular momentum increases.
2018, 35(4): 493-498.
doi: 10.11804/NuclPhysRev.35.04.493
Abstract:
The analysis of the quantum phase crossover behavior in the spherical shell model mean-field plus the geometric quadrupole-quadrupole (Q·Q) and standard pairing model within a single-j shell is reported. Several quantities, such as low-lying excitation energies, the overlaps of excited states, ratios of some B(E2) and electric quadrupole moments of some low-lying states as functions of the control parameter of the model in a j=15/2 shell are calculated. The results show that there are noticeable changes in the crossover region of the rotational-like to the pair-excitation phase transition, such as B(E2;41 → 21)/B(E2;21 → 0g) and B(E2;42 → 21)/B(E2;21 → 0g), especially in the half-filling case. Though the low-lying excitation energies generated from the geometric quadrupole-quadrupole interaction not satisfy the pattern of a rotational spectrum when j is small, these energies follow the pattern of a rotational spectrum when j is sufficiently large.
The analysis of the quantum phase crossover behavior in the spherical shell model mean-field plus the geometric quadrupole-quadrupole (Q·Q) and standard pairing model within a single-j shell is reported. Several quantities, such as low-lying excitation energies, the overlaps of excited states, ratios of some B(E2) and electric quadrupole moments of some low-lying states as functions of the control parameter of the model in a j=15/2 shell are calculated. The results show that there are noticeable changes in the crossover region of the rotational-like to the pair-excitation phase transition, such as B(E2;41 → 21)/B(E2;21 → 0g) and B(E2;42 → 21)/B(E2;21 → 0g), especially in the half-filling case. Though the low-lying excitation energies generated from the geometric quadrupole-quadrupole interaction not satisfy the pattern of a rotational spectrum when j is small, these energies follow the pattern of a rotational spectrum when j is sufficiently large.
2018, 35(4): 499-504.
doi: 10.11804/NuclPhysRev.35.04.499
Abstract:
A recently developed method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is reviewed, that is based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the eveneven core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained by a self-consistent mean-field calculation with the choice of the energy density functional and pairing properties. These quantities are then used as a microscopic input to build the interacting bosonfermion Hamiltonian. Only three strength parameters for the particle-core coupling are specifically adjusted to selected data for the low-lying states of a particular odd-mass nucleus. The method is illustrated in a systematic study of low-energy excitation spectra and electromagnetic transition rates of axially-deformed odd-mass Eu isotopes. Recent applications of the method, to the calculations of the signatures of shapes phase transitions in axially-deformed odd-mass nuclei, octupole correlations in neutron-rich odd-mass Ba isotopes, are discussed.
A recently developed method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is reviewed, that is based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the eveneven core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained by a self-consistent mean-field calculation with the choice of the energy density functional and pairing properties. These quantities are then used as a microscopic input to build the interacting bosonfermion Hamiltonian. Only three strength parameters for the particle-core coupling are specifically adjusted to selected data for the low-lying states of a particular odd-mass nucleus. The method is illustrated in a systematic study of low-energy excitation spectra and electromagnetic transition rates of axially-deformed odd-mass Eu isotopes. Recent applications of the method, to the calculations of the signatures of shapes phase transitions in axially-deformed odd-mass nuclei, octupole correlations in neutron-rich odd-mass Ba isotopes, are discussed.
2018, 35(4): 505-510.
doi: 10.11804/NuclPhysRev.35.04.505
Abstract:
Based on the relativistic Hartree-Bogoliubov theory in nuclear matter, the dineutron correlations and the crossover from Bardeen-Cooper-Schrieffer (BCS) region of neutron Cooper pairs to Bose-Einstein condensation (BEC) are investigated with the one-boson-exchange type of pairing force generated from the relativistic mean field (RMF) model. By introducing an effective factor χ in the RMF effective pairing interaction, the density dependence of the ratios between neutron pairing gap at Fermi surface and neutron Fermi kinetic energy △Fn/eFn and the dimensionless parameter 1/(kFna) are analyzed quantitatively. Then the criteria where dineutron correlations exactly reach the threshold of BCS-BEC crossover or unitary limit are determined to be χ=0.51 or 0.67, respectively. In addition, features of neutron pairing gap, Cooper pair wave function and dineutron coherence length are illustrated, and the value of the probability for partner neutrons correlated within the average inter-neutron distance, namely P (dn) ≃0.80, is obtained as a criterion of BCS-BEC crossover.
Based on the relativistic Hartree-Bogoliubov theory in nuclear matter, the dineutron correlations and the crossover from Bardeen-Cooper-Schrieffer (BCS) region of neutron Cooper pairs to Bose-Einstein condensation (BEC) are investigated with the one-boson-exchange type of pairing force generated from the relativistic mean field (RMF) model. By introducing an effective factor χ in the RMF effective pairing interaction, the density dependence of the ratios between neutron pairing gap at Fermi surface and neutron Fermi kinetic energy △Fn/eFn and the dimensionless parameter 1/(kFna) are analyzed quantitatively. Then the criteria where dineutron correlations exactly reach the threshold of BCS-BEC crossover or unitary limit are determined to be χ=0.51 or 0.67, respectively. In addition, features of neutron pairing gap, Cooper pair wave function and dineutron coherence length are illustrated, and the value of the probability for partner neutrons correlated within the average inter-neutron distance, namely P (dn) ≃0.80, is obtained as a criterion of BCS-BEC crossover.
2018, 35(4): 511-517.
doi: 10.11804/NuclPhysRev.35.04.511
Abstract:
The SD-pair shell model is applied to analyze the evolution of low-lying states of even-even nuclei in A~130 mass region. In the model, the pairing and the quadrupole-quadrupole interactions are taken into account. The results show that there are clear signatures of the crossover from vibrational to rotational or from vibrational to the γ-soft shape phase.
The SD-pair shell model is applied to analyze the evolution of low-lying states of even-even nuclei in A~130 mass region. In the model, the pairing and the quadrupole-quadrupole interactions are taken into account. The results show that there are clear signatures of the crossover from vibrational to rotational or from vibrational to the γ-soft shape phase.
2018, 35(4): 518-522.
doi: 10.11804/NuclPhysRev.35.04.518
Abstract:
A new iterative approach for solving the standard pairing problem is established based on polynomial approach. It provides an efficient way to derive the particle-number conserved pairing wave functions for both spherical and deformed systems, especially for large-size systems. The method reduces the complexity of solving a system for k-pairs polynomial equations into a system for one-pair polynomial equation, which can be efficiently implemented by the Newton-Raphson algorithm with a Monte Carlo sampling procedure for providing the initial guesses step by step. The present algorithm can also be used to solve a large class of Gaudin type quantum many-body problems as a more than 100 orbitals and 50 pairs system such as super-heavy nuclei and nuclear fission.
A new iterative approach for solving the standard pairing problem is established based on polynomial approach. It provides an efficient way to derive the particle-number conserved pairing wave functions for both spherical and deformed systems, especially for large-size systems. The method reduces the complexity of solving a system for k-pairs polynomial equations into a system for one-pair polynomial equation, which can be efficiently implemented by the Newton-Raphson algorithm with a Monte Carlo sampling procedure for providing the initial guesses step by step. The present algorithm can also be used to solve a large class of Gaudin type quantum many-body problems as a more than 100 orbitals and 50 pairs system such as super-heavy nuclei and nuclear fission.
2018, 35(4): 523-530.
doi: 10.11804/NuclPhysRev.35.04.523
Abstract:
Single ∧, Ξ, and ∑ hypernuclei are systematically studied within the framework of relativistic mean-field (RMF) model with YN interactions being constrained according to the experimental data and previous theoretical efforts. By adding a hyperon to 16O, the mean-field potentials and single-particle levels for hyperons (∧, Ξ0,-, and ∑+,0,-) are compared and the impurity effects on the nuclear core are examined. In general, the ∧ and ∑0 hyperons show similar behaviors in bulk properties since both of them are electroneutral and with similar coupling constants; Ξ0 hyperon owns the shallowest mean-field potential well; and Coulomb interactions play vital roles in the charged Ξ-, ∑-, and ∑+ hyperons. As an impurity, the intruded single-hyperon makes the nuclear system more bound in most cases due to the attractive NY interaction. However, very different effects on the nucleon radii are observed for different hyperons. Besides, the effects of the ωYY tensor couplings on the spin-orbit splitting are discussed, and remarkable influences are found which even change the level ordering of Ξ hyperon.
Single ∧, Ξ, and ∑ hypernuclei are systematically studied within the framework of relativistic mean-field (RMF) model with YN interactions being constrained according to the experimental data and previous theoretical efforts. By adding a hyperon to 16O, the mean-field potentials and single-particle levels for hyperons (∧, Ξ0,-, and ∑+,0,-) are compared and the impurity effects on the nuclear core are examined. In general, the ∧ and ∑0 hyperons show similar behaviors in bulk properties since both of them are electroneutral and with similar coupling constants; Ξ0 hyperon owns the shallowest mean-field potential well; and Coulomb interactions play vital roles in the charged Ξ-, ∑-, and ∑+ hyperons. As an impurity, the intruded single-hyperon makes the nuclear system more bound in most cases due to the attractive NY interaction. However, very different effects on the nucleon radii are observed for different hyperons. Besides, the effects of the ωYY tensor couplings on the spin-orbit splitting are discussed, and remarkable influences are found which even change the level ordering of Ξ hyperon.
2018, 35(4): 531-536.
doi: 10.11804/NuclPhysRev.35.04.531
Abstract:
Spin and pseudospin symmetries in the single-particle spectra of atomic nuclei are of great significance for the study of nuclear structure. In this work, taking 132Sn, ∧133Sn, and 2∧134Sn as examples, the spin and pseudospin symmetries in ∧ hypernuclei are studied by using the relativistic mean-field model. For the single-∧ spectra, results show that the spin symmetry maintains well while the pseudospin symmetry is approximately conserved. Besides, as impurities, the ∧ hyperons worsen the spin symmetry of single-neutron spectra while improve the pseudospin symmetry.
Spin and pseudospin symmetries in the single-particle spectra of atomic nuclei are of great significance for the study of nuclear structure. In this work, taking 132Sn, ∧133Sn, and 2∧134Sn as examples, the spin and pseudospin symmetries in ∧ hypernuclei are studied by using the relativistic mean-field model. For the single-∧ spectra, results show that the spin symmetry maintains well while the pseudospin symmetry is approximately conserved. Besides, as impurities, the ∧ hyperons worsen the spin symmetry of single-neutron spectra while improve the pseudospin symmetry.
2018, 35(4): 537-542.
doi: 10.11804/NuclPhysRev.35.04.537
Abstract:
The uncertainty of the nuclear shell model is important but rarely investigated. The present work provides preliminary investigations on the uncertainty of the nuclear force and the effect model space in shell-model calculations. The most important part of the nuclear force is the central force, which is also considered to include the largest contribution from the renormalization effect. If semi-magic nuclei are considered and only the strength of the central force varies, C10 (T,S=1,0) and C11 (T,S=1,1) channels of the central force contribute to the theoretical variances of the description of the levels, while the spin-orbit force and the tensor force are kept unchanged as the bare ones. One set of the strengths of a simple nuclear force gives an 0.2 MeV root mean square (RMS) between observed and theoretical levels from 188 states in Pb and Sn isotopes and N=82 and 126 isotones. However, if levels in these isotopes and isotones are separately considered, RMS are further reduced and found to have two minimums with 15% stronger pp interaction than nn interaction, which indicates a "mirror difference" in medium and heavy nuclei. The enlarge of the model space are of great significance for the description of certain nuclei, such as the inclusion of cross-shell excitations for the nuclei with magic neutron and/or proton numbers. The neutron-rich F isotopes are investigated through three Hamiltonians. Despite the different results among Hamiltonians, the two neutron separation energies and levels are sensitive to and similarly contributed by the cross-shell excitations.
The uncertainty of the nuclear shell model is important but rarely investigated. The present work provides preliminary investigations on the uncertainty of the nuclear force and the effect model space in shell-model calculations. The most important part of the nuclear force is the central force, which is also considered to include the largest contribution from the renormalization effect. If semi-magic nuclei are considered and only the strength of the central force varies, C10 (T,S=1,0) and C11 (T,S=1,1) channels of the central force contribute to the theoretical variances of the description of the levels, while the spin-orbit force and the tensor force are kept unchanged as the bare ones. One set of the strengths of a simple nuclear force gives an 0.2 MeV root mean square (RMS) between observed and theoretical levels from 188 states in Pb and Sn isotopes and N=82 and 126 isotones. However, if levels in these isotopes and isotones are separately considered, RMS are further reduced and found to have two minimums with 15% stronger pp interaction than nn interaction, which indicates a "mirror difference" in medium and heavy nuclei. The enlarge of the model space are of great significance for the description of certain nuclei, such as the inclusion of cross-shell excitations for the nuclei with magic neutron and/or proton numbers. The neutron-rich F isotopes are investigated through three Hamiltonians. Despite the different results among Hamiltonians, the two neutron separation energies and levels are sensitive to and similarly contributed by the cross-shell excitations.
2018, 35(4): 543-548.
doi: 10.11804/NuclPhysRev.35.04.543
Abstract:
In random-interaction ensembles, the electric quadrupole moments (Q) and magnetic moments (μ) of the Iπ=11/2- isomers of the Cd isotopes predominantly present linear correlation with neutron numbers, corresponding to the recently emphasized linear Q and μ systematics in realistic nuclear system. Although the seniority scheme enhances such predominance (more essentially for μ), the configuration mixing due to quadrupolelike and δ-force-like proton-neutron interactions is responsible for the linear Q and μ systematics, respectively, at least in random-interaction ensembles. Especially, the linear μ systematics further requires the proton-neutron interaction have similar relative strength and attractive-repulsive property to realistic nuclear interaction.
In random-interaction ensembles, the electric quadrupole moments (Q) and magnetic moments (μ) of the Iπ=11/2- isomers of the Cd isotopes predominantly present linear correlation with neutron numbers, corresponding to the recently emphasized linear Q and μ systematics in realistic nuclear system. Although the seniority scheme enhances such predominance (more essentially for μ), the configuration mixing due to quadrupolelike and δ-force-like proton-neutron interactions is responsible for the linear Q and μ systematics, respectively, at least in random-interaction ensembles. Especially, the linear μ systematics further requires the proton-neutron interaction have similar relative strength and attractive-repulsive property to realistic nuclear interaction.
2018, 35(4): 549-554.
doi: 10.11804/NuclPhysRev.35.04.549
Abstract:
The density dependence of nuclear fourth-order symmetry energy S4 is studied within the covariant density functional (CDF) theory in terms of the kinetic energy, isospin-singlet, and isospin-triplet potential energy parts of the energy density functional. When the Fock diagram is introduced, it is found that both isospin-singlet and isospin-triplet components of the potential energy plays important roles in determining the fourth-order symmetry energy. Especially, an extra suppression, which comes from the Fock terms via isoscalar meson-nucleon coupling channels, is revealed in the isospin-triplet potential part of the fourth-order symmetry energy. As an useful attempt, the generalized symmetry energy is introduced to describe the various orders of nuclear symmetry energies in a visual and self-consistent way.
The density dependence of nuclear fourth-order symmetry energy S4 is studied within the covariant density functional (CDF) theory in terms of the kinetic energy, isospin-singlet, and isospin-triplet potential energy parts of the energy density functional. When the Fock diagram is introduced, it is found that both isospin-singlet and isospin-triplet components of the potential energy plays important roles in determining the fourth-order symmetry energy. Especially, an extra suppression, which comes from the Fock terms via isoscalar meson-nucleon coupling channels, is revealed in the isospin-triplet potential part of the fourth-order symmetry energy. As an useful attempt, the generalized symmetry energy is introduced to describe the various orders of nuclear symmetry energies in a visual and self-consistent way.
2018, 35(4): 555-560.
doi: 10.11804/NuclPhysRev.35.04.555
Abstract:
In order to study the effect of curvature energy on the thermodynamic driving force (TDF) of nuclear fission, the potential and entropy barrier of 200Pb and 224Th systems are calculated by using the truncated droplet model including curvature energy, respectively. Compared with the liquid drop model, the results show that curvature energy does not affect the saddle point of 224Th, but pushes the saddle point of 200Pb backwards the ground state. The stronger the deformation dependence of the level density parameter is, the closer the saddle point of entropy barrier for these systems is to the ground state. In order to further investigate how curvature energy affects TDF through nuclear potential and entropy, respectively, the prescission neutron multiplicity (PNM) is selected as the probe, some simulations based on two schemes are carried out. The results show that curvature energy reduces the potential driving force of 200Pb and 224Th, and enhances the entropy potential driving force. Combined with the calculations and analyses of PNM, the former effect is more obvious than the latter, so curvature energy weakens TDF of two systems on whole, thus delaying the nuclear fission process of two systems.
In order to study the effect of curvature energy on the thermodynamic driving force (TDF) of nuclear fission, the potential and entropy barrier of 200Pb and 224Th systems are calculated by using the truncated droplet model including curvature energy, respectively. Compared with the liquid drop model, the results show that curvature energy does not affect the saddle point of 224Th, but pushes the saddle point of 200Pb backwards the ground state. The stronger the deformation dependence of the level density parameter is, the closer the saddle point of entropy barrier for these systems is to the ground state. In order to further investigate how curvature energy affects TDF through nuclear potential and entropy, respectively, the prescission neutron multiplicity (PNM) is selected as the probe, some simulations based on two schemes are carried out. The results show that curvature energy reduces the potential driving force of 200Pb and 224Th, and enhances the entropy potential driving force. Combined with the calculations and analyses of PNM, the former effect is more obvious than the latter, so curvature energy weakens TDF of two systems on whole, thus delaying the nuclear fission process of two systems.
2018, 35(4): 561-566.
doi: 10.11804/NuclPhysRev.35.04.561
Abstract:
The observational properties of quark core hybrid star contain dark matter are studied. The influences of containing of strongly or weakly interacting dark matter to global observational features of hybrid stars, mass, radius, gravitational red-shift, rotational period and moment of inertia are studied by using relativistic mean field theory to describe hadron phase, effective mass bag model to quark phase, and Gibbs phase equilibrium conditions to hadron-quark mixed phase respectively. Our results indicate that, both in the strong and weak interacting case, the equation of state for hybrid star matter contain dark matter become softer than that of without dark matter while the mass of dark matter particles larger than 0.5 GeV, which leads to the decrease of the mass and corresponding radius of hybrid star. With the increase of the dark matter particle mass, the equation of state for hybrid star matter become softer, this cause the decrease of the mass and radius of hybrid star obviously. The gravitational red-shift and the rotational period, obviously increase of the moment of inertia of the hybrid stars are influenced by the dark matter particle mass. When the dark matter particle mass is equal to 0.1 GeV, the masses of the star with strong and weak interacting dark matter reach to 2.0 M⊙ and 2.8 M⊙(M⊙ is the solar mass), this result indicates that the giant mass PSR, J1859-0131 and J1931-01, can be a hadron-quark hybrid star and containing dark matter with small dark particle mass. The computational results of all above global observational features of hybrid stars are in the range of astronomical observation data, these also indicate that hybrid star with quark core may contains dark matter.
The observational properties of quark core hybrid star contain dark matter are studied. The influences of containing of strongly or weakly interacting dark matter to global observational features of hybrid stars, mass, radius, gravitational red-shift, rotational period and moment of inertia are studied by using relativistic mean field theory to describe hadron phase, effective mass bag model to quark phase, and Gibbs phase equilibrium conditions to hadron-quark mixed phase respectively. Our results indicate that, both in the strong and weak interacting case, the equation of state for hybrid star matter contain dark matter become softer than that of without dark matter while the mass of dark matter particles larger than 0.5 GeV, which leads to the decrease of the mass and corresponding radius of hybrid star. With the increase of the dark matter particle mass, the equation of state for hybrid star matter become softer, this cause the decrease of the mass and radius of hybrid star obviously. The gravitational red-shift and the rotational period, obviously increase of the moment of inertia of the hybrid stars are influenced by the dark matter particle mass. When the dark matter particle mass is equal to 0.1 GeV, the masses of the star with strong and weak interacting dark matter reach to 2.0 M⊙ and 2.8 M⊙(M⊙ is the solar mass), this result indicates that the giant mass PSR, J1859-0131 and J1931-01, can be a hadron-quark hybrid star and containing dark matter with small dark particle mass. The computational results of all above global observational features of hybrid stars are in the range of astronomical observation data, these also indicate that hybrid star with quark core may contains dark matter.
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