 |
ßäåðíà ô³çèêà òà åíåðãåòèêà
ISSN:
1818-331X (Print), 2074-0565 (Online) |
| Home page | About |
Full text (en) Two-neutron transfer reactions and the quantum chaos measure of nuclear spectra
A. I. Levon, A. G. Magner*
Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine
*Corresponding author. E-mail address:
magner@kinr.kiev.ua
Abstract: A new statistical interpretation of the nuclear collective states is suggested and applied to analysis of states, found recently in rare earths and actinide nuclei by the two-neutron transfer reactions, in terms of the nearest neighbor-spacing distributions (NNSDs). Experimental NNSDs were obtained by using the complete and pure sequences of the collective states through an unfolding procedure. The two-neutron transfer reactions allow to obtain such a sequence of the collective states that meets the requirements for a statistical analysis. Their theoretical analysis is based on a linear approximation of the repulsion level density within the Wigner - Dyson theory. This approximation is successful to evaluate separately the Wigner chaos and Poisson order contributions. We found an intermediate behavior of NNSDs between the Wigner and Poisson limits. NNSDs turn out to be shifted from a chaos to order with increasing the length of spectra and the angular momentum of collective states. The symmetry breaking of states with the fixed projection of angular momenta K is discussed in terms of degree of symmetry – the number of independent integrals of motion beyond the system energy – in relation to the periodic orbit theory.
Keywords: statistical analysis, nuclear collective states, quantum and classical chaos, nearest neighbor-spacing distributions, Wigner and Poisson distributions.
References:1. M.L. Mehta. Random Matrices (San Diego, New York, Boston, London, Sydney, Tokyo, Toronto: Academic Press, 1991). Google books
2. V. Zelevinsky et al. The nuclear shell model as a testing ground for many for many-body quantum chaos. Phys. Rep. 276 (1996) 85. https://doi.org/10.1016/S0370-1573(96)00007-5
3. H.-J. Stöckmann. Quantum Chaos: An Introduction (Cambridge, University Press, Cambridge, England, 1999). https://doi.org/10.1017/CBO9780511524622
4. S. Aberg. Quantum Chaos (Lund: Mathematical Physics, 2002).
5. H.A. Weidenmuller, G.E. Mitchell. Random matrix and chaos in nuclear physics: nuclear structure. Rev. Mod. Phys. 81 (2009) 539. https://doi.org/10.1103/RevModPhys.81.539
6. G.E. Mitchell, A. Richter, H.A. Weidenmuller. Random matrix and chaos in nuclear physics: nuclear reactions. Rev. Mod. Phys. 82 (2010) 2845. https://doi.org/10.1103/RevModPhys.82.2845
7. J.M.G. Gomez et al. Many-body quantum chaos. Recent developments and applications to nuclei. Phys. Rept. 499 (2011) 103. https://doi.org/10.1016/j.physrep.2010.11.003
8. F. Iachello, A. Arima. The Interacting Boson Model (Cambridge, England: Cambridge University Press, 1987). https://doi.org/10.1017/CBO9780511895517
9. V.G. Soloviev. Theory of Atomic Nuclei: Quasiparticles and Phonons (Bristol: Institute of Physics, 1992). Google books
10. B. Gremaud, S.R. Jain. Spacing distributions for rhombus billiards. J. Phys. A 31 (1998) L637. https://doi.org/10.1088/0305-4470/31/37/003
11. E.B. Bogomolny, U. Gerland, C. Schmit. Models of intermediate spectral statistics. Phys. Rev. E 59 (1999) R1315(R). https://doi.org/10.1103/PhysRevE.59.R1315
12. V.V. Flambaum et al. Structure of compound states in the chaotic spectrum of the Ce atom. Phys. Rev. A 50 (1994) 267. https://doi.org/10.1103/PhysRevA.50.267
13. V.V. Flambaum, G.F. Gribakin, F.M. Izrailev. Correlations within Eigenvectors and Transition Amplitudes in the Two-Body Random Interaction Model. Phys. Rev. E 53 (1996) 5729. https://doi.org/10.1103/PhysRevE.53.5729
14. S.H. Tekur, S. Kumar, M.S. Santhanam. Exact distribution of spacing ratios for random and localized states in quantum chaotic systems. Phys. Rev. E 97 (2018) 062212. https://doi.org/10.1103/PhysRevE.97.062212
15. S.H. Tekur, U.T. Bhosale, M.S. Santhanam. Exact distribution of spacing ratios for random and localized states in quantum chaotic systems. Phys. Rev. E 97 (2018) 062212. https://doi.org/10.1103/PhysRevE.97.062212
16. O. Bohigas, M.J. Giannoni, C. Schmit. Characterization of chaotic quantum spectra and universality of level fluctuations. Phys. Rev. Lett. 52 (1984) 1. https://doi.org/10.1103/PhysRevLett.52.1
17. E.P. Wigner. On the statistical distribution of the width and spacings of nuclear resonance level. Proc. Philos. Soc. 47 (1951) 790. https://doi.org/10.1017/S0305004100027237
18. T.A. Brody. A statistical measure for the repulsion of energy levels. Lett. Nuovo Cimento 7 (1973) 482. https://doi.org/10.1007/BF02727859
19. M.V. Berry, M. Robnik. Semiclassical level spacings when regular and chaotic orbits coexist. J. Phys. A 17 (1984) 2413. https://doi.org/10.1088/0305-4470/17/12/013
20. F.M. Izrailev. Quantum localization and statistics of quasi-energy spectrum in a classically chaotic system. Phys. Lett. 134 (1988) 13. https://doi.org/10.1016/0375-9601(88)90538-5
21. C.E. Porter. Statistical Theories of Spectra: Fluctuations (New York: Academy Press, 1965). Google books
22. M.V. Berry. Quantizing a classically ergodic system: Sinai’s billiard and the KKR method. Ann. Phys. 131 (1981) 163. https://doi.org/10.1016/0003-4916(81)90189-5
23. T.A. Brody et al. Random-matrix physics: spectrum and strength fluctuations. Rev. Mod. Phys. 53 (1981) 385. https://doi.org/10.1103/RevModPhys.53.385
24. S.R. Jain, A. Khare. Exactly Solvable Many-Body Problem in One Dimension. Phys. Lett. A 262 (1999) 35. https://doi.org/10.1016/S0375-9601(99)00637-4
25. Z. Ahmed, S.R. Jain. Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices. Phys. Rev. E 67 (2003) 0451006 (R). https://doi.org/10.1103/PhysRevE.67.045106
26. J.F. Shriner Jr., G.E. Mitchell, T. von Egidy. Fluctuation Properties of Spacings of Low-Lying Nuclear Levels. Z. Phys. A 338 (1991) 309. https://doi.org/10.1007/BF01288195
27. J.F. Shriner Jr. et al. Fluctuation Properties of States in 26Al. Z. Phys. A 335 (1990) 393. https://doi.org/10.1007/BF01290186
28. J.F. Shriner Jr., C.A. Grossmann, G.E. Mitchell. Level statistics and transition distributions of 30P. Phys. Rev. C 62 (2004) 054305. https://doi.org/10.1103/PhysRevC.62.054305
29. G. Vidmar et al. Beyond the Berry-Robnik regime: a random matrix study of tunneling effects. J. Phys. A 40 (2007) 13803. https://doi.org/10.1088/1751-8113/40/46/005
30. B. Dietz et al. Chaos and regularity in the doubly magic nucleus 208Pb. Phys. Rev. Lett. 118 (2017) 012501; https://doi.org/10.1103/PhysRevLett.118.012501
L. Munoz et al. Examination of experimental evidence of chaos in the bound states of 208Pb. Phys. Rev. C 95 (2017) 014317. https://doi.org/10.1103/PhysRevC.95.01431731. J.P. Blocki, A.G. Magner. Chaoticity and shell corrections in the nearest-neighbor distributions for an axially-symmetric potential. Phys. Rev. C 85 (2012) 064311. https://doi.org/10.1103/PhysRevC.85.064311
32. A.I. Levon, A.G. Magner, S.V. Radionov. Statistical analysis of excitation energies in actinide and rare-earth nuclei. Phys. Rev. C 97 (2018) 044305. https://doi.org/10.1103/PhysRevC.97.044305
33. A.G. Magner, A.I. Levon, S.V. Radionov. Simple approach to the chaos-order contributions in nuclear spectra. Eur. Phys. J. A 54 (2018) 214. https://doi.org/10.1140/epja/i2018-12645-8
34. A.I. Levon et al. The nuclear structure of 229Pa from the 231Pa(p,t)229Pa and 230Th(p,2n)229Pa reactions. Nucl. Phys. A 576 (1994) 267. https://doi.org/10.1016/0375-9474(94)90260-7
35. A.I. Levon et al. Spectroscopy of 230Th in the (p,t) reaction. Phys. Rev. C 79 (2009) 014318. https://doi.org/10.1103/PhysRevC.79.014318
36. A.I. Levon et al. 0+ states and collective bands in 228Th studied by the (p,t) reaction. Phys. Rev. C 88 (2013) 014310. https://doi.org/10.1103/PhysRevC.88.014310
37. A.I. Levon et al. Spectroscopy of 232U in the (p,t) reaction: More information on 0+ excitations. Phys. Rev. C 92 (2015) 064319. https://doi.org/10.1103/PhysRevC.92.064319
38. M. Spieker et al. Possible experimental signature of octupole correlations in the 0+2 states of the actinide. Phys. Rev. C 88 (2013) 041303(R). https://doi.org/10.1103/PhysRevC.88.041303
39. M. Spieker et al. Higher-resolution (p,t) study of low-spin states in 240Pu: Octupole excitations, α clustering and other structure features. Phys. Rev. C 97 (2018) 064319. https://doi.org/10.1103/PhysRevC.97.064319
40. M. Gutzwiller. Periodic orbits and classical quantization conditions. J. Math. Phys. 12 (1971) 343. https://doi.org/10.1063/1.1665596
41. M. Gutzwiller. Chaos in Classical and Quantum Mechanics (N.Y.: Springer-Verlag, 1990). https://doi.org/10.1007/978-1-4612-0983-6
42. V.M. Strutinsky. Semiclassical theory for nuclear shell structure. Nucleonica 20 (1975) 679.
43. V.M. Strutinsky, A.G. Magner. Quasiclassical theory of nuclear shell structure. Sov. J. Part. Nucl. 7 (1976) 138.
44. M.V. Berry and M. Tabor. Closed orbits and the regular bound spectrum. Proc. R. Soc. Lond. A 349 (1976) 101. https://doi.org/10.1098/rspa.1976.0062
45. M.V. Berry and M. Tabor. Level clustering in the regular spectrum. Proc. R. Soc. Lond. A 356 (1977) 375. https://doi.org/10.1098/rspa.1977.0140
46. A.G. Magner. Quasiclassical analysis of the gross-shell structure in a deformed oscillator potential. Sov. J. Nucl. Phys. 28 (1978) 759.
47. S.C. Creagh, J.M. Robbins, R.G. Littlejohn. Geometric properties of Maslov indices in the semiclassical trace formula for the density of states. Phys. Rev. A 42 (1990) 1907. https://doi.org/10.1103/PhysRevA.42.1907
48. S.C. Creagh, R.G. Littlejohn. Semiclassical trace formulas in the presence of continuous Symmetries. Phys. Rev. A 44 (1991) 836. https://doi.org/10.1103/PhysRevA.44.836
49. S.C. Creagh, R.G. Littlejohn. Semiclsassical trace formulae for systems with non-Abelian symmetries. J. Phys. A 25 (1992) 1643. https://doi.org/10.1088/0305-4470/25/6/021
50. V.M. Strutinsky et al. Semiclassical interpretation of the gross-shell structure in deformed nuclei. Z. Phys. A 283 (1977) 269. https://doi.org/10.1007/BF01407208
51. M. Brack, R.K. Bhaduri. Semiclassical Physics (USA: Westview Press Boulder, 2003) 458 p. Google books
52. A.G. Magner et al. Shell structure and orbit bifurcations in finite fermion systems. Phys. Atom. Nucl. 74 (2011) 1445. https://doi.org/10.1134/S1063778811100061
53. A.G. Magner, M.V. Koliesnik, K. Arita. Shell, orbit bifurcations, and symmetry restorations in Fermi systems. Phys. Atom. Nucl. 79 (2016) 1067. https://doi.org/10.1134/S1063778816060181
54. A.G. Magner, K. Arita. Semiclassical catastrophe theory of simple bifurcations. Phys. Rev. E 96 (2017) 042206. https://doi.org/10.1103/PhysRevE.96.042206
55. A.M. Ozorio de Almeida, J.H. Hannay. Resonant periodic orbits and the semiclassical energy spectrum. J. Phys. A 20 (1987) 5873. https://doi.org/10.1088/0305-4470/20/17/021
56. A.M. Ozorio de Almeida. Hamiltonian Systems: Chaos and Quantization (Cambridge: University Press, 1988). https://doi.org/10.1017/CBO9780511564161
57. J.P. Blocki, A.G. Magner, I.S. Yatsyshyn. The internal excitation of the gas of independent particles in the time-dependent potential. Int. J. Mod. Phys. E 20 (2011) 292. https://doi.org/10.1142/S0218301311017648
58. J.P. Blocki, A.G. Magner, I.S. Yatsyshyn. The internal excitation of the gas of independent particles in the time-dependent potential. Nucl. Phys. At. Energy 11 (2010) 239. https://jnpae.kinr.kyiv.ua/11.3/Articles_PDF/jnpae-2010-11-0239-Blocki.pdf
59. R.F. Casten, D. D. Warner. The interacting boson approximation. Rev. Mod. Phys. 60 (1988) 389. https://doi.org/10.1103/RevModPhys.60.389
60. O. Bohigas, M.P. Pato. Missing levels in correlated spectra. Phys. Lett. B 595 (2004) 171. https://doi.org/10.1016/j.physletb.2004.05.065