1.School of Physics and Microelectronics, Zhengzhou University, Zhengzhou 450001, China
† zw76@pku.org.cn
Scan for full text
Wei Zhang, Wei Gao, Gui-Tao Zhang, et al. Level density of odd-
Wei Zhang, Wei Gao, Gui-Tao Zhang, et al. Level density of odd-
Based on the covariant density functional theory, by employing the core–quasiparticle coupling (CQC) model, the nuclear level density of odd-,A, nuclei at the saddle point is achieved. The total level density is calculated via convolution of the intrinsic level density and the collective level density. The intrinsic level densities are obtained in the finite-temperature covariant density functional theory, which takes into account the nuclear deformation and pairing self-consistently. For saddle points on the free energy surface in the ,, plane, the entropy and the associated intrinsic level density are compared with those of the global minima. By introducing a quasiparticle to the two neighboring even–even core nuclei, whose properties are determined by the five-dimensional collective Hamiltonian model, the collective levels of the odd-,A, nuclei are obtained via the CQC model. The total level densities of the ,234-240,U agree well with the available experimental data and Hilaire’s result. Furthermore, the ratio of the total level densities at the saddle points to those at the global minima and the ratio of the total level densities to the intrinsic level densities are discussed separately.
Level densityCovariant density functional theoryCore-quasiparticle coupling modelSaddle point
A. Koning, S. Hilaire, S. Goriely, TALYS-1.95 A nuclear reaction program: User Manual, NRG, Petten, 2019.
S. Goriely, A new nuclear level density formula including shell and pairing correction in the light of a microscopic model calculation. Nucl. Phys. A 605, 28-60 (1996). doi: 10.1016/0375-9474(96)00162-5http://doi.org/10.1016/0375-9474(96)00162-5.
B. Canbula, Collective effects in deuteron induced reactions of aluminum. Nucl. Instrum. Methods Phys. Res. Sect. B 391, 73-77 (2017). doi: 10.1016/j.nimb.2016.11.006http://doi.org/10.1016/j.nimb.2016.11.006.
H. A. Bethe, Nuclear Physics B. Nuclear dynamics, theoretical. Rev. Mod. Phys. 9, 69-244 (1937). doi: 10.1103/RevModPhys.9.69http://doi.org/10.1103/RevModPhys.9.69.
H. Özdoǧan, Y. A. Üncü, M. Şekerci et al., Estimations of level density parameters by using artificial neural network for phenomenological level density models. Appl. Radiat. Isot. 169, 109583 (2021). doi: 10.1016/j.apradiso.2020.109583http://doi.org/10.1016/j.apradiso.2020.109583.
A. Gilbert, A.G.W. Cameron, A composite nuclear-level density formula with shell corrections. Can. J. Phys. 43, 1446-1496 (1965). doi: 10.1139/p65-139http://doi.org/10.1139/p65-139.
A. Koning, S. Hilaire, S. Goriely, Global and local level density models. Nucl. Phys. A 810, 13-76 (2008). doi: 10.1016/j.nuclphysa.2008.06.005http://doi.org/10.1016/j.nuclphysa.2008.06.005.
Y. Alhassid, S. Liu, H. Nakada, Particle-number reprojection in the shell model Monte Carlo method: Application to nuclear level densities. Phys. Rev. Lett. 83, 4265-4268 (1999). doi: 10.1103/PhysRevLett.83.4265http://doi.org/10.1103/PhysRevLett.83.4265.
Y. Alhassid, S. Liu, H. Nakada, Spin projection in the shell model Monte Carlo method and the spin distribution of nuclear level densities. Phys. Rev. Lett. 99, 162504 (2007). doi: 10.1103/PhysRevLett.99.162504http://doi.org/10.1103/PhysRevLett.99.162504.
Y. Alhassid, M. Bonett-Matiz, S. Liu et al., Direct microscopic calculation of nuclear level densities in the shell model Monte Carlo approach. Phys. Rev. C 92, 024307 (2015). doi: 10.1103/PhysRevC.92.024307http://doi.org/10.1103/PhysRevC.92.024307.
R. A. Sen’kov, M. Horoi, High-performance algorithm to calculate spin- and parity-dependent nuclear level densities. Phys. Rev. C 82, 024304 (2010). doi: 10.1103/PhysRevC.82.024304http://doi.org/10.1103/PhysRevC.82.024304.
V. Zelevinsky, S. Karampagia, A. Berlaga, Constant temperature model for nuclear level density. Phys. Lett. B 783, 428-433 (2018). doi: 10.1016/j.physletb.2018.07.023http://doi.org/10.1016/j.physletb.2018.07.023.
N. Shimizu, Y. Utsuno, Y. Futamura et al., Stochastic estimation of nuclear level density in the nuclear shell model: An application to parity-dependent level density in 58Ni. Phys. Lett. B 753, 13-17 (2016). doi: 10.1016/j.physletb.2015.12.005http://doi.org/10.1016/j.physletb.2015.12.005.
W.E. Ormand, B.A. Brown, Microscopic calculations of nuclear level densities with the lanczos method. Phys. Rev. C 102, 014315 (2020). doi: 10.1103/PhysRevC.102.014315http://doi.org/10.1103/PhysRevC.102.014315.
V.M. Kolomietz, A.I. Sanzhur, S. Shlomo, Self-consistent mean-field approach to the statistical level density in spherical nuclei. Phys. Rev. C 97, 064302 (2018). doi: 10.1103/PhysRevC.97.064302http://doi.org/10.1103/PhysRevC.97.064302.
N.Q. Hung, N.D. Dang, L.T.Q. Huong, Simultaneous microscopic description of nuclear level density and radiative strength function. Phys. Rev. Lett. 118, 022502 (2017). doi: 10.1103/PhysRevLett.118.022502http://doi.org/10.1103/PhysRevLett.118.022502.
N.D. Dang, N.Q. Hung, L.T.Q. Huong, Testing the constant-temperature approach for the nuclear level density, Phys. Rev. C 96, 054321 (2017). doi: 10.1103/PhysRevC.96.054321http://doi.org/10.1103/PhysRevC.96.054321.
B. Dey, D. Pandit, S. Bhattacharya et al., Level density and thermodynamics in the hot rotating 96Tc nucleus. Phys. Rev. C 96, 054326 (2017). doi: 10.1103/PhysRevC.96.054326http://doi.org/10.1103/PhysRevC.96.054326.
B. Dey, N. Quang Hung, D. Pandit et al., S-shaped heat capacity in an odd–odd deformed nucleus. Phys. Lett. B 789, 634-638 (2019). doi: 10.1016/j.physletb.2018.12.007http://doi.org/10.1016/j.physletb.2018.12.007.
S. Hilaire, J. Delaroche, M. Girod, Combinatorial nuclear level densities based on the Gogny nucleon-nucleon effective interaction. Eur. Phys. J. A bf 12, 196-184 (2001). doi: 10.1007/s100500170025http://doi.org/10.1007/s100500170025.
S. Hilaire, S. Goriely, Global microscopic nuclear level densities within the hfb plus combinatorial method for practical applications. Nucl. Phys. A 779, 63-81 (2006). doi: 10.1016/j.nuclphysa.2006.08.014http://doi.org/10.1016/j.nuclphysa.2006.08.014.
S. Goriely, S. Hilaire, A. J. Koning, Improved microscopic nuclear level densities within the Hartree-Fock-Bogoliubov plus combinatorial method. Phys. Rev. C 78, 064307 (2008). doi: 10.1103/PhysRevC.78.064307http://doi.org/10.1103/PhysRevC.78.064307.
F. N. Choudhury, S. D. Gupta, Nuclear level density with realistic interactions. Phys. Rev. C 16, 757-766 (1977). doi: 10.1103/PhysRevC.16.757http://doi.org/10.1103/PhysRevC.16.757.
P. Demetriou, S. Goriely, Microscopic nuclear level densities for practical applications. Nucl. Phys. A 695, 95-108 (2001). doi: 10.1016/S0375-9474(01)01095-8http://doi.org/10.1016/S0375-9474(01)01095-8.
F. Minato, Nuclear level densities with microscopic statistical method using a consistent residual interaction. J. Nucl. Sci. Technol. 48, 984-992 (2011). doi: 10.1080/18811248.2011.9711785http://doi.org/10.1080/18811248.2011.9711785.
D. Vretenar, A. Afanasjev, G. Lalazissis et al., Relativistic Hartree-Bogoliubov theory: static and dynamic aspects of exotic nuclear structure. Phys. Rep. 409,101-259 (2005). doi: 10.1016/j.physrep.2004.10.001http://doi.org/10.1016/j.physrep.2004.10.001.
J. Meng, H. Toki, S. Zhou et al., Relativistic continuum Hartree Bogoliubov theory for ground-state properties of exotic nuclei. Prog. Part. Nucl. Phys. 57, 470-563 (2006). doi: 10.1016/j.ppnp.2005.06.001http://doi.org/10.1016/j.ppnp.2005.06.001.
J. Meng, Relativistic density functional for nuclear structure. WORLD SCIENTIFIC, 2016. doi: 10.1142/9872http://doi.org/10.1142/9872.
S.-G. Zhou, Multidimensionally constrained covariant density functional theories—nuclear shapes and potential energy surfaces. Phys. Scr. 91, 063008 (2016). doi: 10.1088/0031-8949/91/6/063008http://doi.org/10.1088/0031-8949/91/6/063008.
J. Zhao, T. Nikšić, D. Vretenar, Microscopic model for the collective enhancement of nuclear level densities. Phys. Rev. C 102, 054606 (2020). doi: 10.1103/PhysRevC.102.054606http://doi.org/10.1103/PhysRevC.102.054606.
A. Bohr, B. R. Mottelson, Nuclear structure, Vol. 1, Benjamin, New York, 1969.
S. K. Ghosh, B. K. Jennings, The low-energy nuclear density of states and the saddle point approximation (2001). doi: 10.48550/ARXIV.NUCL-TH/0107074http://doi.org/10.48550/ARXIV.NUCL-TH/0107074.
A. Junghans, M. de Jong, H.-G. Clerc et al., Projectile-fragment yields as a probe for the collective enhancement in the nuclear level density. Nucl. Phys. A 629(3), 635-655 (1998). doi: 10.1016/S0375-9474(98)00658-7http://doi.org/10.1016/S0375-9474(98)00658-7.
Z. Kargar, Pairing correlations and thermodynamical quantities in 96,97Mo. Phys. Rev. C 75, 064319 (2007). doi: 10.1103/PhysRevC.75.064319http://doi.org/10.1103/PhysRevC.75.064319.
S. M. Grimes, T. N. Massey, A. V. Voinov, Level density rotational enhancement factor. Phys. Rev. C 99, 064331 (2019). doi: 10.1103/PhysRevC.99.064331http://doi.org/10.1103/PhysRevC.99.064331.
A. Rahmatinejad, T.M. Shneidman, N.V. Antonenko et al., Collective enhancements in the level densities of Dy and Mo isotopes. Phys. Rev. C 101, 054315 (2020). doi: 10.1103/PhysRevC.101.054315http://doi.org/10.1103/PhysRevC.101.054315.
P. Ring, Relativistic mean field theory in finite nuclei. Prog. Part. Nucl. Phys. 37, 193-263 (1996). doi: 10.1016/0146-6410(96)00054-3http://doi.org/10.1016/0146-6410(96)00054-3.
S.-G. Zhou, J. Meng, P. Ring, Spin symmetry in the antinucleon spectrum. Phys. Rev. Lett. 91, 262501 (2003). doi: 10.1103/PhysRevLett.91.262501http://doi.org/10.1103/PhysRevLett.91.262501.
J. Meng, J. Peng, S.Q. Zhang et al., Possible existence of multiple chiral doublets in 106Rh. Phys. Rev. C 73, 037303 (2006). doi: 10.1103/PhysRevC.73.037303http://doi.org/10.1103/PhysRevC.73.037303.
H.Z. Liang, J. Meng, S.G. Zhou, Hidden pseudospin and spin symmetries and their origins in atomic nuclei. Phys. Rep. 570, 1-84 (2015). doi: 10.1016/j.physrep.2014.12.005http://doi.org/10.1016/j.physrep.2014.12.005.
W. Zhang, J. Meng, S. Zhang et al., Magic numbers for superheavy nuclei in relativistic continuum Hartree–Bogoliubov theory. Nucl. Phys. A 753, 106-135 (2005). doi: 10.1016/j.nuclphysa.2005.02.086http://doi.org/10.1016/j.nuclphysa.2005.02.086.
A. Sobiczewski, K. Pomorski, Description of structure and properties of superheavy nuclei. Prog. Part. Nucl. Phys. 58, 292-349 (2007). doi: 10.1016/j.ppnp.2006.05.001http://doi.org/10.1016/j.ppnp.2006.05.001.
N. Wang, E.G. Zhao, W. Scheid et al., Theoretical study of the synthesis of superheavy nuclei with z=119 and 120 in heavy-ion reactions with trans-uranium targets. Phys. Rev. C 85, 041601 (2012). doi: 10.1103/PhysRevC.85.041601http://doi.org/10.1103/PhysRevC.85.041601.
W. Zhang, Z.P. Li, S.Q. Zhang, Description of α-decay chains for 293,294117 within covariant density functional theory. Phys. Rev. C 88, 054324 (2013). doi: 10.1103/PhysRevC.88.054324http://doi.org/10.1103/PhysRevC.88.054324.
B.N. Lu, J. Zhao, E. G. Zhao et al., Multidimensionally-constrained relativistic mean-field models and potential-energy surfaces of actinide nuclei, Phys. Rev. C 89, 014323 (2014). doi: 10.1103/PhysRevC.89.014323http://doi.org/10.1103/PhysRevC.89.014323.
T.T. Sun, W.L. Lv, S.S. Zhang, Spin and pseudospin symmetries in the single- spectrum, Phys. Rev. C 96, 044312 (2017). doi: 10.1103/PhysRevC.96.044312http://doi.org/10.1103/PhysRevC.96.044312.
T.T. Sun, W.L. Lv, L. Qian et al., Green’s function method for the spin and pseudospin symmetries in the single-particle resonant states. Phys. Rev. C 99, 034310 (2019). doi: 10.1103/PhysRevC.99.034310http://doi.org/10.1103/PhysRevC.99.034310.
T.T. Sun, L. Qian, C. Chen et al., Green’s function method for the single-particle resonances in a deformed dirac equation. Phys. Rev. C 101, 014321 (2020). doi: 10.1103/PhysRevC.101.014321http://doi.org/10.1103/PhysRevC.101.014321.
T.H. Heng, Y.W. Chu, Properties of titanium isotopes in complex momentum representation within relativistic mean-field theory. Nucl. Sci. Tech. 33, 117 (2022). doi: 10.1007/s41365-022-01098-8http://doi.org/10.1007/s41365-022-01098-8.
X.N. Cao, X.X. Zhou, M. Fu et al., Research on the infuence of quadrupole deformation and continuum efects on the exotic properties of 15,17,19B with the complex momentum representation method. Nucl. Sci. Tech. 34, 25 (2023). doi: 10.1007/s41365-023-01177-4http://doi.org/10.1007/s41365-023-01177-4.
B.N. Lu, E.G. Zhao, S.G. Zhou, Quadrupole deformation of light hypernuclei in a constrained relativistic mean field model: Shape evolution and shape polarization effect of the hyperon. Phys. Rev. C 84, 014328 (2011). doi: 10.1103/PhysRevC.84.014328http://doi.org/10.1103/PhysRevC.84.014328.
B.N. Lu, E. Hiyama, H. Sagawa et al., Superdeformed hypernuclei within relativistic mean field models. Phys. Rev. C 89, 044307 (2014). doi: 10.1103/PhysRevC.89.044307http://doi.org/10.1103/PhysRevC.89.044307.
T.T. Sun, E. Hiyama, H. Sagawa et al., Mean-field approaches for hypernuclei and current experimental data, Phys. Rev. C 94, 064319 (2016). doi: 10.1103/PhysRevC.94.064319http://doi.org/10.1103/PhysRevC.94.064319.
S.H. Ren, T.T. Sun, W. Zhang, Green’s function relativistic mean field theory for hypernuclei. Phys. Rev. C 95, 054318 (2017). doi: 10.1103/PhysRevC.95.054318http://doi.org/10.1103/PhysRevC.95.054318.
Z.X. Liu, C.J. Xia, W.L. Lu et al., Relativistic mean-field approach for , and hypernuclei. Phys. Rev. C 98, 024316 (2018). doi: 10.1103/PhysRevC.98.024316http://doi.org/10.1103/PhysRevC.98.024316.
C. Chen, Q.K. Sun, Y.X. Li et al., Possible shape coexistence in ne isotopes and the impurity effect of hyperon. Sci. China-Phys. Mech. Astron. 64, 282011 (2021). doi: 10.1007/s11433-021-1721-1http://doi.org/10.1007/s11433-021-1721-1.
W. Zhang, Y. F. Niu, Shape evolution of 72,74Kr with temperature in covariant density functional theory*. Chin. Phys. C 41, 094102 (2017). doi: 10.1088/1674-1137/41/9/094102http://doi.org/10.1088/1674-1137/41/9/094102.
W. Zhang, Y. F. Niu, Shape transition with temperature of the pear-shaped nuclei in covariant density functional theory. Phys. Rev. C 96, 054308 (2017). doi: 10.1103/PhysRevC.96.054308http://doi.org/10.1103/PhysRevC.96.054308.
W. Zhang, Y. F. Niu, Critical temperature for shape transition in hot nuclei within covariant density functional theory. Phys. Rev. C 97, 054302 (2018). doi: 10.1103/PhysRevC.97.054302http://doi.org/10.1103/PhysRevC.97.054302.
W. Zhang, S.S. Zhang, S.Q. Zhang et al., Shell correction at the saddle point for superheavy nucleus. Chin. Phys. Lett. 20, 1694-1697 (2003). http://cpl.iphy.ac.cn/EN/abstract/article_33959.shtmlhttp://cpl.iphy.ac.cn/EN/abstract/article_33959.shtml.
Y.F. Niu, H.Z. Liang, J. Meng, Stability of strutinsky shell correction energy in relativistic mean field theory. Chin. Phys. Lett. 26, 032103 (2009). doi: 10.1088/0256-307X/26/3/032103http://doi.org/10.1088/0256-307X/26/3/032103.
P. Jiang, Z.M. Niu, Y. F. Niu et al., Strutinsky shell correction energies in relativistic Hartree-Fock theory. Phys. Rev. C 98, 064323 (2018). doi: 10.1103/PhysRevC.98.064323http://doi.org/10.1103/PhysRevC.98.064323.
W. Zhang, W. L. Lv, T.T. Sun, Shell corrections with finite temperature covariant density functional theory. Chin. Phys. C 45, 024107 (2021). doi: 10.1088/1674-1137/abce12http://doi.org/10.1088/1674-1137/abce12.
W. Zhang, Z. Li, W. Gao et al., A global weizsäcker mass model with relativistic mean field shell correction. Chin. Phys. C 46, 104105 (2022). doi: 10.1088/1674-1137/ac7b18http://doi.org/10.1088/1674-1137/ac7b18.
T. Nikšić, Z.P. Li, D. Vretenar et al., Beyond the relativistic mean-field approximation. III. collective hamiltonian in five dimensions, Phys. Rev. C 79, 034303 (2009). doi: 10.1103/PhysRevC.79.034303http://doi.org/10.1103/PhysRevC.79.034303.
Y. F. Niu, Z. M. Niu, N. Paar et al., Pairing transitions in finite-temperature relativistic Hartree-Bogoliubov theory. Phys. Rev. C 88, 034308 (2013). doi: 10.1103/PhysRevC.88.034308http://doi.org/10.1103/PhysRevC.88.034308.
J.R. Huizenga, R. Vandenbosc, Nuclear Fission, Academic Press, New York, 1973.
A. Iljinov, M. Mebel, N. Bianchi et al., Phenomenological statistical analysis of level densities, decay widths and lifetimes of excited nuclei. Nucl. Phys. A 543, 517-557 (1992). doi: 10.1016/0375-9474(92)90278-Rhttp://doi.org/10.1016/0375-9474(92)90278-R.
S. Quan, W.P. Liu, Z.P. Li et al., Microscopic core-quasiparticle coupling model for spectroscopy of odd-mass nuclei. Phys. Rev. C 96, 054309 (2017). doi: 10.1103/PhysRevC.96.054309http://doi.org/10.1103/PhysRevC.96.054309.
P.W. Zhao, Z.P. Li, J.M. Yao et al., New parametrization for the nuclear covariant energy density functional with a point-coupling interaction. Phys. Rev. C 82, 054319 (2010). doi: 10.1103/PhysRevC.82.054319http://doi.org/10.1103/PhysRevC.82.054319.
B. Wei, Q. Zhao, Z.-H. Wang et al., Novel relativistic mean field lagrangian guided by pseudo-spin symmetry restoration. Chin. Phys. C 44, 074107 (2020). doi: 10.1088/1674-1137/44/7/074107http://doi.org/10.1088/1674-1137/44/7/074107.
Y. Tian, Z. Ma, P. Ring, A finite range pairing force for density functional theory in superfluid nuclei. Phys. Lett. B 676, 44-50 (2009). doi: 10.1016/j.physletb.2009.04.067http://doi.org/10.1016/j.physletb.2009.04.067.
National nuclear data center (nndc), [Online], http://www.nndc.bnl.gov/http://www.nndc.bnl.gov/.
G. Maino, A. Mengoni, A. Ventura, Collective enhancement of nuclear level density in the interacting boson model. Phys. Rev. C 42, 988-992 (1990). doi: 10.1103/PhysRevC.42.988http://doi.org/10.1103/PhysRevC.42.988.
M. Guttormsen, B. Jurado, J. N. Wilson et al., Constant-temperature level densities in the quasicontinuum of Th and U isotopes. Phys. Rev. C 88, 024307 (2013). doi: 10.1103/PhysRevC.88.024307http://doi.org/10.1103/PhysRevC.88.024307.
A. Rahmatinejad, T.M. Shneidman, G.G. Adamian et al., Energy dependent ratios of level-density parameters in superheavy nuclei. Phys. Rev. C 105, 044328 (2022). doi: 10.1103/PhysRevC.105.044328http://doi.org/10.1103/PhysRevC.105.044328.
0
Views
0
Downloads
0
CSCD
Publicity Resources
Related Articles
Related Author
Related Institution