نوع مقاله: مقاله پژوهشی
نویسندگان
گروه فیزیک، دانشگاه صنعتی ارومیه، صندوق پستی: 57157-419، ارومیه ـ ایران
چکیده
بررسی پایداری ساختار هستهای به عنوان یک سیستم بس- ذرهای اهمیت ویژهای در فیزیک هستهای دارد. آگاهی از خواص آماری و گذارهای فاز میتواند اطلاعات مفیدی را در ارتباط با ساختار و فرایندهای هستهای به همراه داشته باشد. خواص آماری مجموعه ترازهای انرژی یک سیستم به خوبی با معیار جدیدی تحت عنوان نظریهی ماتریس تصادفی در آشوب کوانتومی توضیح داده میشود. افت و خیز ترازهای انرژی
سیستمهای کوانتومی بسته به تقارنهای هامیلتونی در یکی از مجموعههای متعامد (GOE)، یکانی (GUE) و همتافته(GSE)ی گاوسی قرار میگیرد و اگر یک سیستم کوانتومی در ناحیهی انتگرالپذیر قرار داشته باشد در مجموعههای پواسونی قرار خواهدگرفت. تحلیل آماری ترازهای انرژی توسط نظریهی ماتریس تصادفی با محاسبهی ویژه- مقدارهای هامیلتونی سیستم امکانپذیر خواهد بود. یکی از مناسبترین زنجیرهها برای درک ساختار
هستهها زنجیرهی کلسیم است که در اعداد دوبار جادویی نیز نقش بازی میکند. مقالهی حاضر با به کارگیری مدل پوستهای هسته به کمک نظریهی آشوب کوانتومی به بررسی پایداری در ساختار هستهای ایزوتوپهای 50Ca و48Ca میپردازد. یافتهها با نتایج تجربی به دست آمده در آزمایشگاه ایزولد- سرن مقایسه شده است.
کلیدواژهها
عنوان مقاله [English]
Stability Analysis of the Nuclear Structure as a Many Body System by Using Quantum Chaos Theory
نویسندگان [English]
- S Behnia
- V Razazi
چکیده [English]
Stability analysis of the nuclear structure as a many-body system has a particular importance in nuclear physics. Understanding its statistical properties and also phase transitions provide useful information about nuclear structure and nuclear processes. The statistical properties of the set of energy levels of a system are well described by random matrix theory in quantum chaos. Resonance of energy levels depends on the Hamiltonian symmetry that placed in one of the GOE, GUE, GSE ensembles and in the integrable system in the Poissonian ensemble. The statistical analysis of energy levels by random matrix theory will be possible by calculating the Hamiltonian’s eigenvalues of the system. The calcium chain is an ideal test bench for study on the nuclear structure due to its existing double magic isotopes. In the present work, we use quantum chaos theory in order to investigate the stability of the nuclear structure of 50Caand 48Ca isotopes, and the results obtained are compared with those of the Isolde-Cern laboratory.
کلیدواژهها [English]
- Nuclear Shell Model
- Random Matrix Theory
- Quantum Chaos
- Many-Body Systems
[1] P. Watts, Daniel, Nuclear physics: The skin of a nucleus, Nature Physics, 12(2) (2016) 116.
[2] D.J. Dean, T. Engeland, M. Hjorth-Jensen, M.P. Kartamyshev, E. Osnes, Effective interactions and the nuclear shell-model, Progress in Particle and Nuclear Physics., 53(2) (2004) 419-500.
[3] J.M.G. Gómez, K. Kar, V.K.B. Kota, R.A. Molina, A. Relaño, J. Retamosa, Many-body quantum chaos: Recent developments and applications to nuclei, Physics Reports, 499(4) (2011) 103-226.
[4] S. Karampagia, R. Sen'kov, V. Zelevinsky, AB. Brown, Shell Model Nuclear Level Densities using the Methods of Statistical Spectroscopy. Bulletin of the American Physical Society, (2016).
[5] R. Sen’kov, V. Zelevinsky, Nuclear level density: Shell-model approach, Physical Review C., 93 (2016) 064304.
[6] V. Zelevinsky, Quantum chaos and nuclear structure, Physica E., 9 (2001) 450-455
[7] M. Madurga, SV. Paulauskas, R. Grzywacz, D. Miller, DW. Bardayan, JC. Batchelder, NT. Brewer, J.A. Cizewski, A. Fijałkowska, C.J. Gross, M.E. Howard, Evidence for Gamow-Teller Decay of Ni 78 Core from Beta-Delayed Neutron Emission Studies, Physical Review Letters, 117(9) (2016) 092502.
[8] K. Pomorski, J. Dudek, Nuclear liquid-drop model and surface-curvature effects, Physical Review C., 67(4) (2003) 044316.
[9] Heyde, Kris LG, The Nuclear Shell Model, Springer (1994(.
[10] M. Horoi, B.A. Brown, Shell-Model Analysis of the 136Xe Double Beta Decay Nuclear Matrix Elements, Physical review letters., 110(22) (2013) 222502.
[11] M. Alanssari, D. Frekers, T. Eronen, L. Canete, J. Dilling, M. Haaranen, J. Hakala, M. Holl, M. Ješkovský, A. Jokinen, A. Kankainen, Single and Double Beta-Decay Q Values among the Triplet 96Zr, 96Nb, and 96Mo, Physical review letters., 116(7) (2016) 072501.
[12] R.A. Sen'kov, M. Horoi, Accurate shell-model nuclear matrix elements for neutrinoless double-β decay, Physical Review C., 90(5) (2014) 051301.
[13] Y. Iwata, N. Shimizu, T. Otsuka, Y. Utsuno, J. Menéndez, M. Honma, T. Abe, Large-Scale Shell-Model Analysis of the Neutrinoless double-β Decay of 48Ca. Physical review letters, 116(11) (2016) 112502.
[14] E. Mardones, J. Barea, CE. Alonso, J.M. Arias, β-decay rates of 121-131Cs in the microscopic interacting boson-fermion model, Physical Review C, 93(3) (2016) 034332.
[15] R.F. Casten, Shape phase transitions and critical-point phenomena in atomic nuclei, Nature Physics., 2(12) (2006) 811-820.
[16] J. Barea, J. Kotila, F. Iachello, Limits on neutrino masses from neutrinoless double-β decay, Physical Review Letters., 109(4) (2012) 042501.
[17] Horoi, Mihai, Novel Shell Model Analysis of the Double Beta Decay Matrix Elements for 136Xe, APS Division of Nuclear Physics Meeting Abstracts., 1 (2012).
[18] J.E. Lynn, I. Tews, J. Carlson, S. Gandolfi, A. Gezerlis, KE. Schmidt, A. Schwenk, Chiral Three-Nucleon Interactions in Light Nuclei, Neutron-α Scattering, and Neutron Matter, Physical review letters, 116(6) (2016) 062501.
[19] J. Carlson, S. Gandolfi, F. Pederiva, SC. Pieper, R. Schiavilla, KE. Schmidt, RB. Wiringa, Quantum Monte Carlo methods for nuclear physics, Reviews of Modern Physics., 87(3) (2015) 1067.
[20] Baroni, Simone, Petr Navrátil, Sofia Quaglioni, Ab Initio Description of the Exotic Unbound 7He Nucleus, Physical review letters 110(2) (2013) 022505.
[21] S. Liebig, U-G. Meißner, A. Nogga, Jacobi no-core shell model for p-shell nuclei, The European Physical Journal A., 52(4) (2016) 1-18.
[22] Stumpf, Christina, Jonas Braun, Robert Roth, Importance-truncated large-scale shell model, Physical Review C., 93(2) (2016) 021301.
[23] M. Horoi, B.A. Brown, Shell-Model Analysis of the 136Xe Double Beta Decay Nuclear Matrix Elements, Physical review letters., 110(22) (2013) 222502.
[24] N. Shimizu, Y. Utsuno, Y. Futamura, T. Sakurai, T. Mizusaki, T. Otsuka, Stochastic estimation of nuclear level density in the nuclear shell model: An application to parity-dependent level density in 58 Ni, Physics Letters B., 753 (2016) 13-17.
[25] E. Caurier, Shell model code ANTOINE, IReS, Strasbourg 2002, (1989).
[26] B.A. Brown, A. Etchegoyen, WD. Rae, NS. Godwin, The computer code OXBASH, MSU-NSCL Report., 524 (1988).
[27] Shimizu, Noritaka, Nuclear shell-model code for massive parallel computation, KSHELL"." arXiv preprint arXiv:1310 (2013) 5431.
[28] Y. Utsuno, N. Shimizu, T. Otsuka, S. Ebata, M. Honma, Photonuclear reactions of calcium isotopes calculated with the nuclear shell model, Progress in Nuclear Energy., 82 (2015) 102-106.
[29] T. Togashi, N. Shimizu, Y. Utsuno, T. Otsuka, M. Honma, Large-scale shell-model calculations for unnatural-parity high-spin states in neutron-rich Cr and Fe isotopes, Physical Review C., 91(2) (2015) 024320.
[30] Bohigas, Oriol, Marie-Joya Giannoni, Charles Schmit, Characterization of chaotic quantum spectra and universality of level fluctuation laws, Physical Review Letters., 52(1) (1984) 1.
[31] F. Haake, Quantum Signatures of Chaos, Springer, (2010).
[32] Oganesyan, Vadim, A. David, Huse. Localization of interacting fermions at high temperature, Physical Review B., 75(15) (2007) 155111.
[33] YY. Atas, E. Bogomolny, O. Giraud, G. Roux, Distribution of the ratio of consecutive level spacings in random matrix ensembles, Physical review letters., 110(8) (2013) 084101.
[34] N.D. Chavda, Distribution of level spacing ratios using one-plus two-body random matrix ensembles, Pramana, 84(2) (2015) 309.
[35] E. Ideguchi, DG. Sarantites, W. Reviol, AV. Afanasjev, M. Devlin, C. Baktash, RV. Janssens, D. Rudolph, A. Axelsson, MP. Carpenter, A. Galindo-Uribarri, Superdeformation in the Doubly Magic Nucleus , Physical review letters, 87(22) (2001) 222501.
[36] RG. Ruiz, ML. Bissell, K. Blaum, A. Ekström, N. Frömmgen, G. Hagen, M. Hammen, K. Hebeler, JD. Holt, GR. Jansen, M. Kowalska, Unexpectedly large charge radii of neutron-rich calcium isotopes, Nature Physics, 12(6) (2016) 594.